The tritriadic scale with Major Triads (1/1 5/4 3/2) on the Tonic, Subdominant and Dominant degrees, 1/1, 4/3 and 3/2 [respectively].
The scale 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 in JI or 0 2 4 5 7 9 11 12/0 in 12-tone ET or its close approximation in other equal temperaments.
The scale 1/1 9/8 81/64 4/3 3/2 27/16 243/128 2/1 in Pythagorean tuning.
The Lydian Octave Species or Mode lying between C and its octave in the P.I.S. when the component tetrachords are Ptolemy's Intense Diatonic.
[from John Chalmers, Divisions of the Tetrachord]
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The JI version given above may be illustrated on a lattice diagram as follows:
The unison-vectors which define this scale as a periodicity-block are the syntonic comma 81:80 = [-4 4 -1] (which is acting here as the commatic unison-vector) and the ratio 25:24 = [-3 -1 2] (which is acting here as the chromatic unison-vector).
These unison-vectors are drawn here as the solid lines forming a parallelogram, which encloses the points which represent the ratios of the scale.
See also: Paul Erlich's A Gentle Introduction to Fokker Periodicity Blocks,
part 2.
[from Joe Monzo, JustMusic: A New Harmony]
updated: 2002.2.15
