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I'm not sure how the image illustrates the Pythagorean comma. Does the image use a scale of cents? Hyacinth ( talk) 22:42, 26 July 2008 (UTC)
An image or media file that you uploaded or altered, Image:MUSICAL SCALES WITH PYTHAGOREAN COMMA.svg, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Hyacinth ( talk) 00:59, 28 July 2008 (UTC) Hyacinth ( talk) 00:59, 28 July 2008 (UTC)
I have added audio examples to the article. Hyacinth ( talk) 22:41, 13 August 2008 (UTC) Are the higher and lower versions of the note being played simultaneously, or alternately? I can't hear a difference, and some musician friends say they can't either, so this MID file may be sounding both at once. Could someone supply an audio rendition of the comma which would play the two notes alternately, so we can listen for the pitch difference, then simultaneously for a long enough duration that we can hear the beats (roughly 2 per second at Middle C). Perhaps the existing file does this already, and my ear just isn't good enough to hear it. But in any case the caption should explain what it is doing. CharlesHBennett ( talk) 18:49, 11 January 2016 (UTC)
NOTE: This is a spin off of a similar discussion started in another talk page, about the sign of a quantity denoted as ε, which in Pythagorean tuning is supposed to be exactly one twelfth of a Pythagorean comma. In short, we realized that the only way to change the sign of ε was to change the sign of the Pythagorean comma as well, and this is the reason why the discussion was moved here by Glenn L. Paolo.dL ( talk) 13:13, 12 August 2010 (UTC)
The above question was posed to me a few hours ago by frequent music editor Paolo.dL. And yes, I do propose a change in its definition. No, not in its absolute size, but as its currently used reciprocal. Why?
In most meantone temperaments, where the perfect fifth is narrowed by 1/11 of a syntonic comma or more, the sequence of fifths
results in the final note G♯, being flatter than its enharmonic counterpart A♭, and F♯ being flatter than its enharmonic counterpart G♭. Most musicians trained to the subtleties of just intonation and meantone temperament understand that this is a natural arrangement and even expect this. The interval between them is a
diminished second, the same interval defined as the distance between C and D
or between D and E
.
The problem develops on the other side of the 12-TET line:
In these last two cases, we have a negative diminished second, and the above "natural arrangement" has been reversed! Ancient Greek ears may have not had a problem with this, but many "just" and "meantone"-trained ears would be surprised, possibly even a bit upset.
In my humble opinion, the best way to illustrate the changeover in the diminished second is to used a "signed" system to define them. If we remove the virtually-equivalent eleventh-comma and 12-TET systems from the remainder of this discussion, five systems remain, each differing from its adjacent system by one-twelfth of a syntonic comma. The corresponding enharmonic notes likewise set a pattern, differing by a full syntonic comma (81:80 or ≈21.50629 cents). Starting with third-comma meantone, one can take the greater diesis as the starting point and subtract successive commas as follows:
The above redefinition for the Pythagorean comma (as well as the schisma) acknowledges that, in the last two cases, the expected diminished-second pairing of G♯ < A♭ fails and is thus a negative interval. A similar case appears at the top of the Pythagorean interval table.
There is an alternative: One can keep the Pythagorean comma and schisma as positive and make the diaschisma and dieses negative instead. However, this might be construed as even more radical than the other way around.
I now invite comments. − Glenn L ( talk) 18:11, 14 August 2010 (UTC)
Name | Short | Ratio | Cents | ET Cents |
---|---|---|---|---|
diminished second | d2 | 524288/531441 | -23.460 | 0 |
Pythagorean comma | 531441/524288 | 23.460 | 0 |
Thanks for your lengthy response, Paolo. Indeed, your POINT 2 (concerning the Pythagorean diminished second) is precisely why I have taken this stand, as forbidden is it might be outside this Talk page. Be that as it may, I shall take no further action at this point. However, your recent entry here has caused me to place a footnote in this table to note that the Pythagorean diminished second is actually the reciprocal of the Pythagorean comma. − Glenn L ( talk) 05:12, 16 August 2010 (UTC)
I copied here a comment by Glenn L, which in my opinion is extremely effective (especially in what he calls a "poorly-edited number line"), and was posted in Talk:Wolf interval before we realized that the sign of ε was connected with the sign of the Pythagorean comma, and decided to move the discussion here (see above). Paolo.dL ( talk) 15:14, 17 August 2010 (UTC)
In Talk:Wolf interval we agreed with Glenn L that the sign of ε should be, for the sake of consistency, the same as the sign of the comma. And indeed we defined it everywhere as 1/12 of the comma. Moreover, that's the very reason why we moved here, from there, the discussion about the sign of ε, and turned it into a discussion about the sign of the Pythagorean comma (PC). So, can we all agree now about what follows?
− Paolo.dL ( talk) 16:04, 16 August 2010 (UTC)
POINT 1.
I have a few questions for you: what is the reason why you moved the discussion about the sign of ε here, and turned it into a discussion about the sign of the Pythagorean comma (PC)? What's the connection between ε and PC, if you don't want to define ε as 1/12 of a comma? And more importantly, what was the reason why you chose to discuss PC before ε? These questions may seem not useful in this context, because you may simply answer that you changed your mind, and you are perfectly entitled to do so, or that you just wanted commas to be consistent with ε (rather than vice versa). But please indulge me, and think about the reason why you wanted to discuss PC before ε.
ε, in my opinion, does not need to be a unidimensional vector. It works better as a length (see my comment above). In other words, it does not need to have a direction, as a negative sign would only confuse the reader in the context where ε is used. ε is simply used to define intervals within a single tuning system (e.g., right at the end of this section). So, it is convenient to define it as 1/12 of a comma, i.e. as a length, with positive sign. You may ask: what's the difference between a comma and an ε, then? Your answer to my question above might give you insight about this: the difference is that ε is not used for comparisons between tuning systems. For that, we use commas (see table in comma (music)), or fifths. Even your "poorly edited number line", that I copied above, is actually a comparison between the sizes of fifths, not between the sizes of ε, and that's why I like it!
As I wrote in the previous section, I would prefer the PC to be negative, which would imply a negative ε. But this does not mean that I like a negative ε! It would not be wise. The reader would not understand the negative sign in the context where ε is used. Namely, ε is defined at the end of this section as the difference between the size of the fifth and 700:
Definition of ε in Pythagorean tuning |
---|
By definition, in Pythagorean tuning 11 perfect fifths have a size of approximately 701.955 cents (700+ε cents, where ε ≈ 1.955 cents). |
This definition is already crystal clear, and in my opinion it is highly desirable to leave it as it is, as simple as possible. The fact that 701.955 is larger than 700 is so clear, in this definition, that I really can't see the need to give ε a negative sign. It would only decrease readability, with no advantage whatsoever. This is also true in other contexts, such as here, here, or here.
In short, the only advantage of having PC positive, is to have ε positive as well!
− Paolo.dL ( talk) 11:27, 17 August 2010 (UTC)
POINT 2.
By the way, the direction of ε is absolutely clear in this definition, and it happens to be positive (increasing frequency)! So, it does not make sense to give ε a negative sign. However, I guess it might make some sense (but it would slightly decrease readability) to define ε as negative in meantone temperaments where the fifth is tempered to a size narrower than 700 cents. But we cannot do it, because we agreed that, according to the literature, in those tuning systems both d2 and the comma are defined as positive!
I am not implying, however, that this discussion was useless. It is useful to think and be aware about this problem, and this discussion, together with the previous about the sign of PC, already produced a few good edits, even though we are limited by Wikipedia policies.
− Paolo.dL ( talk) 14:54, 17 August 2010 (UTC)
I like your edits on the table in Comma (music), as I like all your (and my) edits inspired by this discussion, but when you use this example here you seem to forget (again, as in your "poorly-edited number line") that commas or fifths are used to compare tuning systems, while ε was created for a totally different reason.
You maintain that to keep ε always positive is "inconsistent". Inconsistent with what? Yes, it is inconsistent with d2, but perfectly consistent with commas. And, consistent with itself as well, its consistence residing in its lack of direction (i.e. in its definition as a length, which is perfectly compatible with mathematics)... Anyway, I disagree that it should be consistent with d2 or with commas. Contrary to what I wrote at the beginning of this discussion, I am now convinced that the main definition of ε is not and should not be based on commas or d2. The correct definition in Pythagorean tuning is given above. One way to summarize my main point is this: ε does not need to be consistent between tuning systems, but only within each tuning system. (BTW, otherwise it would be wise to give it a different symbol for each tuning system.)
However, let's imagine for a moment that ε needed to be also consistent between tuning systems, as you suggest. In this case, as I showed above, in my opinion a reasonable definition of ε would be:
In other words, ε was created to represent the amount by which P5 deviates from 700 (which is the average size for the 12 fifths in 12-tone scales) within a given tuning system. And that definition currently is and should remain the main one, the first one, in all contexts where ε is defined, because it proves to be useful to make the concept crystal clear to the reader. We created ε only to show that, within the tuning system in which it is defined, any interval deviates from the relevant average by a multiple of ε. This is its sense of life, written in its "Genesis" book. We did not create it to compare tuning systems. And this implies that:
This is what logic would dictate if and only if we needed to be also consistent between tuning systems, and it is the opposite of what you propose:
However,
So, because of this, and also because of what I wrote in my POINT 2 above, it might be reasonable to give ε a negative sign in tuning systems with P5 < 700 cents (which is the opposite of what you suggest), but in my opinion we can't do it, because it is more reasonable to keep it always positive, as it always was and still is on Wikipedia. The opposite, i.e. assigning to ε the same sign as d2, is even less reasonable, although mathematically it would work all the same. And please do not forget that the current definition is mathematically correct as well!
− Paolo.dL ( talk) 19:06, 17 August 2010 (UTC)
δ
) or ε (ε
), rather than δ and ε, provided as special characters in Wikipedia standard editor? If not, I suggest you to use the special characters, because they make edits easier.
Paolo.dL (
talk)
18:08, 18 August 2010 (UTC)Totally useless for anyone not already a complete expert in music theory. First section needs an entire rewrite. —Preceding unsigned comment added by 195.112.40.182 ( talk) 09:48, 28 November 2010 (UTC)
Any actual suggestions instead of empty criticisms? Hyacinth ( talk) 11:52, 11 December 2010 (UTC)
In some articles about specific commas (this article, Comma (music), and Syntonic comma ), and in the article about semitone there are pictures showing, in staff notation, an octave + a comma (or semitone), rather than simply a comma (or semitone). On the other hand, the attached audio file typically plays a true comma (not a comma + octave). I tried to remove the picture recently added in this article. And I carefully explained the reason in my edit summary:
However, my edit was unpolitely reverted without explanation.
— Paolo.dL ( talk) 17:50, 3 December 2010 (UTC)
I do not have a software to produce the image. And my point is not exactly the same as yours. You seem to wish only consistency, but an audio file consistent with that picture would be as useless as the picture! I do not need only consistency, but mainly "semplicity and clarity", and pictures and audio files which make the concept clear rather than creating doubts. So, I suggest to delete the picture, and just use the audio file, in all the above mentioned articles. I am not going to do that alone, as I hate edit wars with unpolite people.
I was hoping that Hyacinth, the author of the pictures, would understand my point and fix them, but unfortunately he is also the editor that reverted my edit without explanation, and even ignored my polite request in his talk page.
So, I thank you for your kind support, but I am asking you and other editors to answer this question, regarding all the above-mentioned articles: while we wait for somebody (hopefully the original author) to draw new pictures showing the correct intervals (it may take long, as the author is ignoring my request), is it better to keep those pictures or delete them? — Paolo.dL ( talk) 19:24, 4 December 2010 (UTC)
In this article | In
Comma (music) and Syntonic comma |
In Semitone#Just intonation |
---|---|---|
![]() |
![]() |
![]() |
Don't mean to quibble, but is the sample correct? I only hear a unison. 23.6 cents should make an audible difference, no? The syntonic comma sample is distinct at a slightly narrower interval. — Preceding unsigned comment added by 68.47.101.16 ( talk) 01:02, 20 August 2015 (UTC)
References
Following the above discussion, we have the MIDI file as accurate as possible using the current method. As stated here, a Pythagorean comma = 23.460010 cents. At 23.461914 cents, the interval represented in the MIDI file is not accurate to six decimal places. This is an example of false precision. I have again corrected this error. Burninthruthesky ( talk) 07:39, 28 March 2017 (UTC)
In view of the ongoing edits, I have posted a request for help at the Mathematics WikiProject. Burninthruthesky ( talk) 07:58, 28 March 2017 (UTC)
Re " the file is an estimation of a Pythagorean comma". It doesn't say it's an "estimation", and in fact it isn't. Even if it were properly explained, I still don't believe a discussion of the limits of MIDI precision belongs in this article. As pointed out in the discussion above, it is below the just noticeable difference. Is there any WP:CONSENSUS for this edit? Burninthruthesky ( talk) 08:56, 28 March 2017 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||||
|
I'm not sure how the image illustrates the Pythagorean comma. Does the image use a scale of cents? Hyacinth ( talk) 22:42, 26 July 2008 (UTC)
An image or media file that you uploaded or altered, Image:MUSICAL SCALES WITH PYTHAGOREAN COMMA.svg, has been listed at Wikipedia:Images and media for deletion. Please see the discussion to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Hyacinth ( talk) 00:59, 28 July 2008 (UTC) Hyacinth ( talk) 00:59, 28 July 2008 (UTC)
I have added audio examples to the article. Hyacinth ( talk) 22:41, 13 August 2008 (UTC) Are the higher and lower versions of the note being played simultaneously, or alternately? I can't hear a difference, and some musician friends say they can't either, so this MID file may be sounding both at once. Could someone supply an audio rendition of the comma which would play the two notes alternately, so we can listen for the pitch difference, then simultaneously for a long enough duration that we can hear the beats (roughly 2 per second at Middle C). Perhaps the existing file does this already, and my ear just isn't good enough to hear it. But in any case the caption should explain what it is doing. CharlesHBennett ( talk) 18:49, 11 January 2016 (UTC)
NOTE: This is a spin off of a similar discussion started in another talk page, about the sign of a quantity denoted as ε, which in Pythagorean tuning is supposed to be exactly one twelfth of a Pythagorean comma. In short, we realized that the only way to change the sign of ε was to change the sign of the Pythagorean comma as well, and this is the reason why the discussion was moved here by Glenn L. Paolo.dL ( talk) 13:13, 12 August 2010 (UTC)
The above question was posed to me a few hours ago by frequent music editor Paolo.dL. And yes, I do propose a change in its definition. No, not in its absolute size, but as its currently used reciprocal. Why?
In most meantone temperaments, where the perfect fifth is narrowed by 1/11 of a syntonic comma or more, the sequence of fifths
results in the final note G♯, being flatter than its enharmonic counterpart A♭, and F♯ being flatter than its enharmonic counterpart G♭. Most musicians trained to the subtleties of just intonation and meantone temperament understand that this is a natural arrangement and even expect this. The interval between them is a
diminished second, the same interval defined as the distance between C and D
or between D and E
.
The problem develops on the other side of the 12-TET line:
In these last two cases, we have a negative diminished second, and the above "natural arrangement" has been reversed! Ancient Greek ears may have not had a problem with this, but many "just" and "meantone"-trained ears would be surprised, possibly even a bit upset.
In my humble opinion, the best way to illustrate the changeover in the diminished second is to used a "signed" system to define them. If we remove the virtually-equivalent eleventh-comma and 12-TET systems from the remainder of this discussion, five systems remain, each differing from its adjacent system by one-twelfth of a syntonic comma. The corresponding enharmonic notes likewise set a pattern, differing by a full syntonic comma (81:80 or ≈21.50629 cents). Starting with third-comma meantone, one can take the greater diesis as the starting point and subtract successive commas as follows:
The above redefinition for the Pythagorean comma (as well as the schisma) acknowledges that, in the last two cases, the expected diminished-second pairing of G♯ < A♭ fails and is thus a negative interval. A similar case appears at the top of the Pythagorean interval table.
There is an alternative: One can keep the Pythagorean comma and schisma as positive and make the diaschisma and dieses negative instead. However, this might be construed as even more radical than the other way around.
I now invite comments. − Glenn L ( talk) 18:11, 14 August 2010 (UTC)
Name | Short | Ratio | Cents | ET Cents |
---|---|---|---|---|
diminished second | d2 | 524288/531441 | -23.460 | 0 |
Pythagorean comma | 531441/524288 | 23.460 | 0 |
Thanks for your lengthy response, Paolo. Indeed, your POINT 2 (concerning the Pythagorean diminished second) is precisely why I have taken this stand, as forbidden is it might be outside this Talk page. Be that as it may, I shall take no further action at this point. However, your recent entry here has caused me to place a footnote in this table to note that the Pythagorean diminished second is actually the reciprocal of the Pythagorean comma. − Glenn L ( talk) 05:12, 16 August 2010 (UTC)
I copied here a comment by Glenn L, which in my opinion is extremely effective (especially in what he calls a "poorly-edited number line"), and was posted in Talk:Wolf interval before we realized that the sign of ε was connected with the sign of the Pythagorean comma, and decided to move the discussion here (see above). Paolo.dL ( talk) 15:14, 17 August 2010 (UTC)
In Talk:Wolf interval we agreed with Glenn L that the sign of ε should be, for the sake of consistency, the same as the sign of the comma. And indeed we defined it everywhere as 1/12 of the comma. Moreover, that's the very reason why we moved here, from there, the discussion about the sign of ε, and turned it into a discussion about the sign of the Pythagorean comma (PC). So, can we all agree now about what follows?
− Paolo.dL ( talk) 16:04, 16 August 2010 (UTC)
POINT 1.
I have a few questions for you: what is the reason why you moved the discussion about the sign of ε here, and turned it into a discussion about the sign of the Pythagorean comma (PC)? What's the connection between ε and PC, if you don't want to define ε as 1/12 of a comma? And more importantly, what was the reason why you chose to discuss PC before ε? These questions may seem not useful in this context, because you may simply answer that you changed your mind, and you are perfectly entitled to do so, or that you just wanted commas to be consistent with ε (rather than vice versa). But please indulge me, and think about the reason why you wanted to discuss PC before ε.
ε, in my opinion, does not need to be a unidimensional vector. It works better as a length (see my comment above). In other words, it does not need to have a direction, as a negative sign would only confuse the reader in the context where ε is used. ε is simply used to define intervals within a single tuning system (e.g., right at the end of this section). So, it is convenient to define it as 1/12 of a comma, i.e. as a length, with positive sign. You may ask: what's the difference between a comma and an ε, then? Your answer to my question above might give you insight about this: the difference is that ε is not used for comparisons between tuning systems. For that, we use commas (see table in comma (music)), or fifths. Even your "poorly edited number line", that I copied above, is actually a comparison between the sizes of fifths, not between the sizes of ε, and that's why I like it!
As I wrote in the previous section, I would prefer the PC to be negative, which would imply a negative ε. But this does not mean that I like a negative ε! It would not be wise. The reader would not understand the negative sign in the context where ε is used. Namely, ε is defined at the end of this section as the difference between the size of the fifth and 700:
Definition of ε in Pythagorean tuning |
---|
By definition, in Pythagorean tuning 11 perfect fifths have a size of approximately 701.955 cents (700+ε cents, where ε ≈ 1.955 cents). |
This definition is already crystal clear, and in my opinion it is highly desirable to leave it as it is, as simple as possible. The fact that 701.955 is larger than 700 is so clear, in this definition, that I really can't see the need to give ε a negative sign. It would only decrease readability, with no advantage whatsoever. This is also true in other contexts, such as here, here, or here.
In short, the only advantage of having PC positive, is to have ε positive as well!
− Paolo.dL ( talk) 11:27, 17 August 2010 (UTC)
POINT 2.
By the way, the direction of ε is absolutely clear in this definition, and it happens to be positive (increasing frequency)! So, it does not make sense to give ε a negative sign. However, I guess it might make some sense (but it would slightly decrease readability) to define ε as negative in meantone temperaments where the fifth is tempered to a size narrower than 700 cents. But we cannot do it, because we agreed that, according to the literature, in those tuning systems both d2 and the comma are defined as positive!
I am not implying, however, that this discussion was useless. It is useful to think and be aware about this problem, and this discussion, together with the previous about the sign of PC, already produced a few good edits, even though we are limited by Wikipedia policies.
− Paolo.dL ( talk) 14:54, 17 August 2010 (UTC)
I like your edits on the table in Comma (music), as I like all your (and my) edits inspired by this discussion, but when you use this example here you seem to forget (again, as in your "poorly-edited number line") that commas or fifths are used to compare tuning systems, while ε was created for a totally different reason.
You maintain that to keep ε always positive is "inconsistent". Inconsistent with what? Yes, it is inconsistent with d2, but perfectly consistent with commas. And, consistent with itself as well, its consistence residing in its lack of direction (i.e. in its definition as a length, which is perfectly compatible with mathematics)... Anyway, I disagree that it should be consistent with d2 or with commas. Contrary to what I wrote at the beginning of this discussion, I am now convinced that the main definition of ε is not and should not be based on commas or d2. The correct definition in Pythagorean tuning is given above. One way to summarize my main point is this: ε does not need to be consistent between tuning systems, but only within each tuning system. (BTW, otherwise it would be wise to give it a different symbol for each tuning system.)
However, let's imagine for a moment that ε needed to be also consistent between tuning systems, as you suggest. In this case, as I showed above, in my opinion a reasonable definition of ε would be:
In other words, ε was created to represent the amount by which P5 deviates from 700 (which is the average size for the 12 fifths in 12-tone scales) within a given tuning system. And that definition currently is and should remain the main one, the first one, in all contexts where ε is defined, because it proves to be useful to make the concept crystal clear to the reader. We created ε only to show that, within the tuning system in which it is defined, any interval deviates from the relevant average by a multiple of ε. This is its sense of life, written in its "Genesis" book. We did not create it to compare tuning systems. And this implies that:
This is what logic would dictate if and only if we needed to be also consistent between tuning systems, and it is the opposite of what you propose:
However,
So, because of this, and also because of what I wrote in my POINT 2 above, it might be reasonable to give ε a negative sign in tuning systems with P5 < 700 cents (which is the opposite of what you suggest), but in my opinion we can't do it, because it is more reasonable to keep it always positive, as it always was and still is on Wikipedia. The opposite, i.e. assigning to ε the same sign as d2, is even less reasonable, although mathematically it would work all the same. And please do not forget that the current definition is mathematically correct as well!
− Paolo.dL ( talk) 19:06, 17 August 2010 (UTC)
δ
) or ε (ε
), rather than δ and ε, provided as special characters in Wikipedia standard editor? If not, I suggest you to use the special characters, because they make edits easier.
Paolo.dL (
talk)
18:08, 18 August 2010 (UTC)Totally useless for anyone not already a complete expert in music theory. First section needs an entire rewrite. —Preceding unsigned comment added by 195.112.40.182 ( talk) 09:48, 28 November 2010 (UTC)
Any actual suggestions instead of empty criticisms? Hyacinth ( talk) 11:52, 11 December 2010 (UTC)
In some articles about specific commas (this article, Comma (music), and Syntonic comma ), and in the article about semitone there are pictures showing, in staff notation, an octave + a comma (or semitone), rather than simply a comma (or semitone). On the other hand, the attached audio file typically plays a true comma (not a comma + octave). I tried to remove the picture recently added in this article. And I carefully explained the reason in my edit summary:
However, my edit was unpolitely reverted without explanation.
— Paolo.dL ( talk) 17:50, 3 December 2010 (UTC)
I do not have a software to produce the image. And my point is not exactly the same as yours. You seem to wish only consistency, but an audio file consistent with that picture would be as useless as the picture! I do not need only consistency, but mainly "semplicity and clarity", and pictures and audio files which make the concept clear rather than creating doubts. So, I suggest to delete the picture, and just use the audio file, in all the above mentioned articles. I am not going to do that alone, as I hate edit wars with unpolite people.
I was hoping that Hyacinth, the author of the pictures, would understand my point and fix them, but unfortunately he is also the editor that reverted my edit without explanation, and even ignored my polite request in his talk page.
So, I thank you for your kind support, but I am asking you and other editors to answer this question, regarding all the above-mentioned articles: while we wait for somebody (hopefully the original author) to draw new pictures showing the correct intervals (it may take long, as the author is ignoring my request), is it better to keep those pictures or delete them? — Paolo.dL ( talk) 19:24, 4 December 2010 (UTC)
In this article | In
Comma (music) and Syntonic comma |
In Semitone#Just intonation |
---|---|---|
![]() |
![]() |
![]() |
Don't mean to quibble, but is the sample correct? I only hear a unison. 23.6 cents should make an audible difference, no? The syntonic comma sample is distinct at a slightly narrower interval. — Preceding unsigned comment added by 68.47.101.16 ( talk) 01:02, 20 August 2015 (UTC)
References
Following the above discussion, we have the MIDI file as accurate as possible using the current method. As stated here, a Pythagorean comma = 23.460010 cents. At 23.461914 cents, the interval represented in the MIDI file is not accurate to six decimal places. This is an example of false precision. I have again corrected this error. Burninthruthesky ( talk) 07:39, 28 March 2017 (UTC)
In view of the ongoing edits, I have posted a request for help at the Mathematics WikiProject. Burninthruthesky ( talk) 07:58, 28 March 2017 (UTC)
Re " the file is an estimation of a Pythagorean comma". It doesn't say it's an "estimation", and in fact it isn't. Even if it were properly explained, I still don't believe a discussion of the limits of MIDI precision belongs in this article. As pointed out in the discussion above, it is below the just noticeable difference. Is there any WP:CONSENSUS for this edit? Burninthruthesky ( talk) 08:56, 28 March 2017 (UTC)