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Posted By: Numbered Tuning the 4ths and 5ths Temperament - 06/26/13 12:44 PM
Much has been said against the 4ths and 5ths Temperament/Sequence of tuning, but is it really that problematic and antiquated?

I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.

But the question that needs to be asked is, is this so terrible and backward and unnecessary and is there a better way that will cut all of this backtracking and to and frowing out completely?

My answer is, there is no such system, and I am not going to go into great detail about that except to say that, it is inevitable whatever sysytem you use, there will be some backtracking and refinement needed and that the more you tune a particular system the better you will get at tuning it and the result of that is "Less Backtracking".

Yes, there are good temperament systems and poor ones too, but whether we like it or not there is going to be some sweat, blood and tears in learning to tune it, and the rest of the piano too.

The sitting down and seeking to understand what one is doing and to actually implement what one is doing is difficult and those that persevere, conquer. Those that conquer, are those that have worked hard at it, deserve the congrats, and usually go on to higher ground, learning the never ending intricacies that are involved in tuning, and the other areas of piano technology.

Anway, to get back onto the 4th and 5th temperament. I looked at Mario Igrec's book website, and found what he said on the 4ths and 5ths temperament interesting and helpful to understanding and tuning the temperament using the 4ths and 5ths sequence. Yes, there are other systems, etc...but the question we got to ask again is, which one is the best and why? When that is answered, we can go onto asking another, how much backtracking and fiddling around is involved to get things right?

I would submit, that there is always going to be fiddling around with the temperament sequence, and that for a number of reasons.

Thinking of Bill Bremmers continual seeking to refute the 4ths and 5ths method, and the main reason being is, as he says, there is an accumulation of errors, is valid. On the other hand, we need to ask ourselves, Has Bill himself found that one system that has no fiddling about and backtracking and accumulation of error?

I would submit that, If he had, he would not be changing his tune (temperament sequence, though admittedly he has held to the CM3 sequence), every couple of years of how to go about tuning the temperament, and he has. It is understandable too. This is piano tuning folks and living in an imperfect world.

So has the CM3 sequence got one up on the 4ths and 5ths sequence?

What Mario has said,

" The sequence starts by tuning the middle A to the fork, and establishing a P5 and P4 in the octave. The octave should be just slightly wide but without perceptible beats, and the P4
should beat just slightly faster than the P5, both under 1 bps.

You can spend a little more time on these two notes because they will serve as aural templates for the beat rates of the other P5s and P4s you will tune.

Tune the next five notes to D#4 by tuning P4s up P5s down. Make the beat rates the same as the P5 and P4 you tuned initially. Next, start at the middle A again and tune the five
notes in the opposite direction of the temperament circle. Compare the last note, G#4 with D#4. If this P4 is wider than beatless but beats under 1 bps, congratulations!

If it beats at more than 1 bps, it is too wide—increase the beat rate of the P4s and P5s a touch in both directions. This will narrow the P5s and widen the P4s, and raise the notes tuned during the first half cycle, including the D#4, while lowering the notes in the second half cycle. If the P4 D#4-G#4 beats at less than 1 beat in 2 seconds, doesn’t beat at all, or is narrower than beatless, decrease the beat rates of the P4s and P5s. Make corrections until all the P4s beat at approximately the same rate, slightly faster than the P5s.

Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 01:05 PM
Mario does speak of checks that accompany this system but you will need to purchase his book. So, what I have posted is lacking the checks along the way, that will help one to tune this sequence successfully.

Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 01:26 PM
There are other questions that one can ask too.

If the emphasis today and the "consensis" is that well temperaments are the must and ET is out, then we need to ask ourselves, How far away is a RW from any WT really? I have not received a satisfactory answer yet.

Though I understand the intricacies involved in fine tuning, and am ever learning, I do wonder why such an attack is made against the RW. For an experienced, seasoned and accomplished piano tuner, who for whatever reason did not successfully execute an ET on the piano he was tuning for a concert pianist, how perceptible would it be, without an unnecessary over fussing nit picking, and that would accomplish what?

Why would someone who promotes WT be so vehemently against an RW when an RW could so easliy pass as one of the multitude of WT's that exist and would also pass as a very acceptible tuning?

Anyway, I diverge, from the main topic, but nevertheless it has it's place.



Posted By: Emmery Re: Tuning the 4ths and 5ths Temperament - 06/26/13 01:58 PM
Originally Posted by Mark Davis

....If the emphasis today and the "consensis" is that well temperaments are the must and ET is out...


Although there are a few piano tuners out there who would want to believe this or are trying to actively promote it, the truth and reality is that there are only a very small handful (less than a dozen) amongst the thousands of tuners worldwide who do.

Besides, modern piano's since the turn of the last century are designed and built with a string scaling formula/program which assumes the ideal tuning for that piano is ET and the calculations are formed on this parameter. The speaking lengths/diameters/windings and related individual tensions are all calculated to fine precision based on equal temperament. Tuning to anything outside this parameter will always result in a compromise on the instruments intended design and its intended use. Some people think its not enough to matter, others think it does.

Reverse Well is a non issue in the real world and any tech who tunes by ear which ends up with RW in place of ET should really be reaching for an ETD. An ETD set for ET will not produce RW....period. The majority of techs here in N.A. use an ETD either as stand alone or in some form of hybrid ear/machine collaboration.

When I learned to tune temperaments by ear, one of the very first things taught to us was how to recognize and avoid RW during the process. I know many people who tune using 4ths and 5ths method who produce fine ET tunings in spite of some pitfalls than can accompany it.

Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/26/13 02:44 PM
I simply understand RW as a lack of tempering on the first 5th of the sequence.
If that is, this is a beginner defect, and easy to correct.

Something we can think about too is that we will be enlarging the octaves, if not a lot, at last enough to have the sounding just.
I see no reason why 4ths and 5ths could not as have some progressivement then. It just installs a preparation for stretch within the temperament.

Backtracking is reduced when using ladder of 3ds, hence it's success. But the appreciation of the slow beating Intervals is left aside. They are just used as a tool to obtain the FBI progression. This only can lend to uncontrolled quality of those important intervals.

Also, th 3ds will have variable speed depending of the scaling, it is not always guaranteed that a perfect speed progression of consecutive M3 allows the nicest 5ths.

Whatever sequence is used, I believe it will be more musical to focus on 5 the and 4ths and not judge them by the winning progression of FBI.

It also gives the tuner an excellent ear training to apprehend those intervals directly. Without controlling them by FBI checks.
Open the door to very fast tuning corrections when necessary.

All:

Now here is a subject I can sink my teeth into!

First, is it possible to tune a temperment WITHOUT using 4ths and 5ths? I doubt it. You could say that ALL temperment sequences are 4th and 5th sequences.

Next, where is the dividing line between ET and, well, everything else? Is it just progressive M3s? No, because you could take any set of CM3s and raise them all the same number of cents (well, up to 99 cents theoretically) and still have progressive M3s. How about progressive M3s AND M6s? I would say that is definitely ET, but what accuracy are we talking about? Would you believe to guarantee that all M3s and M6s are progressive each note would have to be +/- 0.25 cents? But in reality with some fudging some notes can be off by 0.5 cents. Still, that is a very high degree of accuracy.

How about the infamous PTG exam standards? Interestingly, the accuracy for tuning progressive CM3s is about the same accuracy required by the exam. It should be no surprise that tuning by CM3 is popular. It is “teaching to the test”!

Anyhoo, of course every sequence requires going back and forth. I wish I understood number theory enough to prove how many steps is required. It seems that every sequence requires 8 or 9 notes to be tuned before the temperment is locked in.

So what intervals do you want to mostly tune until you have the temperment locked in? Well, for me the answer is to use the ones that are affected the least by iH. Those are the ones with the lowest partials. Of the traditional temperment intervals, M3s have the highest (5-4) followed by M6s (5-3), P4s (4-3) and P-5s (3-2).

But what about other, non-traditional temperment intervals? (Yes, those that have read my posts know what is coming next…) How about the P12 (3-1) and the P8 (2-1, 4-2)? A temperment can be tuned with just one P12 and completed with P5s and P8s. The first 8 notes ( in order) to lock in the temperment are: A4, D3, D4, A3, E4, G3, E3 and G4. And not a single M3!

OK, the Topic is about 4th and 5ths sequence. But we all know everyone is going to post what their favorite is. My argument for 4ths and 5ths over M3s and M6s is the amount the partials are changed by iH and it matters little what sequence is chosen. You are going to have to tune 8 or 9 notes before you have it locked in. Besides, you are going to have to tune some 4ths and/or 5ths sooner or later anyway. Why not learn to use them for the entire sequence?
Posted By: kpembrook Re: Tuning the 4ths and 5ths Temperament - 06/26/13 03:11 PM
I learned the 4ths and 5ths temperament as articulated by William Braide White from my father. It's what I grew up with. I moved to a 3rds and 4ths temperament after trying it and finding that I was able to do a better job. At the time I couldn't say exactly why, but my opinion now is this:

1) There are multiple coincident partials with 5ths which can confuse exactly what you are listening for. Although in some instances more has been made of identifying which partial (if any) you are tuning to than is necessary or relevant, in the case of the temperament, it is quite important which set of coincident partials is the the one you are working with.

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

3) 3rds are the "check" for the 4ths & 5ths temperament and the definition of the equal temperament. The single best illustration of the equal temperament is evenly beating and slightly increasing speed with contiguous ascending thirds. So, logically, instead of hoping that this phenomenon occurs with tuning the 4th/5th system, why not simply make it happen? If you get the 3rds right, then the 4ths and 5ths will be OK. Put another way, a 1bps difference in a third is something that is audible and matters. But who cares if a 4th of 5th is a hair faster or slower than what we target?

4) With 3rd/4th tuning, you are able to establish solid anchors within the temperament octave (or slightly beyond if you expand your temperament area). If you tune 3 thirds, you are at the next octave. It is a fairly easy matter to tune three 13-cent-wide thirds within one octave compared to tuning a circle of 4ths or 5ths and arrive back at an octave up at the end of the piano -- or beyond.

In conclusion, whatever works for you is fine with me. And, certainly, there are folk that do very fine work using fourth/fifth temperament. However, I'd suggest that if you give third/fourth temperament a try you may find that, like me, you won't go back.
Posted By: BDB Re: Tuning the 4ths and 5ths Temperament - 06/26/13 03:23 PM
It does not matter whether you use 4th and 5ths or if you use 7th and 29ths. The important thing is understanding and recognizing the characteristics of the temperament you are using and from that, being able to correct any mistakes that are in it. If you need to get from New York to Philadelphia, it does not matter whether you use a plane, a train, a bus, or a transporter as long as you end up in Philadelphia. What you do not want to do is insist on using one method and because of that, end up in Boston.
Quote
I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.


As I see it, this is a recipe for Reverse Well. What is described here is exactly how and why temperaments intended to be ET end up being in fact, Reverse Well. If you don't know what Reverse Well is or sounds like, how would you know if that is what you actually tuned or not?

It seems to me that some people want to believe that what they wish to be the truth actually is. If you had heard the number of times I have heard Reverse Well on pianos, you wouldn't dispute what I am saying at all.

Just wanting to believe that there are only about a dozen tuners world wide who tune pianos in Well Temperaments does not make it true. There are more than that in the city in which I live! It is being taught at the PTG convention in a couple of weeks and not by me but by a PhD who teaches it in numerous venues and has been teaching it for more than two decades. He is not the only one. The number of times I have seen figures pulled out of thin air and published as fact on here has been astounding!

The work I have been doing for 10 years now to find a better way to construct ET is not for my benefit. I became an RPT with a score of 100 in temperament 30 years ago and yes, I used a 4ths & 5ths temperament to do it. And yes, I back tracked and used a myriad of checks to sort out the errors in the 60 minutes I had to tune C3-C5 single strings only. If I had to do that to make a living, I would have been out of business decades ago!

Yes, there is, in fact, a way to construct a temperament one time with no back tracking necessary because each step of the process confirms that the temperament is correct. It is there for anyone who wants to avail themselves of it and the results in how it makes the piano sound are nothing less than stunning! It literally makes the music "float" out of the piano.

Any technician has the right to use whichever method they please or feel comfortable with. One can chose to repeat the first year's experience for a lifetime and never progress beyond that or one may choose to always seek a better and more refined way of practicing one's art and profession. I choose the latter, so if in your mind that qualifies me to be in the "arrogant piano technician" thread for doing so, then please re-post any of my comments there. It would only encourage me.

Reverse Well is indeed possible when using an ETD. It is another example of believing what one wishes were the truth to actually be factual. I am not going to bother to explain how it can happen for your benefit, however. I am only going to say that the use of an ETD does not necessarily lead to the perfection that some people wish it would.

Piano scale design is based upon theoretical ET for the same reason that ETD's use theoretical ET as a paradigm. If you believe that the piano scale is designed only to be tuned in theoretical ET, then you should tune the pianos you service that way and find out for yourself that what you are saying is not true.

Your ignorance is your strength. What you don't know about your own profession would fill an entire book case yet you choose to broadcast what you don't know on a daily basis.
Originally Posted by Bill Bremmer RPT
Quote
I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.


.....

Your ignorance is your strength. What you don't know about your own profession would fill an entire book case yet you choose to broadcast what you don't know on a daily basis.


And what does this last comment say about YOU, Mr. Bremmer?
Originally Posted by kpembrook
.....

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

.....


Please forgive me for zeroing in on this one point. I am singling this out to explain something, not to take it out of context.

The more an interval is tempered from just intonation, the further it can be from ideal and still be progressive. A M3 that is about 7/8 cent too wide will beat the same as the M3 one semitone higher. A P5 that is 1/8 cent too narrow will beat the same as the P5 one semitone higher. This could drive you nuts. However, comparing contiguous P4s or P5s or comparing P4s with P5s that share a common upper or lower note gives an accuracy of about 1/2 cent. It is very useful, IF you can easily compare SBIs. Everyone has different skills and preferences and priorities. Whatever sequence works best is the one to use.

Originally Posted by Bill Bremmer RPT

It seems to me that some people want to believe that what they wish to be the truth actually is.

This entire posting is the perfect example of that.
Originally Posted by Bill Bremmer RPT

Any technician has the right to use whichever method they please or feel comfortable with.

Apparently technicians are not permitted to do this in your world without being insulted.
Originally Posted by Bill Bremmer RPT

Your ignorance is your strength.

And yours is the PTG’s weakness.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 05:11 PM
Bill, your post is shameful and venomous! Pull yourself together man!


Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 05:59 PM
Yes, I learnt to tune using the 4ths and 5ths sequence but I have learned to use the CM3 sequence too.

My journey learning to tune, from 2002, and prior to that, I had been working in a piano restoration workshop for about 9 years, has brought me to learn from many well known piano tuners. I learnt of Bill in about 2006, and began applying the CM3 sequence he was advocating in about 2008.

I have learned from Rick Baldassin, Dan Levitan, Kent Swafford, Rick Butler, Virgil Smith, the PACE series, the PTG resource file, and many others that I forget of at this moment. Each of these people adding new and different perspectives and pertinent information that the other had left out due to lack of space and time in writing what they have.

Anyway, the main reason I started this thread is because I think that what Mario has written on the 4ths and 5ths sequence is valid, interesting and of benefit to those who are interested.

I think that Mario probably may write about "Advanced Temperament/tuning" in his book too.

So, some questions to be asked,

1. will someone who is learning to tune ET from an expert tuner, who is teaching them the 4ths and 5ths temperament, learn how to tune faster or slower than someone who is learning to tune from an expert tuner who is teaching them the CM3 sequence?

2. Will, the person who learned to tune via the 4ths and 5ths sequence, be able to execute an ET as efficiently and accurately as someone who learned the CM3 sequence?







I was trained using the Braid-White method as many were in the early seventies. Still tune using 4ths and 5ths, but have had numerous discussions about temperament sequences and have tried many of them.

Using 4ths and 5ths are difficult for some to hear so best for them to use 3rds and 6ths.

I think it is the difference between using millimetres and centimetres rather than inches and feet.

Both achieve the same result.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 06:06 PM
Originally Posted by UnrightTooner

The more an interval is tempered from just intonation, the further it can be from ideal and still be progressive. A M3 that is about 7/8 cent too wide will beat the same as the M3 one semitone higher. A P5 that is 1/8 cent too narrow will beat the same as the P5 one semitone higher. This could drive you nuts. However, comparing contiguous P4s or P5s or comparing P4s with P5s that share a common upper or lower note gives an accuracy of about 1/2 cent. It is very useful, IF you can easily compare SBIs. Everyone has different skills and preferences and priorities. Whatever sequence works best is the one to use.


Jeff, thanks for this!
What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 06:15 PM
Have you not supplemented your knowledge since you first began learning to tune?

What I find interesting is the changes you have made over the years in your approach to how to tune ET via the CM3 sequence and the employment of the 4th and 5th within that sequence. Anyone who knows your work, knows that you have made changes over the years.

Why is that Bill? Is it not bullet proof? Is it not without accumulation of error? Why the changes?
Originally Posted by Bill Bremmer RPT
What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.


What I find interesting is the fact that more aspiring technicians are driven away from membership in your favorite club by the continued bloviating you do here.


Mark,
Just ignore the postings so that your thread is not destroyed by one person with an agenda.

Let’s just move on with the topic at hand.
All:

Maybe we can get back on track.

One useful thing that M3s can do is fit into an octave as a set of self-checking contiguous intervals. Yes, a P4 and a P5 can also fit into an octave, but are not as useful in setting a temperment as they are not self-checking. Of course when the 9th note is tuned in a strict 4ths and 5ths temperament, a pair of contiguous M3s are formed and can be used as a check in various ways.

For example: In Dr. White's sequence when C#4 is tuned, the first set of contiguous M3s is formed (F3-A3, A3-C#4). The m6 of F3-C#4 can be chromatically compared to the m6 created when the note before was tuned (F#3-D4). And if the error is very early in the sequence, the common, implied interval to these m6s (M6 F3-D4) can be evaluated and corrected to the begining notes of C4 and G3. Then F#3-C#4 P5 can be adjusted before correcting the three middle notes of the sequence (so far) being: A3, E4, B3. I wonder if some tuner's frustration with 4ths and 5th sequences is just not understanding how infered intervals relate to the ones being tuned or checked, like chromatic M3s and the infered P4.

But 4ths, 5ths and octaves can fit into a P12 in a number of ways each of which is not only self-checking, but when used together are cross-checking.

Another possiblility is 4 m3s in an octave, but when there are more than 3 intervals within another interval, the checks are not as certain.
Originally Posted by Bill Bremmer RPT
What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.


Not true.
Posted By: BoseEric Re: Tuning the 4ths and 5ths Temperament - 06/26/13 06:26 PM
One always tunes 4ths and 5ths, the CM3 sequence just sets mileposts for reference and that is a great help, speaking as one that learned and tuned for a number of years the straight 4ths and 5ths sequence. How you treat the 4ths and 5ths as you fit them in the CM3 framework sets the accuracy (or lack of) in your temprement.

There are a couple of agendas here, from both sides of the border. Let's stay on topic.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 07:51 PM
I find what Don Mannino said a while ago pertinent, especially that which I put in bold. Now here is someone with his feet on the ground and who does not have his head in the clouds and who knows his stuff.

I have quoted Don because he brings up something which Bill does like to speak about and that is "The fudge Factor".

Another way of saying that? Compromising and backtracking to make things/the temperament to work, even with the CM3 sequence.

The Fudge Factor, it really is sweet!

So, what I am trying to bring out is, no matter what sequence you use, you may and will need to fudge, whether it is the 4ths and 5ths or the CM3.

from Re: ET via Marpurg Revisited thread, 11/11/10

Originally Posted by KawaiDon

I use the contiguous 3rds to start my temperament, and the only issue that comes up when I teach others about it is that the width of the octaves is somewhat negotiable, and is a part of the tuning process that can confuse setting smooth contiguous 3rds at the start. If one decides in advance to tune precise 4:2 octaves and you verify them it works pretty easily, but I usually tune a little narrower than that, and occasionally a little wider. [/b]So this throws another fudge factor into the initial tuning process[b] that might keep me from being able to claim a truly "perfect" equal temperament. Tuners who try to simply tune a "clean" octave without using a test can then get very confused trying to make the contiguous 3rds work out. The A3-A4 octave might be 4:2, but the F3-F4 might be a little narrow and the contiguous 3rds get goofed up. [/b] And of course, small pianos with not so nice string scales kind of make one have to fudge every step of the way...[b]

Finally, it is interesting to look at a different view of tuning like this, but it is a little dangerous sometimes for people to get overly obsessed with perfection in tuning temperaments. No, I don't mean it's OK to be sloppy, but some tuners do spend an awful lot of time working out a beautiful temperament, only to spoil it with inconsistent octaves and unisons. I think that's what stops a lot of tuners from bothering with trying new temperaments - [/b]they are happy with getting something passable in some of the awful pianos they work with every day, and it just doesn't have relevence to their daily lives to worry too much about this level of perfection.[b]

[/b]I do agree it's nice to have a really well tuned temperament in a good piano that is also in great condition. Especially if the temperament is carried out well into the treble and bass with good octaves, and the unisons sing evenly.[b]

Don Mannino RPT

Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 08:16 PM



Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 08:20 PM
Dan, thanks for chiming in.

Also, thanks to the all who have positively contributed here too.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/26/13 09:22 PM
Has anyone got Arthur Reblitz's first edition book?

I think that in there he teaches the 4ths and 5ths temperament.

Would you mind posting some excerpts on what he has to say, the sequences he taught about, etc...if possible and legal.

You can PM if you like.



Posted By: bkw58 Re: Tuning the 4ths and 5ths Temperament - 06/26/13 11:09 PM
Originally Posted by Mark Davis
Has anyone got Arthur Reblitz's first edition book?

I think that in there he teaches the 4ths and 5ths temperament.

Would you mind posting some excerpts on what he has to say, the sequences he taught about, etc...if possible and legal.

You can PM if you like.



Wish I did. Gave mine away years ago. Public library might be an option. I do not recall the temperament in his first edition.

Clients are most likely to hear problems first in unisons and second, in octaves. Fifths are next. Accordingly, a temperament which places its primary interval emphasis on fifths (and next, fourths, and so on), is a natural. Is it perfect? No. But neither are other temperaments.

That's my two-cents worth. It doesn't get any more unscientific than this. But it works.
Posted By: Gary Fowler Re: Tuning the 4ths and 5ths Temperament - 06/26/13 11:37 PM
There are no short cuts to setting a good temperment. If you are too scared to "back track", than you are too skeered to be a piano tuner. Find a different profession. The fourths and fifths method of setting a temperment is irrelavent. You can tune by thirds and sixths...doesn't matter. But don't be afraid to always go back to the temperment and make necessary adjustments. The results at the end are what counts.
Posted By: Gary Fowler Re: Tuning the 4ths and 5ths Temperament - 06/26/13 11:44 PM
I happen to use fourths and fifths to set the temp, but I'm checking with other stuff to know I am always on track as I go along. As you get into tuning octaves outwards, it lets you know your temperment is on target. It's not unusaul for me to go back to my temperment and tweek it a bit
Posted By: Dave B Re: Tuning the 4ths and 5ths Temperament - 06/27/13 12:34 AM
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks. It all starts with a good solid octave.

An ET can be accomplished across two octaves using only 4ths, 5ths, 8ths, and 12ths. Of course that requires two good solid octaves to get started. What I find interesting is that all three notes of the double octave can be checked against the same note.
Posted By: Ed Foote Re: Tuning the 4ths and 5ths Temperament - 06/27/13 01:43 AM
Greetings,
It might be a little misleading to say what I use for equal temperament. I don't think using fourths and fifths exclusively is going to get anybody near enough to equal to at least pass the guild test, (which is pretty forgiving).

When tuning aurally, I will listen to a fourth or fifth as the pin is moving, but once I know I am on the right side of pure, and tempered like I think it should be, I instantly use thirds and sixths to see where I am. Once I have tuned the interval, I will listen to a cascading series of tests as I progress through the 12 notes. They accumulate as I go, incorporating the 4th and 5th test, 3rd/6th steps, the 3rd/6th brackets, ascending thirds.
The first four notes I tune are C4,F3,F4, Bb3. These allow me to hear what my fifths are going to require of the octave, after that, it is a basic Holder bearing plan with Bill Garlic's refinements.
Regards,
Posted By: kpembrook Re: Tuning the 4ths and 5ths Temperament - 06/27/13 03:03 AM
Originally Posted by Dave B
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks.


Or, you could just tune the 3rds and be done with it.
Posted By: BoseEric Re: Tuning the 4ths and 5ths Temperament - 06/27/13 10:35 AM
Ed...using what fork?
Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/27/13 10:41 AM
Originally Posted by Ed Foote
Greetings,

The first four notes I tune are C4,F3,F4, Bb3. These allow me to hear what my fifths are going to require of the octave, after that, it is a basic Holder bearing plan with Bill Garlic's refinements.
Regards,


I find that octave secured with 4ths and 5ths as the best beginning for tuning (after having played with stacked M3 for decades)Install it from A3 to A4, activity is more noticeable there.
All (referring to various posts):

Ah, yes. How the 5ths sound is important. On oddly scaled pianos, octaves and therefore other intervals, need to be tweaked so that the 5ths are not irritating. It happens both near the breaks and across the breaks.

I remember in my first year of tuning with Dr. White's sequence noticing how when C#4 was tuned, the M3 A3-C#4 could be compared with the M3 C#4-F4, if the F3-F4 octave had also been tuned. I thought I was onto something (this was a CM3 check ...), but soon realized that getting these intervals to be progressive did not mean the 5ths would sound good. This was in the 70's and iH was not understood very well. Heck the EFFECTS of iH are still not understood very well. Let me give my understanding of the subject.

If you consider that iH is different for every note and what the value of any particular note is not as important as the SLOPE formed by a series of notes' iH, you may be able to follow what I am saying. Well scaled pianos have an iH slope that is smooth. When a break is encountered it does not have a sudden jump. And in the lower part of the unwound trichords, there is still a slope, it does not flatten out. Oddly, some piaons have greater iH below the break rather than less.

Also, larger pianos have a steeper iH slope and therefore the difference between the 2:1, 4:2 and 6:3 octaves are small. But smaller pianos have an iH slope that is less steep and therefore there is more of a difference between the octave types. Now get this: ON SMALLER PIANOS THERE IS ALSO A GREATER DIFFERENCE IN THE 3:2 AND 6:4 FIFTHS! If you don't choose an appropriate octave, you can't have a decent sounding fifth when the slope is flatter. And on some pianos the slope even inverts across the break, as I mentioned before.

So what octave type is appropriate for the iH slope? The flatter the slope the narrower the octave type should be. And this will happen if the fifths are listened to and adjustments are made. I suppose that a sequence can rely on RBIs and then adjusted when the fifths are used as checks. But if a tuner is able to tune fifths, well why not just tune fifths that are acceptable to begin with?

I want to be fair to the use of CM3s and in particular to Mr. Bremmer's excellent ET via Marpurg sequence. For a well scaled piano, I cannot think of a more accurate and straight forward way to set the temperment. Yes, there is less going back and forth, but then again, it still takes 9 of the 12 notes (I am not including octaves) before the temperment is locked in. This is because of the temporarily tuned notes. However, I do not find it, or any other RBI sequence, useful for pianos with poor scaling. Only by tuning good fifths can you have good sounding fifths. It only takes one "raisin" to ruin a rabbit stew.
Posted By: bkw58 Re: Tuning the 4ths and 5ths Temperament - 06/27/13 12:27 PM
Originally Posted by Dave B
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks. It all starts with a good solid octave.

An ET can be accomplished across two octaves using only 4ths, 5ths, 8ths, and 12ths. Of course that requires two good solid octaves to get started. What I find interesting is that all three notes of the double octave can be checked against the same note.


thumb
Posted By: Ed Foote Re: Tuning the 4ths and 5ths Temperament - 06/27/13 02:20 PM
Originally Posted by BoseEric
Ed...using what fork?


Greetings,
I used a C fork. tuned C4 to it. Then formed the F octave around it, and then split that octave the other way with the Bb. At this time, I could make my decision on how my octaves and fifths were going to relate. Carrying the temperament outwards from here, I listen by octave, checked by fifth and fourth, and then listened to the double octave and then how the 3rds, then 10ths progress. By that time, I am usually tired of the note, so I go to the next one...

On big pianos, the inharmonic deviation between the C5 pitch of the fork and the second partial of C4 was so far below the piano's natural variability that it was never a problem. When I went to a machine, I started seeing that there were discrepancies on the order of .2 or so cents, which means nothing except in the most clinical settings. I managed to hit the nail squarely on the Guild tests with this thing, which may have been a bit of luck.

Regards,
Posted By: Nick Mauel Re: Tuning the 4ths and 5ths Temperament - 06/27/13 11:57 PM
Originally Posted by kpembrook

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

3) 3rds are the "check" for the 4ths & 5ths temperament and the definition of the equal temperament. The single best illustration of the equal temperament is evenly beating and slightly increasing speed with contiguous ascending thirds. So, logically, instead of hoping that this phenomenon occurs with tuning the 4th/5th system, why not simply make it happen? If you get the 3rds right, then the 4ths and 5ths will be OK. Put another way, a 1bps difference in a third is something that is audible and matters. But who cares if a 4th of 5th is a hair faster or slower than what we target?


This is exactly the reasoning I was taught, but I don't see many others embracing this logic, at least not here on this thread.

The intervals I use to tune (aurally) are M3, 5th, Octave, M3, M3, 5th, M3, M3, 5th, M3, M3, M3.

So, mostly major 3rds and Keith has already stated why.
Posted By: bkw58 Re: Tuning the 4ths and 5ths Temperament - 06/28/13 02:54 AM
If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.



Originally Posted by bkw58
If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.


Precisely! Truer words were never spoken. For many years, I thought (and still believe) that when tuning ET, one must check Slowly Beating Intervals (SBI) against Rapidly Beating Intervals (RBI). Otherwise, one may lead oneself astray by concentrating on one kind of interval alone.

The temperament from Owen Jorgensen's second publication, the Marpurg-Neidhardt Composite Quasi Equal Temperament is a perfect example of that. The Major thirds, when played, sound virtually identical to ET but the 4ths and 5ths are wildly unequal!

The Reverse Well problem that I have for long identified has the opposite problem. The 4ths & 5ths may all sound acceptable but the 3rds & 6ths sound uneven.

With the latest idea that I have been advocating, I set a chain of Contiguous Major thirds first and foremost as a framework. From there, one can tune the whole rest of the piano and get very even sounding RBI's without ever checking them!

The inherent problem in constructing a temperament by starting with a chain 4ths & 5ths and only being able to use any RBI checks after several notes have been literally guessed at as far as tempering is that some cumulative error will inevitably be the result. At that point, when RBI checks become available, it is impossible to know which previous errors have occurred, where they are and how much error is involved in each of them.

Now, it is probably true that some very fine technicians were able to cope with that problem and yield an acceptable and perhaps even a seemingly perfect ET that way, most technicians never really got it right by following a 4ths & 5ths sequence. They end up with uneven Major thirds precisely because of what John Travis identified in the middle of the last century as the "tendency to err towards the just (pure) fifth".

Well Temperaments have about half of the 5ths tuned either pure or nearly so and the rest tempered more than in ET. Reverse Well has exactly the same characteristic but in exactly the opposite manner.

John Travis advocated tuning a temperament from C# rather than C for that reason. He actually said in the tuning chapter of his first publication of A Guide to Restringing that starting from C# would yield a "more equal" temperament!

Considering that he wrote that (I have the book and can prove it) at about the same time that George Orwell wrote the novel, Animal Farm where the pigs declared, "All animals are equal but pigs are more equal", I find it ironic that Mr. Travis was actually trying to find a way to avoid Reverse Well!

While Mr. Travis clearly believed only in ET, he obviously saw that technicians quite often produced a disharmonious temperament if they started the sequence on A or C. If the sequence started on C# however, the first half of the temperament sequence could have pure or nearly pure 5ths. If the last half of the sequence ended up with "wolf" 5th, one could "back up" through the 4ths& 5ths and therefor even everything out.

Lo and behold, John Travis described a way to construct a Well Temperament rather than a true ET! When 10 years ago now, I looked at the whole idea of constructing a true ET, I latched onto John Travis' idea of "Up a third, up a third and down a 5th". This idea worked well to first set a chain of contiguous Major thirds. From there, one could take the "Up a third, up a third, down a 5th" idea and progress to the rest of the temperament.

The next note to be tuned would be F#3 from C#4. That interval could be tempered by estimate and the next note, A#3 again be tuned by estimate but then there would be two Major thirds to check for evenness. The more notes tuned, the more number of checks available would emerge.

I went with that for years until I discovered an even better approach.
Posted By: kpembrook Re: Tuning the 4ths and 5ths Temperament - 06/28/13 05:59 AM
Originally Posted by bkw58
If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.


One would think so . . . but actually not in my experience. When I tune 4ths/5ths, I check with the thirds and go and modify my 5ths until the 3rds are right. When I just make the thirds right, the 4ths/5ths are OK and I don't have to tweak nearly as much.

As I mentioned, I grew up tuning 4ths & 5ths. I was challenged by Let's Tune Up by John Travis to try the thirds approach. Having gone both ways, I find the 3rds approach better for me and there is some basis in objective physics for that to be true.

Now, I should be clear that there was a learning curve for me. If I had given up during that learning time, I might have concluded that it wasn't worthwhile. But it didn't take long. It's an approach that I commend to those who might like to try. If not, I know there are many good folk doing outstanding tunings using approaches that I don't.
Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/28/13 06:02 AM
Originally Posted by bkw58
If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.





Both are probably true, that is a priority question, the M3 can be progressive when focusing of 5th s (even if that logic is not usually learned).

I have heard enough overstretched temperaments with progressive FBI and too disparate 5ths to know that the 2 methods provide different results, harmony wise.

That is also that 5th s are really a foundation in harmony.

And it is challenging to listen to 5ths as if they where FBI...

The goals in my temp sequence (I learned from Alfredo that one, before then I tuned F3 F4 A4) is progressive M3 and M6 in A3 A4, so you imagine well I am using FBI too.
But all intervals must be in the range of acceptability, there is one for the fast beating and one for the slow beatings. The one for the slow beating is large so we think they are less precise.

I for years did not believe it was possible to tune an acceptable temp with progressive 3ds using only 5ths and 4ths, and it is somewhat in absence of checks, for sure, but you may be surprised if you do that right in a good octave, that you will be really near.

Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/28/13 06:39 AM
Originally Posted by kpembrook
Originally Posted by Dave B
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks.


Or, you could just tune the 3rds and be done with it.


That is the pitfall some tuners fall in. Then they tune a temp that is perfect for modern music, but there is not enough consonance job done at the 5th level.
The day they discover they can tune UT in a cycle of 5th, it free their mind of that focusing, and their tuning change (hence the success of UT's)

Not to say an efficient tuner could not even tune "directly" M3, or 10th, whatever, when in doubt in the 5-6th octave I mostly have to listen to the 17 th to know if I can trust my ears or no.

I did not like so much the 5th and 4ths precedently. Find they slowed me, where not as sparkling as FBI's, etc... was a little considering 5th 4ths tuners as "old school"

Tuners may change with age and due to exchanges with other tuners

Both intervals have their characteristics and their use in music - I noticed that our best tuners in concert service where very attentive to 5ths (the M3 are very fast to evaluate).
I was not sure of the reason at that time, as I thought as you "tune the M3 and it is done".

This may be due to the iH and the voicing, but some compromising is done (again) between the progressiveness of the M3 and the good swell of the slow beating ones.

Differences in speed of slow beating intervals is not as much noticed so they do not cause real trouble, but then there is no reason the difference should not be parsed all along the scale is not it ?

It just play a little role in the global congruence, harmonically wise. those ET that lack musicality are probably due to that.





Posted By: rXd Re: Tuning the 4ths and 5ths Temperament - 06/28/13 10:44 AM
I just don't get it why anyone would confine themselves in this way. I sometimes tune in noisy environs and use every check note as it becomes available. Some notes, if the tuning is already close I will use, before they have been tuned as comparison aids from inside and outside the temperament range. All tuning intervals have the same usefulness to me.

I have a sense of tempo and rythm from time spent playing for major ballroom dancing competition orchestras. That helps but is not infallible.

I think that many potential fine tuners were ruined, both in temperament setting and developing excessive stretching habits by a steady diet of spinet pianos early in life. Large pianos are much easier and don't need all that stretch. (spinets don't either if they are reasonably voiced), but trying to lay a good temperament in the usual area is doomed to fail. I say to all tuners in that position, don't expect anywhere near perfection on a spinet but along with a steady diet of spinets comes many big old uprights. There's no excuse for a poor temperament on a big ol' uprite, nor for excessive stretching. If it sounds as though it should be stretched more, perhaps you have developed lazy listening habits. Do yourself a favour and tune them properly then you will always be ready for a better class of work. Never stretch more than half a beat in the whole of the treble and don't stretch at all in the bass. You never hear the drunken warbling 10ths and 17ths that we get fond of on good recordings. Theres a good reason for that. ....properly taught tuners.

Too many tuners are self taught or taught by self taught tuners who never really learned. It's all there in the oldest books but we need a properly taught mentor. As we are discovering, there ain't too many of them.
Originally Posted by Bill Bremmer RPT
.....

The inherent problem in constructing a temperament by starting with a chain 4ths & 5ths and only being able to use any RBI checks after several notes have been literally guessed at as far as tempering is that some cumulative error will inevitably be the result. At that point, when RBI checks become available, it is impossible to know which previous errors have occurred, where they are and how much error is involved in each of them.

.....


I challenge this statement. Any "inherent problem" of using a 4ths and 5ths sequence is you need to be able to recognize a properly tempered SBI. If you can't, then by all means use some other sequence. How rare this ability might be, I really don't know. It is worth developing if possible.
Posted By: rXd Re: Tuning the 4ths and 5ths Temperament - 06/28/13 12:08 PM
I am reading an awful lot about backtracking. I tune all unisons as I go for many reasons. One of the side effects is that it sure does discourage creating the need to backtrack. Backtracking is like a student who starts again every time they play a wrong note. It's an unnecessary habit. And it's only a beginners habit that can persist in spite of added experience.

Once the first 4 notes are right, everything else should follow, otherwise the result is a patched up effort.

Sometimes, for fun, I'll set the A, Bb, B & C on the scale electronically and do the rest by ear.

In a large piano, the beat rates become a rote procedure. On a smaller piano I used to use more minor thirds so that no M6 reflected outside the bearings would be too fast. If the M6th aren't too fast or slow the M3rds and 10ths won't be either. Make sure none of the 4ths & 5ths are too noisy and go. It was never worth any more of my time than that.

With large pianos there no need to re-invent the wheel every time. Too many spinets on the early learning stages might lead a tuner to believe so.


Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 12:47 PM
Ok, I am the one that used the word, "backtracking" first, I think. Allow me to clarify.

What I should have said, instead of backtracking, is one needs to refine.

Kent Swafford says it, so well, with regards to temperament tuning and the refining which is inevitable and necessary,

"The successful piano tuner will understand the difference between the first attempt at laying the bearings and the subsequent refinement of that initial temperament. The objective while tuning through a temperament sequence is not perfect results the first time through.

The tuning resulting from the first (or second or even third)
pass through the temperament sequence only needs to be good enough to allow the refinement procedures to proceed. The purpose of tuning through a temperament sequence is to provide a temperament that can be refined in the separate refinement procedures.

Get through the temperament sequence without belaboring it and move on to temperament refinement. The temperament refinement procedures are where one can achieve close to-perfection tunings. A temperament sequence is only the preparation for fine tuning; it is not fine tuning itself. Great tuning is accomplished during the refinement procedures, not during the temperament sequence."

Mark D.:

I am not so sure about the refinement idea, especially with poorly scaled pianos. What I look for is that ninth tone falling exactly where it should. If it doesn't, and I continue to the end without -backtracking-, when I then try to -refine- I come with some checks that say a note in question should be higher and other checks that say it should be lower.

I know that this is the essence of Mr. Swafford's "Every Which Way" method, but the result is an iffy-wishy temperment that when expanded results in iffy-wishy octaves, 12ths and double octaves. There is a place for it, though. It is great when doing a touch up to be able to quickly get a compromise from various checks to decide which string to tune the rest of a wavering unison to.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 03:15 PM
Jeff

I am not entirely sure where you are coming from and where you are going with regards to what you have written. Can you please explain.

What I am trying to get across, is that there is going to be some refining, and fudging when temperament tuning.

When I tune, I tune from A4 down to A3 and divide that up with the CM3's, A3/C#4, C#4/F4 and F4/A4. I will often run through the A4 to A3 sequence using the 4ths and 5ths and then correct things so that there is a smooth progression of 3rds.

I am reminded of what Don Mannino said, which is important for those of us who do not work on high end pianos all day every day to realise and accept,

"it is a little dangerous sometimes for people to get overly obsessed with perfection in tuning temperaments. No, I don't mean it's OK to be sloppy, but some tuners do spend an awful lot of time working out a beautiful temperament, only to spoil it with inconsistent octaves and unisons. I think that's what stops a lot of tuners from bothering with trying new temperaments - they are happy with getting something passable in some of the awful pianos they work with every day, and it just doesn't have relevence to their daily lives to worry too much about this level of perfection."

I use the whole tone way of tuning the temperament, using the intervals to tell me what is going on and to work things out. In general I work out an ET but not always.

Please do tell me more about the 9th tone.
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 04:44 PM
Originally Posted by UnrightTooner
All:
My argument for 4ths and 5ths over M3s and M6s is the amount the partials are changed by iH and it matters little what sequence is chosen. You are going to have to tune 8 or 9 notes before you have it locked in. Besides, you are going to have to tune some 4ths and/or 5ths sooner or later anyway. Why not learn to use them for the entire sequence?


Jeff, I got the ninth tone issue you are speaking about. I just did not click at the moment I was reading your last post. I thought you were possibly speaking about employing the 9th partial in some way or other.

Originally Posted by UnrightTooner

What I look for is that ninth tone falling exactly where it should. If it doesn't, and I continue to the end without -backtracking-, when I then try to -refine- I come with some checks that say a note in question should be higher and other checks that say it should be lower.


Are you willing to explain in greater detail so as to enlighten me?

Thanks
Posted By: TunerJeff Re: Tuning the 4ths and 5ths Temperament - 06/28/13 04:45 PM
It is interesting to note that the Steinway Voicing and Concert Prep manual still insists on an aural 4th/5ths A-A tuning.

I still tune 4ths/5ths F3-F4, and check with lots of 3rds/6ths along the way. In some ways, this topic confuses me....why does anyone try to insist that ONLY 3rds or ONLY 4ths/5ths is correct? Any competent tuner uses all intervals to tune and check their temperament, don't they?

The fact that I 'lay the bearings' with a 4ths/5ths does not mean I disregard the 3rds and 6ths. Refinement of the orignal settings means that you roll the contiguous and continuous intervals...and adjust accordingly. What's the issue?

Smiling,
No!
Really!
I am,
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 04:54 PM
Thanks Jeff, I agree.

I learnt to tune aurally and and began tuning for clients in 2005. I then began using Tunelab in 2011. It was from the beginning of this year that I have returned to tuning aurally, but do use Tunelab for PR.

Mark D.:

Yeah, the ninth tone might be the place to talk about the whole thing.

I am going to use the classic sequence by Dr. White: C4, F3, G3, D4, A3, E4, B3, F#3, C#4, G#3, D#4, A#3, F4. Yes, it really does end with F4 with the final check being the F3-F4 octave. The ninth tone is C#4. Up to this point if every 4th and 5th was just a hair tempered too much, or tempered too little, it may not be noticeable. But if F4 happened to have been tuned, or if you use the m6 F3-C#4 as a substitute for the M3 C#4-F4, the incorrect tempering will become apparent compared to the m6 F#3-D4 and/or M3 C4-E4. The bps of the m6 F3-C#4 and/or M3 C#4-F4 should fall between the other two. Well, on a small piano it could be off. The test for a 8:4 octave happens to be the m6/M3test.

Another way to put the previous paragraph is that it takes 9 tones in the circle of fifths to construct a ladder of CM3s. If you have everything right, the ninth note proves it, and if you don't the ninth note proves that too!

Then the question is what to do about it? Often the problem is something slipped a little like E4, in which case the check is at fault, not the temperment. But let’s say everything is a little iffy-wishy because all along you planned on refining. So you back up a little, say to B,3 and try to make things better. You run the rest of the temperment start playing chromatic M3s and “refine” things. You know, it is not hard to get the chromatic M3s progressive within just one octave if you are willing to fudge on the rest of the intervals. And that is probably what will happen.

So now you have reasonably progressive M3s in one octave and you start to expand it. You tune F#4 and listen to the M6 A3-F#4. Hmmm, it really isn't beating quite the same speed as the M3 B3-D#4, but didn't somebody that writes posts with thousands of words say that the outside M6\inside M3 test is not to be trusted and they never use it? Ok, ok, as long as the M3s and M10s and M17s are progressive it is ET, right? And sure the resulting 4th and 5th might not sound quite the same as the others, but tuning 4ths and 5ths is "'old school" (Thank goodness!).

This is what I have experienced when “refining” instead of, well, tempering correctly. I better stop before rounding up would put me at 1,000 words. wink
Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 06:20 PM
Thanks Jeff, your posts here have been illuminating.
Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/28/13 09:43 PM
Originally Posted by Mark Davis
Thanks Jeff, your posts here have been illuminating.


ANothyer illuminated, ! please take care, not auto ignition on you !!

I'd add to Jeff comment that you also can secure the first octave with those 4ths and 5ths, then you have very soon fast beating intervals (a M6 A3 F#4 in my case) to tell you where you are going -






Posted By: Numbered Re: Tuning the 4ths and 5ths Temperament - 06/28/13 10:12 PM
Thanks for your post and concern Isaac

Please explain further.





Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/29/13 07:02 AM
Originally Posted by TunerJeff
It is interesting to note that the Steinway Voicing and Concert Prep manual still insists on an aural 4th/5ths A-A tuning.

I still tune 4ths/5ths F3-F4, and check with lots of 3rds/6ths along the way. In some ways, this topic confuses me....why does anyone try to insist that ONLY 3rds or ONLY 4ths/5ths is correct? Any competent tuner uses all intervals to tune and check their temperament, don't they?

The fact that I 'lay the bearings' with a 4ths/5ths does not mean I disregard the 3rds and 6ths. Refinement of the orignal settings means that you roll the contiguous and continuous intervals...and adjust accordingly. What's the issue?

Smiling,
No!
Really!
I am,


+11
Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/29/13 07:08 AM
Originally Posted by Mark Davis
Thanks for your post and concern Isaac

Please explain further.







Hello, Joking is my concern, on a Saturday !

If you secure the initial octave with 2 4th and 2 5th it helps to have sooner fast beating intervals and it is also a strong setup, even if based on slow intervals.


But one may stop focussing on octave types and simply tune "good" octaves, with the tuning done using more 4th an 5th , it is soon easy to tune direct octaves with the same level of precision than iof yopu where making a comparative test at each of them.

A sort of side effect but that makes a difference.

Rartely I need to compare 10th and M3, if I do so they are right usually.






Posted By: Herr Weiss Re: Tuning the 4ths and 5ths Temperament - 06/29/13 01:16 PM
Originally Posted by Olek

+11


Impossible!

In the domain of pure and applied mathematics, Number Theory shows that the Euclidean algorithm in quadratic reciprocity in its distribution of primes(variable integers)with or without the diophantine equations found in modular arithmetic(before the 19th Century), proves that nothing higher than +10 is allowed - this is called Finite Fields.

Of course, there will always be the naysayers, mostly Europeans and Asians, the so called "Young Turks", with their new ideas.
What's next?!? +12??? +13???
Posted By: bkw58 Re: Tuning the 4ths and 5ths Temperament - 06/29/13 02:03 PM
Originally Posted by kpembrook
Originally Posted by bkw58
If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.


One would think so . . . but actually not in my experience. When I tune 4ths/5ths, I check with the thirds and go and modify my 5ths until the 3rds are right. When I just make the thirds right, the 4ths/5ths are OK and I don't have to tweak nearly as much.

As I mentioned, I grew up tuning 4ths & 5ths. I was challenged by Let's Tune Up by John Travis to try the thirds approach. Having gone both ways, I find the 3rds approach better for me and there is some basis in objective physics for that to be true.

Now, I should be clear that there was a learning curve for me. If I had given up during that learning time, I might have concluded that it wasn't worthwhile. But it didn't take long. It's an approach that I commend to those who might like to try. If not, I know there are many good folk doing outstanding tunings using approaches that I don't.


Hi Keith,

The proposition is a mathematical certainty. The real issue is which method easier obtains the goal. Having learned both methods, you are in a better position to say than I.

Often I had this conversation with another tech at the store. He learned exclusively the "3rds" way, I the "5ths." It was like trying to communicate in an "unknown tongue." His tunings were very, very good. An equal part of this equation is application. His skills at setting the pins and the strings, were excellent as well.
Posted By: MU51C JP Re: Tuning the 4ths and 5ths Temperament - 06/29/13 02:27 PM
+14 is what is next !
Posted By: Herr Weiss Re: Tuning the 4ths and 5ths Temperament - 06/29/13 02:52 PM
Originally Posted by Johnkie
+14 is what is next !


Clearly another proponent of tuning 7ths and 9ths. cursing

Posted By: Olek Re: Tuning the 4ths and 5ths Temperament - 06/29/13 05:12 PM
Originally Posted by Herr Weiss
Originally Posted by Olek

+11


Impossible!

In the domain of pure and applied mathematics, Number Theory shows that the Euclidean algorithm in quadratic reciprocity in its distribution of primes(variable integers)with or without the diophantine equations found in modular arithmetic(before the 19th Century), proves that nothing higher than +10 is allowed - this is called Finite Fields.

Of course, there will always be the naysayers, mostly Europeans and Asians, the so called "Young Turks", with their new ideas.
What's next?!? +12??? +13???


Oops sorry I was in binary mode there.. (or was it binaural?)
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