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<font face="Calibri">Ildar,<br>
<br>
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) </font><font face="Calibri">my experience </font><font
face="Calibri">with musical instruments (and with acoustics), as
in charge </font><font face="Calibri">for a long time </font><font
face="Calibri">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.<br>
<br>
I don't claim that "</font><font face="Calibri">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).<br>
<br>
A third – any third – does not refer to "</font><font
face="Calibri">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.) <br>
You write "</font><font face="Calibri">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? <br>
<br>
Of the several melodies you mentioned in a previous message,
presenting "the triad", I have been able to trace only two: the </font><font
face="Calibri">Seikilos epitaph</font> 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 "<font face="Calibri">these are examples
from 25 centuries of history and pretty much global distribution</font>"
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".<br>
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. <br>
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").<br>
<br>
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.<br>
<br>
Nicolas Meeùs<br>
<br>
<br>
<br>
<br>
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