Piano World Home Page
Posted By: MartF most common non ET temperaments in 2020? - 10/21/20 12:56 AM
Hi all, what are the most common temperaments clients and musicians use today, other than 12-TET?

Does every customer want a slight variation, is it mostly Vallotti / Young's 2nd temperament, or something else? Is there a trend regarding temperament choice vs repertoire? Ed mentioned a jazz player using non-ET here but didn't state which temperament.

It's interesting that many digital pianos have presets for Werckmeister III, Kirnberger III, Pythagorean and 1/4 syntonic meantone. I'm guessing none of those are popular today (amongst those who don't use ET), but I could be wrong.

Sorry if this is considered off topic, I'm thinking professional tuners will have the most experience in this area.

Thank you!
I regularly use EBVT as a starting point for those interested in UT. I tune my own piano that way too. It is mild enough not to offend anyone's ears, yet faithfully conveys the characters of the keys (mildly). A good ear detects it right away.

I also tune most spinet and other untunables in EBVT.

Peter Grey Piano Doctor
I've been tuning for a long time. No one has ever asked me for a non ET. They just want me to tune the piano.
Unless the musician is dedicated to pre-1850 music, ET is the best general purpose tuning to use (at least initially). But if they are aware of the fact that the music they are playing was composed and played originally in a UT, then they are usually open to trying it on their piano. However, it is often wise to start off mild (there are numerous mild UT's) and step it up as their ear gets attuned to it. My personal favorite is Thomas Young's rules from 1799 for personal taste with a C-E 3rd at about 5 bps.

Peter Grey Piano Doctor
Posted By: N W Re: most common non ET temperaments in 2020? - 10/21/20 09:59 AM
When he was alive I used to tune for a well known Harpsichord player. He had loads of harpsichords and two pianos. I only tuned the pianos, always equal temp.
One day while we were talking about older music and tunings I asked him if he would like one of the pianos in a different tuning. He said "Good Lord, no! Those tunings only work on harpsichords because there's no sustain...my piano would sound ghastly".
Just saying what he said......
Nick
Most of the pre-loaded temperaments are "too strong" for an introduction, or for modern ears.

Just like LemonColor above, I've been tuning a long time and only 2 people that were knowledgeable have asked for ET, so I tune a mild Well temperament on everything. Even EBVT feels a bit too strong, but many are successfully using that.

Ron Koval
Ron,

Unless I misread things LemonColor tunes exclusively ET. I will stand corrected if wrong.


Once upon a time I thought that Owen Jorgensen was a nut case. This was because I was ignorant of the history of keyboards and tuning, and trained that ET was "HOW" we tune pianos...period...end of discussion. Then I decided to actually try some of what he was talking about. The rest is history (as they say).

Peter Grey Piano Doctor
greetings,

I rarely use ET for pianos, having found the majority of my customers,once introduced to the more musically directed, as opposed to math directed temperaments, prefer the well-tempered sound. Most of the commercial recording studios use ET for convenience, but there are others that have found the WT tracks better with guitars.

given the rarity of amateur players that are comfortable playing in 5 sharps, the WT increases the overall consonance, and I also, to my surprise, have several very professional jazz pianists that have come to fell ET is bland and uninteresting. There are few instances when ET and WT are displayed side by side that ET is preferred. Most of my home tunings are using Coleman 11 or Jorgensens "Broadwood's Best".
Regards
I have never had anyone tell me how to tune. The customers seem to expect whatever is normal. I probably could get away with tuning a non ET, but why risk it? Electronic pianos are set to a normal equal temperament at 440 hertz. I think it is safe to say that people would accept that as the common thing done on pianos too.
I've heard it said by Bill Bremmer that "Reverse Well" is the most common temperament wink
Posted By: N W Re: most common non ET temperaments in 2020? - 10/21/20 05:10 PM
Originally Posted by Ed Foote
greetings,

I rarely use ET for pianos, having found the majority of my customers,once introduced to the more musically directed, as opposed to math directed temperaments, prefer the well-tempered sound. Most of the commercial recording studios use ET for convenience, but there are others that have found the WT tracks better with guitars.

given the rarity of amateur players that are comfortable playing in 5 sharps, the WT increases the overall consonance, and I also, to my surprise, have several very professional jazz pianists that have come to fell ET is bland and uninteresting. There are few instances when ET and WT are displayed side by side that ET is preferred. Most of my home tunings are using Coleman 11 or Jorgensens "Broadwood's Best".
Regards
That's interesting. Do you always tell them they're not getting ET? I'm wondering what happens if they have friends round to sing or play?
Nick
Originally Posted by N W
That's interesting. Do you always tell them they're not getting ET? I'm wondering what happens if they have friends round to sing or play?
Nick

Yes, I tell them. And the normal is that I get calls from "friends" that were impressed with how nice the piano sounded at "so and so's" house. Don't think that somehow the world is automatically predisposed to prefer ET, I have found that to be totally false. It is just tuner's that are attached, for the most part, to the status quo. I will add that I have been charging well above any other tech in the area since 1980, so this is not smoke and mirrors....


As to the commonly stated, "I've never had anyone ask me to tune alternatively" statement, I have often sold a regulation to someone that didn't know their piano needed regulation, ("Whatever that is"), yet afterwards, I hear "I never knew this piano could play this well". I am not letting my customer's ignorance of alternatives keep them from hearing something they actually like better. And, for an added bonus, these WT customers are quite loyal, telling me that when I retire, they would like the name whatever tuner tunes like I do. Few have any interest in going back to ET.
Regards,
Posted By: N W Re: most common non ET temperaments in 2020? - 10/21/20 07:35 PM
That's a really interesting answer.
Thanks Ed.
Nick
Originally Posted by P W Grey
Ron,

Unless I misread things LemonColor tunes exclusively ET. I will stand corrected if wrong.


Once upon a time I thought that Owen Jorgensen was a nut case. This was because I was ignorant of the history of keyboards and tuning, and trained that ET was "HOW" we tune pianos...period...end of discussion. Then I decided to actually try some of what he was talking about. The rest is history (as they say).

Peter Grey Piano Doctor

The point that I was trying to make is that most clients "want the piano tuned". No more, no less. They don't specify ET, they don't specify WT, so it is up to us to tune the piano to the best of our ability. For me, that is WT, for others, it is ET.

Ron Koval
MartF, musicians seem to be using whatever they get, whether they like it or not.
Extremely few people have any knowledge whatsoever about this. To them a tuning is a tuning is a tuning. They pay to get the piano tuned and that's the end of it.

Like Ed, everyone for whom I tune UT (with one exception) loves it. The exception really didn't notice any difference therefore specified ET (and it fits their style too).

I actually find it more difficult to tune UT than ET. ET is a piece of cake...all tests the same, all consistent accelerating and decelerating intervals. UT on the other hand does not contain all consistent tests. You must listen very carefully and slowly to each interval. More time consuming and mentally challenging. Don't bother trying.

Peter Grey Piano Doctor
Another point of realism is that any of us that think we are tuning TRUE ET are basically doing wishful thinking. In reality, ANY DEVIATION whatsoever from the true actual mathematical 12 tone equal sub division of the scale is not ET, but in essence is in fact a mild UT, like it or not.

When Bach created his tweaked out tuning that allowed him to play EQUALLY in all the keys he called it Equal Temperament (or something that implied such). We know from our scientific 20th century standpoint that it was no where near ET as we know it today so we call it Well Temperament, but the terms are relative to the situation.

What we say we tune today as ET is a much closer approximation of true ET, however the anomalies of scale design, environmental factors, human imperfection, etc all combine to make it pretty much impossible to actually apply true ET to almost any piano. And in short order, the humidity change will do number on it anyway.

However, relatively speaking we are tuning much closer to ET than ever before. It depends on how much of a stickler for detail and accuracy you want to use. And as we know, some PSO's cannot accept even an approximation of ET due to their horrible design. Yet, we still "say" that we tuned it in ET. Technically that's a crock (but we tried). Those PSO's actually sound much better in a well crafted WT rather than any attempt at ET.

At any rate, that's the reality. If anyone can prove me wrong on this I'm happy to acquiesce.

Peter Grey Piano Doctor
Posted By: N W Re: most common non ET temperaments in 2020? - 10/22/20 12:30 PM
Peter, that's a very interesting post. I like it all except the very end....surely a well crafted WT will suffer from all the same errors and afflictions of a well crafted ET? So it won't be, in reality, a well crafted WT....?
I'm beginning to think the differences are so small (and of course the more well crafted the attempt the less the cumulative errors and environmental pressures will show) that maybe most players just can't hear what we aim for anyway. Once the music is rolling along it can be said that it's the spaces that matter more than the notes....
I exclude carefully analysed slow chords of course....but how many players do that?
As a previous poster said, people just want their piano tuned. The better players talk of the piano sounding so much better with the harmonics lining up etc. but as the average person can't hear a difference of 3 cents they just hear A as A as long as it's around 440 (sorry, don't mean to start that one off) and matches their flute etc.

Fascinating though, I shall definitely try tuning some alternatives on my own piano and see how I feel about them.
Nick
Greetings,
At some degree of examination, it is true that perfect equality is not attainable on a wooden and steel piano. However, if all thirds are faster than the one below and slower than the one above, it is virtually impossible to distinguish inequality in play. Within the octave, if all thirds obey the above, you will be close to a passable score on the PTG test.

That said, the few cents deviation from ET pitches may not be heard as different notes, but a few cents up on the C and a few cents down on the E will produce a third that has a distinctly different feel in the triad. What it appears to do when I tune a WT is that very few people find a 16 cent third as "out of tune", and nobody hears an 8 cent third as "out", but the feel of the sound is certainly noticed. I ascribe this to the destruction of sameness, a quality much beloved by techs not musically as attractive to pianists as the variety found in WT. There is something about the ever-present "haze" of 14 cent thirds in the classical music that is found to be unattractive once a pianist experiences the texture of a WT. It is common to hear the word "boring" when an WT customer encounters an ET. Modulations in WT create definite changes of emotional response that simple changes of pitch center in ET do not. The composition has a lot to do with this response, but a common reaction from the classical musicians was that the WT was like "power steering" when performing and attempting to create different emotional states with modulation.

Most of my work is for professional pianists. Some, like Ronnie Milsap, couldn't stand the inequality, and he told me that it was like someone moving the furniture around without telling him! Others were instinctively drawn to the textural difference and found they could compose with new harmonic resources. I can now say, after 30 years of using WT's that the vast majority of customers really prefer the piano tuned that way. I used to pursue the ideal idea of perfect evenness, but I now think that the consistency is more attractive to us harmonic mechanics than it is to the musicians.
regards,
Posted By: VladK Re: most common non ET temperaments in 2020? - 10/22/20 03:36 PM
I am curious, when you tune to any WT, what anchor point do you use, A, or C?
And do you keep A 440 pitch or use any historic one?
And how do you achive desired pitch if you anchor C?
Originally Posted by VladK
I am curious, when you tune to any WT, what anchor point do you use, A, or C?
And do you keep A 440 pitch or use any historic one?
And how do you achive desired pitch if you anchor C?

Greetings,
I keep the A at 440. I use pre-loaded offsets in a SAT for the various temperaments now. I apply these to my own recorded, repeated, and refined aural ET's that I have archived in the machine for all sizes of Steinways and Yamahas that we had. In truth, the modern programmable ETD's all produce a very close to ideal ET if one is fastidious about taking the original measuements. i still felt better using recorded versions of my aural tuning that I had massaged via repeated uses of the machine.

When Jorgensen first published the "Historical Temperaments by Ear", I worked my way through a couple of them. Given the interpretative nature of these things, the dead-nut accuracy required by ET is not so important. When the big Red "(Tuning) came out, he gave the offsets from ET that would allow a machine to replicate the temperaments. I tried them, compared them to my aural versions, and found that there was no distinguishable difference, so I use the machine for ease and trustworthy consistency. This is important when asking a faculty to judge the sound, as I know that every time I put a Kirnbeger or Young, etc. on a piano, it was exactly the same as the last time I put it on. This removes a variable and allows for a more valid feedback, as the pianists heard the exact same version each time they used the piano.
Regards,
Originally Posted by P W Grey
When Bach created his tweaked out tuning that allowed him to play EQUALLY in all the keys he called it Equal Temperament (or something that implied such). We know from our scientific 20th century standpoint that it was no where near ET as we know it today so we call it Well Temperament, but the terms are relative to the situation.
Maybe I misunderstood, but are you talking about "Das wohltemperierte Klavier?" If so, that doesn't mean equal temperament. It literally means well temperament, or good temperament (passable). It was also know as a circulating temperament. Basically it implied that we could use all 12 keys in some kind of musically acceptable way. But, it never meant equal. All 12 major and minor keys were different for sure.

I just want to say that equal temperament is not the end of an evolutionary process. The concept of equal temperament has basically always been with us. It is not a new concept by any means. It is a mathematical and musical application problem that had to be figured out. The Chinese and the Italians both worked it out around 1600. Whether or not people ever were able to tune equal temperament is a different issue.
I was of course splitting hairs, but doing so to try to point out that being adamant about tuning ET is really quite relative. Claiming that this is the "standard" and that all pianos should be tuned this way (there was a time when I did that), and that UT or WT is inferior or even sloppy/lazy (yes I have seen this assertion right here on PW) is an unwise position to take. Why? Because if one were to scrupulously analyze most tuners application of what they are calling ET, they would come up short to one degree or another...some seriously so. However, in the average scheme of things, ET is the goal for most, and we TRY to achieve it (close enough as was pointed out above).

Once I experienced good WT I understood better what was being heard, what was "built" into the music itself in WT, and since I generally play in simpler keys I came to really like those slower beating 3rds etc. They seemed to really complement my music. I actually DON'T like the very fast intervals in therefore keys, but since I don't/can't play there anyway it's irrelevant to me...l'll never use them. So I get to enjoy the parts I like and not be bothered by the parts I don't.

Interestingly, the very good musicians that I find enjoy the WT actually like some of that shimmering sound they get in keys of 4, 5, 6 flats or sharps. But more importantly what they tell me is that they like the CHOICES now available, and the ability to RESOLVE from an aggressive tonality to a calm one, much of which was built right into the music they're playing, but the intended effect is not there in ET...it is there in WT.

Most WT's are basically the same in the sense that they enhance the calmness of the simple keys, esp key of C, then in varying degrees they introduce dissonance in all the other keys, but essentially the patterns are the same, some more, some less.

Modern music generally sounds better in ET due to the fact that it is constructed without any musical rules. The ability to change randomly from one key to another without striking tonal changes is important to the modern composer. Also, according to Owen Jorgensen (as I recall) ET (or the essence of it) was in fact known and basically understood by many early musicians/composers, but when presented with an instrument tuned this way (or some reasonable facsimile) they did not like it, since the tonal palette they had come to know and love in WT was largely washed away. They rejected it as inferior.

So, that brings me back to the relativity of all of this. Relative to ones limes and dislikes, relatively the music being played, and the era in which it was created, relative to the specific instrument being played on, etc etc.

Yes, Bach may not have actually used the term ET specifically, but his work has been historically categorized as being ET by many who claim to be able to interpret it. This of course is not accurate. Jorgensen made this statement numerous times.

Peter Grey Piano Doctor
Posted By: VladK Re: most common non ET temperaments in 2020? - 10/22/20 07:15 PM
Bach's WTC being written with ET in mind is a myph which can't be confirmed or refused based on documents we know so far, and there are multiple works on the subject from scholars and practicians.
IMHO, it was not. Here is one cool hint from his own manuscript which might be true:
https://www.rolf-musicblog.net/what-tunings-did-bach-use/
Here is a deeper examination: https://www.colinbooth.co.uk/bach-n-tuning-02.pdf
I'm going to be a bit of a contrarian here based on my own experience.

First of all, let me say that I've been aware of (and open to) historical temperaments since I was 18 years old and Owen Jorgensen took me to my first PTG chapter meeting.
I've heard some of Owen's recitals (and others since) and have found them interesting and informative. I recall a lecture when I was tuning at Interlochen about the different key tonalities and how they were used to convey different feelings in classical opera. As I recall, for example, C-Major was the "military marching" tonality whereas B-minor (or was it B-flat minor??) was the key of illicit sexual desire.
At one time, I have had my home piano (don't laugh, a 50s-era Baldwin Hamilton) tuned to a version of Bill Bremmer's Equal-Beating Victorian Temperament for several months. It was interesting and enjoyable. But ultimately I didn't keep it. My violinist wife (who clearly has to be able to hear) didn't seem to care one way or the other when the piano is used to accompany her or for her level of direct piano use.

I've also tuned some of the more radical temperaments like Pythogorian and Meantone.

However...
Equal temperament has a particular provision for musicality that has nothing to do with mathematical concepts or the convenience of not retuning the instrument every time you want to play in unrelated keys. It's the main point of the temperament procedure described in Travis's Let's Tune Up. It's not about beat counting but rather it's about listening to the partials line up as you tune thirds from pure to wide. You can hear it and it makes for a nice tuning.
With UT, the partials don't line up the same way and as a result have a dissonance in the higher coincident partials.
Also, I tried doing the EBVT for my customer with the most discriminating ear (get's grumpy if it's longer than 6 weeks before I can re-tune his piano and notices subtle voicing issues). I didn't tell him that I had done anything different until the following tuning. (We have that kind of relationship where he trusts me to try stuff that I think he might like). Anyway, when I mentioned I had used the unequal temperament he said he "hadn't noticed anything different".

So...
I don't want to dissuade anyone who enjoys UT from continuing to do so and I myself will keep it as an option in my bag of tricks. But I offer this as a different perspective for consideration.
Well thank you for offering it - I enjoyed that!
Posted By: VladK Re: most common non ET temperaments in 2020? - 10/22/20 10:34 PM
Thanks for sharing all this first hand experience.
Probably the easiest way to compare various temperaments is Pianoteq with any decent digital piano. If only I was good enough to generate any meaningful conclusions by playing it cry
For me any temperament sounds good enough.
Originally Posted by P W Grey
I was of course splitting hairs, but doing so to try to point out that being adamant about tuning ET is really quite relative. Claiming that this is the "standard" and that all pianos should be tuned this way (there was a time when I did that), and that UT or WT is inferior or even sloppy/lazy (yes I have seen this assertion right here on PW) is an unwise position to take.
I don’t take the position that WT is inferior work. History shows that equal, mean tone, and well temperaments have all existed concurrently. It appears that each period has had preferences, based on instrument builders, texts, compositions, etc. But, it was not a timeline evolution from mean tone, to well, to equal temperament. Nonetheless, it can be argued that each period had a de facto standard. The de facto standard of the time that we are living in now is 440 equal temperament. That doesn’t mean that I agree with that standard. I think people should be able to set their own standards, but I think that it should be done with full-disclosure so that there can be a kind of informed consent.

Originally Posted by P W Grey
if one were to scrupulously analyze most tuners application of what they are calling ET, they would come up short to one degree or another...some seriously so.
Here’s an analogy for you. A circle is mathematical construct. It exists only in the mind. As soon as you try to put pencil to paper, the thickness of that arc, no mater how small, turns it in to a cylinder. Any slight deviation from perfection means it is something different from a circle.

I think it can be argued that for musical purposes, the concept of a circle can exist beyond the mathematical construct. We know a circle when we see it. Being mathematically perfect isn’t the defining characteristic of either ET or a circle. If the intent is to minimize differences between key areas, and fast beating intervals are progressing smoothly, then I think we can safely call it ET. It may or not be a good ET, but it is ET nevertheless.
Originally Posted by VladK
Thanks for sharing all this first hand experience.
Probably the easiest way to compare various temperaments is Pianoteq with any decent digital piano. If only I was good enough to generate any meaningful conclusions by playing it cry
For me any temperament sounds good enough.


Digital pianos do not produce the same partials as an acoustic piano, and the effects of tempering occur between upper partials, not fundamentals. Digital pianos I have heard don't give a very clear image of what WT's are all about
Posted By: VladK Re: most common non ET temperaments in 2020? - 10/23/20 01:47 AM
Originally Posted by Ed Foote
Originally Posted by VladK
Thanks for sharing all this first hand experience.
Probably the easiest way to compare various temperaments is Pianoteq with any decent digital piano. If only I was good enough to generate any meaningful conclusions by playing it cry
For me any temperament sounds good enough.


Digital pianos do not produce the same partials as an acoustic piano, and the effects of tempering occur between upper partials, not fundamentals. Digital pianos I have heard don't give a very clear image of what WT's are all about

Thanks. I assume you mean harmonics; important clarification for me personally.
Originally Posted by VladK
Thanks. I assume you mean harmonics; important clarification for me personally.

Partials are related to harmonics. In the piano, the relationship is theoretical to real-world. The idea of a harmonic is a whole-number fraction of the fundamental -- octave = ½ ; twelfth = 3/2, etc.

In reality, due to the existence of inharmonicity, the strings in pianos do not divide up into perfect fractional segments due to the thickness and stiffness of the wire. So, what theoretically would be a 1:2 division for the first octave, when actually measured, turns out to be something slightly off -- like maybe 1:1.998, for example (mathematicians, you can do your thing here). So since these divisions are only "part" of the theoretical harmonic, they are called "partials".
Originally Posted by N W
When he was alive I used to tune for a well known Harpsichord player. He had loads of harpsichords and two pianos. I only tuned the pianos, always equal temp.
One day while we were talking about older music and tunings I asked him if he would like one of the pianos in a different tuning. He said "Good Lord, no! Those tunings only work on harpsichords because there's no sustain...my piano would sound ghastly".
Just saying what he said......
Nick

I would agree with that. I play a moderate amount of Baroque and early music and only want my acoustic piano tuned to equal temperament. Up until the late 17th mean tone was the dominant tuning. Werckmeister published his work in this area between 1681 and 1691. Work of Kirnberger and Valotti was later, well into the 18th century, although there may have been significant lags (in decades) between the work being done, and being published.

But a digital piano is different from an acoustic piano. You can choose the temperament for each piece. You can choose which tone to use as the root of the temperament. A piece in Ab major may be difficult to play in meantone rooted on C but may work fine in meantone rooted on Ab. The inplementation of temperaments on digital instruments opens up a whole new avenue of exploration that is not feasible on an acoustic keyboard instrument.
Correction in red.

Originally Posted by N W
When he was alive I used to tune for a well known Harpsichord player. He had loads of harpsichords and two pianos. I only tuned the pianos, always equal temp.
One day while we were talking about older music and tunings I asked him if he would like one of the pianos in a different tuning. He said "Good Lord, no! Those tunings only work on harpsichords because there's no sustain...my piano would sound ghastly".
Just saying what he said......
Nick

I would agree with that. I play a moderate amount of Baroque and early music and only want my acoustic piano tuned to equal temperament. Up until the late 17th century, mean tone was the dominant tuning. Werckmeister published his work in this area between 1681 and 1691. Work of Kirnberger and Valotti was later, well into the 18th century, although there may have been significant lags (in decades) between the work being done, and being published.

But a digital piano is different from an acoustic piano. You can choose the temperament for each piece. You can choose which tone to use as the root of the temperament. A piece in Ab major may be difficult to play in meantone rooted on C but may work fine in meantone rooted on Ab. The inplementation of temperaments on digital instruments opens up a whole new avenue of exploration that is not feasible on an acoustic keyboard instrument.
Posted By: N W Re: most common non ET temperaments in 2020? - 10/23/20 09:56 AM
"It's the main point of the temperament procedure described in Travis's Let's Tune Up. It's not about beat counting but rather it's about listening to the partials line up as you tune thirds from pure to wide. You can hear it and it makes for a nice tuning.
With UT, the partials don't line up the same way and as a result have a dissonance in the higher coincident partials."

I think this is a most interesting point you make Keith.
Very few of my clients can hear beats as such. (And in fact why would you help someone hear them when they kind of ruin everything musical once you can hear them) But they often say things like "I love how sweet it all sounds when the harmonics line up" (using harmonics and partials interchangeably for a moment as most layman do).
It's this lining up that seems to make a tuning sweet perhaps?

I also found the comments on electronic keyboards interesting. What an interesting thread this is.
Nick
Posted By: MartF Re: most common non ET temperaments in 2020? - 10/23/20 10:38 AM
Thank you everyone, there are a lot of interesting comments here, more than I was expecting. I'm still reading through them.
Originally Posted by VladK
Thanks. I assume you mean harmonics; important clarification for me personally.

Greetings,
No, I meant partial. They, harmonics, and "overtones" are not the same. We speak of partials when we refer to the various frequencies produced by a string, and that includes the lowest, which is the"fundamental". The fundamental is not a "harmonic" and has to be recognized when describing intervals i.e. the major third is a 5:4 interval so we must include all the parts to use this term. This can follow from two ways of looking at things; in the C-E third, the fifth partial of the C is an E two octaves above and the fourth partial of the E is the same E. Hence, the 5:4 designation. The major third is also the interval between the 5th and 4th partial of a string's series of spectrum.

The first "overtone" is the second partial and some may refer to the 2nd partial as the first harmonic. So, Harmonics may refer to overtones, but unless we want to call the fundamental a harmonic they must be assigned their own definition. I think it is important to distinguish these terms from one another if we want to avoid confusion.
regards,
Is the fundamental not called the First Harmonic?
https://www.physicsclassroom.com/class/sound/Lesson-4/Fundamental-Frequency-and-Harmonics#:~:text=The%20lowest%20frequency%20produced%20by,first%20harmonic%20of%20the%20instrument.
Harmonics are fingered.

A fundamental and overtones are blown.

Partials are parts of a describing a whole.
I think the term "partial" was chosen simply as a suitable substitute term since the piano string subdivisions are not actually harmonic to the fundamental. At least this true when freely vibrating. If you bow them they act more like a violin or cello string. Whether they would be TRULY harmonic then I don't know for sure. Stiffness may still be a factor.

Peter Grey Piano Doctor
Posted By: N W Re: most common non ET temperaments in 2020? - 10/23/20 03:19 PM
I was taught that the fundamental was the first harmonic and that the second harmonic was the first partial.....
Have I remembered that right?
Originally Posted by N W
I was taught that the fundamental was the first harmonic and that the second harmonic was the first partial.....
Have I remembered that right?

Greetings,
For clarity, piano techs have usually numbered the "overtone series" beginning with 1 for the fundamental. The fundamental can't be an overtone, and overtones and harmonics are often mixed, interchangeably. Designating the fundamental as the first 'partial' allows us to compute combinations of intervals more easily and avoids the semantic confusion of overtones and harmonics. A guitar player will usually call the first overtone the "harmonic" in that touching the string without fretting at the 12th fret produces the first harmonic.
hence confusion.
Regards,
Originally Posted by N W
I was taught that the fundamental was the first harmonic and that the second harmonic was the first partial.....
Have I remembered that right?

That's kinda how I remembered it as well. Until I checked up, for the new "Electronic Tuning" page of my website.

As I understand it now in relation to vibrating strings:

HARMONICS are integer multiples of the fundamental frequency. The first integer is 1, so the first harmonic is the fundamental frequency multiplied by 1, which is the fundamental frequency. Harmonics are theoretical numbers.

PARTIALS are the actual frequencies produced, rather than the theoretical harmonics. The First partial is also the Fundamental. The second partial will be near, but not exactly, the value of the second harmonic, etc.

OVERTONES are the partial frequencies ABOVE the fundamental. The First Overtone is the Second Partial. It is possibly best to avoid talking of Overtones at all, in relation to piano technology.
Ah, I was typing at the same time as Ed!
Originally Posted by Ed Foote
Originally Posted by VladK
Thanks for sharing all this first hand experience.
Probably the easiest way to compare various temperaments is Pianoteq with any decent digital piano. If only I was good enough to generate any meaningful conclusions by playing it cry
For me any temperament sounds good enough.


Digital pianos do not produce the same partials as an acoustic piano, and the effects of tempering occur between upper partials, not fundamentals. Digital pianos I have heard don't give a very clear image of what WT's are all about

Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from. Modelled pianos will be a bit different (as you can change the inharmonicity factor) but they can still be extremely close to real pianos.
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
From a theoretical perspective, this is false, because the overtone series is infinite, and piano samples are finite.

From a practical perspective, piano samples may contain all audible overtones. Frequencies beyond the Nyquist limit will be filtered out, as will harmonics at amplitudes below the dynamic range floor of the mics used when sampling. The latter perhaps could lead to audible differences, but I'm not sure. The advertised dynamic range specs of the best mics would suggest audible harmonics should be captured, but the issue is complex.
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
Having the same partials doesn't mean that a digital will function the same as an acoustic piano. With the digital pianos, the partials will just beat. With acoustic pianos, the partials get pulled together. Some tuners sense this as the tone getting "sucked in/together." That effect doesn't happen on the digital piano.
Originally Posted by Sweelinck
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
From a theoretical perspective, this is false, because the overtone series is infinite, and piano samples are finite.

From a practical perspective, piano samples may contain all audible overtones. Frequencies beyond the Nyquist limit will be filtered out, as will harmonics at amplitudes below the dynamic range floor of the mics used when sampling. The latter perhaps could lead to audible differences, but I'm not sure. The advertised dynamic range specs of the best mics would suggest audible harmonics should be captured, but the issue is complex.

If you think our ears have infinite bandwidth you're sorely mistaken. I'll grant you the non-linear mixing effect of the human ear drum could potentially introduce intermodulation artifacts from ultrasonic partials but I suspect these are below the noise floor of the ear anyway.


Originally Posted by piano411
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
Having the same partials doesn't mean that a digital will function the same as an acoustic piano. With the digital pianos, the partials will just beat. With acoustic pianos, the partials get pulled together. Some tuners sense this as the tone getting "sucked in/together." That effect doesn't happen on the digital piano.

Good point about the Weinrich effect - but this occurs during tuning, no? Once a note is tuned, all the sympathetic locking is, well, locked in. I would posit that in a blind trial of a piano tuned in ET and then retuned in software to a WT would be indistinguishable from the same piano tuned to exactly the same WT first - with both then played back through the same audio chain.
Originally Posted by David Boyce
Originally Posted by N W
I was taught that the fundamental was the first harmonic and that the second harmonic was the first partial.....
Have I remembered that right?

That's kinda how I remembered it as well. Until I checked up, for the new "Electronic Tuning" page of my website.

As I understand it now in relation to vibrating strings:

HARMONICS are integer multiples of the fundamental frequency. The first integer is 1, so the first harmonic is the fundamental frequency multiplied by 1, which is the fundamental frequency. Harmonics are theoretical numbers.

PARTIALS are the actual frequencies produced, rather than the theoretical harmonics. The First partial is also the Fundamental. The second partial will be near, but not exactly, the value of the second harmonic, etc.

OVERTONES are the partial frequencies ABOVE the fundamental. The First Overtone is the Second Partial. It is possibly best to avoid talking of Overtones at all, in relation to piano technology.

Partials are the components you get when decomposing the waveform into simple wave components, each of a single frequency. You need both frequency (term in the Fourier series) and amplitude (coefficient of the term in the Fourier series) to describe a partial.

There can be many more partials than just the principal and harmonics of a single wave vibrating in a plane. For instance, piano notes with 2 or 3 strings experience interference between the strings, and sympathetic resonance of undamped strings, which gives rise to a set of partials significantly more complex than just the harmonic series of a single vibrating string.
Good points, thank you.
Originally Posted by pyropaul
Good point about the Weinrich effect - but this occurs during tuning, no? Once a note is tuned, all the sympathetic locking is, well, locked in.
It's been a long time since I read his lectures on piano acoustics. I'd have to go reread them to see how they apply.

So in one respect, yes sympathetic locking occurs at the time of tuning. There is a difference if you resonate a single note alone while tuning, vs. resonating other intervals together while tuning the note. It all will produce different results. But, even after it is set, there is still a "pull" on each note. So a C, if used as a root (of a chord), 3rd, 5th, 7th, 9th, etc. on an acoustic piano will get pulled in different directions when measured. C doesn't just stay in a fixed place and "beat" like a digital piano. There are literal shifts that take place based on what is resonating. This can be measured. Ideally, the tuner will tune the piano in such as way there is maximum flexibility in this respect. That allows the piano to sound more in tune with itself, but it also allows it sing more. For those that are familiar with the "bell-like resonance" of the golden age of pianos and tuning, this is what is going on.
Posted By: MartF Re: most common non ET temperaments in 2020? - 10/24/20 01:51 AM
Originally Posted by P W Grey
I regularly use EBVT as a starting point

Thanks Peter, that's this one isn't it? Oddly I can't find it on rollingball.com.

Originally Posted by LemonColor
No one has ever asked me for a non ET. They just want me to tune the piano.

That's what I was expecting most people to say :-)

Originally Posted by P W Grey
My personal favorite is Thomas Young's rules from 1799 for personal taste with a C-E 3rd at about 5 bps.

Is that Young's first or second temperament? And now I'm not sure if that's your preference or EBVT is!

Originally Posted by N W
He said "Good Lord, no! Those tunings only work on harpsichords because there's no sustain...my piano would sound ghastly".

Right, and I know some others prefer ET too. I wonder if he tried it or just imagined how bad it would be!

Originally Posted by RonTuner
only 2 people that were knowledgeable have asked for ET, so I tune a mild Well temperament on everything.

I like that approach! If you don't ask, you get WT. Next time, if they don't specify, maybe try La Monte Young's "The Well-Tuned Piano" :-)

Originally Posted by Ed Foote
there are others that have found the WT tracks better with guitars.

Interesting. Maybe it's because guitars are often poorly tempered! Some slight differences between instruments probably makes it sounds more.. human.

truetemperament.com make squiggly fret WT guitar necks. Reviewers/bloggers think it's ET with better intonation, which it is (straight frets don't quite work as each string bends sharp a different amount when fretted).

But it's also a WT inspired by Bradley Lehman's Bach temperament. This used to be on their website (and can be found via archive.org), but now they're more vague about it. My hunch is explaining WT was confusing to customers. They still list the offsets from ET on their How to tune page though.

There's also evidence that EVH and Frusciante tuned the B string down to get pure major thirds (though in Frusciante's case it's not clear if it was intentional).

Originally Posted by Ed Foote
given the rarity of amateur players that are comfortable playing in 5 sharps, the WT increases the overall consonance

I'm a complete newbie, and the first two pieces I decided to try.. one had 6 flats and the other 5 sharps!

Originally Posted by Ed Foote
to my surprise, have several very professional jazz pianists that have come to fell ET is bland and uninteresting.

Yes that's what started me on this journey - sometimes picking up the guitar and feeling everything sounds bland. I'd be interested to know what these jazz pianists use, and whether they talk about it, or if it's their "secret sauce". I wonder what e.g. Nina Simone, Monk and the other greats used, and how much they understood about temperaments.

Originally Posted by pyropaul
I've heard it said by Bill Bremmer that "Reverse Well" is the most common temperament wink

Is that similar to the unwell?

Originally Posted by piano411
MartF, musicians seem to be using whatever they get, whether they like it or not.

Absolutely. In 20 or 50 years time, maybe digital pianos will come with a different default, and that will then be what most people use.

Originally Posted by VladK
Here is one cool hint from his own manuscript

Thank you, I'm familiar with larips.com but hadn't seen those articles before.

Originally Posted by kpembrook
With UT, the partials don't line up the same way and as a result have a dissonance in the higher coincident partials.

Isn't this true of ET as well? I think you're making a good point, but I'm not sure I understand it.

Originally Posted by kpembrook
I tried doing the EBVT for my customer with the most discriminating ear ... he said he "hadn't noticed anything different".

Maybe he's drawn to other aspects of the sound and tuning?

Originally Posted by VladK
If only I was good enough to generate any meaningful conclusions by playing it ... for me any temperament sounds good enough.

Um I think you just came to your own meaningful conclusion :-)

If you want to experiment though, I would go straight to pure/just intonation, meantone or quarter tones arabic-style. Get familiar with something really different. Try a 7/4 "harmonic 7th" like Michael Harrison for example.

Originally Posted by piano411
I think people should be able to set their own standards, but I think that it should be done with full-disclosure so that there can be a kind of informed consent.

Yes, I get the impression temperaments are not part of most people's musical education, and therefore many don't realise alternatives even exist.
I just entered the world of temperaments when my first tuning on my brand new August Forster 215 resulted in a different sound than I was accustomed - so much so that I had the piano retuned to a second temperament and am quite pleased now. Below are the tuner's notes:

First tuning -

Tuning style followed the pattern found: Sharp 4-2 tuning in bass, excessive stretch
In the 7th octave(6-3 bass and modified 4-1 tuning were used in the 7th octave used by me
double octave 4ths and 5ths in the middle of the piano)
Established pitch at 443 Hz(1st tuning)
Fine tuned to A=443 Hz(2nd tuning)

Second tuning-

Tuning style: OTS 3, 8/4 bass .5 cent treble octaves, 7th & 8th octaves: 2/1
Established pitch at 443 Hz(1st tuning)
Fine tuned to A=443 Hz(2nd tuning)

Which of the two styles above are more common?
Originally Posted by blueviewlaguna.
Which of the two styles above are more common?
blueviewlaguna, those are notes about how the octaves are stretched. That's different from temperament. A temperament is how the notes between the octaves are divided.

It seems like that information applies to a specific software. For example, I don't know what "OTS 3" stands for.
Originally Posted by pyropaul
Originally Posted by Sweelinck
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
From a theoretical perspective, this is false, because the overtone series is infinite, and piano samples are finite.

From a practical perspective, piano samples may contain all audible overtones. Frequencies beyond the Nyquist limit will be filtered out, as will harmonics at amplitudes below the dynamic range floor of the mics used when sampling. The latter perhaps could lead to audible differences, but I'm not sure. The advertised dynamic range specs of the best mics would suggest audible harmonics should be captured, but the issue is complex.

If you think our ears have infinite bandwidth you're sorely mistaken.
I don't think I said that, nor that our ears have infinite dynamic range, which I think is what you were trying to say. I don't think the tone of the SK-EX patch in my DP sounds identical to an SK-EX. There are audible differences. But as I said, from a practical perspective, piano samples may contain all audible overtones, but I'm not sure. Were you planning to offer any rigorous analysis to substantiate your claim that they are identical, even within the audible limits of human hearing?
Originally Posted by piano411
Originally Posted by blueviewlaguna.
Which of the two styles above are more common?
blueviewlaguna, those are notes about how the octaves are stretched. That's different from temperament. A temperament is how the notes between the octaves are divided.

It seems like that information applies to a specific software. For example, I don't know what "OTS 3" stands for.


Thanks for the clarification - I do recall my tech advising that he was changing from "favoring fifths" to "favoring thirds". The interesting part is that I had my previous Schimmel grand tuned by a different tech and I never took issue with how the tuning sounded.
Originally Posted by blueviewlaguna.
I do recall my tech advising that he was changing from "favoring fifths" to "favoring thirds".
Oh, well, that does sound like unequal temperament language! It sounds like they are moving from a well temperament to meantone temperament. But, meantone is very harsh in the extended key areas. Basically it doesn't work. I'd be surprised if that is really what they did.

Did you ask for an unequal temperament or anything special? Does the tuner know what kind of music you play?
Originally Posted by piano411
Originally Posted by blueviewlaguna.
I do recall my tech advising that he was changing from "favoring fifths" to "favoring thirds".
Oh, well, that does sound like unequal temperament language! It sounds like they are moving from a well temperament to meantone temperament. But, meantone is very harsh in the extended key areas. Basically it doesn't work. I'd be surprised if that is really what they did.

Did you ask for an unequal temperament or anything special? Does the tuner know what kind of music you play?


No, that comment just relates to the stretch. The second tuning (referencing OTS) used Reyburn Cyber Tuner and the first tuning is cryptic enought to possibly be the notes from an aural tuning or perhaps Tunelab? If it was an aural tuning, then it is possible that the temperament was also skewed.

Ron Koval
Originally Posted by kpembrook
With UT, the partials don't line up the same way and as a result have a dissonance in the higher coincident partials.


Isn't this true of ET as well? I think you're making a good point, but I'm not sure I understand it.

****************

No. This is something that can be empirically observed. Actually, it's a function of the inharmonicity of piano wire which results in the the higher partials being sharp to whole number multiples (see ample discussion above about harmonics, partials and overtones). So, the widened thirds of ET put the higher partials "in tune" at the expense of a few beats at the fundamental or lower partials. The other tunings try for "purer" intervals but the "pure" in practice is at the fundamental or lower partial level, thus leaving the higher partials less consonant. So, the more "consonant" intervals a given tuning has the more those intervals will not be consonant at higher coincident partials. So, it's not about UT as a concept, per se. It's that the more untempered or less-tempered thirds there are, the more out-of-tune higher coincident partials there will be.

The way I learned setting the temperament from Travis's book doesn't involve counting beats. (Who can really count--or even estimate-- whether a particular third is 6.2 bps or 6.1, anyway?). I tune the thirds so that the upper partials "line up" and then the beat rates will be correct (or acceptable, or closely matching somebody's theory). The test is that 3 stacked thirds should equal an octave and that's what I get.

On a separate "note" (so-to-speak cool ), I'd like to bring back something I had mentioned before regarding the usage of electronic devices to "measure" what we are doing. I gained a helpful term from Brian Capleton's Theory and Practice of Piano Tuning (and I confess I haven't read all 680 pages yet). Capleton's term to describe "what we hear" is "soundscape". Electronic devices (at least not yet) do not measure the soundscape in its entirety but rather extract a single aspect of that soundscape and presents that information in some sort of display or definable quantity. The complex interactions and events of multiple-note chords (even basic two-note intervals) remains to be explored and described using scientific devices. (Not saying it can't happen -- just that it hasn't yet). My comment here is in regard to people incorrectly using what is reported by measuring devices as somehow "correct" and "true" when, in fact, they are still operating at more of a Middle Ages level in comparison to the richness perceived by the human ear even though we can't attach numerical quantities to our perceptions. Hearing is nonetheless valid.
Nice points. Capleton's book is quite something, isn't it. I really like your last two sentences above - we have yet to see a recital delivered to an audience of appreciative Electronic Tuning Devices.....
Originally Posted by Sweelinck
Originally Posted by pyropaul
Originally Posted by Sweelinck
Originally Posted by pyropaul
Well most modern digitals use samples of real pianos so they absolutely have the same partials as the acoustic they were sampled from.
From a theoretical perspective, this is false, because the overtone series is infinite, and piano samples are finite.

From a practical perspective, piano samples may contain all audible overtones. Frequencies beyond the Nyquist limit will be filtered out, as will harmonics at amplitudes below the dynamic range floor of the mics used when sampling. The latter perhaps could lead to audible differences, but I'm not sure. The advertised dynamic range specs of the best mics would suggest audible harmonics should be captured, but the issue is complex.

If you think our ears have infinite bandwidth you're sorely mistaken.
I don't think I said that, nor that our ears have infinite dynamic range, which I think is what you were trying to say. I don't think the tone of the SK-EX patch in my DP sounds identical to an SK-EX. There are audible differences. But as I said, from a practical perspective, piano samples may contain all audible overtones, but I'm not sure. Were you planning to offer any rigorous analysis to substantiate your claim that they are identical, even within the audible limits of human hearing?

I don't have any rigorous proof but there have been plenty of studies done. Many years ago I took part in a demo of DSD audio. There were musicias in a room and a small audience in another room with high quality speakers etc. There were two sources - one was direct from the performers and the other passed through a DSD audio chain (which, for fun, was also transmitted over laser so the demonstrator at one point could cut the audio by blocking beam). We had to sit through a performance while the sources were switched and we had to write down which we though was "live" and which passed through the DSD chain. To cut a long story short, at the end no one could tell the difference between the two (the audience was blind to which was which). Then a fun discussion about how it all worked and cutting of the laser beam etc. Of course, this was a live performance, not fixed piano samples so I take the points about any dynamic resonance changes introduced by the tuning are not produced by replaying/retuning the samples. This is one for the Pianoteq guys to add if it's significant (it could well be).
Originally Posted by kpembrook
[
Electronic devices (at least not yet) do not measure the soundscape in its entirety but rather extract a single aspect of that soundscape and presents that information in some sort of display or definable quantity. The complex interactions and events of multiple-note chords (even basic two-note intervals) remains to be explored and described using scientific devices. (Not saying it can't happen -- just that it hasn't yet). My comment here is in regard to people incorrectly using what is reported by measuring devices as somehow "correct" and "true" when, in fact, they are still operating at more of a Middle Ages level in comparison to the richness perceived by the human ear even though we can't attach numerical quantities to our perceptions. Hearing is nonetheless valid.

Greetings,
I doubt electronic devices will be developed that will match the perception of the human ear, (there won't be enough money in it!). However, they can have an advantage in making comparisons. They do not suffer the subjective, and usually variable, response that human perception automatically comes with, as 'wetware" is fickle and usually dependent on an emotional basis, whereas the computer delivers information with a very consistent validity. What we do with that is another matter, but whatever its 'facts' are are replicable, which is a valuable asset in any kind of comparison.
Regards,
Originally Posted by pyropaul
I don't have any rigorous proof but there have been plenty of studies done. Many years ago I took part in a demo of DSD audio. There were musicias in a room and a small audience in another room with high quality speakers etc. There were two sources - one was direct from the performers and the other passed through a DSD audio chain (which, for fun, was also transmitted over laser so the demonstrator at one point could cut the audio by blocking beam). We had to sit through a performance while the sources were switched and we had to write down which we though was "live" and which passed through the DSD chain. To cut a long story short, at the end no one could tell the difference between the two (the audience was blind to which was which). Then a fun discussion about how it all worked and cutting of the laser beam etc. Of course, this was a live performance, not fixed piano samples so I take the points about any dynamic resonance changes introduced by the tuning are not produced by replaying/retuning the samples. This is one for the Pianoteq guys to add if it's significant (it could well be).

The dynamic range of DSD well exceeds the dynamic range of human hearing, which in turn exceeds that of 16x44.1kHz. It takes 20 bits to fully encode the dynamic range of human hearing. But that range includes very loud sound pressure levels that would damage the inner ear and result in hearing loss. If you limit the level on the loud end of the range, I doubt the dynamic range of human hearing is remapped so that it translates into sufficient resolution on the quiet end of the range still attain the same full dynamic range.
I would add that the dynamic range of human hearing lessens as frequency increases. As harmonics increase in frequency, they decrease in amplitude, and our ability to hear them also decreases.

Also, a large hall to accommodate an audience will attenuate high frequencies much moreso than your living room due to travelling further. This will filter out high frequency harmonics.
Originally Posted by P W Grey
Once upon a time I thought that Owen Jorgensen was a nut case. This was because I was ignorant of the history of keyboards and tuning, and trained that ET was "HOW" we tune pianos...period...end of discussion. Then I decided to actually try some of what he was talking about. The rest is history (as they say).

Peter Grey Piano Doctor

There is history, and there is Jorgensen's account of history, but in neither were there pianos with the tonal sustain of a modern piano in the first half of the 19th century.
Originally Posted by Sweelinck
Originally Posted by P W Grey
Once upon a time I thought that Owen Jorgensen was a nut case. This was because I was ignorant of the history of keyboards and tuning, and trained that ET was "HOW" we tune pianos...period...end of discussion. Then I decided to actually try some of what he was talking about. The rest is history (as they say).

Peter Grey Piano Doctor

There is history, and there is Jorgensen's account of history, but in neither were there pianos with the tonal sustain of a modern piano in the first half of the 19th century.

Greetings,
This brings up another interesting difference between temperaments where all thirds are equally tempered (at 14 cents out of "tune") and the irregular, circulating temperaments that follow the common form of tonic thirds being widened as the keys follow the circle of fifths from C,(or, in the Valotti model, F). In this form of ascending widths of thirds, virtually all WT's are the same, so it appears that it was a form so common that it composers could take for granted that the key of C would be far more consonant than the key of C#, etc. Indeed, a study of key usage for various levels of expression tends to support that thesis. The use of modulation also supports this, as it is rare, if ever, that a resolution moves towards a more highly tempered triad. Doing this in a WT leaves an uncomfortable and unsettled feeling in the listener.

It is often stated that the greater sustain of the modern piano is the reason that original pedal markings in much classical music cannot be used, that the increased sustain creates a "muddiness" or blurring of the harmony. I, and many others have found that this is not necessarily true. In my own experience, of listening to numerous pieces performed on numerous temperaments, and comparing numerous pieces on the same WT, what becomes apparent is that with a well-tempered piano, the original pedal markings do NOT create any blurring, but rather, a reinforcing of the harmony. A particularly striking example is the first 17 measures or so of the 3rd mvt. of the "Waldstein" sonata. LVB writes to hold the pedal down the entire time! In ET the results are horrendous, on a Young or Kirenberger, it's a completely different effect.

When every third, tenth, and seventeenth is busily beating, the dampers must be used to clean the harmony up by removing residual dissonance. When these same intervals are tuned far closer to consonant, there is nothing to clean up, and the resulting sound builds upon itself.The modern piano offers a perfect tool to amplify this asset.

Just another reason to consider that the composers between Bach and Chopin may have written what they did, in the keys that they did, to take advantage of the various harmonic resources found in a tuning system of their time.
Regards,
I have to agree!

Okay...so it's true that OJ had a particular viewpoint in these matters and some of the conclusions he came to may have been not exactly on the money, but the research that he did (while not being the end of it) is certainly significant. I can say with absolute certainty that ALL of the pianists I have introduced to WT (playing exclusively period appropriate music) would never go back to ET willingly. They tolerate ET on other pianos because they have no choice, but on their own instrument it's WT. It's kind of like a cherished family recipe, I guess.

Peter Grey Piano Doctor
Originally Posted by Ed Foote
A particularly striking example is the first 17 measures or so of the 3rd mvt. of the "Waldstein" sonata. LVB writes to hold the pedal down the entire time! In ET the results are horrendous, on a Young or Kirenberger, it's a completely different effect.
You're talking about the Rondo? Where would you get that idea that it is a 17 measure pedal? Even LvB's original manuscript is crystal clear. It is an 8 bar pedal. Even so, it's a 4 measure phrase repeated. The only harmony involved is I and V642 - 6 measures of tonic and 2 measures of dominant.

That does not sound horrendous in ET!
Fortepianist Tom Beghin is a recognized authority on historically accurate performance of early piano music. Here he discusses the damper instructions for the Moonlight Sonata, and how the reduced tonal sustain made it work on Beethoven's piano. There is no mention of temperament in that context.

https://youtu.be/LJuNgjb2HcY

I used to own a clavichord that I tuned myself. I'm not particularly good at tuning, but I could set a usable meantone on an unfretted clavichord. Piano literature has moved beyond unequal temperaments. I would only consider an unequal temperament on my acoustic piano if it were a 2nd piano. Digital instruments offer a much wider palette of exploration of historical temperaments, for reasons I stated above.
Quote
...given the rarity of amateur players that are comfortable playing in 5 sharps...
Seriously? There are quite a few amateur pianists on PW who have advanced far beyond the point of being intimidated by playing in 5 or 6 sharps or flats.
Originally Posted by Sweelinck
Quote
...given the rarity of amateur players that are comfortable playing in 5 sharps...
Seriously? There are quite a few amateur pianists on PW who have advanced far beyond the point of being intimidated by playing in 5 or 6 sharps or flats.

Greetings,
Yes, seriously. The pianists on PW may or may not be a representative sampling, though I would suspect they are more serious about the instrument and its literature than the general public. I am speaking of the pianists I have encountered over the last 45 years as I did the 37,000 tunings that I have done. Aside from the 38 years at a university's school of music, and even more years on Music Row dealing with professionals, the majority of the home pianos I have serviced are played by amateurs that play music in keys with less than 5 accidentals. I know this because I ask, and look at the literature that is around the piano, (most techs do this). So don't take it personally, I am speaking of the"piano public" at large that I have personally encountered.

Beyond this, a survey of the literature written between 1700 and 1900 will show that all keys were not employed equally, but rather, show a bias towards the keys closer to C than F#(the harmonic extremes in the circle of fifths). I am away from my home computer, but upon return, I can publish the breakdown of keys favored by major composers during this time. It correlates with the developement of tuning equality, and argues against a sudden move from restrictive meantime to totally equal.
regards,
Originally Posted by Ed Foote
It is often stated that the greater sustain of the modern piano is the reason that original pedal markings in much classical music cannot be used, that the increased sustain creates a "muddiness" or blurring of the harmony. I, and many others have found that this is not necessarily true. In my own experience, of listening to numerous pieces performed on numerous temperaments, and comparing numerous pieces on the same WT, what becomes apparent is that with a well-tempered piano, the original pedal markings do NOT create any blurring, but rather, a reinforcing of the harmony.
The muddiness that people are complaining about comes from the approach. If you choke off the piano with a temperament strip, then you are only listening to the beginning of the sound, and not how the sound effects the rest of the piano as a whole. A muddy and blurry damper pedal is the signature of someone that only cares about the attack. Tune with two mutes and the damper pedal, and that problem goes away.

The best way to judge the quality of a tuning is to use the damper pedal. Does the damper pedal help, or hurt the music? Pianist use damper pedal all the time. If we want it to work, and be musically functional, then we need to be able to tune with it. There is a huge difference between those that tie up the piano, and those tuners that allow the piano to resonant freely during the tuning process.
Posted By: N W Re: most common non ET temperaments in 2020? - 10/26/20 04:55 PM
Originally Posted by piano411
Originally Posted by Ed Foote
It is often stated that the greater sustain of the modern piano is the reason that original pedal markings in much classical music cannot be used, that the increased sustain creates a "muddiness" or blurring of the harmony. I, and many others have found that this is not necessarily true. In my own experience, of listening to numerous pieces performed on numerous temperaments, and comparing numerous pieces on the same WT, what becomes apparent is that with a well-tempered piano, the original pedal markings do NOT create any blurring, but rather, a reinforcing of the harmony.
The muddiness that people are complaining about comes from the approach. If you choke off the piano with a temperament strip, then you are only listening to the beginning of the sound, and not how the sound effects the rest of the piano as a whole. A muddy and blurry damper pedal is the signature of someone that only cares about the attack. Tune with two mutes and the damper pedal, and that problem goes away.

The best way to judge the quality of a tuning is to use the damper pedal. Does the damper pedal help, or hurt the music? Pianist use damper pedal all the time. If we want it to work, and be musically functional, then we need to be able to tune with it. There is a huge difference between those that tie up the piano, and those tuners that allow the piano to resonant freely during the tuning process.
Presumably this on a second pass. I like to check through as you describe and adjust but surely you can't start a tuning this way?...any sounds from anywhere but the string you are tuning will be out as the tuning is incorrect at the start. All the harmonics will be wrong until you've tuned it won't they?
Nick
Originally Posted by Ed Foote
Yes, seriously. The pianists on PW may or may not be a representative sampling, though I would suspect they are more serious about the instrument and its literature than the general public. I am speaking of the pianists I have encountered over the last 45 years as I did the 37,000 tunings that I have done. Aside from the 38 years at a university's school of music, and even more years on Music Row dealing with professionals, the majority of the home pianos I have serviced are played by amateurs that play music in keys with less than 5 accidentals. I know this because I ask, and look at the literature that is around the piano, (most techs do this). So don't take it personally, I am speaking of the"piano public" at large that I have personally encountered.
I didn't take it personally. Sure, there are pianists at all levels who need their pianos tuned. But a beginning or intermediate player who is intimidated by reading something in Db major would do well to play more music in 5 or 6 sharps/flats, not less. Such a player would be unlikely have the historical and theoretical knowledge to choose a temperament, and if presented with the information that equal temperament was the only temperament usable for all piano literature, would they choose an unequal temperament? Surely, a technician would not tune an unequal temperament on a piano for a customer who just asked to have their piano tuned with no discussion of temperament.

You would be hard pressed to conceptualize what is in my repertoire from what is on my piano's music desk at some arbitrary point in time.
Originally Posted by Sweelinck
Surely, a technician would not tune an unequal temperament on a piano for a customer who just asked to have their piano tuned with no discussion of temperament.
That is exactly what has been going on for a very long time now. Technicians feel that piano owners don't understand what unequal temperament is all about anyway, so they end up tuning however they want. For some reason, they think they know what is best for someone else. They justify their actions by saying things like the uneducated piano populous is unlikely to play in the extended keys to know better.
Originally Posted by N W
Presumably this on a second pass. I like to check through as you describe and adjust but surely you can't start a tuning this way?...any sounds from anywhere but the string you are tuning will be out as the tuning is incorrect at the start. All the harmonics will be wrong until you've tuned it won't they?
Yep, I basically tune that way all the time. It can take a while to get used to listening to the "tone" resonating through the system instead of the "sound" of the strings beating. You have to learn to focus on a different part. Instead of listening to the sound of the intervals beating progressively, all of the effort instead go to ensuring that the beats get sucked into the tone of the instrument and used musically as quickly as possible. It is all about tone. I want to build the piano's tone in a musically useful way, not mathematically manage beat rates. I want the beats to equally and evenly go away.
Quote
In this form of ascending widths of thirds, virtually all WT's are the same, so it appears that it was a form so common that it composers could take for granted that the key of C would be far more consonant than the key of C#, etc. Indeed, a study of key usage for various levels of expression tends to support that thesis.

Which composer? Chopin composed his Preludes in the winter of 1838/1839, and earlier works like Nocturne 27/2 in Db in 1835, and Nocturne 9/3 in B major and Op 10 Etudes (10/5 in Gb major) were composed during 1829-1832.

I remember years ago a tuner who was a proponent of Jorgensen's recommendations claiming to me that Chopin's pianos were tuned using a Werckmeister temperament, likely incorrect by the time early works like Op 9 and 10 were composed.
Originally Posted by piano411
Originally Posted by Sweelinck
Surely, a technician would not tune an unequal temperament on a piano for a customer who just asked to have their piano tuned with no discussion of temperament.
That is exactly what has been going on for a very long time now. Technicians feel that piano owners don't understand what unequal temperament is all about anyway, so they end up tuning however they want. For some reason, they think they know what is best for someone else. They justify their actions by saying things like the uneducated piano populous is unlikely to play in the extended keys to know better.

hmm, I can't say what has been going on for a very long time with others, but I have been offering a choice to my clientele for the last 27 years. I always offer to return the piano to ET for free if they are not happy with the well-temperament I select for them. So far, exactly three of them have done so, but the normal response is that the piano sounds better the way I chose for them. A common response is nothing short of epiphany for may classical pianists. Since I charge significantly more than anyone in the state, and these customers have been loyal for years, I think I am on to something more than smoke and mirrors.

And to the point that extended keys sound worse, that is the argument offered by ignorance of the musical qualities. Extended keys have better fifths and fourths to go along with the more expressive thirds, and much music, old and new, actually creates a more intense response for it. Chopin is a prime example. His melodic lines, supported and contrasted by a very brilliant harmony, tend to have an ethereal effect, (according to a number of my more professional customers).

The staunch supporters of ET are arguing that a 13.7 cent third is tempered as far as the ear can tolerate. This leaves them supporting a temperament in which EVERY third is maxed out. In this temperament, there is an out of tune quality to every key. Just because they are all out the same doesn't change the fact that everything is out and the ear just has to get used to it.

I am amused by the defenders of the commonly sold product, but I have enough years of selling tunings to know where the job security and profit is. It ain't ET.

If ET was the common tuning during the classical era, we are left with no explanation why all the composers, (except Chopin) favored the choice of key in similar ways.The 'extended' keys were used least, the closer keys, used most. There is a pattern to choice of key that directly correlates to the width of the thirds in a WT. Coincidence? I don't think so, and neither does my clientele.
Originally Posted by Sweelinck
Quote
In this form of ascending widths of thirds, virtually all WT's are the same, so it appears that it was a form so common that it composers could take for granted that the key of C would be far more consonant than the key of C#, etc. Indeed, a study of key usage for various levels of expression tends to support that thesis.

Which composer? Chopin composed his Preludes in the winter of 1838/1839, and earlier works like Nocturne 27/2 in Db in 1835, and Nocturne 9/3 in B major and Op 10 Etudes (10/5 in Gb major) were composed during 1829-1832.

Chopin is the exception, sorta. When one graphs his compositions according to key usage, what we find is a reversed mirror image of the graphs of all others. He did not use all 12 keys equally, but the pattern is still the same, just backwards. I would think a Werckmeister would be a poor choice. However, just for something to compare, when I produced the CD "Six Degrees of Tonality", I used an atypical temperament, the DeMorgan, for Chopin, which reversed the key colors of a normal WT. It removed some of the brilliance, but it will have to be heard before a credible critique can be offered. This CD also has a Mozart piece in three different tunings. For those that want to hear what meantime and ET do to his composition.
Chopin is not a classical era composer.
Originally Posted by Ed Foote
I can't say what has been going on for a very long time with others, but I have been offering a choice to my clientele for the last 27 years. I always offer to return the piano to ET for free if they are not happy with the well-temperament I select for them.

I am amused by the defenders of the commonly sold product, but I have enough years of selling tunings to know where the job security and profit is. It ain't ET.
The issue wasn't about choice, it was about informed consent. If you are informing your customers, and offering to re-tune back to the standard for free, then I don't have a problem with what you are doing. Of note is that you acknowledge with your policy that you know there is an expectation or standard ET to return too.

It's interesting that you would characterize your tuning as a product that ensures job security and profit. The same people have hired me for decades because of who I am and what I can do with their piano, not because I have a magic temperament I sell them. People invest in me, not the name of the temperament that I tune. Again, I encourage people try WTs as much as possible. My experience is totally different than yours. The professional musicians I work with go right back to ET.

Maybe I don't know how to tune well temperaments very well, or maybe you don't know how to tune ET in a way that it is musically useful. The way you describe ET doesn't sound very appealing.
Originally Posted by piano411
Maybe I don't know how to tune well temperaments very well, or maybe you don't know how to tune ET in a way that it is musically useful. The way you describe ET doesn't sound very appealing.


Gee, Maybe I don't know how to "tune ET in a way that is "musically useful?" When a producer is responsible for a recording session that'll cost anywhere from $15,000 to $25,000, they consider me and my tuning to be useful. When Yo Yo Ma and Edgar Meyer record with my ET and both find the tuning to be "wonderful", I think that is useful. When the dean of a major university's school of music tells me, (after 38 years) that he is appreciative of never having a problem on stage with my tuning,I tend to relax about the quality of my work.

I was trained by perhaps the most highly regarded tuner and teacher in the trade, which allows me to feel like my tuning passes the most stringent muster available, and after tuning, displaying, and discussing my tunings at numerous PTG Institutes, in front of the most critical,(and, at times, skeptical) audiences available, I have often been told that my tunings were appealing, so I think I have the hang of it. I certainly am not afraid to put my name on my work instead of anonymously throwing innuendo around with those I don't agree with. Talk is cheap when it doesn't have to be claimed.
So, Ed_Foote, like you told someone else, don't take it personally.

Honestly, it's not helpful to see what you say that other people say about how you tune ET vs. unequal temperaments. Unless you are suggesting that we individually contact the people you mentioned to ask further questions? Anyway, before you were saying that only 3 people asked for a return to the standard ET, from your normal approach of unequal temperament, and now it seems you are saying you tune ET all the time and people love it. I can't judge you on what you say other people say about your work.

I can, however, judge on you on how you describe your own ET work. You described the pedal as being muddy and blurring of the harmony. That is what you said. Since that is happening to you, then no, the way that you are tuning ET is not musically useful. If the pedal make the harmony blurry, then something is wrong with what you are doing.That is probably why you do better with unequal temperaments. Your tone doesn't build up in a musically useful manner in ET. It might beat perfectly and mathematically correct, but musicians can't use "beats" musically. That's not how music works. Musicians work with tone and resonance, not beats.

If you want to talk about specifics, then we could compare and contrast your Mozart examples. I can go into more details, but the ET that you put on the piano was extraordinarily dry and not musically useful. It seemed mathematically fine, but it was dry and boring. ET doesn't need to be like that. It's probably just the way that you learned to tune. That's fine. But, that is not what I am looking for in ET on the pianos that I work with.

I want my pianos to sing, I want the tone to build up in a musically useful way, and I want the piano to have an open resonant presence (like it is in a hall, even though it is in a room). My objectives and your objectives with piano sound are different. And, that is OK. You think a dry tone and messy pedal is good quality. I don't. I go for a wet tone that combines in the piano into something musically usable.
Originally Posted by Ed Foote
The issue wasn't about choice, it was about informed consent. If you are informing your customers, and offering to re-tune back to the standard for free, then I don't have a problem with what you are doing. Of note is that you acknowledge with your policy that you know there is an expectation or standard ET to return too.
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
Originally Posted by Sweelinck
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
I don't have the insert in front of me to quote the exact verbiage that Ed_Foote used for the CD, but apparently the changes in unequal temperament used for the recording was such that it necessitated a complete restringing before the piano was put back into service.
Originally Posted by Sweelinck
Originally Posted by Ed Foote piano411
The issue wasn't about choice, it was about informed consent. If you are informing your customers, and offering to re-tune back to the standard for free, then I don't have a problem with what you are doing. Of note is that you acknowledge with your policy that you know there is an expectation or standard ET to return too.
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
My apologies for the incorrect quote attribution.
Posted By: N W Re: most common non ET temperaments in 2020? - 10/27/20 10:27 AM
Originally Posted by piano411
Originally Posted by Sweelinck
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
I don't have the insert in front of me to quote the exact verbiage that Ed_Foote used for the CD, but apparently the changes in unequal temperament used for the recording was such that it necessitated a complete restringing before the piano was put back into service.
No! Are you serious? Any chance of the actual verbiage? Surely something else was going on too?

Nick
Originally Posted by N W
Originally Posted by piano411
[quote=Sweelinck]How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
I don't have the insert in front of me to quote the exact verbiage that Ed_Foote used for the CD, but apparently the changes in unequal temperament used for the recording was such that it necessitated a complete restringing before the piano was put back into service.
No! Are you serious? Any chance of the actual verbiage? Surely something else was going on too?

Nick[/quote

Our hall's D was due to be restrung, so I had no qualms about moving it into a meantone tuning for the last example of the recordings. It would have been a small chore to re-stabilize it but I didn't have to. The dramatic change in tension on selected notes posed no danger to the piano, (according to Steinway engineers I spoke with). it didn't need to be restrung because it had been tuned in any particular way, it needed to restrung because 20 years of heavy use.

Moving a piano from ET to most of the WT''s requires less than half the notes to move 3-5 cents, and I haven't yet seen the pianos's stability suffer from it. Normal between seasons changes in pianos have a greater departure that a change of temperament.
regards,
Originally Posted by piano411
Originally Posted by Sweelinck
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
I don't have the insert in front of me to quote the exact verbiage that Ed_Foote used for the CD, but apparently the changes in unequal temperament used for the recording was such that it necessitated a complete restringing before the piano was put back into service.


It is exactly this type of misquote/misrepresentation that causes unnecessary problems. Yes, it was stated that he couldn't recall the exact verbiage, but the CONCLUSION that it had to be restrung BECAUSE of the tuning changes is so far into outer space as to be ridiculous. However an uninformed reader could be swayed by this. This is the power of propaganda.

I'm not being mean. It would have been better to ask Ed to comment on the matter before reaching an erroneous conclusion.

Peter Grey Piano Doctor
Originally Posted by P W Grey
However an uninformed reader could be swayed by this. This is the power of propaganda.
Propaganda is done from a position of power, which tries to control the narrative of what other people think. I think people are smart enough to think for themselves.

He had a chance to clarify the statement. This is what I get out of the statement. He would have had qualms tuning the piano to meantone, had he not planed to restring the piano afterwards; since he was going to restring the piano, he had no qualms tuning to meantone. What were the qualms about? There was a reason he put the disclaimer out there. And there was a reason why he's talking about qualms now. If it is a complete non-issue, then a person would not have "an uneasy feeling about the rightness of a course of action."

For the record, I don't have any qualms about it. But, again, I'm not the one that wrote it down as a disclaimer. I'm also not the one that described the re-stabilization back to ET as a small chore. In fact going from ET, to an unequal temperament, then back to ET is a lot of work. It is not like turning nobs.
piano411 - Since we all recognize that you are indeed a genius, perhaps you can be extraordinarily generous and explain to the rest of us dim bulbs just exactly what Ed could have done to make necessary the complete restringing of the piano before going back into service.

While I wait for your reply (with bated breath!!), I will conjecture that Ed has super powers that he is hiding from us. Yeh, that's it, I am sure of it.
True

Peter Grey Piano Doctor
Posted By: David-G Re: most common non ET temperaments in 2020? - 10/27/20 03:49 PM
Originally Posted by piano411
In fact going from ET, to an unequal temperament, then back to ET is a lot of work. It is not like turning nobs.

As a non-professional, but very interested in the topic, I have been following this thread with keen interest (and, I must say, with some surprise at the tone of some of the posts).

I would like to probe a little deeper regarding the above point. I am sure it is a lot of work - all tuning seems to me to be a lot of work - but is retuning to UT, and then back to ET more work than, say, a couple of pitch raises?
Originally Posted by David-G
I would like to probe a little deeper regarding the above point. I am sure it is a lot of work - all tuning seems to me to be a lot of work - but is retuning to UT, and then back to ET more work than, say, a couple of pitch raises?
No, it's probably the same as a few pitch raises. When you tune UTs the coincident partials get locked in, kind of like of like a magnet, so it takes a little bit of effort to pull them apart and then reset.
Posted By: David-G Re: most common non ET temperaments in 2020? - 10/27/20 03:59 PM
Not sure if you mean the coincided partials get locked into the piano or into the ear of the tuner? I can sort of understand the latter - I can't see any reason for the former.
*coincident partials. They get locked into the piano, not the tuner(person). If you put the damper pedal down, you can hear how they are locked into the system as a whole.
Posted By: N W Re: most common non ET temperaments in 2020? - 10/27/20 04:16 PM
Originally Posted by Ed Foote
Originally Posted by N W
Originally Posted by piano411
[quote=Sweelinck]How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?
I don't have the insert in front of me to quote the exact verbiage that Ed_Foote used for the CD, but apparently the changes in unequal temperament used for the recording was such that it necessitated a complete restringing before the piano was put back into service.
No! Are you serious? Any chance of the actual verbiage? Surely something else was going on too?

Nick[/quote

Our hall's D was due to be restrung, so I had no qualms about moving it into a meantone tuning for the last example of the recordings. It would have been a small chore to re-stabilize it but I didn't have to. The dramatic change in tension on selected notes posed no danger to the piano, (according to Steinway engineers I spoke with). it didn't need to be restrung because it had been tuned in any particular way, it needed to restrung because 20 years of heavy use.

Moving a piano from ET to most of the WT''s requires less than half the notes to move 3-5 cents, and I haven't yet seen the pianos's stability suffer from it. Normal between seasons changes in pianos have a greater departure that a change of temperament.
regards,
Phew! I thought there must be another reason. I can't see how altering the temperament could upset the stability of the piano. Altering the pitch, yes, but not the temperament.
Nick
Posted By: N W Re: most common non ET temperaments in 2020? - 10/27/20 04:20 PM
Originally Posted by piano411
Originally Posted by David-G
I would like to probe a little deeper regarding the above point. I am sure it is a lot of work - all tuning seems to me to be a lot of work - but is retuning to UT, and then back to ET more work than, say, a couple of pitch raises?
No, it's probably the same as a few pitch raises. When you tune UTs the coincident partials get locked in, kind of like of like a magnet, so it takes a little bit of effort to pull them apart and then reset.
I say 411, you are usually urging scientific data. "Kind of like a magnet" won't wash. Do you mean that you're tuning them out and then they magically go back to where they were?
I'd like to be able to understand exactly what you mean.
Nick
Originally Posted by N W
you are usually urging scientific data. "Kind of like a magnet" won't wash. Do you mean that you're tuning them out and then they magically go back to where they were?
Yes, I continue to argue scientific reasoning and observation.

So, the statement was tuning a piano is not like turning nobs on a mechanical device. When we turn the tuning pin, all of the partials do not move consistently in the same way. We can hear this, but we can also see it if we use a spectrum analyzer to see what is going on. If the tuning pin were like a nob, the everything would move together as a unit. It doesn't happen like that in the piano. The reason it doesn't work like that is because the strings are coupled to a resonating system. The 200+ strings are the piano's resonating system. The energy in that system flows like a current. When it is close, it will combine, when it gets further away it will create turbulence.

I didn't use the term magically, I used the term magnetically. I could have used gravity, but gravity is a concept that is difficult to internalize (I'm not a planet passing another planet, so I don't know what that is like). Many people have played with magnets, so that is similar property taking place for people to understand what is going on. But, again, it is not actual magnetic property. It just a way to describe an effect.

It takes work to reset the system. I wouldn't go straight from one to the other. I would literally reset the whole tuning system. Piano tuning 101 is to tighten the coils. In order to do that, we lower the tension down a 5th on a pair of strings, tighten the two coils, then tune to ET target. If you don't do that, there is going to be false beats happening in the sustain of the piano. That is the "magnetic" part of the partials interacting on the system.
I have not found this to be the case but it would be unwise for me to argue the point since I have no data to back me up.

However, if I am reading this correctly, it sounds like what is being described is the coupling of the strings at the bridge, often referred to as the "Weinrich effect" after Gabriel Weinrich, "Coupled Motions of Piano Strings", Scientific American, 1969 (I think). If so (and I could be wrong), this happens when two or three strings are within about a quarter of a cent of each other, and the mass of the bridge "forces" or "entrains" them to vibrate in phase (or extremely close to in phase) with each other. If you play them separately they are different, play them together they are the same. This is well documented, however it has nothing to do with UT or ET as it will occur either way. It could be colorfully described as "magnetic", but it's just physics at work.

Please correct me if I am wrong on this.

I certainly would NEVER drop the all the pitches a 5th and bring them back up again simply to switch from UT to ET or vice versa. That would create tremendous instability, not to mention unnecessary wear in the pinblock. Then again, perhaps I am reading this wrong.

Peter Grey Piano Doctor
Originally Posted by P W Grey
I certainly would NEVER drop the all the pitches a 5th and bring them back up again simply to switch from UT to ET or vice versa. That would create tremendous instability, not to mention unnecessary wear in the pinblock. Then again, perhaps I am reading this wrong.
I love playing around with UTs. I do it as much as I can, but when I am done, I go back to ET. If you don't reset the system, and you go straight there, then your damper pedal and sustain will be blurry and full of false beats, waves, and fuzziness. Sometimes technicians notice the pitch falling or raising after the attack. What is going on is that the partials are being pulled in different directions because they are still locked on to different parts of the system.

Setting the coil is step one in piano tuning. I believe it continues to be in most manufactures protocols for preparing a piano for the showroom. Instability comes from the coil not being tight. Not from moving a pitch down a 5th, which is approximately 1/64 of a turn. That's not going to wear out a pinblock. We can't tighten a coil at pitch, so, you have to go down to do the job.

Everyone knows that setting the coil is important, but very few technicians ever bother to take this basic step when tuning a piano. Most of them just tune the piano where ever it is. But, all of those technicians are dealing with blurry and messy sounding damper pedals and tunings full of false beats.

Reset the system like you are supposed to, and both of the aforementioned problems go away.
Originally Posted by P W Grey
it sounds like what is being described is the coupling of the strings at the bridge, often referred to as the "Weinrich effect" after Gabriel Weinrich, "Coupled Motions of Piano Strings", Scientific American, 1969 (I think). If so (and I could be wrong), this happens when two or three strings are within about a quarter of a cent of each other, and the mass of the bridge "forces" or "entrains" them to vibrate in phase (or extremely close to in phase) with each other. If you play them separately they are different, play them together they are the same.
What you are describing seems to deal only with unisons. I don't remember what Weinrich looked into. If that is the only thing he described, then no it appears we are talking about two similar yet very different things. I am talking about how the piano circulates energy thorough the entire system. The energy doesn't just stay on the string of a unison. It gets transduced into the board and recirculated throughout the rest of the system of strings. When the sustain is tuned, the piano has a wet, reverberant, musical quality that can build energy. When only the attack is tuned, the pedal will be messy, full of false beats, and appear noisy and dry.
Originally Posted by David-G
Originally Posted by piano411
In fact going from ET, to an unequal temperament, then back to ET is a lot of work. It is not like turning nobs.

As a non-professional, but very interested in the topic, I have been following this thread with keen interest (and, I must say, with some surprise at the tone of some of the posts).

I would like to probe a little deeper regarding the above point. I am sure it is a lot of work - all tuning seems to me to be a lot of work - but is retuning to UT, and then back to ET more work than, say, a couple of pitch raises?

Well, it depends on the temperament! As Ed already stated, many of the mild well temperaments in use only alter a few cents (100 cents=1/2 step) from ET on any single note. So really there's no problem to switch back and forth - it's just like a regular tuning.

Going back and forth from a strong temperament would be more like a pitch raise/fine tuning to get everything to line up right.

Ron Koval
Originally Posted by Sweelinck
Originally Posted by Ed Foote
The issue wasn't about choice, it was about informed consent. If you are informing your customers, and offering to re-tune back to the standard for free, then I don't have a problem with what you are doing. Of note is that you acknowledge with your policy that you know there is an expectation or standard ET to return too.
How does a change from ET to a WT and back to ET in a short period of time (say 2 weeks) affect tuning stability?

Not at all, if treated like a pitch raise & fine tuning for stronger temperaments. Mild temperaments are a breeze and don't really cause any problems.

Ron Koval
Originally Posted by piano411
Originally Posted by N W
you are usually urging scientific data. "Kind of like a magnet" won't wash. Do you mean that you're tuning them out and then they magically go back to where they were?
Yes, I continue to argue scientific reasoning and observation.

So, the statement was tuning a piano is not like turning nobs on a mechanical device. When we turn the tuning pin, all of the partials do not move consistently in the same way. We can hear this, but we can also see it if we use a spectrum analyzer to see what is going on. If the tuning pin were like a nob, the everything would move together as a unit. It doesn't happen like that in the piano. . (snip)


.

I haven't seen evidence that points to this being true. The testing I've done with the Verituner would suggest that the relationship between the partials of a single string/note is stable through the tuning of strings close to pitch - at least 1/4 step(25 cents - I've never tuned an alternate temperament with an offset bigger than this), perhaps more.

That is not to say that you don't get great results, just the reasons you give may not be behind what is actually producing those results.

Ron Koval
Posted By: N W Re: most common non ET temperaments in 2020? - 10/27/20 09:43 PM
Originally Posted by piano411
Originally Posted by P W Grey
I certainly would NEVER drop the all the pitches a 5th and bring them back up again simply to switch from UT to ET or vice versa. That would create tremendous instability, not to mention unnecessary wear in the pinblock. Then again, perhaps I am reading this wrong.
I love playing around with UTs. I do it as much as I can, but when I am done, I go back to ET. If you don't reset the system, and you go straight there, then your damper pedal and sustain will be blurry and full of false beats, waves, and fuzziness. Sometimes technicians notice the pitch falling or raising after the attack. What is going on is that the partials are being pulled in different directions because they are still locked on to different parts of the system.

Setting the coil is step one in piano tuning. I believe it continues to be in most manufactures protocols for preparing a piano for the showroom. Instability comes from the coil not being tight. Not from moving a pitch down a 5th, which is approximately 1/64 of a turn. That's not going to wear out a pinblock. We can't tighten a coil at pitch, so, you have to go down to do the job.

Everyone knows that setting the coil is important, but very few technicians ever bother to take this basic step when tuning a piano. Most of them just tune the piano where ever it is. But, all of those technicians are dealing with blurry and messy sounding damper pedals and tunings full of false beats.

Reset the system like you are supposed to, and both of the aforementioned problems go away.

Are you talking about setting up a new piano or are you saying you retighten the coils every time you tune the piano?
(I think wires are getting crossed in this discussion (pardon the intentional pun)).
If you do it every tuning.....why is it necessary?
I totally agree about doing it when I restring or change something big. Most tuning instability comes from the coil in my opinion. In fact, the tension around the coil is the highest tension section of the string.
I was once forced to use a hexacore string (in a great emergency) before a concert. It wasn't long enough and I only just got the wire through the hole in the pin. I tuned up and went and sat at the side of the stage in terror, ready to rush on when it flew off....
What actually happened was that the string didn't even go out of tune. Not at all. Not even in the second half. I checked at the interval in some shock.There was no coil at all remember.
So I went home and experimented. I'd never dare do this on a client's piano but I can promise you that if you string with no coil at all the tuning stability is amazing.
I later discovered that this effect is well known by guitarists who fit locking tuners which clamp the string so that no coil is necessary and the selling point of these tuners is purely tuning stability.
Nick
That's very interesting Nick.
Originally Posted by N W
I totally agree about doing it when I restring or change something big. Most tuning instability comes from the coil in my opinion. In fact, the tension around the coil is the highest tension section of the string.
I was once forced to use a hexacore string (in a great emergency) before a concert. It wasn't long enough and I only just got the wire through the hole in the pin. I tuned up and went and sat at the side of the stage in terror, ready to rush on when it flew off....
What actually happened was that the string didn't even go out of tune. Not at all. Not even in the second half. I checked at the interval in some shock.There was no coil at all remember.
Thank you N_W for your contribution! Hopefully your experience will begin to influence others. Getting that coil tight is so important. It can be a difficult process to master. But, setting the coil is really important. Most technicians don't do this basic step any more.

No, I don't do it every tuning. I do it if the piano is new to me(if I'll be maintaining the piano), if the pedal is messy/blurry sounding, or there is any kind of falseness happening in the string. Sometimes a string pair just needs a reset. After making the adjustment, it will go right to pitch. It's also part of my seasonal concert prep, but after a few years, it really gets locked in and is no longer necessary. Basically, you can feel it when you tune and how the string responds.

I deeply appreciate your story because I've experienced a similar thing. I've been experimenting using 2 turns in the bass, in stead of the more common 3. Just for fun, I tried only 1 turn. What you have stated is all true. With the 1 turn in the coil, the string goes right to pitch, and stays there. I've also tried 4 turns in the treble, as there was a manufacture that did that at one point in history. Getting 4 turns to stabilize in the treble was a nightmare, it would be impossible in the bass.
At the risk of a controversial posting, I will say that it is my belief that modern proponents of unequal temperament for romantic era music use very late estimates for the rise of ET. ET may have been virtually universal by 1900, but that does not mean it was a rarity in 1895. The opposite is true. ET gradually became more prevalent over a period of 80-90 years culminating in its widespread use by 1900, not starting in 1900.

Even in the early 17th century, compositions like Bull's Hexachord Fantasy and Sweelinck's Fantasia Chromatica clearly sound better to many listeners in ET than in meantone. Tunings of Werckmeister, Kirnberger, Vallotti, and Young were not yet developed. (Michael Praetorius had a temperament that closed the circle of 5ths, published in 1620).

But the discovery of logarithms by Dutch mathematicians in the early 17th century clarified the arithmetic and calculation of ET intervals, and ET had been known among lutenists since the 15th century. I think it is most likely that Bull and Sweelinck tuned their harpsichord or virginal with ET for at least some of their compositions. Fantasia Chromatica is often played on organ as well, and the organs in the Oude Kerk were unlikely tuned to ET then, but the piece is composed without requiring use of pedals, likely with harpsichord primarily in mind.

This article has some interesting info regarding the history of tuning and temperament. An interesting claim is that Bach set his own temperament by ear for the well-tempered clavier, and there is no written spec for it. This would suggest that we never will know how Bach tuned his harpsichord for WTC and later works.

http://huygens-fokker.org/docs/Kroesbergen_Bach_Temperament.pdf

A critique of some WT's:

https://casfaculty.case.edu/ross-duffin/why-i-hate-vallotti-or-is-it-young-1-1/

https://casfaculty.case.edu/ross-duffin/why-i-hate-vallotti-or-is-it-young-2-1/

https://casfaculty.case.edu/ross-duffin/why-i-hate-vallotti-or-is-it-young-3-1/
Posted By: David-G Re: most common non ET temperaments in 2020? - 10/28/20 01:02 AM
More years ago than I care to remember, when I was a mathematics student, I attended a lecture course on non-linear equations. Because it was so many years ago I remember rather little of it - but one thing that I do recall vividly was a discussion of coupled oscillators of slightly different frequencies, and how the coupling can bring the two to oscillate synchronously. This sounds very much like the Weinrich Effect that Peter referred to above.

I find Piano411's idea of coincident partials being locked into the system as a whole to be very interesting. But as a scientist I am not convinced by mention of "energy circulating through the entire system". I am sure it seems like that subjectively, but I feel that more precise understanding would be valuable. It is surely a question of frequencies and resonance rather than energy. I wonder if the Weinrich effect can apply to partials as well as to fundamental frequencies - it seems to me not at all unlikely that it would do. This could perhaps be the scientific basis for Piano411's observations.
411,

Now I'm curious since stability has not been a problem for me for a very long time. Just how, where, and why would coils "loosen" when under 150-230 lbs. If tension 24/7 365? What specifically are you "resetting"? I have not observed this phenomenon on any piano that was set up correctly in the first place...ever.

Peter Grey Piano Doctor
In the article I linked above, Ross Duffin (professor of early music at Case Western Reserve U.) highlights the biggest issue with tuning a modern acoustic piano with an unequal temperament-- it creates huge challenges playing with other musicians, mostly eliminating the possibility. Early music instrumentalists and singers will often be able to perform in ET and one UT-- highly skilled ones probably could manage multiple UTs.

Jazz, pop, and rock musicians, and classical musicians who do not specialize in early music likely will tell you to go jump in a lake when you say that your piano is tuned in a "superior" manner but it means that scales and intervals vary depending on key, and they have to adjust accordingly. Guitarists, of course, cannot adjust.
Originally Posted by David-G
It is surely a question of frequencies and resonance rather than energy. I wonder if the Weinrich effect can apply to partials as well as to fundamental frequencies - it seems to me not at all unlikely that it would do. This could perhaps be the scientific basis for Piano411's observations.
Oh, I'm sure it is all about frequencies and resonance. How ever I used the term energy, it was just done loosely to describe what is being observed, like the pull on the partials acting magnetically. Magnets have nothing to do with what is going on. There is a "pull" that happens to the partials, in that we can effect the bandwidth at the coincident partials, but we can also feel that pull/resistance at the tuning hammer itself. It is tactile. The more we tune the resonance of the system, the stronger that pull becomes. Basically, even though we are dealing with ET, the resonance in system is powerful enough to pull things into sounding in-tune (like coupled oscillators). This is the wet/singing quality of old master tuners. Today, the way so many technicians understand what they are doing is that they only deal with the beginning of the sound. They literally mute off the entire resonating system while they tune. They don't care about what is happening with that "pedal sound" at all. That is why it is blurry and never in tune.

Originally Posted by David-G
one thing that I do recall vividly was a discussion of coupled oscillators of slightly different frequencies, and how the coupling can bring the two to oscillate synchronously.
Was that the clocks on the wall discussion?
Posted By: MartF Re: most common non ET temperaments in 2020? - 10/28/20 02:52 AM
I like Dr Duffin's other articles too (https://casfaculty.case.edu/ross-duffin/).

Originally Posted by Sweelinck
Guitarists, of course, cannot adjust.

We'll see about that :-)

Anything
https://www.microtonalguitar.org

Mild WT
https://www.truetemperament.com

ET with pure 3rds
https://www.youtube.com/watch?v=I34lvLQxDK4
https://www.youtube.com/watch?v=Daw93bRHe4Y

1/4 syntonic meantone
https://www.youtube.com/watch?v=8nQrarL2z9o
https://www.youtube.com/watch?v=E0pUt_Wvht0

1/6 syntonic meantone
https://www.youtube.com/watch?v=9X_XywSQxG4
I'm sorry Sweelinck, I'll try and stop talk about these other issues. This thread should be more about unequal temperaments.

I skimmed the material you linked. I'll reread it later. It is excellent material. I agree with everything you wrote. I hope others will chime in.

ET as been around for as long as everything else. I've been saying this for years. ET is not the pinnacle of an evolutionary process. It has always been with us, and musicians have essentially always used it. I use a very loose definition of ET, which goes more to intent, rather than mathematical perfection.
Originally Posted by MartF

Well, yes, it would take a specialized guitar and specialist to play it, or a conventional guitar with frets re-aligned to match the piano's temperament. There are lutes for early music specialists with very wide necks and two sets of strings so that two temperaments are supported.
Posted By: MartF Re: most common non ET temperaments in 2020? - 10/28/20 06:34 AM
Originally Posted by kpembrook
the widened thirds of ET put the higher partials "in tune" at the expense of a few beats at the fundamental or lower partials. The other tunings try for "purer" intervals but the "pure" in practice is at the fundamental or lower partial level, thus leaving the higher partials less consonant. So, the more "consonant" intervals a given tuning has the more those intervals will not be consonant at higher coincident partials. So, it's not about UT as a concept, per se. It's that the more untempered or less-tempered thirds there are, the more out-of-tune higher coincident partials there will be.
...
I tune the thirds so that the upper partials "line up" and then the beat rates will be correct (or acceptable, or closely matching somebody's theory). The test is that 3 stacked thirds should equal an octave and that's what I get.

I'd like to come back to this. With a regular C-E-G chord don't all the notes have a similar amount of inharmonicity? If we're tuning ET, C might be 261.6 Hz and E 329.6 Hz. We'd expect C's 5th partial to be about 1308.1 Hz and E's 4th partial to be about 1318.1 Hz. Even if C's partials are sharper than that, won't E's be as well, so they still won't line up?

This chart implies there's no inharmonicity in the middle octaves, but I don't know if that's accurate:
https://en.wikipedia.org/wiki/Piano_tuning#Stretch

What further confuses me, is if this makes sense for the major 3rd, what about the other intervals? The 4#/5b and major 6th are in a similar position (flat), but the 4th and 5th are already close to pure, and the minor 3rd / 6th are already sharp.

Are there any good videos or audio demonstrations? I've only seen one decent tuning video, but he only talks about beats:
https://www.youtube.com/watch?v=lNY7Eyntlt0
https://www.youtube.com/watch?v=bC8p1PmB6sk

This also has me wondering if any synthesizers have/fake inharmonicity.
Originally Posted by Sweelinck
In the article I linked above, Ross Duffin (professor of early music at Case Western Reserve U.) highlights the biggest issue with tuning a modern acoustic piano with an unequal temperament-- it creates huge challenges playing with other musicians, mostly eliminating the possibility. Early music instrumentalists and singers will often be able to perform in ET and one UT-- highly skilled ones probably could manage multiple UTs.

Greetings,
This has not been my experience. String players' pitches are not ET until the piano begins. I have sat in the audience with my SAT in my lap and watched it happen. The human ear doesn't have a wide third in place, automatically. We naturally gravitate towards consonance, which makes the dissonance so stimulative when it occurs. In ET, the dissonance is everywhere and the ear becomes insensitive to it. As a member of the Blair Quartet once told me, that "When the piano begins, everything about pitch changes". It ain't natural, just institutionalized.

Having a piano in a WT on stage at Blair School of Music for many years, (a mild Colemann 11, which is close to Jorgensen's "Broadwood's Best") was instructive. The other D was in ET. The WT piano was chosen with regularity by singers and instrumentalists. One memorable performance was by a piano/violinist from the Royal Academy of Scotland,(I have lost their names but they were the heads of their dept. and this was maybe 10 years ago). I only found out when I arrived that they were using the WT piano, having had both in tune that morning. When I asked him afterwards if the piano had presented any problem, his quote was "Goodness no, for the first time I can remember, all the overtones lined up perfectly!" I remember that because when I told him the piano was in a well-temperament, he said that he didn't care how it was tuned, he just wish they were all tuned like that.

Well-tempered pianos are NOT restrictive. Having thirds of various widths is more akin to the human's musical sense of consonance/dissonance that having them all alike. An example; A master class with the "master" from Curtis some years before used both pianos on stage when I had been told that only one was to be employed. When I attended, there they were, both of them with the "master" sitting at one tuned in a Young, the students at the other in ET. Afterwards, asking him what he thought of the WT, he replied, "You mean, the pianos were tuned differently?" I was stunned, but since only music was played, not analytical measurements, the differences escaped a man with 50 years teaching experience.

There have been numerous similar examples at PTG presentations, and in every one of them, the WT piano has been favored as sounding better. Peer review is always better than my own "genius", so I tend to pay attention to the feedback, from both artists and technicians.
Regards,
Originally Posted by Sweelinck
In the article I linked above, Ross Duffin (professor of early music at Case Western Reserve U.) highlights the biggest issue with tuning a modern acoustic piano with an unequal temperament-- it creates huge challenges playing with other musicians, mostly eliminating the possibility. Early music instrumentalists and singers will often be able to perform in ET and one UT-- highly skilled ones probably could manage multiple UTs.

Jazz, pop, and rock musicians, and classical musicians who do not specialize in early music likely will tell you to go jump in a lake when you say that your piano is tuned in a "superior" manner but it means that scales and intervals vary depending on key, and they have to adjust accordingly. Guitarists, of course, cannot adjust.

Again, there is a world of difference between a meantone tuning which may have single notes 20 cents from ET, and a well temperament like the Broadwood's Best which has a 5 cent maximum offset. I've posted a scalable temperament on the Rollingball.com website if you want to see visualizations of some interval widths - the offset for C becomes the strength indicator. The "almost ET" eqwell has a maximum offset of 1.3, while the one most favored by those that want a little more flavor (Victorian) has a 2.1 cent offset for C.

Ron Koval
I also have found no problem switching from ET to EBVT or back (although going back to ET has only happened once). There is not enough tension difference to require a second pass...maybe a few backup tweaks here and there but that's about it. EBVT can also be tweaked in such a way so as to be considered "a loose definition of ET".

Peter Grey Piano Doctor
Originally Posted by Ed Foote
Originally Posted by Sweelinck
In the article I linked above, Ross Duffin (professor of early music at Case Western Reserve U.) highlights the biggest issue with tuning a modern acoustic piano with an unequal temperament-- it creates huge challenges playing with other musicians, mostly eliminating the possibility. Early music instrumentalists and singers will often be able to perform in ET and one UT-- highly skilled ones probably could manage multiple UTs.

Greetings,
This has not been my experience. String players' pitches are not ET until the piano begins. I have sat in the audience with my SAT in my lap and watched it happen. The human ear doesn't have a wide third in place, automatically. We naturally gravitate towards consonance, which makes the dissonance so stimulative when it occurs. In ET, the dissonance is everywhere and the ear becomes insensitive to it. As a member of the Blair Quartet once told me, that "When the piano begins, everything about pitch changes". It ain't natural, just institutionalized.

Having a piano in a WT on stage at Blair School of Music for many years, (a mild Colemann 11, which is close to Jorgensen's "Broadwood's Best") was instructive. The other D was in ET. The WT piano was chosen with regularity by singers and instrumentalists. One memorable performance was by a piano/violinist from the Royal Academy of Scotland,(I have lost their names but they were the heads of their dept. and this was maybe 10 years ago). I only found out when I arrived that they were using the WT piano, having had both in tune that morning. When I asked him afterwards if the piano had presented any problem, his quote was "Goodness no, for the first time I can remember, all the overtones lined up perfectly!" I remember that because when I told him the piano was in a well-temperament, he said that he didn't care how it was tuned, he just wish they were all tuned like that.

Well-tempered pianos are NOT restrictive. Having thirds of various widths is more akin to the human's musical sense of consonance/dissonance that having them all alike. An example; A master class with the "master" from Curtis some years before used both pianos on stage when I had been told that only one was to be employed. When I attended, there they were, both of them with the "master" sitting at one tuned in a Young, the students at the other in ET. Afterwards, asking him what he thought of the WT, he replied, "You mean, the pianos were tuned differently?" I was stunned, but since only music was played, not analytical measurements, the differences escaped a man with 50 years teaching experience.

There have been numerous similar examples at PTG presentations, and in every one of them, the WT piano has been favored as sounding better. Peer review is always better than my own "genius", so I tend to pay attention to the feedback, from both artists and technicians.
Regards,

Can you reference a recording of a piano concerto (piano and full orchestra) done in UT? Please explain why they are rare at best. Recordings of solo piano or concertos done on two pianos can be found. But if pianos in ET are indeed the problem everyone else has to compromise to meet, why are pianos still tuned in ET and why are recordings of piano and orchestea in UT a rarety?

The ear also adapts to the ET third. Play a C major scale and intervals in just intonation for a few minutes, then switch to ET and the thirds sound dissonant. Play the same in ET for a few minutes and the perception of a dissonant third melts away.

But sometimes the piano just sounds out of tune when a WT is used for Chopin's music, as in various parts of this example:

https://youtu.be/I-W8oRAd6Bw
Originally Posted by Sweelinck
Can you reference a recording of a piano concerto (piano and full orchestra) done in UT? Please explain why they are rare at best. Recordings of solo piano or concertos done on two pianos can be found. But if pianos in ET are indeed the problem everyone else has to compromise to meet, why are pianos still tuned in ET and why are recordings of piano and orchestea in UT a rarety?

Here is a pretty good violinist playing Brahms with an UT pianist. I would say she is struggling to get the intonation to line up with the piano. She is trying, but she having a hard time finding where to go because the piano conflicts with the resonance of her own instrument.
https://youtu.be/LQXEq3XOrjU?t=676

Here is orchestra and UT piano. The piano sounds beautiful. I have no complaints with the piano sound at all. But, notice how the orchestra struggles with intonation. It is hard for them to predict where the pitch should be.
https://youtu.be/mnTDkj5dYYc?t=1755

Here is a chopin in UT. It's OK. It's not awesome. It's not particularity special. I wouldn't say I like that.
https://youtu.be/mnTDkj5dYYc?t=1755
Posted By: MartF Re: most common non ET temperaments in 2020? - 10/28/20 11:44 PM
Originally Posted by RonTuner
I've posted a scalable temperament on the Rollingball.com website

Rollingball is great, thank you. The only thing is I wonder if the charts would look better with C in the middle rather than at the edges. Also note some links are long dead (rollingball.com/A01d.htm).

I've been going through my own process of understanding and chart creation (www.fidolab.org), still very much work in progress though.

A bit off topic, some piano+strings in just intonation if anyone's interested:
https://www.youtube.com/watch?v=iNiX5XxL2d0
Another view...

From: http://www.terryblackburn.us/music/temperament/stoess.htm

Quote
Equal temperament is the only practical temperament for the modern piano.
© Piano World Piano & Digital Piano Forums