[Smt-talk] Harmonics

[Nicolas Meeùs]

Ildar,

My comments so far have nothing "Schenkerian"; on the contrary, I 
avoided mentioning Schenker, because his case is not so clear in this 
respect (especially in American translations, let me add nevertheless) – 
let's leave that for another occasion. And my comments indeed have 
nothing new: they merely reproduce common knowledge in acoustics (i.e., 
among acousticians). My comments stem from (a) my experience with 
musical instruments (and with acoustics), as in charge for a long time 
of one of the major museums in this domain, the Brussels Museum of 
Instruments; (b) my commitment with at least half a dozen PhD's on 
Oriental music (and about as many of the functioning of tonality) that I 
directed in the Sorbonne.

I don't claim that "not all partials are exactly harmonic", I claim that 
many partials are not harmonic at all – and that the very notion of 
"partial" becomes problematic in such cases. The perception of the tone 
A (as about 440Hz, or 415 Hz, or whatever you like) is not a "zone", it 
is a convention, based much more on the meaning of "A" within a 
(Western) notational system than on specific frequencies. I am perfectly 
aware that the perception of pitches and intervals is a matter of 
"zones". I am not the one, I think, to have claimed here that it is a 
perception of numerical ratios of whole numbers (Pythagorean or others).

A third – any third – does not refer to "the third contained in the 
natural overtone series". Consonant thirds do refer to the fusion of 
overtones in their respective overtone series (which, by the way, 
provides a much better justification of the minor third than overtones 5 
and 6 of the 'fundamental' series); but violinists know that they don't 
always want to play that type of thirds, that they often want to play 
wider melodic thirds, etc. etc. (Note that the harmonic series, how far 
you continue it, NEVER contains an overtone in the ratio 6:5, nor in the 
ratio 4:3, above any octave of its fundamental. You may say that this is 
because the whole affair is but a matter of "zones"... I am more 
interested to know that two notes in the ratio of 6:5 or 4:3 have 
harmonic overtone series that fusion to a large extent, that two 
overtone series of notes in the ratio of 4:3, for example, fusion better 
than those of notes in the ratio of 5:4, etc.)
     You write "The thirds that we take vary and deviate from the ideal 
pitch of the fourth harmonic" (probably meaning "the fifth harmonic"). 
This reminds me of Maurice Emmanuel, much convinced of the "truth" of 
the overtone series, expressing in "Histoire de la langue musicale" his 
astonishment at seeing "primitive" people sing minor thirds instead of 
the major ones dictated by nature! Is it so difficult to imagine that, 
perhaps, his notion of what is dictated by nature, or your idea of "the 
ideal pitch of the [fifth] harmonic", merely may not be the right ones, 
that perhaps "primitive" people may have been determined by other 
considerations?

Of the several melodies you mentioned in a previous message, presenting 
"the triad", I have been able to trace only two: the Seikilos epitaph 
and Victimae paschali laudes. I am rather doubtful that we could know a 
13th century Arabic melody (in what type of notation?), but I won't 
argue as this famous melody is unknown to me. I cannot say anything of 
the Morning Raga that you recently heard, nor about the Bashkirian song 
that you mention. Your claim that "these are examples from 25 centuries 
of history and pretty much global distribution" seem to me somewhat far 
fetched: without arguing about the date of the Seikilos epitaph, I think 
that a distribution between Europe and India is far from "global".
     Anyway, neither of the two melodies that I am aware of, the 
Seikilos one or Victimae paschali laudes, present a triad properly 
speaking. They do present notes a fifth and a third apart (a major third 
in the first case, a minor one in the second). Whether and how these 
notes were sung "in tune" (in just intonation?) we shall never know – 
you'll say that it is but a matter of "zone", and I'll agree. Whether 
they were sung as triads, let me very much doubt – unless we don't agree 
on what "triad" really means: to me, a triad is a chord, understood as a 
chord, that is, as one block of the construction game that is music.
     Victimae paschali laude is one case that Maurice Emmanuel would 
have dismissed as resulting from these "primitives" not understanding 
that nature told them to sing in major. It is a typical example of the 
medieval (because the song probably dates from the 11th century) 
implicit consciousness of the pentatonic substrate of Gregorian chant. 
As so many pentatonic melodies, it stresses the trihemitonic interval 
(the "minor third") but contains rather few major thirds (the "ditone").

There's a lot more to say, among others about the idea that tonal 
harmony should boil down to triads. As far as I know, triadic music 
could be (and has been) written that hardly could be considered tonal. 
But that is another discussion.

Nicolas Meeùs




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