[Smt-talk] Fwd: Re: a la mode

[Nicolas Meeùs]

Le 2013-12-02 18:24, Ildar Khannanov a écrit :

    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...

Ildar,

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 /systema teleion/, 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.

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.

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.

Tonality is a phenomenon of utterly different nature.

Nicolas Meeùs
University Paris-Sorbonne




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