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#1350157 - 01/15/10 03:38 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
BTW BDB,

You have not said what you do on the difficult (and easyer) pianos.

Do you use a fifths/fourths based sequence?
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1350171 - 01/15/10 04:01 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Gadzar]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21303
Loc: Oakland
On the more difficult pianos, I tune contiguous thirds, fourths and fifths between one major third, and contiguous thirds to fill in the rest of the fourths and fifths, with the addition of tests from the Travis method. The all-important final step is to check everything afterwards. Note that I say I use tests that are based on Travis' method, rather than using his method exactly. Also note that I do not say what note I start with. Once you develop the method and understand the method, none of that stuff matters. You can start anywhere and do things in different orders. The final result is what matters, and that is a result of the final check.

On the easier pianos, I tune contiguous thirds, fourths and fifths between one major third, and contiguous thirds to fill in the rest of the fourths and fifths, with the addition of tests from the Travis method. The all-important final step is to check everything afterwards. Note that I say I use tests that are based on Travis' method, rather than using his method exactly. Also note that I do not say what note I start with. Once you develop the method and understand the method, none of that stuff matters. You can start anywhere and do things in different orders. The final result is what matters, and that is a result of the final check.

For those who are not familiar with the Travis method, he tuned contiguous thirds, and then a fourth, and contiguous thirds from that, comparing with his original thirds. I feel it is better to fill a third with fourths and fifths, and once you have done this, you can compare the rest of the fourths and fifths with the thirds that you have tuned initially.

Lots and lots of checks, not just in the initial temperament octave, but everywhere you tune, makes for a very well-tuned piano.
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Semipro Tech

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#1350175 - 01/15/10 04:11 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
So there is another CM3s tuner.

I am afraid there is no "let the piano tell you" sequence based on fifths/fourths tempering.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1350236 - 01/15/10 07:29 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: BDB]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
All:

I can only say what I do and why I do it. I cannot say what others do what they do or why they get the results they do.

If the very first time you tried to set a temperment the sequence worked, most any one would favor that sequence. That is the case with me and BW. I have made just the modification of including F4 and A#3 at the beginning of the sequence.

The sequences that include CM3s all sound wonderful, but do not work as well for me.

To me, setting an octave to start with without listening to its effects on the sound of the fourths and fifths is the tuner telling the piano, not the piano telling the tuner. And setting the octave is always done before tuning fourths and fifths in CM3 sequences.

I cannot explain what properly tempered fourths and fifths sounds like. If you don’t know, it would be best not to try to tune with them.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1350254 - 01/15/10 08:18 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Gadzar:

It seems again that you had already decided that what you are asking for does not exist in fourth and fifth tuning. Of course “the piano tells you” for any sequence if a true ET is the result. What else could tell you? The question is: in what part of the sequence is the piano telling you?

Perhaps your thinking is locked into the glib statement of “let the piano tell you” meaning what it was meant to convey in whatever article it came from. Which seems to be that fourth and fifth tuning is about arbitrarily choosing beat rates for intervals which are then used to adjust the fourths and fifths. If you look at fourth and fifth tuning as distributing the comma so that all RBIs are progressive you may see that “the piano tells you” if you are tempering correctly.

In a fourth and fifth tuning (and perhaps all sequences), the ninth note is what proves if things have gone correctly. As I said in an earlier post, “I know G-A# is very, very close because I know what tempered fourths and fifths sound like. Then "the piano tells me" what the beat speed of G-A# is for how those fourths and fifths are tempered. Later this will be confirmed or not.” Comparing F#-A# to F-A and G-B is how “the piano tells me” if the fourths and fifths are correct. And when the fourths and fifths are correct. then the intervals that they create are correct. It is about beat progression, not beat rates. And, yes, it takes nine notes or eight fourths or fifths to get to that point. That requires great accuracy, but I think you have to be able hear the tempering of fourths and fifths, not just their beats.

Let me add some comments so you can understand the value of G-A# in the sequence. A m3 is made from 2 fourths and 1 fifth. A M3 is made from 2 fourths and 2 fifths. A M6 is made from 1 fourth and 2 fifths. If there is a tendency to tune the fifths insufficiently tempered it will show up more in comparing a m3 to a M3 than it will comparing a M6 to an M3. And by checking the one fifth that is used to form the m3 with an octave and a fourth, the m3 can be consider to be tuned with 3 fourths and an octave - the octave that “the piano tells you” is correct because of how the fourths and fifths sound. So now there is a limit for how fast the M3s can beat and will point out any tendency for the fifths to not be tempered enough. This is especially valuable when tuning E. If C-E is not slower than G-A#, then the place to look is in the fifths that form C-E: G-D and A-E. Notice that these are not involved in the tuning of G-A# and, of course, C can be depended upon as it is the starting note. After E is verified by having made sure C-E beats slower than G-A#, the next 2 intervals are fourths and brings us to the ninth note without tuning any more fifths.

I don’t think you will benefit from this post; I can only hope other readers might. I continue to think that the purpose of this Topic is to bash, not understand, fourth and fifth tuning.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1353777 - 01/19/10 11:32 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
Originally Posted By: UnrightTooner
I cannot explain what properly tempered fourths and fifths sounds like. If you don’t know, it would be best not to try to tune with them.


How can I understand what the "piano is telling me" when tuning a fifth, if even an experienced fifth's tuner like you can not explain how it should sound like?

What you say about a m3 being two fourths and 1 fifth; and a M3 being 2 fourths and 2 fifths sounds interesting however and much less arbitrary than tuning 0.5 bps narrow fifths and 1 bps wide fourths.

If you prefer to tune the octave by tuning the 4th + 5th and 5th + 4th, (instead of tuning it directly by testing 6:3 and 4:2 types), I have no objection: yes, you are tuning a good sounding octave, taking into account partials 2, 3, 4 and 6 of the notes involved.

But the the question is still blowing in the wind: how do we tune fourths and fifths?

Originally Posted By: UnrightTooner
In a fourth and fifth tuning (and perhaps all sequences), the ninth note is what proves if things have gone correctly. As I said in an earlier post, “I know G-A# is very, very close because I know what tempered fourths and fifths sound like. Then "the piano tells me" what the beat speed of G-A# is for how those fourths and fifths are tempered. Later this will be confirmed or not.” Comparing F#-A# to F-A and G-B is how “the piano tells me” if the fourths and fifths are correct. And when the fourths and fifths are correct. then the intervals that they create are correct.



Yes, if they are correct, but what happens if they happen to not be correct?

You say it takes 10 notes to have an answer, and that is too much to know how to correct them. There are too many intervals to tweak to have a right progression of FBI's.


Edited by Gadzar (01/20/10 12:14 AM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1353811 - 01/20/10 12:21 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Gadzar]
Jim Moy Offline
Full Member

Registered: 05/06/07
Posts: 292
Loc: Fort Collins - Loveland, CO
If I may interject, I believe what Rafael means when he says "let the piano tell you," is something specific, and that is a sequence by which the following occurs:
  • Octave width in the temperament area is chosen ahead of time.
  • Two octaves are tuned, with one or two overlapping M3rds, one of which is initially estimated.
  • The note between the remaining two M3rds is adjusted such that the beat rate of the middle of the three contiguous M3rds is "in-between" the two outer ones.
  • Once the middle M3rd beat rate is discovered, the piano has "told you" how wide it should be, for the given octave widths, and for the iH of the piano in that range.
  • Given the fixed octave widths, the rest of the M3rd beat rates "fall out" naturally when tuned for smoothly increasing beat rates, as do the beat rates of the 4/5ths.
So the question about whether a similar sequence exists for 4/5ths tuners is one of strategy. In the steps I describe above, the octave widths are chosen ahead of time with the assumption that you can make a wise choice (how that happens is another topic), and given that assumption, the rest of the sequence can be performed mechanically, and produce good results.

My impression is that with 4/5ths tuning, the high level strategy is different, that one does not choose octave widths as a high level guide, and therefore such a sequence may not exist, hence Rafael's query.
_________________________
Jim Moy, RPT
Moy Piano Service, LLC
Fort Collins and Loveland, Colorado
http://www.moypiano.com

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#1353842 - 01/20/10 01:22 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Jim Moy]
Thomas Dowell Offline
Full Member

Registered: 11/18/09
Posts: 122
Loc: Twin Lakes, WI
Has anyone looked at Virgil Smith's temperment? I'm not sure if it's a 4ths/5ths method, per se, but you work with the A3-A4 octave, guess F3, use 4/5 for the D octave, and then use a fourth for the speed of the a major third. I know it's complicated, but I'm not sure if I'd be breaking any rules by copying a copyrighted work on a public domain. His book is only $7 or something.

I don't personally use this, but I thought it does bridge a few gaps.

Regards.
_________________________
Thomas Dowell, R.P.T.
Dowell Piano
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#1353924 - 01/20/10 08:02 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Thomas Dowell]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Gadzar:

I can no more tell you what properly tempered 4ths and 5ths sound like than I could tell you what the color blue looks like. But I could point to the sky and tell you that is the color blue. And if you are not color blind, you will know what I mean. And you can listen to a well tuned piano to see what properly tempered 4ths and 5ths sound like. But if you do not recognize the tempering (which is really best discerned while tuning) and only hear beats, then you will not know what I mean.

Jim:

If what you described is what Gadzar is really asking about, then he would recognize that a 4ths and 5ths sequence does the same thing as a CM3 sequence, but in more steps (which adds accuracy). This is why I do not believe that is the purpose of this Topic. And when starting out there is no reason that a 4ths and 5ths sequence cannot be used with a predetermined octave or a predetermined 12th or a predetermined 17th.

Tdowel:

I know that Virgil Smith’s sequence is on the internet already. I believe I saw it on this Forum. If I remember right, it starts with a specific beat rate, or color, for an initial 5th. I think there may be more to this that I thought at first. With a shorter piano this will produce a narrower octave than on a larger piano which is exactly what you want! It was posted recently about a master tuning committee having difficulty in discerning the difference between the 4:2 and 6:3 octave on a particular piano because of low iH. Perhaps a wider than 6:3 would have been best on this piano and could have been obtained through using a predetermined 5th instead of a predetermined octave. Thanks for putting this thought in my head!

[Edit:] Maybe that is just what I am doing but didn't realise it....


Edited by UnrightTooner (01/20/10 08:49 AM)
Edit Reason: added comment
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Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1354012 - 01/20/10 10:39 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Thomas Dowell]
Jim Moy Offline
Full Member

Registered: 05/06/07
Posts: 292
Loc: Fort Collins - Loveland, CO
Originally Posted By: Tdowel
...Virgil Smith's temperment ... you work with the A3-A4 octave, guess F3, use 4/5 for the D octave, and then use a fourth for the speed of the a major third...

Yes, I have his book, but have not studied his sequence in much detail (was more interested in his approach and philosophy).

I do not get the impression it is a 4/5th's temperament per-se. More that he uses all the interval checks he thinks appropriate to get the balances he wants. For example, in the part you referenced, his actual text is:

Originally Posted By: Virgil Smith
Tune D3 and D4 to A3 until: a) octave is beatless, b) D3-F3 m3rd beats faster than F3-A3 M3rd, but slower than F3-D4 M6th, c) D3-A3 5th beats slightly slower than A3-D4 4th, and d) F3-A3 M3rd beats slower than F3-D4 M6th.

I'm sure I'll get around to trying the sequence out, but I'm still working on my ET and EBVT aurally, and that's enough for me to wrestle with for now shocked
_________________________
Jim Moy, RPT
Moy Piano Service, LLC
Fort Collins and Loveland, Colorado
http://www.moypiano.com

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#1354044 - 01/20/10 11:45 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Gadzar]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Gadzar:

Maybe I am being unnecessarily rough on you. Let me try an apologetic approach.

In any given CM3 sequence, how many notes, after the initial set of CM3s, must be tuned before any of these additional notes are verified?

What is the total number of notes that have been tuned at that point?

How does this number compare with a 4th and 5th sequence?

You have posted, “You say it takes 10 notes to have an answer, and that is too much to know how to correct them. There are too many intervals to tweak to have a right progression of FBI's.”

How many notes are too many?

Why wouldn’t one know how to correct them?

Can there be too many intervals to tweak if the result is a right progression of FBIs?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1354639 - 01/21/10 08:27 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
All:

I did some checking on a simulator. Setting the 4ths to 1 bps and the 5ths to ½ bps in the temperament gives an appropriate octave width for a given inharmonicity. For a large piano this is between a 6:3 and a 4:2 octave. For a small piano it is a 4:2 octave.

The more arguments I hear against 4th and 5th tuning, the more I am convinced of my choice after further study. But I understand that others will confirm their different choices in consideration of their own personal preferences and experiences.

Still, you can’t go far wrong with 1 bps 4ths and ½ bps 5ths in the temperament. BW was right again, but again for the wrong reason.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1354651 - 01/21/10 08:48 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3190
Loc: Madison, WI USA
Jeff, I am itching to see how well the student I will tutor on Saturday does with his BW style temperament. He says he has studied it for 5 years now. Quite frankly, I am not very hopeful. I am going to record the numeric values of what he comes up with for discussion. If he does well, fine, I will work with him on what he can do but if the results are what I expect them to be and he has little or no understanding of how to improve upon it, I will take another approach and that will most definitely start with the CM3s.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1354654 - 01/21/10 08:56 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Bill Bremmer RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Bill:

I hope it will be a good tutoring session for both of you. I know I am in the minority, but that is nothing new.

Do you understand or agree with the beat speeds of SBIs being able to set the proper octave width for a piano's iH?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1355048 - 01/21/10 08:00 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3190
Loc: Madison, WI USA
Originally Posted By: UnrightTooner
Bill:
Do you understand or agree with the beat speeds of SBIs being able to set the proper octave width for a piano's iH?


I am sorry, I do not. That would be an example of the tuner trying to tell the piano what to do and the piano may say, "No, I am doing my own thing."
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Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1355119 - 01/21/10 10:33 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Bill Bremmer RPT]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
I'd like to contribute a little to this discussion, as the way I have been taught to tune may shed a bit of light on the question of the piano telling you how much to temper 4ths and 5ths.

I've learnt to tune a F - E temperament. There are no octaves involved in my temperament whatsoever. I use a C4 523.3 tuning fork, and tune C3 to it using an A#3 equal beating test with the fork and the C3 note. I'm beginning to realise this may be the a large source of inaccuracy in the temperament, but this is not relevant to this discussion. Let's assume that this C3 is tuned accurately.

My basic sequence is tuning F3-C3, then G3-C3, D3-G3 and A3-D3 using predefined beat rates. The 4th is set at 1bps, which (I don't know much about theoretical analysis of iH) seems to hold true for very nearly all pianos. But the salient point here which I think sheds a bit of light on the situation, is the tempering of the 5ths. I learned to use the 6:4 partial match to temper the 5ths, with an initial estimate of 3bps. 3bps is a very easy beat rate to estimate in your head, and also a lot easier to perceive than possibly 1/2 a beat a second, which has a massive margin for error. 3.5bps sounds wrong, as does 2.5, but both produce a similar beat rate on the 3:2 partial match.
After tuning the first four intervals, there is M6 - M3 test to see what is what. The check here is the 8bps M6. 8bps is very easy to count by subdividing the second, and 8 holds true as a beat rate for very nearly all pianos. Our teacher taught us this rate holds true even when there is a jump in iH such as there being a wound string on the F. I've tuned good temperaments on spinets using this method and I support this view.

So on checking the 8bps M6, and comparing for a slightly slower M3, we can see whether our two initial 5ths are correct. The pianos we learnt on were average height uprights, Welmars. On those pianos, if the 6:4 was at 3bps on the 5ths, and the 4ths were at 1bps, the M6th would be 8bps. So any error was obvious. As long as the 4th was at 1bps, I knew if the M6th was slow, the 5ths were too narrow, if the 6th too fast, the 5ths too pure.

But what about on other pianos with different iH?

On smaller pianos with higher iH, this sends the 6:4 partials further up the piano, and so increases their beat rate for a correctly tempered 5th. The way this manifests is by the F3-D3 6th still being too slow when the 4th has been confirmed at 1bps and the 5ths confirmed at 3bps on the 6:4 and both even. This is then addressed by slightly increasing the 6:4 beat rates on the 5ths, evenly. Only a slight change is needed, but this change is obvious against the 3bps pulse, and so easily done.

On larger pianos with lower iH, the converse is true. The 6:4 partials are flatter, and beat slower, so 3bps on the 6:4 partial will produce a fast F3-D3 M6. So the 5ths are widened until the 8bps is achieved.

After these rates are adjusted until the 8bps condition is met, and if the F3-A3 M3 is slightly slower than the M6 then I continue. After this, every new note produces a M3 or a M6 to check with the others.

Next is E3-A3, giving a G3-E3 6th which should be slightly faster than F3-D3 (about 1bps). Then B3-E3, giving our first inside M3 outside M6 check. If this holds we can move forward, if not, there is a systematic error somewhere.

I won't continue with the sequence as I realise it is getting rather verbose. But the point I am trying to get across is that the initial five notes after the fork note C3 let the piano tell us how much iH to allow for.

I believe this works very well using the 6:4 test, because of how low down the 3:2 partial match is on the series. This is also why I think the 1 bps 4th is very accurate. Changes in iH do not move the 4:3 partials enough so that 1bps is no longer accurate, nor do they move the 3:2 enough on the 5th. But a higher iH will push the 6:4 partials up noticeably, and the M6 and M3 checks show this to me. If the checks still tell me something is wrong even though the 5ths now seem to be at the right rate, only then do I look to the 4ths as a source of systematic error.

Of course it is impossible to tune 1bps 4ths completely accurately. There is no need. If every 4th matches the previous ones, and the first checks held, then if the checks continue to hold, the 4ths will be correct. The same with the 5ths. The tempering amount of the 5ths is found using the first few checks. The piano tells me how much to temper them.

After the temperament is set (B-E, B#-F, F#-B, C#-F#, G#-C#, D#-G#, B#-E# confirm) then the temperament itself sets the size of the octave. F4 is tuned to F3 according to what will give the best progression on the RBIs, and the best evenness with the SBIs. Simple as that.

This is how I believe the SBIs are "able to set the proper octave width for a piano's iH?"

This is also a "letting the piano tell you" 4ths & 5ths sequence, as far as I understand the term. It uses the pianos iH to correct your tempering of the 4ths and 5ths.

It does require some counting of beats, and bit of guesswork at the beginning, but only two notes need moving if the first M6 test seems wrong. And then if the M3 test also seems wrong, only 3 notes need moving, if the 4ths are right.
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Phil Dickson
The Cycling Piano Tuner

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#1355281 - 01/22/10 03:29 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Phil D]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7264
Loc: France
that is interesting, a first time to me to see a temperament without an initial octave (while I recall tuning sometime by 3ds and 4ths till the octave comes in, but on pianos i was acquainted with).

Yes may be A#2 should be better to test against C4 but aint less good than checking A440 with the 10th F3 A4.
if you are used to listen at higher partial ranges you may well compare the speed at the good level anyway (C5).

I am unsure to understand however if you are willing to get a "standard" beat rates which should apply to the RBI, or if this can be conceived that their speed will vary depending of the piano, as it is the case with methods that put emphasis on 4ths/5ths.

it seem to me more based toward a standard set of rate, with octaves as a result.

I like to heard that in real time. the tone may be a tad "greasy" , that's interesting (not criticizing there !) makes me think of the pop music piano, but may be I am plain wrong and it is adapted to resonance of the instrument afterthat by stretch. it is precise enough, anyway, good learning temperament.

What is the name of that tempering method ?

The EDT use one partial in the medium range, generally the 3d so they can put you in the ballpark and provide an even progression of 12ths or 5ths, but the RBI will not be as even then. Or you use the 4ths partial, the display is jumpy, and you have a smoother progression of RBI's.

They can be more accurate if they record the partial ladder of each note (during tuning) and recompute the tuning at that moment (Verituner's use that method).

I've always find that the justness of the 1 partial driven EDT give me the impression that the tuning is "holding by the noze" as some zones are purer than others and the display push you in its direction, slightly changing your global hearing and emotions.
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#1355393 - 01/22/10 09:10 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Olek]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
N a M:

Yes, that is quite a contribution. I am glad that you are willing to jump in.

The sequence of notes is straight BW (Braid White). The m3-M3 test for the 6:4 5th is additional, although is available by looking at any theoretical beat rate tables, which Dr. White suggests that tuners do.

What the tests and checks you mention for getting F-D correst are really based on is the relationship between the beat rates of M3s compared to M6s (which includes the test for 4:3 fourths) and the relationship between the beat rates of m3s compared to M3s (which includes the test for 6:4 fifths). A 3 bps difference between the m3 and M3 in a 6:4 fifth test seems way, way too much. This would cause F-G# to beat over 1 bps faster than G#-F which is the 6:3 octave test and would also indicate a very narrow 2:1 octave. Maybe you mean something else?

Also, even if F-D always beat 8 bps (which I respectfully disagree with), just how accurately can a person hear a difference between 8.00 bps and what an interval is actually beating? 1/10 bps? ¼ bps? ½ bps? And how accurate must the beat rate be in order to guarantee that the result will be that all M3s and M6s beat progressively, or at least to hope that all RBIs could beat progressively?

Here is how accurate. To guarantee all RBIs beat progressively the error must be less than 0.3 cents which is a difference of 0.15 bps. To hope that all RBIs could beat progressively the error must be less than 1 cent which is a difference of 0.5 bps. And since the theoretical beat rate of F-D is actually 7.92 bps, we are already half way to being unable to guarantee progressive M3s and M6s and one sixth the way to being unable to hope for progressiveness by using 8.00 bps as a standard.

I used to think just as you are thinking, including the value of the M3 inside M6 outside test. But after further study and review of Dr. White’s book, I realize that the difference between actual and theoretical beat rates is really not important after all because it is not the beat rates that are important but the beat rate progressions. Certainly if the beat rates while tuning are discernibly different than theoretical, then there is the opportunity to make corrections before continuing further. But until there is a set of three chromatic M3s (or possibly their m6 inversions) there are not enough notes to prove the progression is correct. On a straight BW sequence this happens on the tenth note when G# is tuned.

But then that is what I prefer about 4th and 5th tuning. It is right or it isn’t. Everything has to be right for the sequence to be right. With up a third, up a third, down a fifth, you can have four augmented chords (sets of CM3s) that are perfectly in tune to themselves and produces perfectly progressive M3s, but not have very progressive M6s or m3s and uneven sounding 4ths and 5ths. I suspect that those that use this method may listen more to the M3s than to M6s and m3s.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1355394 - 01/22/10 09:11 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: Olek]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3190
Loc: Madison, WI USA
Thanks Mongoose, that was interesting. It explains a thought process of 4ths & 5ths tempering better than I have ever seen it before and I am glad it works for you. You seem to understand what you are doing and you seem to get consistent and correct results and that is all anyone would be after.

Having said that, can you and everyone else see how a person who first learned to tune with an ETD but who now wants to take a tuning exam (where tuning the two central octaves aurally is required) would most likely not be able to follow that logic or learn that sequence very easily?

While I have seen many people pass those exams, I have also seen many failures. I have tried to find out why those people have failed and what other strategy may work better for them. I've also looked at exam master tunings of the same piano done by different committees that had different results and identified the reasons why the results were not closer to each other.

If I want to try to correct an attempt at ET or to bring an ET as close to perfection as humanly possible (such as starting with one technician's best attempt at an initial tuning which is then reviewed for a master tuning), it is always done by comparing the octave sizes of both A3-A4 and F3-F4 and then verifying the CM3s from F3 to A4. Until and unless those intervals are correct, none of the rest of the temperament will be.

It would not matter to me if the initial tuning had been done using 4ths & 5ths or with an ETD. The above points are those I would check and correct first. That would not involve any guessing whatsoever. What is the octave size of A3-A4? Is it a 4:2 or slightly larger? Either is OK within a certain margin. Now, without regard at this point to the CM3s, is the F3-F4 octave of the same or at least very similar type? If not, the temperament cannot be ET. One octave or the other must be changed in size so that they both have at least approximately the same width. If the CM3s don't fit after that, then they must be shifted so that they do.

After that, virtually any known sequence of checks and any combination of checks can be used to make the rest of the intervals fit within that framework. If, on the other hand, taking an extreme example but which I have seen more than a few times, the A3-A4 is wide enough to be a 6:3 octave (or close to it) but the F3-F4 octave is narrow enough to be a 2:1 (or close to it), the CM3s cannot possibly fit. 4ths & 5ths will not fit, all sounding similarly and M3s & M6s could not progress and digress evenly.

To me, this is how "the piano tells you". I cannot imagine the piano telling you in any other way. That expression, by the way is attributed to Jack Stebbins RPT who is the chief instructor at the North Bennett Street School in Boston. He has also been a tuning examiner for some 30 years. He teaches ET tuning using a CM3 approach and also conducts exam master tunings the same way I do. He has presented classes at numerous PTG conventions with that title.

One of the most amusing things I ever read on Pianotech was from a novice who said, "Somewhere, I read something about the piano being able to tell you when the temperament is correct or not. Well, I have been at this about 6 months now and so far, the piano ain't talking!" That was many years ago but I took it upon myself to show that technician just exactly how the piano can tell you when the temperament is correct or not. He quickly learned the method and became an RPT and has been ever since. He had first learned to tune with an ETD, had tried 4ths & 5ths tuning sequences but did very poorly. All it took to put him on the right path was to teach him a few very reliable techniques which work consistently well and he did just fine.
_________________________
Bill Bremmer RPT
Madison WI USA
www.billbremmer.com

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#1355415 - 01/22/10 09:41 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: UnrightTooner]
Phil D Offline
500 Post Club Member

Registered: 01/15/10
Posts: 551
Loc: London, England
Thanks for the encouragement guys, I'm glad not to have been jumped on for putting my oar in! wink

Originally Posted By: kamin
I am unsure to understand however if you are willing to get a "standard" beat rates which should apply to the RBI, or if this can be conceived that their speed will vary depending of the piano, as it is the case with methods that put emphasis on 4ths/5ths.

The standard beat rates are used at the beginning of the temperament to give something to work from. When the sequence is complete and it is time to check through the progression of all the intervals, then I ignore the standard beat rates and concentrate on getting the smooth progressions. When all the intervals progress smoothly, they can be used to give a size for the F3-F4 octaves. The result, if done very well, sounds extremely good and very accurate.

Originally Posted By: UnrightTooner
The sequence of notes is straight BW (Braid White). The m3-M3 test for the 6:4 5th is additional, although is available by looking at any theoretical beat rate tables, which Dr. White suggests that tuners do.

What the tests and checks you mention for getting F-D correst are really based on is the relationship between the beat rates of M3s compared to M6s (which includes the test for 4:3 fourths) and the relationship between the beat rates of m3s compared to M3s (which includes the test for 6:4 fifths). A 3 bps difference between the m3 and M3 in a 6:4 fifth test seems way, way too much. This would cause F-G# to beat over 1 bps faster than G#-F which is the 6:3 octave test and would also indicate a very narrow 2:1 octave. Maybe you mean something else?


I'm actually only vaguely aware of the m3-M3 test for 5ths. I think maybe I missed this part of the course. The 3bps I am referring to is not the difference between the m3 and the M3, it is the beat rate of the 6:4 partial as I hear it ie. the beat rate at C5 for the C3-F3 5th. Could you explain the m3-M3 test for me, and explain how I might make use of it?

As I mention above, none of these beat rates are set in stone by the time the temperament is finished. The emphasis is as you as on the beat rate progressions. The 8bps is, however, a firm basis to start from. We were initially taught to go for 8-9-10 bps rates for the M6s from F, F# and G, and 7-7.5-8-8.5-9 etc for the progression of M3s. But obviously it is ridiculous to think of these in this way, it just gives an idea of how they should progress.


Bill: In posting, I was trying to give my answer to the original poster's topic. I don't know anything about EDTs, and I've never been taught about CM3s. I now wish I had been taught about CM3s and the augmented chord basis for the temperament. The concept of using octaves to set the temperament is also completely new to me, but I can see massive value in it in my first attempts.
I have a very firm grasp of how my BW sequence is supposed to work, getting the beats to progress correctly is the aim. This is what I always aim for, and if I spend enough time doing it, I will achieve it. But using CM3s, I have achieved the same level of accuracy in the same amount of time already, and I haven't practiced it nearly enough for it to come naturally to me like the BW sequence does. In time I feel I will be able to produce a close ET quicker using the methods you describe. That's all I'm going to say on that particular matter, as I'm not interested in going off topic in order to join in the CM3s vs P4P5 turf war!
_________________________
Phil Dickson
The Cycling Piano Tuner

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#1355450 - 01/22/10 10:34 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Phil D]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
N a M:

My hat is off to you for hearing the beat of the 6:4 partial match directly. I do not, but have not tried all that hard. Instead I hear a “color” to the fifths that I attribute to a blend of the beat rates of the 3:2 and 6:4 partials.

The m3-M3 test does this indirectly. The difference between the beat rate of the m3 and the M3 is the beat rate of the 6:4 partial match. In case you didn’t know, the M3-M6 test for a fourth works the same way. If F-A beats 7 bps and F-D beats 8 bps then the 4:3 partial match of the fourth beats 1 bps. And if the F is raised so that the F-A beats 6 bps and F-D beats 7 bps, the A-D fourth still beats 1 bps. This is not explained in Dr. Whites book.

Still, 3 bps seems awfully fast. Perhaps you are hearing 3 half beats per second, like up-down-up. Theoretically the 6:4 beats twice the speed of the 3:2, but actually beats a little more than double because of iH. So 1-1/2 bps seems more like it and agrees with the actual difference in beat rates of the m3s and M3s. F-G# usually beat the same as B-D# on a real piano. And since M3 progress about ½ bps for each semi-tone, then F-G# would beat about 1-1/2 bps faster than G#-C.

And I understand what you are saying to Bill about the F-F octave just working out correctly even without starting there. I have wondered about how this could always be so when iH can require different octave sizes. I now believe that the beat rate of the fourths and fifths differs very little due to the scaling. There are definitely self-correcting effects of iH on beat rates. I hadn’t realized that they are to the extent that the correct width of the octave for the piano’s scale is one of them.

I know that others disagree. And in all fairness, if someone chose to tune the octave with a definite beat in it, it would be a challenge to use a 4th and 5th sequence. But to find an octave that truly fits the piano, you cannot be far off by having 4ths beat 1 bps and 5ths beat ½ bps.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#1355962 - 01/23/10 12:53 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence exist? [Re: UnrightTooner]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
Originally Posted By: UnrightTooner
How many notes are too many?


Two of them are too many.

In fact I can tune only one note at a time.

First I make an estimate on this note and proceed to tune other notes which confirm or correct this one note. Once this note is corrected I tune the next one.

Take for example F3 in the CM3 setting. First we estimate F3, then we tune F4 and C#4 to check the progression. If CM3s are not progressing evenly we retune F3, until we have a correct set of CM3s.

After that we tune a note which forms a 4th with one of the tuned notes using the same approach: first we make an estimate, then we tune auxiliary notes that will confirm or reject our estimate, etc…

The procedure is error free or more precisely: self correcting, one step at a time.

If you have to tune 10 notes before you can conclude anything, there are too many possible errors involved.


Originally Posted By: UnrightTooner
Can there be too many intervals to tweak if the result is a right progression of FBIs?


No, if the result is right there is nothing to tweak, of course, but if the result is an uneven progression then you’ll have a bad time to figure out the culprits.

That is precisely the opposite of what I am searching.

I am looking for a sequence free of guessing, where the piano tells you what it needs.


Edited by Gadzar (01/23/10 12:55 AM)
_________________________
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1356027 - 01/23/10 03:19 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Phil D]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7264
Loc: France
Originally Posted By: Not a Mongoose
Thanks for the encouragement guys, I'm glad not to have been jumped on for putting my oar in! wink


The standard beat rates are used at the beginning of the temperament to give something to work from. When the sequence is complete and it is time to check through the progression of all the intervals, then I ignore the standard beat rates and concentrate on getting the smooth progressions. When all the intervals progress smoothly, they can be used to give a size for the F3-F4 octaves. The result, if done very well, sounds extremely good and very accurate.


Hello, thanks for the answer. In case you could record some music or some chords on a piano tuned with that method I sure wish to hear it (I have something in mind, just want to see if I am right). SO if you could, would me much appreciated (your tuning or the one of the instructor but please say so (or not !)

Funny you dont relate beat rate ratios with tests. I also wonder if it is told actually in Europe it was not when I learned. Learning to listen to a whole tone is also better than hearing too much at beat's level, I suppose.

Have anice week end !


Edited by Kamin (01/23/10 04:33 AM)
_________________________
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#1356174 - 01/23/10 10:12 AM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Olek]
Bill Bremmer RPT Offline
3000 Post Club Member

Registered: 08/21/02
Posts: 3190
Loc: Madison, WI USA
"I am looking for a sequence free of guessing, where the piano tells you what it needs."

Rafael, the "Up a third, up a third, down a 5th" sequence on my website is best for that. After the initial CM3s (where, as you know, there is only one estimate which is self correcting), each of the rest of the notes is tuned as a 4th or 5th (more 4ths than 5ths, the 4th is more reliable than the 5th) and is checked by RBI's. The name of the sequence only tells you the next note to be tuned. You do not tune M3s.

As the sequence progresses, you get increasing availability of checks. The weakest spot in it is G3, tuned from D4 as a 5th. At that point, there is only the minor third, G3-A#3 to check but it can be compared to the F#3-A3 minor third which is right next to it for similarity. The next note, B3 is tuned from F#3 as a 4th. If the G3-B3 M3 is not quite correct, you only have the B3 itself and the G3 previously tuned to adjust in order to find a smooth chromatic progression of F3-A3, F#3-A#3 and G3-B3.
_________________________
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Madison WI USA
www.billbremmer.com

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#1356364 - 01/23/10 02:23 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Bill Bremmer RPT]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
Thank you Bill,

I know the sequence "up a third, up a third, down a fifth" in your site. I've studied it some time ago in great detail. I even set you a PM with some questions and doubts I experienced when trying it. But this is a sequence based on CM3 to set the bearings.

What I want in this thread is to discuss if there is a sequence a la Braid-White, not based on CM3s but on a circle of 5ths while being self-correcting.

The great problem I've found on this type of procedures to tune ET is that after tuning four fifths when you finally have a third, there is nothing avialable to know if this third is correctly tempered. Then after other five fifths/fourths tuned you have the complete picture but if something is going wrong there are several possible causes and it's difficult to know what is wrong. So you are forced to a very painful trial and error guessing game to get a correct temperament.

They say that 1 bps wide fourths, 0.5 bps narrow fifths, and 8 bps wide major sixth F3-D4 do the trick, and are universally correct for any piano with any iH. But what I've experienced in my dayly work denies this.

First of all, it is extremely difficult to temper an accurate 0.5 bps narrow fifth, there are two pairs of strong coincident partials sounding simultaneously. Even the tuners that tune this way can not explain how they do it.



And for the 1 bps fourths and 8 bps M6th, I've found that small pianos, spinets, need slower thirds, not of 7 bps in F3-A3 but 6 bps which gives 7 (not 8) bps for the Major sixth F3-D4, with a slow wide fourth but I can not say if it is 1 bps, or 0.8, or 1.1 etc.

And here is the problem: Can we tell the piano how we want to tune it? Would it accept those imposed beat rates?

I personally have found that it doesn't work. Each piano needs different beat rates, so we need a sequence that takes this into consideration and gives us the possibility of finding the correct beat rates in an orderly self correcting procedure.


Edited by Gadzar (01/23/10 02:28 PM)
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1356368 - 01/23/10 02:28 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Gadzar]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21303
Loc: Oakland
Quote:
And here is the problem: Can we tell the piano how we want to tune it? Would it accept those imposed beat rates?

What choice does it have?
_________________________
Semipro Tech

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#1356373 - 01/23/10 02:33 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
Originally Posted By: BDB
Quote:
And here is the problem: Can we tell the piano how we want to tune it? Would it accept those imposed beat rates?

What choice does it have?


It can sound bad, for example. Or it can get tuned in a Reverse Well Temperament.

If I tune a small spinet imposing it a F3-A3 M3 beating at 7 bps, I will have too wide octaves, very harsh 10ths, and the overall piano will be too much stretched.
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1356383 - 01/23/10 02:38 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Gadzar]
BDB Offline
Yikes! 10000 Post Club Member

Registered: 06/07/03
Posts: 21303
Loc: Oakland
That must be because you are not a good piano tuner. Other people can do it.
_________________________
Semipro Tech

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#1356399 - 01/23/10 02:49 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: Gadzar]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
And the if I want to avoid this overstretching then I will tune more narrower fifths.

You see, the first fifths I tuned were too wide, giving a too wide F3-A3 M3. Then I must narrow the remaining fifths in order to close the circle and have a correct octave. The result is: Reverse Well Temperament.

In a well temperament the first fifths we tune are narrower, in order to form quiet M3s, as we progress in the circle of fifths they become less narow and some of them are even tuned pure, giving more lively beating thirds in the remote keys.

By imposing a beat rate of 8 bps to the M6 F3-D4 in a small piano with a lot of iH, we are enlargening fifths, those of the simpler keys. And to close the circle we must tune narrower fifths for the remote keys. This is by definition "Reverse Well Temperament".
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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#1356404 - 01/23/10 02:56 PM Re: Does a "Let the piano tell you" ET 5ths/4ths sequence ex [Re: BDB]
Gadzar Offline
1000 Post Club Member

Registered: 12/15/06
Posts: 1610
Loc: Mexico City
Originally Posted By: BDB
That must be because you are not a good piano tuner. Other people can do it.


If you want to be offensive, you must accept unpolite answers.

This time I'll let it go, but please don't insist.

If someone dares to qualify me as a bad tuner, he must at least be a good tuner.

Why don´t you put some audio on the internet of a piano you have tuned to show me the good tuner you are?

For my part I offer to show you my piano as I usually tune it in EBVT III or if you want so I can retune it in ET and let you judge if I am a bad tuner.


Edited by Gadzar (01/23/10 03:08 PM)
_________________________
Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx

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