User:VectorGraphics/Vector's introduction to 15edo/Intervals: Difference between revisions

!Cents

!Approximate Ratios

|-

|Unison

|0

|1/1

|-

|Semitone

|80

|'''25/24,''' 16/15

|-

|Minor tone

|160

|'''10/9'''

|-

|Major tone, wolf third

|240

|'''8/7''', 9/8

|-

|Minor third

|320

|'''6/5'''

|-

|Major third

|400

|'''5/4'''

|-

|Perfect fourth

|480

|'''4/3''', 21/16

|-

|Small tritone, diminished fifth, wolf fourth

|560

|'''11/8''', 7/5

|-

|Large tritone, augmented fourth, wolf fifth

|640

|'''16/11''', 10/7

|-

|Perfect fifth

|720

|'''3/2''', 32/21

|-

|Minor sixth

|800

|'''8/5'''

|-

|Major sixth

|880

|'''5/3'''

|-

|12

|960

|'''7/4''', 16/9

|-

|13

|1040

|'''9/5'''

|-

|Major seventh

|1120

|'''48/25,''' 15/8

|-

|Octave

|1200

|2/1

|}

Let's take a look at the zarlino diatonic scale (more elaboration on the structure of this scale in the page linked at the top). Zarlino is an MV3 scale, meaning that there are at most 3 sizes of any given interval.

* the ptolemaic semitone, or syntonic comma, found by stepping up 4 and left 1 on the table. This separates standard intervals from "wolf" intervals.

* the compound semitone, or diaschisma, found by stepping up 4 and right 2 on the table. This separates fifth-generated "diatonic" intervals and their augmented or diminished zarlino counterparts. Note that this "compound semitone" is actually the ''complement'' of the just diaschisma, since the diaschisma proper is a negative interval in 15edo.