# EdV

**EdV** means **Division of a fifth interval into n equal parts**.

Division of a fifth (e. g. 3/2 or 13/9) into n equal parts

Division of e. g. the 3:2 or the 13:9 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has mostly not even been posed yet. The utility of 3:2, 13:9 or another fifth as a base though, is apparent by being used at the base of classical triadic harmony. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.

Incidentally, one way to treat 3/2 or 13/9 as an equivalence is the use of the 8:9:10:(12) or 9:10:11:(13) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 or 11/9 to get to 9/8 or 10/9 (tempering out the comma 15625/15552 or 1779570/1771561). So, doing this yields 9, 11, and 20 note MOS for ED(3/2)s or ED(13/9)s, the 20 note MOS of the two temperaments being mirror images of each other (9L 11s for ED(3/2)s vs 11L 9s for ED(13/9)s). While the notes are rather closer together, the scheme is uncannily similar to meantone.

## Individual pages for EDVs

**Equal Divisions of the Perfect Fifth (3/2)**

- most famously Carlos Alpha, Beta and Gamma, but lots of others, too

**Equal Divisions of the Tridecimal High Tritone (13/9)**

**Equal Divisions of the Septimal High Tritone (10/7)**