Ed4/3

EdIV means Division of a fourth interval into n equal parts.

Division of a fourth (e. g. 4/3 or 15/11) into n equal parts

Division of e. g. the 4:3 or the 15:11 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence has not even been posed yet. The utility of 4:3, 15:11 or another fourth as a base though, is apparent by being used at the base of so much Neo-Medieval 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 4/3, 15/11, or 7/5 as an equivalence is the use of the 12:13:14:(16), 11:12:13:(15), or 10:11:12:(14) 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 eight 7/6, 13/11, or 6/5 to get to 13/12 or 12/11 (tempering out the comma 5764801/5750784, 815730721/808582500, or 42875/42768). So, doing this yields 13, 15, and 28 note MOS for ED(4/3)s; 11, 13, and 24 note MOS for ED(15/11)s or ED(7/5)s, the 24 note MOS of the two temperaments being mirror images of each other (13L 11s for ED(15/11)s vs 11L 13s for ED(7/5)s). While the notes are rather closer together, the scheme is uncannily similar to meantone.

Individual pages for EDIVs

Equal Divisions of the Perfect Fouth (4/3)

• 3 - Cube Root of P4
• 5 - Quintilipyth scale
• 6 - Sextilipyth scale
• 9 - Noleta scale

Equal Divisions of the Septimal Narrow Tritone (7/5)

• 4 - Fourth root of 7/5
• 5 - Fifth root of 7/5
• 7 - Seventh root of 7/5
• 11 - Eleventh root of 7/5
• 13 - Thirteenth root of 7/5
• 24 - 24th root of 7/5

Equal Divisions of the Undecimal Semiaugmented Fourth (15/11)

• 13 - Thirteenth root of 15/11

Equal Divisions of the Tridecimal Ultramajor Third (13/10)

• 2 - Square root of 13 over 10