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Topic Options
#2241106 - 03/04/14 07:01 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: Robert Scott]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

A demonstration would prove that what you refer to is a lame theory but, yes..

Alfredo, what kind of demonstration would you accept, that does require my traveling to Italy, or your traveling to the USA? Would you, for example, take my word for it if I said I tuned a rank of pipes with 2:1 ET and measured the beat rate of thirds and found them to be uniformly faster as I went up the scale?


Hi Robert,

No need to come to Europe :-) I would take your word for it, perhaps adding a few ten-thousandths to the ratio you used.

What I think is that we approach 'exatitude' and what we may define 'perfect' in different ways. I was not addressing the thirds beat rate progression only, but all intervals within a theoretical 2:1 octave.

What I can say is that there is only one way to combine fourths, fifths, thirds and octaves in an exponential scale and obtain a 'perfect' octave: that is when you combine 4 (the double octave) and 3 (the octave + fifth). In this case, the 'perfect' octave is not 2:1 but a little bit wider, a bit more than five ten-thousandths wider than 2:1.

As mentioned, you would probably hear those approximations only when you check all intervals, including 12ths. Did you?

Of course, I would be happy to check non-iH 2:1 octaves aurally, even if it was a simulation: progressive thirds, tenths and 17ths, and consistent fourths, fifths, octaves and 12ths.

In fact, I would look forward.
_________________________
alfredo

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#2241129 - 03/04/14 08:12 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: DoelKees]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Originally Posted By: DoelKees
Originally Posted By: alfredo capurso
Originally Posted By: DoelKees
Originally Posted By: alfredo capurso

You will see now (and I hope you acknowledge) that 4/3 (the conventional fourth) multiplied by 3/2 (the conventional fifth) will not reach 2 (as in the 2:1 ratio). Leave all 'tuning errors' aside, that is why we cannot have 'perfectly' progressive intervals on the basis of 12th root of two.

I was taught in elementary school that 4/3 * 3/2 = 2.

Kees


Me too.

So we've all been taught wrong? What is 4/3 * 3/2 according to you, if it is not equal to 2?

Kees


I think that decimal approximations of exact values are being mis-understood and mis-used to further a theory.

Alfredo, the value of pi, for example, is an exact quantity defined by the ratio of the circumference of a circle to its diameter. The decimal approximation of pi is not exact and not used in conceptual mathematics. It is used in technological applications.

Top
#2241347 - 03/04/14 03:26 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

A demonstration would prove that what you refer to is a lame theory but, yes..

Alfredo, what kind of demonstration would you accept, that does require my traveling to Italy, or your traveling to the USA? Would you, for example, take my word for it if I said I tuned a rank of pipes with 2:1 ET and measured the beat rate of thirds and found them to be uniformly faster as I went up the scale?


Hi Robert,

No need to come to Europe :-) I would take your word for it, perhaps adding a few ten-thousandths to the ratio you used.

What I think is that we approach 'exatitude' and what we may define 'perfect' in different ways. I was not addressing the thirds beat rate progression only, but all intervals within a theoretical 2:1 octave.

What I can say is that there is only one way to combine fourths, fifths, thirds and octaves in an exponential scale and obtain a 'perfect' octave: that is when you combine 4 (the double octave) and 3 (the octave + fifth). In this case, the 'perfect' octave is not 2:1 but a little bit wider, a bit more than five ten-thousandths wider than 2:1.

As mentioned, you would probably hear those approximations only when you check all intervals, including 12ths. Did you?

Of course, I would be happy to check non-iH 2:1 octaves aurally, even if it was a simulation: progressive thirds, tenths and 17ths, and consistent fourths, fifths, octaves and 12ths.

In fact, I would look forward.



Hi Alfredo,
Here is a link to a simulation of ET with no iH. It is just a portion of the full compass but shows that the intervals are progressive.

Top
#2241415 - 03/04/14 05:56 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

A demonstration would prove that what you refer to is a lame theory but, yes..

Alfredo, what kind of demonstration would you accept, that does require my traveling to Italy, or your traveling to the USA? Would you, for example, take my word for it if I said I tuned a rank of pipes with 2:1 ET and measured the beat rate of thirds and found them to be uniformly faster as I went up the scale?


Hi Robert,

No need to come to Europe :-) I would take your word for it, perhaps adding a few ten-thousandths to the ratio you used.

What I think is that we approach 'exatitude' and what we may define 'perfect' in different ways. I was not addressing the thirds beat rate progression only, but all intervals within a theoretical 2:1 octave.

What I can say is that there is only one way to combine fourths, fifths, thirds and octaves in an exponential scale and obtain a 'perfect' octave: that is when you combine 4 (the double octave) and 3 (the octave + fifth). In this case, the 'perfect' octave is not 2:1 but a little bit wider, a bit more than five ten-thousandths wider than 2:1.

As mentioned, you would probably hear those approximations only when you check all intervals, including 12ths. Did you?

Of course, I would be happy to check non-iH 2:1 octaves aurally, even if it was a simulation: progressive thirds, tenths and 17ths, and consistent fourths, fifths, octaves and 12ths.

In fact, I would look forward.



Hi Alfredo,
Here is a link to a simulation of ET with no iH. It is just a portion of the full compass but shows that the intervals are progressive.


Thank you, Prout, I appreciate your effort.

Yes, I said 'simulation', but meaning a simulation of non-iH 'sounds', what do you call them, recorded sounds or notes in a scale, say like Pianoteq's, so that one can check them aurally?

Anyway, look at the values for A0, A1, A2, and A3, relative to M3, P4, P5 and M6, perhaps you will notice two facts: how fifths (P5) get divaricated, comparing them to M3, P4 and M6 (imagine what 12ths would sound like), and how decimal approximations (roundings?) are inconsistent: on A3, the M6 would slow down, as the M3 (1.09 - 2.18 - 4.37 - 8.73) is unstable.

Regards, a.c.
.
_________________________
alfredo

Top
#2241459 - 03/04/14 08:03 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Originally Posted By: alfredo capurso
Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

A demonstration would prove that what you refer to is a lame theory but, yes..

Alfredo, what kind of demonstration would you accept, that does require my traveling to Italy, or your traveling to the USA? Would you, for example, take my word for it if I said I tuned a rank of pipes with 2:1 ET and measured the beat rate of thirds and found them to be uniformly faster as I went up the scale?


Hi Robert,

No need to come to Europe :-) I would take your word for it, perhaps adding a few ten-thousandths to the ratio you used.

What I think is that we approach 'exatitude' and what we may define 'perfect' in different ways. I was not addressing the thirds beat rate progression only, but all intervals within a theoretical 2:1 octave.

What I can say is that there is only one way to combine fourths, fifths, thirds and octaves in an exponential scale and obtain a 'perfect' octave: that is when you combine 4 (the double octave) and 3 (the octave + fifth). In this case, the 'perfect' octave is not 2:1 but a little bit wider, a bit more than five ten-thousandths wider than 2:1.

As mentioned, you would probably hear those approximations only when you check all intervals, including 12ths. Did you?

Of course, I would be happy to check non-iH 2:1 octaves aurally, even if it was a simulation: progressive thirds, tenths and 17ths, and consistent fourths, fifths, octaves and 12ths.

In fact, I would look forward.



Hi Alfredo,
Here is a link to a simulation of ET with no iH. It is just a portion of the full compass but shows that the intervals are progressive.


Thank you, Prout, I appreciate your effort.

Yes, I said 'simulation', but meaning a simulation of non-iH 'sounds', what do you call them, recorded sounds or notes in a scale, say like Pianoteq's, so that one can check them aurally?

Anyway, look at the values for A0, A1, A2, and A3, relative to M3, P4, P5 and M6, perhaps you will notice two facts: how fifths (P5) get divaricated, comparing them to M3, P4 and M6 (imagine what 12ths would sound like), and how decimal approximations (roundings?) are inconsistent: on A3, the M6 would slow down, as the M3 (1.09 - 2.18 - 4.37 - 8.73) is unstable.

Regards, a.c.
.


Hi Alfredo,

Again, I think you are missing the fact that the numbers presented are approximations only, rounded to 2 decimal places. Had I chosen to round them to a larger number of decimal places, they could be as accurate as you could desire. What is important to note is that the beat rates of the P4 and P5 within the octave are exact when the number of decimal places is increased to an arbitrarily large number (common language used for 'arbitrarily large number' is 'infinity').

Top
#2241680 - 03/05/14 01:46 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Hi Alfredo,

Here is a wav file of simulated M3s from F3A3 to C#4F4. They show a perfectly progressive increase in beat rate within the perfect 2:1 F3F4 octave. Hope this helps validate the math of no iH ET.

Regards.

Top
#2241787 - 03/05/14 04:42 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

A demonstration would prove that what you refer to is a lame theory but, yes..

Alfredo, what kind of demonstration would you accept, that does require my traveling to Italy, or your traveling to the USA? Would you, for example, take my word for it if I said I tuned a rank of pipes with 2:1 ET and measured the beat rate of thirds and found them to be uniformly faster as I went up the scale?


Hi Robert,

No need to come to Europe :-) I would take your word for it, perhaps adding a few ten-thousandths to the ratio you used.

What I think is that we approach 'exatitude' and what we may define 'perfect' in different ways. I was not addressing the thirds beat rate progression only, but all intervals within a theoretical 2:1 octave.

What I can say is that there is only one way to combine fourths, fifths, thirds and octaves in an exponential scale and obtain a 'perfect' octave: that is when you combine 4 (the double octave) and 3 (the octave + fifth). In this case, the 'perfect' octave is not 2:1 but a little bit wider, a bit more than five ten-thousandths wider than 2:1.

As mentioned, you would probably hear those approximations only when you check all intervals, including 12ths. Did you?

Of course, I would be happy to check non-iH 2:1 octaves aurally, even if it was a simulation: progressive thirds, tenths and 17ths, and consistent fourths, fifths, octaves and 12ths.

In fact, I would look forward.



Hi Alfredo,
Here is a link to a simulation of ET with no iH. It is just a portion of the full compass but shows that the intervals are progressive.


Thank you, Prout, I appreciate your effort.

Yes, I said 'simulation', but meaning a simulation of non-iH 'sounds', what do you call them, recorded sounds or notes in a scale, say like Pianoteq's, so that one can check them aurally?

Anyway, look at the values for A0, A1, A2, and A3, relative to M3, P4, P5 and M6, perhaps you will notice two facts: how fifths (P5) get divaricated, comparing them to M3, P4 and M6 (imagine what 12ths would sound like), and how decimal approximations (roundings?) are inconsistent: on A3, the M6 would slow down, as the M3 (1.09 - 2.18 - 4.37 - 8.73) is unstable.

Regards, a.c.
.


Hi Alfredo,

Again, I think you are missing the fact that the numbers presented are approximations only, rounded to 2 decimal places. Had I chosen to round them to a larger number of decimal places, they could be as accurate as you could desire. What is important to note is that the beat rates of the P4 and P5 within the octave are exact when the number of decimal places is increased to an arbitrarily large number (common language used for 'arbitrarily large number' is 'infinity').


Thank you, Prout, for addressing approximations.

For me what is important to note also, it is that even if we extend the number of decimal places to infinity, we are unable to remedy an 'arbitrary' model, as the first ET is.

Now I hope Robert will offer us a sound reproduction of a non-iH 12th root of two tuning.
.

Edit: Sorry, I had not seen your latest post, ...arriving at home from work I just replied to your second last post. I will listen to that file and reply asap.


Edited by alfredo capurso (03/05/14 04:46 PM)
_________________________
alfredo

Top
#2241791 - 03/05/14 04:54 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy

Prout, sure that wav file is OK? Are you yourself able to reproduce it? I can only hear two very low notes that go on chromatically. Perhaps there is something wrong with my LT?
_________________________
alfredo

Top
#2241810 - 03/05/14 05:23 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Hi Alfredo,

I now realize that the file I posted is not correct for our discussion. Each M3 in the file is the result of two essentially pure sine waves interfering with each other. The resultant sound is interesting, but incorrect. For example, the F3A3 sound (first 5 seconds) produces a clearly heard set of harmonics based on about 8.6 (8.6, 17.2, 25.8, etc.) that are a result of the 174.61 Hz and 220.00 Hz. This is not the beat rate from the upper harmonics, since there are no upper harmonics.

Sorry, I will try to add some harmonic distortion to the mix.

Regards.

Top
#2242322 - 03/06/14 06:00 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy

Hi Robert,

If you like, have a look at this (below), it is down this page:

http://www.pykett.org.uk/temperament_-_a_study_of_anachronism.htm

..."Appendix 2 – Arithmetical Precision required in Temperament Studies

The degree of precision required in numbers and arithmetic operations to do with temperament arises as follows.

Consider the process of tuning by beats. Let there be two flue pipes, one of which is already in tune and one which is to be tuned to it. Tuning becomes progressively more critical and difficult the higher the frequency because the beats, which are frequency differences, become faster as those frequencies increase for a given change in length of the pipes.

A verdict of “pretty well in tune” would probably be given if there was, say, one beat in around ten seconds for any pair of pipes. Although stricter criteria could be adopted there is no point in making things too difficult, partly because of the tuning drift which occurs naturally due to temperature variations etc after an organ has been carefully tuned. Therefore, using this criterion, the two pipes would have to be tuned until their fundamental frequencies did not differ by more than about 0.1 Hz, because one beat in ten seconds implies a frequency difference of 0.1 Hz.

Remembering that tuning is most critical in the upper reaches of the compass, consider the fifth C on the keyboard, i.e. the C below top C on a 61-note organ keyboard. Even higher notes could be chosen, but again we have to adopt reasonable parameters if the discussion is to remain sensible and practical. The fundamental frequency of this note on an 8 foot stop is 1046.5 Hz for an organ tuned to A = 440.00 Hz in Equal Temperament. For simplicity we shall use the approximate figure of 1000 Hz.

A frequency tolerance of about 0.1 Hz at a frequency of about 1000 Hz implies a tuning accuracy of the order of 0.0001 or 0.01%. This is therefore also the precision required in temperament calculations which have to deliver the frequencies of the notes in a particular temperament. But because there are usually several steps in the calculation of each frequency, it is necessary that the numerical precision of the numbers used in each step is greater than that required in the final answer, otherwise the answer will not be accurate enough owing to truncation or rounding errors. Therefore at least one more significant figure is required throughout the calculations, meaning that numbers must be represented to at least a precision of 0.00001 or 0.001%. This is the same as a precision of 1 part in 100,000, or 6 significant figures, as stated in the main body of this article."...

Is that what you where referring to, few posts ago, mentioning 'tuning errors'?

Regards, a.c.
.
_________________________
alfredo

Top
#2242401 - 03/06/14 09:08 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada

I find that article pedantic crackpottery.

Kees

Top
#2242405 - 03/06/14 09:13 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
Robert Scott Offline
Full Member

Registered: 12/19/03
Posts: 285
Loc: Minnesota
Originally Posted By: alfredo capurso

Hi Robert,

If you like, have a look at this (below), it is down this page:

http://www.pykett.org.uk/temperament_-_a_study_of_anachronism.htm

..."Appendix 2 – Arithmetical Precision required in Temperament Studies...

No, not exactly. That appendix 2 describes the degree of precision to achieve 0.1 Hz accuracy at higher and higher frequencies. But it does not take that much accuracy to achieve the goal of having progressive beat rates. All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower. To have progressive thirds, for example, all you need to do is tune to 2:1 ET with an accuracy of 0.0114%, or 0.2 cents. (The proof is left as an exercise for the reader.) However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before. That's 0.03 cents! But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths. With randomly occurring errors it is unlikely they would all conspire so perfectly to mess things up, so in practice you can get away with lesser accuracy and still have progressive intervals.
_________________________
Robert Scott
Hopkins, Minnesota
http://www.tunelab-world.com

Top
#2242809 - 03/07/14 06:22 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Robert Scott]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

Hi Robert,

If you like, have a look at this (below), it is down this page:

http://www.pykett.org.uk/temperament_-_a_study_of_anachronism.htm

..."Appendix 2 – Arithmetical Precision required in Temperament Studies...

No, not exactly. That appendix 2 describes the degree of precision to achieve 0.1 Hz accuracy at higher and higher frequencies. But it does not take that much accuracy to achieve the goal of having progressive beat rates. All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower. To have progressive thirds, for example, all you need to do is tune to 2:1 ET with an accuracy of 0.0114%, or 0.2 cents. (The proof is left as an exercise for the reader.) However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before. That's 0.03 cents! But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths. With randomly occurring errors it is unlikely they would all conspire so perfectly to mess things up, so in practice you can get away with lesser accuracy and still have progressive intervals.


Hi Robert, thank you.

You say: ..."That appendix 2 describes the degree of precision to achieve 0.1 Hz accuracy at higher and higher frequencies. But it does not take that much accuracy to achieve the goal of having progressive beat rates."...

Well, one might say that the two things, 'accuracy...' and 'progressive beat rates' are somehow related?

..".All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower."...

I am sure this has to do with my poor English: how can 'progressive beat rates' be '...as fast as the same interval starting one semitone lower', would not 'as fast as..' mean 'equal' beat rates?

..."To have progressive thirds..."...

This is interesting. One fresh question, would a ratio wider than 2:1 modify the accuracy %?

..."However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before."...

Should I understand that you have heard progressive (narrow) fifths, perhaps on a pipe organ tuned with non-iH ET? If positive, how did you like that, at higher frequencies?

..."But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths."...

Sincerely, I do not follow this reasoning, again, probably because of my English, 'worst-case way' or best-case, what is it that we know for sure?

..."With randomly occurring errors it is unlikely they would all conspire so perfectly to mess things up, so in practice you can get away with lesser accuracy and still have progressive intervals."...

I must say, I do not rely on luck, anyway... your last line should end with '..progressive...(not intervals, but) thirds'?

Regards, a.c.
.
_________________________
alfredo

Top
#2242820 - 03/07/14 06:37 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
accordeur Offline
1000 Post Club Member

Registered: 06/23/06
Posts: 1207
Loc: Québec, Canada
Alfredo, you should be happy that Robert is still answering to your posts. He is the creator of tunelab, and usually does not participate in these esoteric discussions.

Then again I never participate as well. But this time since Robert answered, I felt the need to as well.

Tunelab does consistently produce progressive thirds so.....
_________________________
Jean Poulin

Musician, Tuner and Technician

www.actionpiano.ca

Top
#2242875 - 03/07/14 08:59 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
Robert Scott Offline
Full Member

Registered: 12/19/03
Posts: 285
Loc: Minnesota
Originally Posted By: alfredo capurso

..".All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower."...

I am sure this has to do with my poor English: how can 'progressive beat rates' be '...as fast as the same interval starting one semitone lower', would not 'as fast as..' mean 'equal' beat rates?

"at least as fast" means "faster or the same". They just should not be slower.
Quote:

..."To have progressive thirds..."...

This is interesting. One fresh question, would a ratio wider than 2:1 modify the accuracy %?

Yes, but only to this extent: The faster the beat rates the easier it is to make them progressive. The so called RBI (rapidly beating intervals) do not take as much accuracy to make them progressive as the SBI (slowly beating intervals). If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive. But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards.
Quote:


..."However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before."...

Should I understand that you have heard progressive (narrow) fifths, perhaps on a pipe organ tuned with non-iH ET? If positive, how did you like that, at higher frequencies?

I have never found a pipe organ tuned accurately enough to draw these esoteric distinctions. Accuracy of 0.0016% would be nearly impossible on real pipes.
Quote:

..."But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths."...

Sincerely, I do not follow this reasoning, again, probably because of my English, 'worst-case way' or best-case, what is it that we know for sure?

'worst-case way' means the errors are arranged so they do the most damage to the progressive intervals. It is helpful to think of it as a game. The rules of the game are you are allowed to introduce tuning errors, but you are not allowed to make those errors too big. You can win the game if you can make the thirds not progressive. I claim you can only win that game if you are allowed to make tuning errors of more than 0.0114%. But you would have to make those errors in a worst-case way. That is, given C-E and C#-F, you could make them not-progressive if C and F were made as low as possible and E and C# were made as high as possible (within the limits of what you are allowed to do).
_________________________
Robert Scott
Hopkins, Minnesota
http://www.tunelab-world.com

Top
#2243055 - 03/08/14 09:53 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: accordeur]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: accordeur
Alfredo, you should be happy that Robert is still answering to your posts. He is the creator of tunelab, and usually does not participate in these esoteric discussions.

Then again I never participate as well. But this time since Robert answered, I felt the need to as well.

Tunelab does consistently produce progressive thirds so.....


Jean Poulin, perhaps you are misinterpreting. If you read carefully you will see that nobody here is doubting TL's performances.

We are expanding on non-iH progressive intervals, accuracy and intonation when you put 12th_root_of_two into practice.

I am certainly happy to hear what Robert has to say (it is being more than four years that Robert and I are in contact on this board), especially when our discussions, in general, can add on public knowledge. Do contribute with your experience, if you wish, how would you like progressive narrow fifths on higher frequencies?

Regards, a.c.
.
_________________________
alfredo

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#2243094 - 03/08/14 11:23 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
Robert Scott Offline
Full Member

Registered: 12/19/03
Posts: 285
Loc: Minnesota
Originally Posted By: alfredo capurso
[.... how would you like progressive narrow fifths on higher frequencies?

I gather that you are suggesting that using an octave wider than 2:1 would slow down the fifths that might otherwise be objectionable, especially at higher frequencies. Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good. Slowing down the 5ths is a good side effect of that stretch. But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat. People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible. So in the trade off between clean octaves and clean 5ths on a pipe organ, I think the attention should be given primarily to the octaves, which means 2:1 octaves.
_________________________
Robert Scott
Hopkins, Minnesota
http://www.tunelab-world.com

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#2243101 - 03/08/14 11:33 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7897
Loc: France
that is , the octaves scream too much when they are enlarged, even without audible beats. The organ players may find that effect highly uncomfortable. (as with harpsichords)

That said, we had a colleague that tuned harpsichords in pure 5th (no pure octave then), and that was appreciated for movies music and other in a recording studio I worked for, strangely.

possibly the strength of the pure ratio (the same may happen with pure 12 of 12/15 balance) gives an "in tune" impression that can hide the beating octaves somewhat.

as if the ear/brain switch on another listening mode.
_________________________
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#2243130 - 03/08/14 12:26 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Good day all,

I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1. I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7).

It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful.


Edited by prout (03/08/14 12:39 PM)

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#2243308 - 03/08/14 06:07 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Robert Scott]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso
[.... how would you like progressive narrow fifths on higher frequencies?

I gather that you are suggesting that using an octave wider than 2:1 would slow down the fifths that might otherwise be objectionable, especially at higher frequencies. Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good. Slowing down the 5ths is a good side effect of that stretch. But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat. People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible. So in the trade off between clean octaves and clean 5ths on a pipe organ, I think the attention should be given primarily to the octaves, which means 2:1 octaves.


Hi Robert,

You wrote: ..."I gather that you are suggesting that using an octave wider than 2:1 would slow down the fifths that might otherwise be objectionable, especially at higher frequencies."...

Yes, a talk about a non_noticeable_wide 'beating octave'. Not only fifths would slow down, also octave + fifths and double-octaves + fifths and so on. That is also why I look forward to listening to a non-iH ET tuning of 2:1 octaves on a pipe organ and to checking all intervals aurally, not only thirds and fifths (as mentioned a few days ago).

..."Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good."...

I guess you mean 'numerical' stretch, though still non-beating octaves? Is that correct?

..."Slowing down the 5ths is a good side effect of that stretch."...

I wonder if on a piano, stretched_but_non-beating octaves would slow down fifths. So I wonder if the side effect you mention is actually (instead) given by octaves that are stretched beyond the (2:1 +iH) non-beating threshold.

..."But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat."...

Sure, but I guess that the beat rate would be proportionate to the deviation, so, perhaps for very very small deviations the beat would be very very slow?

Really, I do not know, does the beat start at a fixed beat rate? On pianos and harpsichords the beat rate is strictly related to that (in fact, any) deviation. As you say, it starts '..immediately..', but not immediately fast, nor annoying.

..."People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible."...

Well, in a way I am saying the same thing, be it pianos, harpsichords or pipe organs, octaves can sound as clean as possible, meaning 'in tune' and well related to all other intervals. As for what 'people have gotten used to...', I would not be that concerned, I believe that people, really, love hearing an instrument that sounds in tune.

..."So in the trade off between clean octaves and clean 5ths on a pipe organ, I think the attention should be given primarily to the octaves, which means 2:1 octaves."...

I do not look at it as either 'clean octaves' or 'clean 5ths', because 'clean' seems to presuppose the absence of beats. I now understand beats as color but I know, this of mine may be a professional bias.
.
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alfredo

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#2243312 - 03/08/14 06:27 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Olek]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: Olek
that is , the octaves scream too much when they are enlarged, even without audible beats. The organ players may find that effect highly uncomfortable. (as with harpsichords)

That said, we had a colleague that tuned harpsichords in pure 5th (no pure octave then), and that was appreciated for movies music and other in a recording studio I worked for, strangely.

possibly the strength of the pure ratio (the same may happen with pure 12 of 12/15 balance) gives an "in tune" impression that can hide the beating octaves somewhat.

as if the ear/brain switch on another listening mode.



Hi Isaac,

Thanks for joining. I have to report that progressive wide octaves on harpsichords (as you say 'without audible beats') were not heard as 'uncomfortable' at all.

Is that 'pure fifths' colleague still around? I am still curious about that tuning practice, do you have any sample?

..."...possibly the strength of the pure ratio (the same may happen with pure 12 of 12/15 balance) gives an "in tune" impression that can hide the beating octaves somewhat."...

I am not sure there is something that needs to be hidden, the beating octave I talk about is like a starry sky that looks still but it is not.

Un caro saluto,

Alfredo
.
_________________________
alfredo

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#2243319 - 03/08/14 06:55 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: prout
Good day all,

I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1. I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7).

It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful.


Hi Prout,

You wrote: ..."I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1."...

Well, the difference is (approximately) .0005... with no iH. What makes it, as you say, 'little'?

..."I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7)."...

Prout, here I would agree with Robert, if 'the octaves beat audibly' it might not be that good.

..."It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH."...

Perhaps Tunewerk can help.

Tunewerk, would you please explain in good English why octaves, together with thirds, fourths, fifths, M6ths, 10ths, 12ths, 15ths, 17ths and all intervals need to be stretched before iH?
.
_________________________
alfredo

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#2243338 - 03/08/14 08:24 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
prout Offline
500 Post Club Member

Registered: 11/14/13
Posts: 834
Originally Posted By: alfredo capurso
Originally Posted By: prout
Good day all,

I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1. I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7).

It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful.


Hi Prout,

You wrote: ..."I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1."...

Well, the difference is (approximately) .0005... with no iH. What makes it, as you say, 'little'?

..."I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7)."...

Prout, here I would agree with Robert, if 'the octaves beat audibly' it might not be that good.

..."It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH."...

Perhaps Tunewerk can help.

Tunewerk, would you please explain in good English why octaves, together with thirds, fourths, fifths, M6ths, 10ths, 12ths, 15ths, 17ths and all intervals need to be stretched before iH?
.




Hi Alfredo,

Using an octave stretch of 2.0005 yields a 0.014 bps at A0 and 1.047 bps at C7. This yields a negligible benefit over no stretch as all the other intervals exhibit a negligible change as well (the stretch is -1.7 cents at A0 increasing to 1.4 cents at C8).

As an organist I can tell you that the best sound from an organ tuned in ET is still terrible because the beating harsh intervals are sustained. On the piano at least, the upper partials decrease rapidly in intensity and cause a significant reduction in the obviousness of the beating. Organs tuned in a meantone variant or a well temperament show a marked reduction in beating in the appropriate keys and are therefore much more harmonious.

Regarding stretching of all intervals by some predetermined amount beyond the desired temperament widths (on a 12 note per octave instrument) before consideration of iH - this makes no sense. The only reason for stretch is to compensate for iH.

I have not heard an organ tuned in a stretched octave ET, and, as such , cannot offer an opinion on the euphonious quality of such a temperament.

Regards.






Edited by prout (03/09/14 02:33 PM)

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#2243882 - 03/09/14 08:38 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: prout
Good day all,

I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1. I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7).

It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful.


Hi Prout,

You wrote: ..."I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1."...

Well, the difference is (approximately) .0005... with no iH. What makes it, as you say, 'little'?

..."I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7)."...

Prout, here I would agree with Robert, if 'the octaves beat audibly' it might not be that good.

..."It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH."...

Perhaps Tunewerk can help.

Tunewerk, would you please explain in good English why octaves, together with thirds, fourths, fifths, M6ths, 10ths, 12ths, 15ths, 17ths and all intervals need to be stretched before iH?
.




Hi Alfredo,

Using an octave stretch of 2.0005 yields a 0.014 bps at A0 and 1.047 bps at C7. This yields a negligible benefit over no stretch as all the other intervals exhibit a negligible change as well (the stretch is -1.7 cents at A0 increasing to 1.4 cents at C8).

As an organist I can tell you that the best sound from an organ tuned in ET is still terrible because the beating harsh intervals are sustained. On the piano at least, the upper partials decrease rapidly in intensity and cause a significant reduction in the obviousness of the beating. Organs tuned in a meantone variant or a well temperament show a marked reduction in beating in the appropriate keys and are therefore much more harmonious.

Regarding stretching of all intervals by some predetermined amount beyond the desired temperament widths (on a 12 note per octave instrument) before consideration of iH - this makes no sense. The only reason for stretch is to compensate for iH.

I have not heard an organ tuned in a stretched octave ET, and, as such , cannot offer an opinion on the euphonious quality of such a temperament.

Regards.


Hi Prout,

You wrote: ..."Using an octave stretch of 2.0005 yields a 0.014 bps at A0 and 1.047 bps at C7. This yields a negligible benefit over no stretch as all the other intervals exhibit a negligible change as well (the stretch is -1.7 cents at A0 increasing to 1.4 cents at C8)."...

You mean.. on a piano?

..."As an organist I can tell you that the best sound from an organ tuned in ET is still terrible because the beating harsh intervals are sustained."...

As a musician I would agree, but I do not know, was the one we heard ET? And, how about the temperament expansion, was it still ET? I doubt it, in any case I think we need a sample, a recording of all intervals, in order to evaluate the ET sound.

..."On the piano at least, the upper partials decrease rapidly in intensity and cause a significant reduction in the obviousness of the beating."...

Well, yes, if partials beat in the wrong way, you may want a "reduction".

..."Organs tuned in a meantone variant or a well temperament show a marked reduction in beating in the appropriate keys and are therefore much more harmonious."...

Even when you play 6ths, 10ths, 12ths, 15ths and 17ths? Hmmm.... Let me hear that.

..."Regarding stretching of all intervals by some predetermined amount beyond the desired temperament widths (on a 12 note per octave instrument) before consideration of iH - this makes no sense."...

Prout, I would like to know your real name. I would tell you that many times I have explained on this board why all intervals need to be stretched, though it will not be here nor now that we go through the same issue.

..."The only reason for stretch is to compensate for iH."...

Fair enough, it must a matter of horizons.

..."I have not heard an organ tuned in a stretched octave ET, and, as such, cannot offer an opinion on the euphonious quality of such a temperament."...

I recorded a simulation with digital sounds and it strengthened my opinion, if you like I can PM you the link.

Regards, a.c.
.
_________________________
alfredo

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#2244906 - 03/11/14 07:18 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Robert Scott]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

..".All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower."...

I am sure this has to do with my poor English: how can 'progressive beat rates' be '...as fast as the same interval starting one semitone lower', would not 'as fast as..' mean 'equal' beat rates?

"at least as fast" means "faster or the same". They just should not be slower.
Quote:

..."To have progressive thirds..."...

This is interesting. One fresh question, would a ratio wider than 2:1 modify the accuracy %?

Yes, but only to this extent: The faster the beat rates the easier it is to make them progressive. The so called RBI (rapidly beating intervals) do not take as much accuracy to make them progressive as the SBI (slowly beating intervals). If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive. But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards.
Quote:


..."However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before."...

Should I understand that you have heard progressive (narrow) fifths, perhaps on a pipe organ tuned with non-iH ET? If positive, how did you like that, at higher frequencies?

I have never found a pipe organ tuned accurately enough to draw these esoteric distinctions. Accuracy of 0.0016% would be nearly impossible on real pipes.
Quote:

..."But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths."...

Sincerely, I do not follow this reasoning, again, probably because of my English, 'worst-case way' or best-case, what is it that we know for sure?

'worst-case way' means the errors are arranged so they do the most damage to the progressive intervals. It is helpful to think of it as a game. The rules of the game are you are allowed to introduce tuning errors, but you are not allowed to make those errors too big. You can win the game if you can make the thirds not progressive. I claim you can only win that game if you are allowed to make tuning errors of more than 0.0114%. But you would have to make those errors in a worst-case way. That is, given C-E and C#-F, you could make them not-progressive if C and F were made as low as possible and E and C# were made as high as possible (within the limits of what you are allowed to do).


I Robert,

Sorry I have had to wait a bit, these are pretty busy days.

You wrote: ...""at least as fast" means "faster or the same". They just should not be slower."...

So, do you call 'progressive beat rates..', beat rates that may be 'the same'?

..."Snip//... The faster the beat rates the easier it is to make them progressive. The so called RBI (rapidly beating intervals) do not take as much accuracy to make them progressive as the SBI (slowly beating intervals)."...

I look at those intervals in a different way: all the accuracy you need will be in favor of both RBI's and SBI's. In a way, simply saying '..progression...' makes it easy, (AFAIAC) it has to be a 'smooth' progression and we need accuracy on and for both types of intervals.

..."If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive."...

The above sentence is deformed/contorted, unless the point is to go by with less tuning accuracy. In fact, 'a ratio wider than 2:1..', per se, means nothing. Yet, 'accuracy' is what is needed, and yes, you need extreme accuracy for smooth-progressive intervals.

..."But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards."...

I see, when you say '..it is not so important...' I understand how differently we interpret 'tuning' and intonation. In any case, a non-backwards fifth and a non-backwards contiguous fourth can make an octave narrow. This, to you, should be clear: a fifth a little bit too narrow (flat) and a contiguous fourth a bit too_slow (clean) will produce a narrow octave. I hope you can see how thirds, fourths, fifths and octaves are all in the same boat, all intervals are strictly related to each other.

..."I have never found a pipe organ tuned accurately enough to draw these esoteric distinctions. Accuracy of 0.0016% would be nearly impossible on real pipes."...

My question would be: have you ever found a pipe organ that could satisfy your 'artistic' expectations? And what does 'nearly impossible' mean? Have you ever succeeded?

Regards, a.c.
.
_________________________
alfredo

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#2245191 - 03/12/14 05:58 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
Robert Scott Offline
Full Member

Registered: 12/19/03
Posts: 285
Loc: Minnesota
Originally Posted By: alfredo capurso

So, do you call 'progressive beat rates..', beat rates that may be 'the same'?
Practically speaking, there is no way distinguish between "the same or greater" and "strictly greater" but you may assume the definition of "progressive" to mean beat rates that are "strictly greater" as you go up the scale.
Quote:

..."If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive."...

The above sentence is deformed/contorted, unless the point is to go by with less tuning accuracy. In fact, 'a ratio wider than 2:1..', per se, means nothing. Yet, 'accuracy' is what is needed, and yes, you need extreme accuracy for smooth-progressive intervals.

The point was to quantify what accuracy is needed to achieve the very specific goal or progressive intervals. We don't need to rely on vague terms like "extreme accuracy" when we can put a number on that accuracy so we know how "extreme" it is. The fact is, it takes more "extreme accuracy" to guarantee progressive SBIs than to guarantee progressive RBIs.
_________________________
Robert Scott
Hopkins, Minnesota
http://www.tunelab-world.com

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#2245216 - 03/12/14 08:34 AM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
Olek Online   content
7000 Post Club Member

Registered: 03/14/08
Posts: 7897
Loc: France
Hello Alfredo, about that "pure 5th" tuning, that is a question of taste, I have a colleague, also organist that tune both styles.

I suggest that if the tuning rely on a similar partial matching all along, or on most of the scale, it gives a coherence to the tone, along with the raise in sympathetic resonance of each note played , a lively instrument under the fingers is the result.

I mean the mix tactile perceptions thru the fingers, mixed with the level of energy perceived with the ears.

Eventually the tuner can also loose a little his sense of intonation, when caught in those resonances, but at last it is something reliable he can use, whatever tuning scheme he follows.
_________________________
It is critical that you call your Senators and Representatives and ask them to cosponsor S. 2587 and H.R. 5052. Getting your legislators to cosponsor these bills


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#2245527 - 03/12/14 06:36 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: Olek]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy

..."Practically speaking, there is no way distinguish between "the same or greater" and "strictly greater"...

Hi Robert, what do you mean? That you would not be able to distinguish beat rates that are the same, from beat rates that are greater as you go up the scale?

..."The point was to quantify what accuracy is needed to achieve the very specific goal or progressive intervals. We don't need to rely on vague terms like "extreme accuracy" when we can put a number on that accuracy so we know how "extreme" it is."...

I think we got on a point when you wrote ..."All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower. To have progressive thirds, for example, all you need to do is tune to 2:1 ET with an accuracy of 0.0114%, or 0.2 cents. (The proof is left as an exercise for the reader.) However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before. That's 0.03 cents! But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths. With randomly occurring errors it is unlikely they would all conspire so perfectly to mess things up, so in practice you can get away with lesser accuracy and still have progressive intervals."

I am still puzzled and cannot really understand what you want to say, as you wrote that 'in practice' we "...can get away with lesser accuracy and still have progressive intervals", and "...Practically speaking, there is no way distinguish between "the same or greater" and "strictly greater".

..."The fact is, it takes more "extreme accuracy" to guarantee progressive SBIs than to guarantee progressive RBIs."

No doubt, progressive SBI's require more accuracy but, should that be a reason (this is what I understood) for not tuning the octave a tiny bit wider than 2:1?

- . - . - . -

Originally Posted By: Olek
Hello Alfredo, about that "pure 5th" tuning, that is a question of taste, I have a colleague, also organist that tune both styles.

I suggest that if the tuning rely on a similar partial matching all along, or on most of the scale, it gives a coherence to the tone, along with the raise in sympathetic resonance of each note played , a lively instrument under the fingers is the result.

I mean the mix tactile perceptions thru the fingers, mixed with the level of energy perceived with the ears.

Eventually the tuner can also loose a little his sense of intonation, when caught in those resonances, but at last it is something reliable he can use, whatever tuning scheme he follows.


Hi Isaac,

You wrote: ..."..about that "pure 5th" tuning, that is a question of taste, I have a colleague, also organist that tune both styles."...

Yes, why not, once we achieve the accuracy that is required, I would believe that our tunings can somehow represent our taste; otherwise, implying 'taste' sounds like self-indulgence.

..."I suggest that if the tuning rely on a similar partial matching all along, or on most of the scale, it gives a coherence to the tone, along with the raise in sympathetic resonance of each note played, a lively instrument under the fingers is the result."...

I agree, in my experience too it is as you say, 'coherence' all across the scale and 'resonance'.

..."I mean the mix tactile perceptions thru the fingers, mixed with the level of energy perceived with the ears."...

Yes, through '..the fingers..', I share that feeling, and tone energy that is clearly perceivable.

..."Eventually the tuner can also loose a little his sense of intonation, when caught in those resonances, but at last it is something reliable he can use, whatever tuning scheme he follows."

Yes, resonances might be deceptive at times, but we have beats that we can check and perhaps time to rest.

Regards, a.c.
.
_________________________
alfredo

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#2247175 - 03/15/14 07:48 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: alfredo capurso]
alfredo capurso Offline
1000 Post Club Member

Registered: 07/10/07
Posts: 1073
Loc: Sicily - Italy

Originally Posted By: prout
Originally Posted By: alfredo capurso
Originally Posted By: prout
Good day all,

I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1. I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7).

It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful.


Hi Prout,

You wrote: ..."I ran a spreadsheet starting with a 2.0005 octave suggested by Alfredo on 12ET with no iH. There was little difference from 2:1."...

Well, the difference is (approximately) .0005... with no iH. What makes it, as you say, 'little'?

..."I increased the width to 2.0038 and found that the fifths become almost pure (0.0bps at A0 to -0.19bps at F7, giving a stretch of 13.1 at A0 to 10.7 at C8. The problem is that the octaves beat audibly from about C2 up. However, using the 2.0038 octave width as a starting point for tuning my piano using its iH, produces a relatively good tuning curve, which, not surprisingly, closely matches the calculated tuning curve from my own work and that of other ETD programmes (-18.7 to 24.7)."...

Prout, here I would agree with Robert, if 'the octaves beat audibly' it might not be that good.

..."It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH."...

Perhaps Tunewerk can help.

Tunewerk, would you please explain in good English why octaves, together with thirds, fourths, fifths, M6ths, 10ths, 12ths, 15ths, 17ths and all intervals need to be stretched before iH?
.



Hi Alfredo,

Using an octave stretch of 2.0005 yields a 0.014 bps at A0 and 1.047 bps at C7. This yields a negligible benefit over no stretch as all the other intervals exhibit a negligible change as well (the stretch is -1.7 cents at A0 increasing to 1.4 cents at C8).

As an organist I can tell you that the best sound from an organ tuned in ET is still terrible because the beating harsh intervals are sustained. On the piano at least, the upper partials decrease rapidly in intensity and cause a significant reduction in the obviousness of the beating. Organs tuned in a meantone variant or a well temperament show a marked reduction in beating in the appropriate keys and are therefore much more harmonious.

Regarding stretching of all intervals by some predetermined amount beyond the desired temperament widths (on a 12 note per octave instrument) before consideration of iH - this makes no sense. The only reason for stretch is to compensate for iH.

I have not heard an organ tuned in a stretched octave ET, and, as such , cannot offer an opinion on the euphonious quality of such a temperament.

Regards.


Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso
[.... how would you like progressive narrow fifths on higher frequencies?

I gather that you are suggesting that using an octave wider than 2:1 would slow down the fifths that might otherwise be objectionable, especially at higher frequencies. Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good. Slowing down the 5ths is a good side effect of that stretch. But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat. People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible. So in the trade off between clean octaves and clean 5ths on a pipe organ, I think the attention should be given primarily to the octaves, which means 2:1 octaves.


Hi Robert,

You wrote: ..."I gather that you are suggesting that using an octave wider than 2:1 would slow down the fifths that might otherwise be objectionable, especially at higher frequencies."...

Yes, a talk about a non_noticeable_wide 'beating octave'. Not only fifths would slow down, also octave + fifths and double-octaves + fifths and so on. That is also why I look forward to listening to a non-iH ET tuning of 2:1 octaves on a pipe organ and to checking all intervals aurally, not only thirds and fifths (as mentioned a few days ago).

..."Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good."...

I guess you mean 'numerical' stretch, though still non-beating octaves? Is that correct?

..."Slowing down the 5ths is a good side effect of that stretch."...

I wonder if on a piano, stretched_but_non-beating octaves would slow down fifths. So I wonder if the side effect you mention is actually (instead) given by octaves that are stretched beyond the (2:1 +iH) non-beating threshold.

..."But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat."...

Sure, but I guess that the beat rate would be proportionate to the deviation, so, perhaps for very very small deviations the beat would be very very slow?

Really, I do not know, does the beat start at a fixed beat rate? On pianos and harpsichords the beat rate is strictly related to that (in fact, any) deviation. As you say, it starts '..immediately..', but not immediately fast, nor annoying.

..."People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible."...

Well, in a way I am saying the same thing, be it pianos, harpsichords or pipe organs, octaves can sound as clean as possible, meaning 'in tune' and well related to all other intervals. As for what 'people have gotten used to...', I would not be that concerned, I believe that people, really, love hearing an instrument that sounds in tune.

..."So in the trade off between clean octaves and clean 5ths on a pipe organ, I think the attention should be given primarily to the octaves, which means 2:1 octaves."...

I do not look at it as either 'clean octaves' or 'clean 5ths', because 'clean' seems to presuppose the absence of beats. I now understand beats as color but I know, this of mine may be a professional bias.
.



Originally Posted By: alfredo capurso
Originally Posted By: Robert Scott
Originally Posted By: alfredo capurso

..".All that is needed for progressive beat rates is to have each beat rate be at least as fast as the same interval starting one semitone lower."...

I am sure this has to do with my poor English: how can 'progressive beat rates' be '...as fast as the same interval starting one semitone lower', would not 'as fast as..' mean 'equal' beat rates?

"at least as fast" means "faster or the same". They just should not be slower.
Quote:

..."To have progressive thirds..."...

This is interesting. One fresh question, would a ratio wider than 2:1 modify the accuracy %?

Yes, but only to this extent: The faster the beat rates the easier it is to make them progressive. The so called RBI (rapidly beating intervals) do not take as much accuracy to make them progressive as the SBI (slowly beating intervals). If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive. But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards.
Quote:


..."However, to have progressive 5ths, it is much harder. Then the accuracy would need to be 0.0016% to guarantee each fifth is slightly faster than the one before."...

Should I understand that you have heard progressive (narrow) fifths, perhaps on a pipe organ tuned with non-iH ET? If positive, how did you like that, at higher frequencies?

I have never found a pipe organ tuned accurately enough to draw these esoteric distinctions. Accuracy of 0.0016% would be nearly impossible on real pipes.
Quote:

..."But that is assuming that one can pick the errors in the worst-case way to try to mess up the progressive fifths."...

Sincerely, I do not follow this reasoning, again, probably because of my English, 'worst-case way' or best-case, what is it that we know for sure?

'worst-case way' means the errors are arranged so they do the most damage to the progressive intervals. It is helpful to think of it as a game. The rules of the game are you are allowed to introduce tuning errors, but you are not allowed to make those errors too big. You can win the game if you can make the thirds not progressive. I claim you can only win that game if you are allowed to make tuning errors of more than 0.0114%. But you would have to make those errors in a worst-case way. That is, given C-E and C#-F, you could make them not-progressive if C and F were made as low as possible and E and C# were made as high as possible (within the limits of what you are allowed to do).


I Robert,

Sorry I have had to wait a bit, these are pretty busy days.

You wrote: ...""at least as fast" means "faster or the same". They just should not be slower."...

So, do you call 'progressive beat rates..', beat rates that may be 'the same'?

..."Snip//... The faster the beat rates the easier it is to make them progressive. The so called RBI (rapidly beating intervals) do not take as much accuracy to make them progressive as the SBI (slowly beating intervals)."...

I look at those intervals in a different way: all the accuracy you need will be in favor of both RBI's and SBI's. In a way, simply saying '..progression...' makes it easy, (AFAIAC) it has to be a 'smooth' progression and we need accuracy on and for both types of intervals.

..."If a ratio wider than 2:1 made some interval beat slower, it would take more tuning accuracy to ensure they are progressive."...

The above sentence is deformed/contorted, unless the point is to go by with less tuning accuracy. In fact, 'a ratio wider than 2:1..', per se, means nothing. Yet, 'accuracy' is what is needed, and yes, you need extreme accuracy for smooth-progressive intervals.

..."But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards."...

I see, when you say '..it is not so important...' I understand how differently we interpret 'tuning' and intonation. In any case, a non-backwards fifth and a non-backwards contiguous fourth can make an octave narrow. This, to you, should be clear: a fifth a little bit too narrow (flat) and a contiguous fourth a bit too_slow (clean) will produce a narrow octave. I hope you can see how thirds, fourths, fifths and octaves are all in the same boat, all intervals are strictly related to each other.

..."I have never found a pipe organ tuned accurately enough to draw these esoteric distinctions. Accuracy of 0.0016% would be nearly impossible on real pipes."...

My question would be: have you ever found a pipe organ that could satisfy your 'artistic' expectations? And what does 'nearly impossible' mean? Have you ever succeeded?

Regards, a.c.
.


Hi All,

I decided to re-post some statements and questions, in case someone is able and willing to contribute further.

In the first quotation Prout wrote: "It is my opinion that pure (integer) harmonic octaves are a requirement for no or extremely low iH conditions, and that some octave stretch, variable according the circumstances, is an obvious requirement for normal instruments with iH. A generic formula that does not include the unique measured iH of the instrument being tuned, is not useful."

- . - . - . -

Personally, I wonder how "...a generic formula that does not include the unique measured iH of the instrument being tuned..", as 12th root of two is, could take us where we are; should I think it is a miracle? And what should we think about the past and present literature on temperaments?

From the second quote above:

Robert: ..."Well, on instruments with IH, like a piano, some stretch is necessary just to make the octaves sound good."...

Me: I guess you mean 'numerical' stretch, though still non-beating octaves? Is that correct?

Robert: ..."Slowing down the 5ths is a good side effect of that stretch."...

Me: I wonder if on a piano, stretched_but_non-beating octaves would slow down fifths. So I wonder if the side effect you mention is actually (instead) given by octaves that are stretched beyond the (2:1 +iH) non-beating threshold.

Robert: ..."But on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat."...

Me: Sure, but I guess that the beat rate would be proportionate to the deviation, so, perhaps for very very small deviations the beat would be very very slow?

Really, I do not know, does the beat start at a fixed beat rate? On pianos and harpsichords the beat rate is strictly related to that (in fact, any) deviation. As you say, it starts '..immediately..', but not immediately fast, nor annoying.

Robert: ..."People have gotten used to hearing beating thirds and even 5ths, but when it comes to organs, people expect octaves to be as clean as possible."...

- . - . - . -

Sincerely, I would like to know more, do you All normally tune stretched-non-beating octaves?

I was saying: I wonder if on a piano, stretched_but_non-beating octaves would slow down fifths. So I wonder if the side effect you mention is actually (instead) given by octaves that are stretched beyond the (2:1 +iH) non-beating threshold.

Is anyone able and willing to offer a feedback?

Robert, you wrote .."..on non-IH instruments, which we were discussing, any departure from 2:1 octaves immediately causes octaves to beat..", do you mean to say that octaves 'immediately' beat fast?

From the third quote:

Robert: "..."But then, for very slowly beating intervals, it is not so important artistically that they be strictly progressive, as long as they are not backwards."...

Me: ..a fifth a little bit too narrow (flat) and a contiguous fourth a bit too_slow (clean) will produce a narrow octave.... ...have you ever found a pipe organ that could satisfy your 'artistic' expectations? And what does 'nearly impossible' mean? Have you ever succeeded?

- . - . - . -

I still wonder how the first ET is being expanded in these days, perhaps others can say how they manage 4ths and fifths outside the temperament? And 10ths, 12ths, double-octaves and 17ths? Do you do that "by size or beats?".

Regards, a.c.
.
_________________________
alfredo

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#2247183 - 03/15/14 08:06 PM Re: Do we hear 'in tune' intervals by size or beats? [Re: prout]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1760
Loc: Vancouver, Canada
To state the obvious: non-beating octaves don't exist when there is inharmonicity.

Kees

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