User:Lhearne/15edo: Difference between revisions

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=Scales=

Some scales commonly used in 15edo, written in a common mode, in steps of 15edo:

=== MOS Scales ===

Augmented[6]: 414141

Porcupine[7]: 3222222

Hanson/Keemun/Orgone[7]: 1313133

Porcupine[8]: 21222222

Augmented[9]: 311311311

Blackwood[10]: 2121212121 (Blackwood Decatonic)

=== Other Scales ===

Zarlino/Ptolemy JI Major: 3213231

=Notation=

Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243|Pythagorean limma]] is tempered out. This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches. This also has the effect of making the [[2187/2048|Pythagorean apotome]] equal to the [[9/8|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents. There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis.

@@ Line 353: / Line 353: @@
 | |[[Blackwood]]/[[blacksmith]]
 |}
+=Scales=
+Some scales commonly used in 15edo, written in a common mode, in steps of 15edo:
+=== MOS Scales ===
+Augmented[6]: 414141
+Porcupine[7]: 3222222
+Hanson/Keemun/Orgone[7]: 1313133
+Porcupine[8]: 21222222
+Augmented[9]: 311311311
+Blackwood[10]: 2121212121 (Blackwood Decatonic)
+=== Other Scales ===
+Zarlino/Ptolemy JI Major: 3213231
 =Notation=
 Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243|Pythagorean limma]] is tempered out.  This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches.  This also has the effect of making the [[2187/2048|Pythagorean apotome]] equal to the [[9/8|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents.  There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis.