Talk:Undertone series

message: ...the undertone series is considered by many to be purely theoretical.
:I'm pretty sure Paul Hindemith makes this argument, so I'll probably have a reference when my university's music library opens tomorrow.
When describing the overtone series, it is conventional to start with C.
:This is pretty trivial, so we might want to just leave it out. The starting pitch doesn't matter.
During the experiments with temperament and tunings systems in the 1500s and onward, the discovery of the overtone series largely contributed to the rise in popularity of equal temperament and the major triad.
:This one doesn't even make sense to me. The overtone series would lead people to use just intonation, not equal temperament, right? This one definitely needs a source or it has to go.
Many people in this time used this as proof that equal temperament should be used because the physics of sound implied it with the major triad.
:Ditto for this one. How in the world is it a "proof that equal temperament should be used"? —Keenan Pepper 23:52, 2 September 2006 (UTC)
thread_title:  Missing references 

message: I came to read this article almost by accident, because a link to it has been added in Riemannian theory. It seems to me that there is a confusion, both in the article itself and in the comments above, between two related but somehow independent phenomena.
The first is the phenomenon of harmonic partials, those that arise when producing one single complex periodic tone. The very fact that this tone is called "complex" denotes that it consists in partial tones, as suggested by Fourier's theorem. Partial tones can only be equal or higher in frequency as the complex tone itself. It is a matter of a whole and its parts: no part of a whole can exceed the whole itself; or a matter of boundary conditions: nothing falling under boundary conditions can have boundaries outside those considered. Lower harmonic partials ("undertones") are impossible both from a logical and from a physical point of view. And if Riemann thought otherwise, it only is because he at first only had a confused idea of what harmonic partials were; he eventually recognized his mistake in this respect.
The second phenomenon is the production of sounds described as "subharmonics" by a variety of means, e.g. by specific techniques of violin playing beyond the ordinary limits of vibration. Such sounds always results from distortions creating abnormal sound productions. The article mentions them, but without enough stressing the distortive aspect. As it states, "there are '...only fairly restricted conditions' that will lead to the 'nonlinear phenomenon known as subharmonic generation'", the important word being "nonlinear". Differential tones, for instance (Tartini tones) result from nonlinearities. And the production of "undertones" on bowed instruments involves a high pressure of the bow forcing the string outside its normal modes of vibration. The article puzzingly indicates that the production of such sounds "has nothing to do with the undertone series", probably because by "undertone series" it still expresses a belief in the possibility of "subharmonic partials".
It has for a while been thought, I think to remember, that even harmonic partials resulted from nonlinearities: they were described as "subjective", because one believed that they arose in the nonlinearities of individual ears. If this were so, two different hearers would have heard them differently, and they might not have existed outside individual ears. It has been proved early in the 18th century, however, that harmonic partials are "objective" and that they exist even in the absence of any hearing subject.
Nonlinearities on the other hand, as needed for the production of undertones, are not "objective" in the same way. They may exist independently of human ears and of hearers, but they would still belong to specific conditions – the acoustics of a given space, for instance, within which the sound might be distorted up to giving an impression of undertones.
The article is not too bad in making this difference between overtones and undertones. It induces some doubt, however, when it says that "The overtone series can be produced physically in two ways—either by overblowing a wind instrument, or by dividing a monochord string." In this it forgets a third (or the main) way or producing the overtone series, by producing any periodic sound with a rich timbre.
I don't know whether anything can be done about this. The article also shows that a belief in the quasi natural existence of undertones is still very much among us. I trust that convincing references could be found to explain that harmonic partials are utterly different from undertones. This is so obvious to me that I am afraid I won't bother to seek these references ... — Hucbald.SaintAmand (talk) 21:35, 14 November 2019 (UTC)
thread_title:  Undertones and uppertones 

message: The subsection "Resonance" of this article includes a puzzling statement:
Helmholtz argued that sympathetic resonance is at least as active in under partials as in over partials.
Helmholtz indeed may seem to say that. He writes more precisely:
To make experiments [...] on the sympathetic vibrations of strings, [...] press down the key of the string (for c ' suppose) which you wish to put into sympathetic vibration. [...] The motion [of the c ' string] is greatest when one of the under tones of c ' is struck [...]. Some, but much less, motion also occurs when one of the upper partial tones of c' is struck [...]
But what does it mean to say that "sympathetic resonance is active in the partials"? Is that really what Helmholtz says? I don't think so. Sympathetic resonance, in all cases, occurs in the c ' string and there only. If the note struck is one of its undertones, then one of the harmonic partials of that undertone is in unison with the c ' string and causes it to vibrate by sympathy. If the note struck is one of the upper tones, then the corresponing upper harmonic partial of the c ' string is set in sympathetic vibration with it, but that effect is much less than in the first case because here only an upper partial vibrates.
By "under tone" of a note, Helmholtz means the tones of which the note considered is an upper harmonic partial, and certainly not a "lower harmonic partial" of this note (Helmholtz merely does not believe in lower harmonic partials). But that does not seem to be the meaning of the title of our article, Undertone series or, at least, the article is ambiguous on this point. The general definition in the lead, "a sequence of notes that results from inverting the intervals of the overtone series," might describe undertones as Helmholtz understands them, as resulting from a mere inversion of intervals. (What is meant by that is not entirely clear.) But the article soon raises the question whether these undertones could be subharmonics of some kind.
Our article is about undertones: Helmholtz' quotation is therefore justified, if its particular meaning is more clearly explained. What is not justified, on the other hand, is that it appears under the heading "Resonance," which has nothing to do with our article (and is not at all mentioned in the Cowell book quoted after). And this particular meaning, which implies that undertones are no subharmonics, redounds on the article as a whole, which might perhaps make this distinction clearer from the start.
I really don't know what to do. Advices would be welcome. — Hucbald.SaintAmand (talk) 12:18, 30 December 2021 (UTC)
thread_title:  Resonance? 

message: I had a closer look at what Henry Cowell has to say of this otherwise unknown Nicolas Garbusov, who would have built an instrument producing undertones. He writes this:
Professor Garbusov shows that such resonating chambers [e.g. the violin "wooden sound-chamber"], under certain circumstances, respond only to every other vibration of the original sounding body, or that some part of the resonator will respond only to every other vibration, even if part of the resonator responds normally to every vibration. The part of the resonator which responds only to every other vibration is then vibrating at one-half the speed of the fundamental and produces a tone one octave lower. Under other circumstances a part of the resonator will vibrate at one-third the speed of the fundamental, thus producing a tone one octave and a fifth below that of the original sounding body. Through an extention of this principle, a series of tones is formed downwards from the fundamental which contains the same relative intervals as the overtone series, counting downwards instead of upwards, and which produces a different actual set of tones.
It is however improper to call the body of a violin (or of other similar instruments) a "resonator" or a "resonating chamber". Such bodies, on the contrary, are built so as not to resonate because that would undily reinforce some notes of the instrument. It is difficult to imagine what Garbusov (or Cowell) refers to when speaking of "some part of the resonator" responding to only some of the vibrations. This may remind the experiment where a tuning fork hits a sheet of paper which is pushed away and comes back to touching the tuning fork only at one vibration on two: the sheet then vibrates at half the frequency of the tuning fork. But it would be utterly impossible to produce a series of undertones in this manner: the sheet cannot vibrate at several frequencies at the same time. 
Similarly, it seems utterly improbable that Garbusov's "resonator", or different parts of it, could vibrate at a series of undertones. Cowell continues in the obvious conviction that undertones are subharmonics. He writes:
just as the first four overtones form a major triad, the first four undertones form a minor triad, the necessary contrast to the major. Chords formed from the undertones are generated downwards; therefore their roots are really the top notes!
This apppears similar to what Hugo Riemann believed, in his "dualist" conception, until one shew him that he was wrong. But once again, I don't know what to do. I think more and more that the article needs a thorough revision. — Hucbald.SaintAmand (talk) 18:29, 30 December 2021 (UTC)
thread_title: Cowell and Garbusov

message: "The tritare, a guitar with 'Y' shaped strings" ...
I've been playing and teaching guitar for 40 years and I have never seen, or heard of a "Y-shaped" guitar string.  Is the cross-sectional area y-hshaped?  Is the string split into three branches that instersect at a point?  Are multiple strings tied together?
This phrase needs some explanation or perhaps an illustration.  — Preceding unsigned comment added by 74.95.43.253 (talk) 23:27, 18 March 2022 (UTC)
thread_title:  "Y-shaped strings"? 

message: The first sentence of the article appears to say that the terms "undertone" and "subharmonic" are synonyms. The section on terminology is mainly devoted to the meanings of "subharmonic", but includes odd statements, e.g.
* subharmonic does not relate to the subharmonic series
* In a very loose third sense, subharmonic is sometimes used or misused...
The article is a redirection of "Subharmonic:" it seems probable that a former article "Subharmonic" appeared misleading in that the term often was misused for "Undertone," but that parts of this article were copied here without change. The section on terminology appears to be about the meaning of "subharmonic;" it fails to explain the difference between the two terms. Further in the article, there is frequent mention of an "undertone series," probably coming from mentions of "subharmonic series." But there is no particular reason why the undertones should form a series...
Is it possible to read the discussion that led to the fusion of the two articles? — Hucbald.SaintAmand (talk) 12:32, 20 November 2022 (UTC)
thread_title:  Undertones, or subharmonics? 

message: Let x be the original frequency
subharmonic x/4, x/5, x/6 form the minor triad
now let’s multiply by the denominators’ Least Common Multiple, 60
now they are 15x, 12x, 10x
Multiplying by 60 is multiplying by 2^2 * 3 * 5
multiply by 2 is to go up P8
multiply by 3 is to go up P5 + P8
multiply by 5 is to go up M3 + 2P8
together to go up M7 + 5P8  
interlocking suharmonic and harmonic? Ziconium (talk) 15:50, 21 December 2022 (UTC)
thread_title:  A way to reconcile the two views about the minor triad