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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,

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

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!

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
For me any temperament sounds good enough.

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.

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.

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.

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".

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.


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.

"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

Thank you everyone, there are a lot of interesting comments here, more than I was expecting. I'm still reading through them.

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