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Re: Help with best octave sizes [Re: Mark Cerisano] #2404845
03/31/15 09:45 AM
03/31/15 09:45 AM
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Bradford County, PA
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Rafael:

"Closing the circle" Hmmmm...

Yes, a set of CM3s "closes the circle" as does a set of 4 Cm3s, 2 TTs, 6 M2s, 12 semitones or 12 SBIs. Depending on the number of intervals and the amount of tempering, each of these require different levels of accuracy to have those particular intervals progressive, and even different levels of accuracy to have other intervals progressive.

I don't think your point for preferring CM3s is valid, although it could be valid by making other points.

For instance, I could say "Wait a minute! why go back and forth between two notes to 'close the circle' when you can do so with just one? It is much better to tune an octave and then a tritone (TT) and go on from there." Your likely reply would have to do with how much more accurate CM3s are compared to CTTs and where would you go from there anyway? Then I could say "So? Are CM3s accurate enough to guarantee that the M6s will be progressive? And where are you going to go from a set of CM3s that I cannot go with a set of CTTs?"

Please don't think I am attacking. Let's just use each other to hone our arguments, shall we? smile


Jeff Deutschle
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Who taught the first chicken how to peck?
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Re: Help with best octave sizes [Re: Mark Cerisano] #2404859
03/31/15 10:21 AM
03/31/15 10:21 AM
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This topic has certainly run off the rails!


Semipro Tech
Re: Help with best octave sizes [Re: Mark Cerisano] #2404870
03/31/15 10:35 AM
03/31/15 10:35 AM
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Mexico City
Gadzar Offline
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Jeff,

I respect your opinion about tuning sequences. I was only explaining what I mean by "self correcting" and "error compounding".

I know very fine tuners who use P4/P5 sequences. I've seen Rick Buttler tuning a very nice ET by tuning a circle of fifths without listening to a single RBI! I can't do that. But that doesn't mean it's impossible.


Last edited by Gadzar; 03/31/15 10:38 AM.

Rafael Melo
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Re: Help with best octave sizes [Re: BDB] #2404876
03/31/15 10:40 AM
03/31/15 10:40 AM
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Originally Posted by BDB
This topic has certainly run off the rails!


I am not so sure. Where else could it go? The idea that there is an ideal octave that should be started with, leads to the question of why do you need it and what is the next step. Of course the train tracks lead to temperament sequences and even how we characterize them.


Jeff Deutschle
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Who taught the first chicken how to peck?
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Re: Help with best octave sizes [Re: BDB] #2404878
03/31/15 10:42 AM
03/31/15 10:42 AM
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Boston, MA
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BDB, I think it started with Mark stating a rational/mathematical/engineering premise on which he was going to base a class at the PTG National in Denver. Given the number of cavils and disagreements with that premise on this board, I would not want to be Mark as he now prepares that class. At this point I have no idea whether the premise is true or false, and, if true, how it relates to real-world pianos.


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: bellspiano] #2404887
03/31/15 10:51 AM
03/31/15 10:51 AM
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Oakland
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It started as a request for people to take a test. It seems to have become "How can aural tuners learn to tune like an electronic device?"


Semipro Tech
Re: Help with best octave sizes [Re: Gadzar] #2404888
03/31/15 10:53 AM
03/31/15 10:53 AM
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Bradford County, PA
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Originally Posted by Gadzar
Jeff,

I respect your opinion about tuning sequences. I was only explaining what I mean by "self correcting" and "error compounding".

I know very fine tuners who use P4/P5 sequences. I've seen Rick Buttler tuning a very nice ET by tuning a circle of fifths without listening to a single RBI! I can't do that. But that doesn't mean it's impossible.


Does Mr. Butler have AP, like Mr. Stopper and BB have? Hmmm? wink

But you miss my point. Yes I understand what "self correcting" and "error compounding" are, even though the one is assumed to be miraculous and the other debilitating. In actuality they exist in every step of every tuning sequence to some degree.

This should be remembered when discussing the relative merits of tuning sequences, otherwise there is no real discussion. Did you understand my point about how different intervals all "close the circle"?


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: Mark Cerisano] #2405067
03/31/15 05:50 PM
03/31/15 05:50 PM
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Canberra, ACT, Australia
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Mark, in the end do have any results on your survey? What kind of octaves corresponded with peoples preferences?


Chris Leslie ARPT
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Re: Help with best octave sizes [Re: Gadzar] #2405129
03/31/15 10:30 PM
03/31/15 10:30 PM
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Vancouver, Canada
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Originally Posted by Gadzar

In the ET Via Marpurg sequence, errors can not add/cancel. As soon as you tune a bad interval another interval shows you your error.

Within the P4/P5's that span each M3 yes, but if your initial CM3's are off there is no way to detect errors. At least not in the original scheme published by Bill Bremmer. My problem is always the F4A4 beatrate detection. It's hard to judge such a fast beat, unless you have a nice clean grand. So it's great for passing the tuning examn, but what about regular consumer grade piano's?

I've had better aural results with the up M3 up M3 down P5 sequence that Bill so kindly published on his website.

Also to tune the P5's spanning a M3 (after tuning the CM3's) I have had better results from tuning the P4/P5's directly to make them equal beating rather than starting with the pure ones and then subdividing once more. So from F3A3 you get G3 C4 and D4 by tweaking these 3 to make F3C4, G3C4, G3D4, and A3D4 all equal beating.

Mathematically the way to do this is to first tune C4 pure to F3 and D4 pure to A3, then make G3 equal beating to C4 and D4, the retune C4 to make F3C4 and G3C4 equal beating and then retune D4 to make G3D4 and A3D4 equal beating. This is theoretically better as you have to to only one note at a time, but in practice just moving the 3 notes around (GCD) worked better for me. Probably because I have errors at every step and my "G3 equal beating to C4 and D4" is usually off.

I like this scheme because I've been using it for decades to tune UT's: just tune F3A3 at the speed you like, then fill in the GCD, and then decide on how you want A major to sound and you get C# and you're done with your temperament for the piece you want to play.

Of course all these schemes assume you know how to tune A3A4 and F3F4 octaves "optimally". What the "best" octave is, is unclear in theory, and everyone has his own ideas about this it seems so in my opinion Mark's attempt to come up with a "recipe" to tune those octaves optimally is well motivated. Even if no clear solution will emerge (apart from "using you judgement") and "in practice" this is not a problem, whatever that means, I think this is a good topic to discuss and will lead to better understanding despite disagreements.

One thing seems clear: best octave size depends on the inharmonicity, so some aural way of "measuring" this is required. m3's are most affected by this so any aural "IH detections" scheme should probably use them.

Maybe even m7th beatrates could be used? Not to tune, but just to establish how far off beatrates are from the twelfth root of 2 theory that Alfredo thinks is the state of the art? By listening to those beat rates it should be possible to quantify inharmonicity and then decide on the best octave size using empirical data such as Mark is trying to collect.

Sorry for the sermon, I guess this is not church smile

Kees

Re: Help with best octave sizes [Re: Mark Cerisano] #2405130
03/31/15 10:33 PM
03/31/15 10:33 PM
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Mexico City
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Originally Posted by UnrightTooner
Does Mr. Butler have AP, like Mr. Stopper and BB have? Hmmm wink


I don't think so, he used a tuning fork to set A4, he then checked with F2, and finally he raised A4 to make a pitch correction pass. He tuned A3 to A4 and then resumed tuning a sequence of P4s/P5s. When he tuned the last note, he checked the closing interval and it was ok. Then he checked the M3s And they were ok. I couldn't believe it!

And for what I know BB has not AP. Doesn't he claim it doesn't exist?

I do not understand what you mean. You say all intervalls close the circle. That's true if they are correctly tempered. I can not tune tritones because I have not a clue about how they must sound and I do not know how to correctly temper them. I like tuning CM3s because I only have to tune 2 notes, namely F and C#, and once I have estimated F, I can try C#. If it doesn't fit, I know F is in fault and I also know how to correct it.

I can not tune 12 semitones because there are too many notes to tune and I have no means to know which ones are in fault.

I can not tune a circle of fifths for the very same reason.

I can not tune 4 chains of CM3s also for the same reason.

When tuning CM3s, the fact that there are only two notes to tune, plus the fact that the beat rates of M3s in the temperament region are easily discerned and estimated, makes it possible to correctly temper them.

Last edited by Gadzar; 03/31/15 10:43 PM.

Rafael Melo
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Re: Help with best octave sizes [Re: Mark Cerisano] #2405137
03/31/15 11:08 PM
03/31/15 11:08 PM
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Mexico City
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Kees,

Great post!

I am a seasoned M3 divider. Mostly in meantone, dividing a M3 into four P5s is bread and butter.

Once you've tuned CE to the desired size (tempering) you have to divide it into 4 P5s namely CG, GD, DA, AE. And the best way is to directly temper them and retune them until AE sounds good.

For the best size of the octaves A3A4 and F3F4 I think it goes beyond iH.Rick Baldassin has explained it in a very clear and eloquent way in his book On Pitch. What kind of octave sounds best in a specific point of the scale? It depends of course on the iH but also on the relative strength of each partial in the two notes of the octave. Thats why we tune 6:3 octaves in the bass, 4:2 in the tenor and 2:1 in the treble.

The relative prominence of partials has a lot to do with the kind of the best sounding octave.

Last edited by Gadzar; 03/31/15 11:11 PM.

Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: Gadzar] #2405161
04/01/15 12:48 AM
04/01/15 12:48 AM
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Vancouver, Canada
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Originally Posted by Gadzar
Kees,

Great post!

I am a seasoned M3 divider. Mostly in meantone, dividing a M3 into four P5s is bread and butter.

Glad to know at least 1 person understands me.

They used to claim butter is bad for you but that seems to be no longer true smile

Kees

Re: Help with best octave sizes [Re: Gadzar] #2405253
04/01/15 07:15 AM
04/01/15 07:15 AM
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Bradford County, PA
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Originally Posted by Gadzar
Originally Posted by UnrightTooner
Does Mr. Butler have AP, like Mr. Stopper and BB have? Hmmm wink


I don't think so, he used a tuning fork to set A4, he then checked with F2, and finally he raised A4 to make a pitch correction pass. He tuned A3 to A4 and then resumed tuning a sequence of P4s/P5s. When he tuned the last note, he checked the closing interval and it was ok. Then he checked the M3s And they were ok. I couldn't believe it!

And for what I know BB has not AP. Doesn't he claim it doesn't exist?

I do not understand what you mean. You say all intervalls close the circle. That's true if they are correctly tempered. I can not tune tritones because I have not a clue about how they must sound and I do not know how to correctly temper them. I like tuning CM3s because I only have to tune 2 notes, namely F and C#, and once I have estimated F, I can try C#. If it doesn't fit, I know F is in fault and I also know how to correct it.

I can not tune 12 semitones because there are too many notes to tune and I have no means to know which ones are in fault.

I can not tune a circle of fifths for the very same reason.

I can not tune 4 chains of CM3s also for the same reason.

When tuning CM3s, the fact that there are only two notes to tune, plus the fact that the beat rates of M3s in the temperament region are easily discerned and estimated, makes it possible to correctly temper them.


OK. Then your preference for "closing the circle" with CM3 is due to that is the only way you can - which is fine. But it is not because it is the only way.

I was thinking about the term "closing the circle". If you start with an octave, you are really "filling the circle". If you tune intervals that create an octave you are then truly "closing the circle".

Bill Bremmer insist there is no such thing as perfect pitch, but admits he has absolute pitch.

A tritone has a 7:5 partial match. If I remember right, stacked tritones have a 2:3 beat ratio. You can tune an octave, tune a pure TT to the lower note and then adjust it so that the CTTs are proportionate. It isn't very accurate, though, as it is tempered about 18 cents and uses high partials.

Another way to fill the circle is with 4ths and 5ths. I believe it is just as accurate as CM3s. Just make the 4ths beat 1 bps. You would then have notes 2 semitones apart and when constructing CM3s from these, would produce a whole tone scale with an M3 available at each note for checking the beatrate progression. There may also be a M6/M3 outside/inside check, too, depending on which octaves you tune.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: DoelKees] #2405341
04/01/15 11:23 AM
04/01/15 11:23 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT

After tuning CM3, set D4 by tuning it so that:

F3A3 < F3D4 < A3C#4

This works because we expect F3D4 to equal G3B3.

And the CM3 window we bisect sets up

F3A3 < G3B3 < A3C#4

Does anyone else see the beauty of this approach? - We have tuned a wide P4 by exactly the amount that iH requires in order to have progressive RBI.

I see the beauty but also a flaw. F3D4 is closer to G#3C4 than to G3B3 even on low IH instruments and more so on high IH instruments.

You are correct in stating
F3A3 < F3D4 < A3C#4
if the "<" mean less than, but if this equation means that the beatrate of F3D4 should be the average of the beatrates of F3A3 and A3C#4, it is not true. It should be closer to the beat rate of A3C#4 than to the beatrate of F3A3, not in the middle.

Theoretically speaking, if you ignore this subtlety you will end up with non progressive M3's. That's OK because no-one can tune progressive M3's aurally anyways, but something to consider.

Another thing that comes to mind here is that you have stated a number of times that you have measured human abilities (tolerances) for beat rate progressions detection, which you have. However you measured the ability to detect beat rate differences for beating sine waves, not real piano tones. Clearly the real accuracy will be lower, possibly by a large factor.

I don't intend to "shoot you down" and knowing beat rate discriminatation for beating sine waves is obvious better than knowing nothing at all, but if you claim you have "proved" beat rate discrimination limits and don't mention these caveats you should expect to be challenged on this.

The value I see in your pursuit of determining "objectively best octave size in the temperament octave" is as follows. On a good day you just listen and find the best octave. On a bad day you can't decide and would like to have some method to do what you'd do on a good day. If you had an ETD you'd just measure IH and let the software figure it out. It usually does a good job, which is why 90% of PTG member tune electronically

If not what you can do is to listen to beat rates of m3's and M3's and see how much off they are from what would be predicted from a simple no-inharmonicity model using a twelfth root of 2 relation between pitches which Alfredo incorrectly thinks people use.

By listening to this you can get an idea of how much IH you have under your fingers, and then, using the data collected from your survey you can make a recommendation for a 4:2, 4:2/6:3, or even a 2:1/4:2 octave. For BDB: the symbol ":" does not indicate division here as you learned in elementary school, it has a different meaning.

Kees


Thanks Kees,

Yes, having a way to decide which tests to use is the goal. But from my survey, I've concluded that tuning octaves in isolation produces a wide range of preferences.

So, is that because of taste or the looseness of the method? Either way, an aural tuner needs to have a way to ensure they are being precise. That is the real benefit for octave checks. On a good day, they can confirm.

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2405355
04/01/15 11:56 AM
04/01/15 11:56 AM
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Vancouver, Canada
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Originally Posted by Mark Cerisano, RPT

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Well, one of us must be wrong. I use IH curves measured from actual pianos and then compute a theoretically perfect temperament on F3A4, with all consonant intervals progressive.
Then I compute the beat rates, which I posted here long time ago, you can find this stuff in the old thread I referenced earlier.

For example for Steinway D the beat rates for the case under discussion are:
F3D4 = 8.0, G3B3 = 7.8, G#3C4 = 8.2.

For my Heintzman upright the result is:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For Pat's Hellas Helsinki:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For a Wurlitzer spinet:
F3D4 = 8.3, G3B3 = 7.7, G#3C4 = 8.2.

Kees


Re: Help with best octave sizes [Re: DoelKees] #2405382
04/01/15 01:16 PM
04/01/15 01:16 PM
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Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Well, one of us must be wrong. I use IH curves measured from actual pianos and then compute a theoretically perfect temperament on F3A4, with all consonant intervals progressive.
Then I compute the beat rates, which I posted here long time ago, you can find this stuff in the old thread I referenced earlier.

For example for Steinway D the beat rates for the case under discussion are:
F3D4 = 8.0, G3B3 = 7.8, G#3C4 = 8.2.

For my Heintzman upright the result is:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For Pat's Hellas Helsinki:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For a Wurlitzer spinet:
F3D4 = 8.3, G3B3 = 7.7, G#3C4 = 8.2.

Kees



I get similar results. The test is still very practical.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: Mark Cerisano] #2405580
04/02/15 01:46 AM
04/02/15 01:46 AM
Joined: Dec 2006
Posts: 2,758
Mexico City
Gadzar Offline
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"The test is still very practical"

How do you use it?



Rafael Melo
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Serving Mexico City and suburbs.

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Re: Help with best octave sizes [Re: Gadzar] #2405648
04/02/15 07:08 AM
04/02/15 07:08 AM
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Bradford County, PA
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Originally Posted by Gadzar
"The test is still very practical"

How do you use it?



I see it as a way to prevent what I call a "Marpurg error" where the M3s are progressive, but the M6s are not.

It also compares the tempering of the 4ths with the tempering of the 5ths. If the amount of error of the 4ths is the same as the amount of error of the 5ths, but in the opposite direction, the beatrate of the M3s will not be affected, but the beatrate of the M6s will be. This is because the M3s are made from two 4ths and two 5ths, but the M6s are made from one 4th and two 5ths.

But, you know, I might not be paying enough attention to how the M6s beat about 1/2 bps faster due to iH. Perhaps that is why I only get so close to progressive RBIs, and perhaps why trying to tune with RBIs alone failed. To make the outside M6/inside M3 test beat equally, with typical iH, requires an error of 1 cent, which could be in one or more notes. I've got a P22 tomorrow morning that I can take my time with...


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: DoelKees] #2405693
04/02/15 08:50 AM
04/02/15 08:50 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Well, one of us must be wrong. I use IH curves measured from actual pianos and then compute a theoretically perfect temperament on F3A4, with all consonant intervals progressive.
Then I compute the beat rates, which I posted here long time ago, you can find this stuff in the old thread I referenced earlier.

For example for Steinway D the beat rates for the case under discussion are:
F3D4 = 8.0, G3B3 = 7.8, G#3C4 = 8.2.

For my Heintzman upright the result is:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For Pat's Hellas Helsinki:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For a Wurlitzer spinet:
F3D4 = 8.3, G3B3 = 7.7, G#3C4 = 8.2.

Kees



How did you arrive at a theoretically perfect temperament considering iH? What criteria?

I used theoretically calculated B values considering different octave spread. (Octave spread, my own term, is the cents deviation between the 6th and 3rd partials of a pure 4:2), and tried to produce as close to perfect ET using progressive M3, m3, M6, and P4 at 1bps +/- 0.2bps. I programmed my sequence into a spread sheet and could get very close to that using the appropriate sequence for the octave spread.

Also, I'm very curious, how did you measure inharmonicity? It's probably simple but I wouldn't know where to start. Could you help?

Regards,

Last edited by Mark Cerisano, RPT; 04/02/15 08:56 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2405709
04/02/15 09:49 AM
04/02/15 09:49 AM
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I am sure I missed a memo somewhere. But why would one plan out a octave-based tuning class in great and rational detail, triple-check all the math, get the class accepted for the PTG national convention and then -- much later -- do a survey of what octaves sound good to interested techs? Isn't the ultimate purpose to have a pleasing piano? So why would one leave the aural test of the hypothesis (viz: pianos tuned by this mathematical method have a "better" sound) until way after the math chapters, so to speak, are published?

I guess one area of confusion for me is, in fact, the statement of the hypothesis. What is all this work trying to prove or disprove?


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: bellspiano] #2405712
04/02/15 09:54 AM
04/02/15 09:54 AM
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Originally Posted by bellspiano
I am sure I missed a memo somewhere. But why would one plan out a octave-based tuning class in great and rational detail, triple-check all the math, get the class accepted for the PTG national convention and then -- much later -- do a survey of what octaves sound good to interested techs? Isn't the ultimate purpose to have a pleasing piano? So why would one leave the aural test of the hypothesis (viz: pianos tuned by this mathematical method have a "better" sound) until way after the math chapters, so to speak, are published?

I guess one area of confusion for me is, in fact, the statement of the hypothesis. What is all this work trying to prove or disprove?


Dorrie: What is trying to be "proved" is not so much about tuning as it is about a tuning teacher. And therein lies the problem. Sigh...


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Help with best octave sizes [Re: Mark Cerisano] #2405715
04/02/15 10:16 AM
04/02/15 10:16 AM
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Vancouver, Canada
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Originally Posted by Mark Cerisano, RPT
Originally Posted by DoelKees
Originally Posted by Mark Cerisano, RPT

As for F3D4 not equal to G3B3, I've never heard that and in my spreadsheet with measured and calculated multiple B curves, F3D4 and G3B3 are within 2%.


Well, one of us must be wrong. I use IH curves measured from actual pianos and then compute a theoretically perfect temperament on F3A4, with all consonant intervals progressive.
Then I compute the beat rates, which I posted here long time ago, you can find this stuff in the old thread I referenced earlier.

For example for Steinway D the beat rates for the case under discussion are:
F3D4 = 8.0, G3B3 = 7.8, G#3C4 = 8.2.

For my Heintzman upright the result is:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For Pat's Hellas Helsinki:
F3D4 = 8.2, G3B3 = 7.8, G#3C4 = 8.2.

For a Wurlitzer spinet:
F3D4 = 8.3, G3B3 = 7.7, G#3C4 = 8.2.

Kees



How did you arrive at a theoretically perfect temperament considering iH? What criteria?

I used theoretically calculated B values considering different octave spread. (Octave spread, my own term, is the cents deviation between the 6th and 3rd partials of a pure 4:2), and tried to produce as close to perfect ET using progressive M3, m3, M6, and P4 at 1bps +/- 0.2bps. I programmed my sequence into a spread sheet and could get very close to that using the appropriate sequence for the octave spread.

Also, I'm very curious, how did you measure inharmonicity? It's probably simple but I wouldn't know where to start. Could you help?

Regards,

Criterium for perfect: "with all consonant intervals progressive. "

Tunelab to measuring IH.

Kees

Re: Help with best octave sizes [Re: UnrightTooner] #2405720
04/02/15 10:34 AM
04/02/15 10:34 AM
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Thank you! It is all becoming clear now --


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: bellspiano] #2405821
04/02/15 04:50 PM
04/02/15 04:50 PM
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Dorrie, I agree.

Concerning the application of math to this problem.. it can be very helpful and articulate, unless it is misapplied. Unfortunately using the type of math described here will do no more than what a tuning machine does.

The reason why this problem hasn't been solved to a greater depth yet is because you can't apply a model curve to anything on the piano with just a single measurement of 'B'. Even a few samples are still ineffective. Literally every string has to be sampled because every string on a piano is different. Models get us very close, but to transcend that last 10%, every string has to be taken into account to refine the model.

The result from that type of best fit analysis will never result in any kind of smooth, continuous curve. You could model the deviations with regressive polynomials.. but why? It's just an erratic engineering problem best solved with raw data.

Octave sizes for ideal tuning must vary because of partial density and bandwidth availability at the octave as opposed to other partials - if we are to use the definition that Kees supplied above, which I believe is accurate. Cent width for each semitone will always be slightly unequal to reflect the ideal balance from irregularity in the scale itself.

This is highly variable and will change to reflect the differences in instruments, nevermind subjective taste..


www.tunewerk.com

Unity of tone through applied research.
Re: Help with best octave sizes [Re: Mark Cerisano] #2406001
04/03/15 07:09 AM
04/03/15 07:09 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Dorrie,

I have been tuning by measuring octave spread and choosing an appropriate sequence to help me tune accurate ET with little or no refining for some time. It works for me and it is fun. When I submitted the class to the PTG, they accepted it.

I could give the class now, based on my own opinions but I would like it to be a bit more concrete than that.

Octave sizes for instance. Specifically, the first octaves tuned, need to be tuned as they will be in the final temperament, without any references other than, "Does it sound good?", if my goal is "accurate ET with least refinement". Octave spread helps me do that. I think the octaves I tune using octave spread are very good, but I need to find out if others have the same conclusion or the method would not be interesting to them. That's the reason for the thread. Also, the topic still fascinates me.

This thread is part "gather more research to back up what I use" and part "just for the fun of it".

You did not miss anything if you find the posts interesting. You needn't read them in the context of "this sounds like someone who is unsure of themselves, yet giving a PTG class".

You can never be too unsure when you are trying to prove something. There will always be someone who will try to make you look like a fool. Thanks to some people here on PW, I have come to realize that. They may sound mean and spiteful, but they do provide a service.

Last edited by Mark Cerisano, RPT; 04/03/15 07:22 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406030
04/03/15 08:40 AM
04/03/15 08:40 AM
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Thank you, Mark. I appreciate your clarification, as well as your willingness to teach and learn.


Dorrie Bell
retired piano technician
Boston, MA
Re: Help with best octave sizes [Re: Chris Leslie] #2406039
04/03/15 09:03 AM
04/03/15 09:03 AM
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Mark Cerisano Offline OP
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Originally Posted by Chris Leslie
Mark, in the end do have any results on your survey? What kind of octaves corresponded with peoples preferences?


There was no obvious preference for any one octave.

Here are my thoughts as to why:
1. The octaves were open. Rolling unisons could have made choosing difficult.
2. The octaves themselves were not tuned well enough for this test. Some were too close to each other.
3. The design of the test was not ideal. Having to choose between only two octaves resulted in the subject's preference for the best size possibly not being available.

Recommendations:
1. Use only single strings
2. Use a better test
3. Use a better test

I am working on a web app that allows the user to listen to an A3A4 octave and tweak A3 until they consider the sound the best possible.

I am using actual recorded piano strings and altering the a3's using Audacity.

I will have multiple pairs of strings that have different iH.

One problem I find is that Audacity can only change the pitch by 0.058% which corresponds to about 1 cent.

I am going to code it anyway since I can't find a way to get anything more precise. Hopefully I will be able to measure a difference using checks that will provide some insight.

My hypothesis is that best octave sizes tuned with no other criteria other than best sound, may have a quite large window.

My sequences still produce more accurate interval sizes than I could any other way, mainly because I am using RBI all the time so my ear gets better over the tuning and as I use the method through the years.

A question I have for those who seem to criticize the RBI approach is:
How do you check your temperament when you are finished? Don't you check the RBI progression? If so, then using an RBI sequence will improve your ability to hear the progressions. Do not misread this. SBI are necessary and required as a check to make sure the RBI are as you hear them - the ear can be fooled.

In the end, the RBI approach for me is just a workout to improve my filtering ability and sensitivity to beat speed differences.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Help with best octave sizes [Re: Mark Cerisano] #2406065
04/03/15 10:33 AM
04/03/15 10:33 AM
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Mexico City
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Originally Posted by Mark Cerisano, RPT
My hypothesis is that best octave sizes tuned with no other criteria other than best sound, may have a quite large window.

My sequences still produce more accurate interval sizes than I could any other way


I ask me why then you have not yet "discovered" that in spinets and some consoles the best sounding octave is a narrow 4:2 / wide 2:1

I still remember when you used to say that a 6:3/4:2 balanced octave was the unique option.

That kind of octave allowed you to use what you called the P4 window. Which is severely altered with any other octave size.

Now you have accepted the possibilty of a narrow 6:3 with a pure 4:2. And you have modified your P4 window concept accordingly.

But you still ignore the case of a narrow 4:2/wide 2:1, which reverses your "P4 window"

This would force you to accept the P4 window is not valid in all pianos!

I agree with you that a good sounding octave is a too wide range but IMO if you tune a pure 4:2 in a spinet you are definitely out of this large window. How is it that you have not noticed that?

You do not have to believe me! You can ask other tuners. Ask Ron Koval which kind of octaves he uses for tuning the smallest pianos. Or better: use your own ears! Tune a good sounding octave in a spinet, put it right in the middle of the "good sounding" large window and measure its size with the m3M6, M3M10 and M10M17 tests. You will find, as me and many others, that it is a narrow 4:2 / wide 2:1

If you open your mind an accept this fact, then the way to tune accurate octaves of the same size is to tune A3A4 as the best sounding octave, leaned to the wide side, and then measure it. You can then tune the same size of octave for F3F4.

And for your P4 window, I think it is of a limited use as it is not universal. It is valid only in some regions of the scale of some selected pianos with specific octaves's sizes.


Last edited by Gadzar; 04/03/15 10:41 AM.

Rafael Melo
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

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Re: Help with best octave sizes [Re: Mark Cerisano] #2406079
04/03/15 11:19 AM
04/03/15 11:19 AM
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Mexico City
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It is a commonly accepted fact that, when tuning the temperament, fourths must beat at approx 1bps and fifths must beat slower, at approx 1/2 bps.

That's how I was taught. But I used to have a little console. It was my practice piano. It was on this piano that I learned to set the temperament. I soon realised that in this piano if I tuned a narrow fifth D4A4 beating at around 0.5 bps and then a wide fourth A3D4 beating at 1 bps, the resulting A3A4 was not clean. For it to be clean I should have the P4 A3D4 purer than the P5 D4A4.

This was against all I were been taught!

At that time I supposed I was wrong as I was a beginner. But now I know I was right. In this piano, complementary fourths must be tuned purer than fifths in order to have clean octaves. In other words this piano requires narrow 4:2 octaves in the temperament region.

I know almost all aural tuners will say no! But I am comfident I'm right. I've seen numerous tuners who use this kind of setting in their Verituners, but I have never seen an aural tuner tuning A3D4 purer than D4A4, except Alfredo Capurso if memory doesn't fail.




Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Help with best octave sizes [Re: Mark Cerisano] #2406086
04/03/15 12:16 PM
04/03/15 12:16 PM
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Mark Cerisano Offline OP
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When I look back, I am truly amazed at how much I have changed my approach to tuning.

Yes, I used to advocate 4:2+/6:3- as the best size.
Yes, I now recognize a variety of sizes between pure 4:2 and wide 4:2.
Yes, I have found a piano recently that its F or A octave tuned well as a pure 2:1, narrow 4:2.

Through the PTG I was taught to tune 4:2+/6:3-. This approach worked on many pianos, but not those that sounded best as pure 4:2/very narrow 6:3. Now I have found a system that refines that approach to include more pianos.

Yes, I see narrow 4:2 in the field, specifically with reversed octaves where the 6:3 is wide. But, IMHO, they are anomalies created by scaling errors. I have not found on these pianos that many of the octaves in the temperament have this same relationship. This is confirmed by the one or two wild B numbers seen around the break/coil change section in an iH graph.

When teaching my method, I will just mention to be aware of these possibilities, check neighbouring octaves to make sure it is an anomaly, and try to compromise if somethings don't fit.

Thanks for your comments.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
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