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15 equal temperament

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15 equal temperament

In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is a tempered scale derived by dividing the octave into 15 equal steps (equal frequency ratios). Each step represents a frequency ratio of 152 (=2(1/15)), or 80 cents (Play). Because 15 factors into 3 times 5, it can be seen as being made up of three scales of 5 equal divisions of the octave, each of which resembles the Slendro scale in Indonesian gamelan. 15 equal temperament is not a meantone system, rather being a superpyth system (tempering out 64:63, the septimal comma).

Guitars have been constructed for 15-ET tuning. The American musician Wendy Carlos used 15-ET as one of two scales in the track Afterlife from the album Tales of Heaven and Hell. Easley Blackwood, Jr. has written and recorded a suite for 15-ET guitar. Blackwood believes that 15 equal temperament, "is likely to bring about a considerable enrichment of both classical and popular repertoire in a variety of styles".

Easley Blackwood, Jr.'s notation of 15-EDO creates this chromatic scale:

B/C, C/D, D, D, E, E, E/F, F/G, G, G, A, A, A, B, B, B/C

Ups and Downs Notation uses up and down arrows, written as a caret and a lower-case "v", usually in a sans-serif font. One arrow equals one edostep. In note names, the arrows come first, to facilitate chord naming. This yields this chromatic scale:

B/C, ^C/^D, vC/vD,

D, ^D/^E, vD/vE,

E/F, ^F/^G, vF/vG,

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musical tuning system with 15 pitches equally-spaced on a logarithmic scale
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