Talk:Neutral third

Neutral vs three-quarter third
Would people object to me re-writing this article to consider the just neutral third to be more fundamental? The "quarter-tone" neutral third is only an approximation to this third. Other equally-tempered tuning systems, such as 31 equal temperament, 41 equal temperament, and 53 equal temperament approximate this interval with other intervals. The closeness of the fit is defined by the closeness to the just interval. The 350 cents interval has little or no significance outside of the 24 equal temperament. —Preceding unsigned comment added by Cazort (talk • contribs) 00:39, 28 December 2007 (UTC)


 * I don't think the just neutral third is necessarily more fundamental. It depends on where you're coming from. If you're working with 24-EDO and decide you like the sound of the neutral third, you can't really be said to be approximating the just interval, because the sonority you're using is the one you're hearing. &mdash; Gwalla | Talk 23:35, 16 February 2008 (UTC)
 * The difference between the quarter-tone neutral third and just neutral third (about 2.6 cents) is below the threshold for comprehension by most humans, which is about 5 cents from what I've read. For comparison it's only a tiny bit larger than the difference between a perfect fifth in just intonation and 12-EDO.  It's more of a theoretical quibble than about the actual sound of it.  Cazort (talk) 20:23, 20 February 2008 (UTC)

Request: Indian music
Does anyone know much about the occurrence of this interval in the classical music of India? This would be an important and valuable addition to this page. Cazort (talk) 16:24, 6 March 2008 (UTC)

Requested audio
I have added audio examples to the article. Hyacinth (talk) 08:46, 9 August 2008 (UTC)

Suggestion to mention 7 equal in the section on equal temperaments
The section currently says "Although there are no neutral thirds in any of the commonly used equally tempered tuning systems with less than 24 divisions of the octave...".

Actually, two steps of seven equal take you to 342.8571 cents which is within 5 cents of 347.4079 for 11/9. And seven equal could be considered an ET in reasonably common use, at least in the form of "near seven equal", as it is a tuning used for Thai music as well as the Ugandan Chopi tradition of music. Equal_temperament.

Posting this as a suggestion first. If there is no objection, I'll go ahead and add it in a few days time. Robert Walker (talk) 20:24, 30 January 2015 (UTC)


 * I've now added this, also added cents values and numbers of steps for the other equal temperaments mentioned. I've also added refs to the xenharmonic wiki. Though Wikipedia guidelines discourage citations of other wikiss - this is most important for wikis that can be anonymously edited. The Xenharmonic wiki is a closed wiki maintained by microtonalist specialists including composers and professional mathematicians, some of whom have published papers on relevant topics.


 * So - though a peer reviewed publication would certainly be a better source according to wikipedia guidelines, if one can be found, it should do for the time being at least for simple calculations like that which hardly count as WP:OR. It is a good course for this as it has all the ETs listed systematically. I don't know of another source that does this easily available. The numbers themselves can be checked easily also by simple mathematical calculations.


 * I thought at any rate, this seems better than no citation source, at least until anyone else comes up with another preferred citation source. Robert Walker (talk) 22:37, 17 March 2015 (UTC)

Fundamentals of ratios?
The article contains the following paragraph that I find puzzling:
 * Neutral thirds expressed in the form of a ratio of two whole numbers can also be considered as the interval between the harmonics of the same order. For instance, an undecimal neutral third, with a ratio of 11:9, is the interval between harmonics 11 and 9. The fundamental is then four octaves and a tone (9:1) below the lower of the two tones, or four octaves and a narrow fourth (11:1) below the higher of the two tones – or, if octaves are neglected, a tone (9:8) below the lower note and a narrow fourth (11:8) below the higher one.

Not only don't I see why it may be important to know that the interval expressed as a ratio of two whole numbers also is the interval between harmonics of the same order, with a fundamental equal to 1 (this is true, but what's the point?), I also fail to see why is it important to know how distant the fundamental of these two harmonics is, or what it becomes if octaves are neglected. The example given is the ratio 11:9. If octaves are neglected, the fundamental becomes 8 and the distances are 9:8 for the lower note, 11:8 for the higher one. So what?

Considering that all intervals (and not neutral thirds exclusively) expressed in ratios of whole numbers can also be seen as intervals between harmonics of the same order, I cannot figure out why it is important to say this here. This seems to belong to the definition of the harmonic series as a series of whole numbers. I see that created this paragraph myself in December 2017, trying to clarify another one that said that the fundamental of the undecimal neutral third [11:9] "implied a root a tone lower than the lower of the two tones" – which not only was obscure, but also was wrong (it is true only if one neglects octaves). The initial purpose may have been to explain that a neutral third is made of a tone plus a neutral second, but here again, I don't see the point.

I'd suggest to remove this paragraph entirely, unless some reader has another opinion. – Hucbald.SaintAmand (talk) 17:36, 2 June 2019 (UTC)


 * I remove this paragraph now (after all, I had written it myself, in this form at least). If anyone has objections, just say so. — Hucbald.SaintAmand (talk) 18:23, 4 June 2019 (UTC)