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Le 2013-12-02 18:24, Ildar Khannanov a écrit :
<blockquote>
<div style="color:#000; background-color:#fff;
font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial,
Lucida Grande, sans-serif;font-size:12pt"><span>Tetrachord,
pentachord, heptachord--do not imply dia--. Tetrachord--four
strings, nothing else. Trichord--three strings. Where is the
dia--? And what does this dia- in this case mean? An easy
question? Hmmm...</span></div>
</blockquote>
Ildar,<br>
<br>
The Greek name of the perfect four (tetrachord) is "diatessaron",
i.e. "through four degrees"; and the perfect fifth is "diapente",
"through five degrees". The Greek (as many other early theorists)
were particularly interested in describing the fourth (the
tetrachord) because it has the capacity of describing the whole
scale – the "system", the <i>systema teleion</i>, as they named
it. Indeed, the system can be described as a concatenation of
alternatively conjunct and disjunct tetrachords, much as we
describe it as a concatenation of disjunct octaves.<br>
<br>
Any scale formed of diatonic tetrachords is diatonic; but the
tetrachord itself may be STT, or TST, or TTS, and tetrachords may
be either disjunct or conjunct. This gives a choice of six
diatonic octave scales. Fa–Sol–La–Ti (TTT) is not a valid
tetrachord; as a result neither Fa–Sol–La–Ti | Do–Re–Mi–Fa nor
Do–Re–Mi–Fa | Fa–Sol–La–Ti (that you mentioned) are diatonic
properly speaking, in Greek terms at least.<br>
<br>
It is counterproductive to believe that "diatonic" may have kept
the same sense from Greek Antiquity to our days. Another
definition, proposed by François-Auguste Gevaert among others, is
based on the cycle of fifths: any scale the degrees of which can
be joined by a cycle of at most 6 perfect fifths (i.e. at most 7
degrees) is diatonic; any scale that needs between 7 and 11 fifths
is chromatic; and any scale of more than 11 fifths is enharmonic.
This definition is not concerned with the number of degrees in the
scale, but only with the number of steps in the cycle of fifths
necessary to produce it: the anhemitonic pentatonic scale is
"diatonic" (less than 6 steps), the harmonic major and minor are
"chromatic" (more than 6 steps, but less than 11), etc. This
definition may seem questionable, but it is explicit and
unambiguous.<br>
<br>
Tonality is a phenomenon of utterly different nature.<br>
<br>
Nicolas Meeùs<br>
University Paris-Sorbonne<br>
<br>
<br>
<br>
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