31edo: Difference between revisions

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See [[#Rank-2 temperaments]] for a table of MOSes and their temperament interpretations.

=== Harmonic ~~Scale~~ ===

=== Harmonic scales ===

31edo approximates Mode 8 of the [[harmonic series]] okay, but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated okay, but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the [[13-limit]].

The steps are: 5 5 4 4 4 3 3 3

{| class="wikitable"

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* [[Strictly proper]] [[Strictly proper 7-note 31edo scales|7-note 31edo scales]].

* Interesting (to somebody) [[9-note 31edo scales]].

* the [[Euler-Fokker genus]] (technically [[JI]] but representable in 31)

~~Some of the popular ones:~~

* 31-tone major: 5 5 3 5 5 5 3

* Meantone[12] (Eb-G#): 2 3 3 2 3 2 3 2 3 3 2 3

* Harmonic scale 8: 5 5 4 4 4 3 3 3

* the [[Euler-Fokker ~~genera~~]] (technically [[JI]] but representable in 31)

== Regular temperament properties ==

@@ Line 707: / Line 707: @@
 See [[#Rank-2 temperaments]] for a table of MOSes and their temperament interpretations.
-=== Harmonic Scale ===
+=== Harmonic scales ===
 edo approximates Mode 8 of the [[harmonic series]] okay, but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated okay, but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the [[13-limit]].
+The steps are: 5 5 4 4 4 3 3 3
 {| class="wikitable"
@@ Line 834: / Line 836: @@
 * [[Strictly proper]] [[Strictly proper 7-note 31edo scales|7-note 31edo scales]].
 * Interesting (to somebody) [[9-note 31edo scales]].
+* the [[Euler-Fokker genus]] (technically [[JI]] but representable in 31)
-Some of the popular ones:
-* 31-tone major: 5 5 3 5 5 5 3
-* Meantone[12] (Eb-G#): 2 3 3 2 3 2 3 2 3 3 2 3
-* Harmonic scale 8: 5 5 4 4 4 3 3 3
-* the [[Euler-Fokker genera]] (technically [[JI]] but representable in 31)
 == Regular temperament properties ==