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Re: Octave Sizes [Re: Mark Cerisano] #2621412
03/08/17 09:52 AM
03/08/17 09:52 AM
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Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Originally Posted by Mark Cerisano, RPT
Hi Chris,

Maybe you are right. I have noticed what I can only define as "Aural Illusion". Much like an optical illusion where we think we see something that is not there.

Try this:
Play the contiguous M3's. Listen to the bottom and top one, then the three together.

I.e.
Play F3A3-C#4F4
then F3A3-A3C#4-C#4F4

I sometimes get the sensation that F3A3-C#4F4 is a lot closer when I play F3A3-A3C#4-C#4F4, than when I play F3A3-C#4F4. Sometimes I can't tell them apart.

I'm working on the math and it is not easy.

As for finding reversed octave Kees, have you been looking for them? I look for them every time I tune. I've recorded a few. I'll dig them up. If I can prove to you that reversed octaves exist, does that prove that pure 4:2/pure 6:3 can exist?

For the purpose of defining pure 4:2/pure 6:3 aurally, we only need the tests to be within 2-3%.

Found the recording. Here it is:

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)

Here is a recording of the filtered beats. I have often posted that bandpassing beat rates is a great tool. It helped me just now not to be so arrogant. (I thought the 4:2 was pure when listening to the unfiltered recording)

https://www.dropbox.com/s/xq89szaznszn0qw/A%20Filtered%20Reversed%20F3F4%20Octave.mp3?dl=0


Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?

Last edited by Mark Cerisano, RPT; 03/08/17 09:53 AM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
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Re: Octave Sizes [Re: Mark Cerisano] #2621432
03/08/17 10:58 AM
03/08/17 10:58 AM
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Bradford County, PA
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Originally Posted by Mark Cerisano, RPT
...

Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?


Well, you asked. I cannot speak for others, but I don't think you know what you are talking about and tend to hear what you want to hear. You also do not receive the views of others gracefully. So, for myself, I choose not to waste the time or experience the aggravation in following up your claims.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Octave Sizes [Re: Mark Cerisano] #2621456
03/08/17 11:48 AM
03/08/17 11:48 AM
Joined: May 2010
Posts: 2,503
Vancouver, Canada
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Originally Posted by Mark Cerisano, RPT
Originally Posted by Mark Cerisano, RPT
Hi Chris,

Maybe you are right. I have noticed what I can only define as "Aural Illusion". Much like an optical illusion where we think we see something that is not there.

Try this:
Play the contiguous M3's. Listen to the bottom and top one, then the three together.

I.e.
Play F3A3-C#4F4
then F3A3-A3C#4-C#4F4

I sometimes get the sensation that F3A3-C#4F4 is a lot closer when I play F3A3-A3C#4-C#4F4, than when I play F3A3-C#4F4. Sometimes I can't tell them apart.

I'm working on the math and it is not easy.

As for finding reversed octave Kees, have you been looking for them? I look for them every time I tune. I've recorded a few. I'll dig them up. If I can prove to you that reversed octaves exist, does that prove that pure 4:2/pure 6:3 can exist?

For the purpose of defining pure 4:2/pure 6:3 aurally, we only need the tests to be within 2-3%.

Found the recording. Here it is:

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)

Here is a recording of the filtered beats. I have often posted that bandpassing beat rates is a great tool. It helped me just now not to be so arrogant. (I thought the 4:2 was pure when listening to the unfiltered recording)

https://www.dropbox.com/s/xq89szaznszn0qw/A%20Filtered%20Reversed%20F3F4%20Octave.mp3?dl=0


Some people have made some pretty clear accusations. Namely that a pure 4:2/pure 6:3 is not possible. And that a pure 4:2/wide 6:3 is not possible. I've offered that if I could prove a pure 4:2/wide 6:3 exists, then the pure 4:2/pure 6:3 could exist as well.

I've posted recordings that show the pure 4:2/wide 6:3 can exist, but nobody has commented. Why not?

I haven't commented because I can't download the audio in those links.

Kees

Re: Octave Sizes [Re: Mark Cerisano] #2621460
03/08/17 11:54 AM
03/08/17 11:54 AM
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Kees,

Do you have a Dropbox account? That may be the issue. I will email you the mp3's.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Octave Sizes [Re: Mark Cerisano] #2621495
03/08/17 01:24 PM
03/08/17 01:24 PM
Joined: May 2010
Posts: 2,503
Vancouver, Canada
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Originally Posted by Mark Cerisano, RPT

https://www.dropbox.com/s/5bgim46ckedipzw/A%20Reversed%20F3F4%20Octave.m4a?dl=0

I measured the beat rates as:
C#3F3 = 8.1
C#3F4 = 8.5
Difference = 4.7%
F3G#3 = 8.4
G#3F4 = 10.1
Difference = 19.9%

The 4:2 is not strictly pure but the 6:3 is much wider so theoretically it could have been tuned as a pure 4:2/wide 6:3 if I was a better tuner :-)


I get:

C#3F3 = 8.6
C#3F4 = 8.9
F3G#3 = 8.2
G#3F4 = 9.7

So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.

Kees

Re: Octave Sizes [Re: Mark Cerisano] #2621506
03/08/17 02:03 PM
03/08/17 02:03 PM
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As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Octave Sizes [Re: Mark Cerisano] #2621519
03/08/17 02:50 PM
03/08/17 02:50 PM
Joined: Nov 2008
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Bradford County, PA
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Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


Sure there is a proof that this can happen. It seems to be very rare. What piano was this and were any wound strings involved?


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Octave Sizes [Re: Mark Cerisano] #2621521
03/08/17 02:52 PM
03/08/17 02:52 PM
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Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


No he didn't say that, he said:

Quote
So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.


Paul.

Re: Octave Sizes [Re: Mark Cerisano] #2621524
03/08/17 03:01 PM
03/08/17 03:01 PM
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Some years ago I remember AL Sanderson talking in a class about inharmonicity and the question that someone brought up was: "Does inharmonicity essentially progress the SAME way in all piano?". He started off saying basically "yes", but then he stopped and said:"Except for the Astin-Weight...that is one weird piano, I don't exactly know how they did it but it to has reverse inharmonicity in it".

I do not measure or care much about inharmonicity, but I have had experience with three Astin-Weight Pianos and can attest to the fact that they certainly sound and behave differently from "normal".

So it is possible to engineer a piano that has a scale that could do what Mark is suggesting.

Pwg


Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
https://www.youtube.com/watch?v=PK0T7_I_nV8
Re: Octave Sizes [Re: P W Grey] #2621526
03/08/17 03:06 PM
03/08/17 03:06 PM
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Bradford County, PA
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Originally Posted by P W Grey
Some years ago I remember AL Sanderson talking in a class about inharmonicity and the question that someone brought up was: "Does inharmonicity essentially progress the SAME way in all piano?". He started off saying basically "yes", but then he stopped and said:"Except for the Astin-Weight...that is one weird piano, I don't exactly know how they did it but it to has reverse inharmonicity in it".

I do not measure or care much about inharmonicity, but I have had experience with three Astin-Weight Pianos and can attest to the fact that they certainly sound and behave differently from "normal".

So it is possible to engineer a piano that has a scale that could do what Mark is suggesting.

Pwg


It is only when the slope is much steeper than normal, that his can happen, not when it is "reversed", which is hard to believe.


Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?
Re: Octave Sizes [Re: Mark Cerisano] #2621550
03/08/17 04:10 PM
03/08/17 04:10 PM
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All I am saying is that if "reverse" is possible (though very strange), it follows that almost any other combination of inharmonicity curves is theoretically possible, and probably already has been designed into some pianos. Therfore what Mark is saying probably could be in existence.

Dr. Al Sanderson was one who knew more about inharmonicity than just about anyone else on the planet, and was very deliberate to make sure he had his facts straight. I trust his judgement in the matter. He was also a REALLY nice guy.

Now, what I am about to say is probably likely to get misinterpreted so I want to make it clear that the following is not meant to be disrespectful or antagonist, or even impolite. Here goes:

Who cares? What difference does it make if an octave has pure 4:2 and 6:3 partials at the same time? Or whatever? It doesn't change the fact that we would need to figure out a way to tune the thing so that it maximizes the musicality available in that piano as a whole.

I would like to hear more expressions about what specifically is being heard in that (or any other) octave that makes you decide that that is the "best" sounding octave.

Can anyone do that? What makes you "decide" that the octave sounds better at the pure 4:2 vs pure 6:3 vs pure 8:4 OR something in between? What are YOU listening for to make that decision?

In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

I would be very interested and I am sure others would be too.

Pwg

Last edited by P W Grey; 03/08/17 04:11 PM.

Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
https://www.youtube.com/watch?v=PK0T7_I_nV8
Re: Octave Sizes [Re: Mark Cerisano] #2621562
03/08/17 04:39 PM
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I would posit that if a string has inharmonicity (which it does) then it is mathematically impossible to tune an octave and have all partials beatless simultaneously. I don't think it matters what the inharmonicity constants are for the strings involved, unless those constants are zero. Higher partials are always proportionately sharper than lower ones so you can't have 4:2 beatless at the same time as 6:3 or any other combination. Of course, you can tune so that the sound of the inevitable beating is minimized (and with weaker upper partials, a pure 4:2 or 2:1 may sound "beatless" overall), but you can't have them all beating at the same speed (which includes zero). All bets are off, though, if different partials have different inharmoncity constants! How that works, physically, though, I'm not sure.

Paul.

Re: Octave Sizes [Re: P W Grey] #2621585
03/08/17 05:43 PM
03/08/17 05:43 PM
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Originally Posted by P W Grey
In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

Pwg


thumb



Rafael Melo
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rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Octave Sizes [Re: pyropaul] #2621586
03/08/17 05:45 PM
03/08/17 05:45 PM
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Originally Posted by pyropaul
..., but you can't have them all beating at the same speed (which includes zero). All bets are off, though, if different partials have different inharmoncity constants!...

Paul.


thumb


Rafael Melo
Piano Technician
rafaelmelo@afinacionpianos.com.mx

Serving Mexico City and suburbs.

http://www.afinacionpianos.com.mx
Re: Octave Sizes [Re: pyropaul] #2621598
03/08/17 06:18 PM
03/08/17 06:18 PM
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Montreal, Quebec, Canada
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Mark Cerisano Offline OP
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Originally Posted by pyropaul
Originally Posted by Mark Cerisano, RPT
As Kees alluded to, he performed a mathematical proof that shows that one can have a piano with pure 4:2/pure 6:3 if the iH of the top note is 4 times that of the bottom note.


No he didn't say that, he said:

Quote
So indeed nearly pure 4:2 and wide 6:3. So the IH of F4 must be more than 4 times the IH of F3. You could check that with tunelab.


Paul.


Hi Paul,

I think you are referring to the recordings. The recordings were of a "nearly pure 4:2 and wide 6:3"

The mathematical proof that Kees made was done on a google doc I created and proves that the pure 4:2/pure 6:3 occurs when the iH of the top note is 4 times that of the lower.


Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Octave Sizes [Re: P W Grey] #2621603
03/08/17 06:32 PM
03/08/17 06:32 PM
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Mark Cerisano Offline OP
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Originally Posted by P W Grey
All I am saying is that if "reverse" is possible (though very strange), it follows that almost any other combination of inharmonicity curves is theoretically possible, and probably already has been designed into some pianos. Therfore what Mark is saying probably could be in existence.

Dr. Al Sanderson was one who knew more about inharmonicity than just about anyone else on the planet, and was very deliberate to make sure he had his facts straight. I trust his judgement in the matter. He was also a REALLY nice guy.

Now, what I am about to say is probably likely to get misinterpreted so I want to make it clear that the following is not meant to be disrespectful or antagonist, or even impolite. Here goes:

Who cares? What difference does it make if an octave has pure 4:2 and 6:3 partials at the same time? Or whatever? It doesn't change the fact that we would need to figure out a way to tune the thing so that it maximizes the musicality available in that piano as a whole.

I would like to hear more expressions about what specifically is being heard in that (or any other) octave that makes you decide that that is the "best" sounding octave.

Can anyone do that? What makes you "decide" that the octave sounds better at the pure 4:2 vs pure 6:3 vs pure 8:4 OR something in between? What are YOU listening for to make that decision?

In the interest of full disclosure, I subscribe to the idea that you CANNOT tune an octave such that ALL partials are beatless (meaning pure) at the same time. You must make a choice (or two).

I would be very interested and I am sure others would be too.

Pwg


Hi Peter,

You are right. We cannot have more than two partial pairs beatless.

The reason why I care about this is that tuning an octave using checks is much more precise than just tuning it directly, without checks. Theoretically there could be some techs who have great precision when tuning octaves, but I'm not one of them. :-)

I also created an online survey that shows that not many of us are.

When one can and does tune a pure 4:2/pure 6:3, it does sound very clean to me. But more importnatly, a pure 6:3 allows for pure 19ths to be tuned as well as pure 11/12/22.

Example:

When tuning pure 4:2 and pure 12, we have

M3 = M10 < M17 = M6

Add to that the pure 22

M3 = M10 < M17 = M6 = m6down

The pure 22 is at

M17 = m6down

The pure 11 is the

M6 = m6down

But with a pure 6:3, we have

m3 = M6

Using the same M6 in

M3 = M10 < M17 = M6 = m6down

We get

M3 = M10 < M17 = M6 = m6down = m3down

The pure 19 is here

m3down = M17

So, a piano that has mid range octaves that can be tuned at, or very near, the pure 4:2/pure 6:3, can have pure 11/12/19/22.




Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Octave Sizes [Re: Mark Cerisano] #2621625
03/08/17 07:39 PM
03/08/17 07:39 PM
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Mark,

When you say "22", are you referring to the 22nd partial? Or something else?

Pwg


Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
https://www.youtube.com/watch?v=PK0T7_I_nV8
Re: Octave Sizes [Re: Mark Cerisano] #2621653
03/08/17 08:51 PM
03/08/17 08:51 PM
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22 = triple octave
11 = octave plus fourth
12 = octave plus fifth
19 = two octaves plus fifth

By the way, most pianos I tune are very well scaled and I have trouble hearing the difference between the M3/M10 and the m3/M6 when I try to tune them equal. Because of human limitations in detecting beat speed differences, these are pure within 3%.

I did a study a while ago and recorded 20 or 30 piano octaves and analyzed then all. Many were pure 4:2/pure 6:3, about half.


Last edited by Mark Cerisano, RPT; 03/08/17 08:55 PM.

Mark Cerisano, RPT, B.Sc.(Mech.Eng), Dip.Ed.(Music)
www.howtotunepianos.com
Re: Octave Sizes [Re: Mark Cerisano] #2621661
03/08/17 09:16 PM
03/08/17 09:16 PM
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Got it.

So, tell me how you "prove" that the triple octave is in fact pure? What RBI's do you use to confirm this, other than simply playing the triple octave and listening to it?

I admit that I have great difficulty in understanding how one can have single, double, and triple octaves all pure and beatless without having severely constricted octaves, which would sound quite flat musically, especially in an arpeggio.

Virgil Smith used to claim he could do this, but then he would turn around and say that (for instance) RCT did not have an octave stretch that could match his! They were all too narrow! I have great difficulty in accepting this rationale based on 40+ years of experience, though I am willing to be proven wrong if this can be done, which is why I am asking for more information.

Pwg


Last edited by P W Grey; 03/08/17 09:17 PM.

Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
https://www.youtube.com/watch?v=PK0T7_I_nV8
Re: Octave Sizes [Re: Mark Cerisano] #2621698
03/08/17 11:00 PM
03/08/17 11:00 PM
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If you look at the P4 window, you can see the tests. It clearly shows that you can have pure 11/12/19/22 but not pure 15 (double octave) at the same time. If we tune pure double octaves, the 11/12/19/22 will all have to be narrow.

P4 Window
M3 = M10 < M17 = M6 = m6down = m3down

The M3 < M17 proves a wide double octave.
To have a pure double octave, you need

M3 = M10 = M17

That produces a pure 2:1. I don't know why anyone advocates a pure double octave. You need a pure 2:1 and that's just too narrow imho. But even tunelab has a setting for pure double octaves.

Pure 22 triple octave test
m6down = M17

I always use beat speeds to set intervals and then check the actual intervals now and then.

Thanks for the question.


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