Talk:Syntonic comma

Didymus?
I don't know which of the people on Didymus this comma is referring to - it was named after the first person to suggest using 5:4 for tuning a major third, but I don't know who that would have been. Anybody know? --Camembert


 * (Lest anybody thinks I must be thicker than thick for not guessing it was Didymus the Musician, he wasn't on the Didymus page at the time I wrote the article. --Camembert)

Confusing
I think this page is hard to read, and I know quite a lot about music theory. How could we make this more accessible? I think the comment that the syntonic comma is the difference between the major and minor whole tones (9:8 and 10:9) is more fundamental and should go closer to the top; it's also something people can understand more readily even if they don't understand what a "limit" or "comma" is (and we can wikify the page so that they can click through if they don't understand this). Cazort (talk) 17:42, 26 January 2008 (UTC)

Requested audio
I added an audio example to the article. Hyacinth (talk) 01:39, 7 August 2008 (UTC)


 * I think it would be easier to understand if the two notes were played separately first, one after the other, before playing both at the same time. —David Eppstein (talk) 02:54, 7 August 2008 (UTC)


 * It might also help to use a plainer sound than a piano, although it is nice to have an audio example at all, so thanks! I did one for the Diesis page, trying to make clear how an octave is slightly wider than three just-tuned major thirds in a row. I thought the audio example worked pretty well and considered trying to make more for other commas. But none are so simple as the Diesis. It might not be possible, but it would be impressive if one could demonstrate through audio how four just-tuned perfect fifths in a row does not end up at the same pitch as two octaves and a just major third in a row. More than I can attempt, but still something I hope might be possible. Pfly (talk) 07:06, 7 August 2008 (UTC)

Is there a Typo in referencing A to D as a "Sixth"?
Because this is my first contribution, I want to be sure that I have not misunderstood the original article.

In the frame on the right I see musical notation of an A and a D referenced as a "Sixth". In standard musical notation, that interval would be called a FIFTH.

I invite the original author to reply to this post.

Thanks, Marcelde Marcelde (talk) 17:23, 25 July 2011 (UTC)


 * I'm not the original author, but it's an old request, and I just saw it, so I fixed it. I modified the illustration text to, "The perfect fifth above D (A+) is a syntonic comma higher than the (A♮) that is a just major sixth above C, assuming C and D are 9/8 apart." It's a complex explanation, but that's the shortest way to say it accurately, given the illustration, which is not actually a simple example. If anyone knows how to fold this topic up, please do, since it's resolved. 38.86.48.38 (talk) 04:14, 13 May 2015 (UTC)

OR: Comma pump
Neologism. Hyacinth (talk) 10:27, 19 September 2012 (UTC)


 * Hyacinth, you wrote that the section "Comma pump" may contain original research. Did you mean that the term comma pump is a neologism? Or did you refer to what I wrote at the end of the section?
 * What I wrote is just another way to describe the comma pump. Everything is based on well known notions such as
 * "descending P4" = P5 - P8
 * which is based on the well known method of "multiplication of ratios" to compute the ratio of an interval formed by two or more stacked intervals. An equation based on well known arithmetics, such as 6-2 = 2+2 = 4 (two equivalent ways to describe 4).
 * Our articles are not a collage of literature. They are sometimes better than articles on other Encyclopedias, and sometimes clearer than the literature they are based upon. What we do when we
 * explain or
 * translate or
 * organize
 * concepts, using our own words to make them understandable to everybody, is not original research. It is just a convenient rearrangement of what is already known, aimed to enhance readability and guide the reader toward a deeper and more complete understanding.
 * Paolo.dL (talk) 12:46, 21 September 2012 (UTC)


 * The idea of a "comma pump" is not original research. It's centuries old. However, this sentence bothers me in the explanation, "The syntonic comma arises in "comma pump" (comma drift) sequences such as C G D A E C, when each interval from one note to the next is played with just intonation tuning." It bothers me because of the end, "played with just intonation tuning." It implies that there is only one way to engineer that progression of note names in just intonation, and that "just intonation" is somehow the villain or cause of the comma pump. It is not. Just Intonation is perfectly capable of producing intervals that don't pump. The comma pump only happens when you intentionally (and incorrectly) use a 5/4 to complete the cycle in that example. It's either an ignorant misunderstanding of how just harmony actually works or, worse, a specious argument intending to make just intonation look bad (which I think at some points in history was the intention) by intimating that the comma pump is an inevitable byproduct and flaw of all just intonation. The truth is simple and logical; using a 5/4 at that point takes you to a completely different key. If your intention is to modulate keys that way, and there are pieces that do, then fine, but if your intention is to return home, that's the wrong bus! Considering those pitches as the roots of a chord progression, by going C G D A E, you've already gone out on the spiral (not circle) of fifths to what is effectively (in roman-numeral harmonic analysis) the V of V of V of V (of I), assuming C as tonic. That's four extensions of the prime 3 in the numerator of your ratios (which gives you the odentity 81 in Partch's terms). You can't then expect to use a prime 5 to cancel all those prime 3. The only way to come back home in just harmony (in real harmony) is to undo the same number of fifths, to move back by the same extent of the prime 3, this time in the denominator. In other words, the interval you actually want has to be some power of two over 81, such as 64/81, which is the so called Pythagorean Major Third (descending), and which is kind of ugly (or "strong" or "rich" or "dissonant" if you prefer), but for good reason. I mean, after all, you can't expect to jump all the way home from such a grand harmonic distance in one go without using a rather-rich-sounding interval. A better (more musical) way to come home would be to step back through the same roots again but descending by fifths this time to A, D, G, and finally C. In real harmony, you have to "unwind" everything to get home, because no power of any prime will ever equal any power of another prime. You can only do those artificial harmonic circles and loops in tuning systems that intentionally add errors to make stuff line up when it shouldn't. 38.86.48.38 (talk) 03:40, 13 May 2015 (UTC)
 * Slightly modified the Comma Pump section to explain that it happens with a 4/5 third in the sequence but not with a 64/81 third. 108.60.216.202 (talk) 19:37, 18 May 2015 (UTC)
 * The definitive sequence “C G D A E C” is spelled incorrectly and should end with a B#. The concept of enharmonic equivalence needs to be noted somewhere in this section or the general preamble to the article. Unless somebody else beats me to it, I’ll be tending to that as soon as I’ve read through the related articles. Also, comma drift — labeled as such — is a fundamental consideration in the discussion of just tuning. It is in common use in that sense (with better ways of deriving and illustrating it than via the C—B# sequence) and it would provide a more recognizable heading for the present section than does comma pump. Absent objection here, I’ll also be making that change. Unless a citable source for the latter term is provided in the interim, I’ll probably remove it from the article entirely. —Futhark|Talk 07:57, 1 June 2021 (UTC)

The section on the Syntonic comma in the history of music hardly makes sense
I must come back once again on an idea that I have been trying to make clear in various WP pages, mainly about "tempering out the comma", which makes no sense. The section gives no reference at all and the idea that Pythagorean tuning "prevented musicians from using triads and chords, forcing them for centuries to write music with relatively simple texture" is wishful thinking. The section further says that in 1/4-tone meantone tuning "the number of major thirds was maximized, and most minor thirds were tuned to a ratio which was very close to the just 6:5", which shows that "tempering out" the syntonic comma for the major third does not fully "temper it out" for the minor third.

I utterly fail to see how it is possible to construct the expression "temper out" in English – it merely does not exist. I also fail to understand what it means to "temper out" a comma. The single interval that is ever tempered, in any tempered tuning system, is the fifth. And a "tempered fifth" is so named because, even although tempered, it remains a fifth. I cannot imagine a fifth being "tempered out" (or what that would mean).

Tempering the fifths by 1/4 of a syntonic comma produces pure major thirds. Tempering them by 1/3 of a syntonic comma produces pure minor thirds. 1/4 and 1/3 comma meantones make some of the commas vanish, but not all of them. And making them vanish is not at all the same thing as "tempering them out". Nobody, that I know, ever tempered a comma.

At the same time, I fail to see how the top part of the figure below illustrates the syntonic comma, as the caption says. Translating the ratios in cents would give 1200 (for 2:1) 702 (for 3:2) and 386 (for 5:4). Comparing these values to the ones at the bottom, 1200, 700 and 400, does not obviously produce a syntonic comma. I wonder how many viewers noticed that the upper line (in red and blue) is slightly shorter than the second one (in black), and of those who did, how many realized that the difference is the syntonic comma. It would be simpler, and more in line with the text of the section, to show a Pythagorean major third, a just one, and a tempered one in 12TET.

— Hucbald.SaintAmand (talk) 09:38, 29 January 2020 (UTC)