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Encyclopedia of Microtonal Music Theory

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pyknon ( πυκνον )

(Greek: "condensation", plurals: pykna, pyknomata, pyknoma)

[John Chalmers, Divisions of the Tetrachord]

Intervallically dense region of non-diatonic, i.e., chromatic or enharmonic, genera.

The width of the pyknon is less than or equal to 1/2 of the Fourth.

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[Joe Monzo]

That is, the widest possible pyknon has the irrational interval-size of 4/3(1/2) [or sqrt(4/3)] = ~1.154700538 ratio = ~249.0224996 cents.

The _pyknon_ indicates 'compression', and refers to the grouping together of small intervals at the bottom of the tetrachord.

Ancient Greek theorists held that each tetrachord in a tuning system was bounded by two fixed notes ('ηστοτησ = hestotes) a perfect-4th apart, and the other two notes inside that 4th were moveable (κινουμενου = kinoumenoi). The pyknon is the group of small intervals found between lichanos and hypate in the chromatic and enharmonic genera:

      DIATONIC           CHROMATIC                    ENHARMONIC

A mese       ----    A     mese   ----             A mese      ----

G lichanos   ----

                     Gb lichanos  ---- \
F parhypate  ----    F  parhypate ----  |pyknon  Gbb lichanos  ---- \
                                        |         Fv parhypate ----  | pyknon
E hypate     ----    E  hypate    ---- /           E hypate    ---- /

According to Aristoxenos, the higher of these two notes (either paranete or lichanos) could move within the locus of a tone -- i.e., from G down to Gbb in the diagram above, and the lower of them (either trite or parhypate) could move within the locus of a diesis -- i.e., from F down to Fv.

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