Harmonisma: Difference between revisions

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== Temperaments ==

Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 × 14/11 (→[[182/121]]) on the lower end and 11/9 × 16/13 (→[[176/117]]) on the higher end, and this interval is not mapped to 3/2. However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[~~Subgroup_temperaments#Parapyth_~~.~~28Rank_3.29~~|~~parapyth~~]].

Tempering out this comma in the full 13-limit gives the rank-5 '''harmonismic temperament'''. Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 × 14/11 (→[[182/121]]) on the lower end and 11/9 × 16/13 (→[[176/117]]) on the higher end, and this interval is not mapped to 3/2. However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[parapyth]].

== Etymology ==

The harmonisma was named by [[Margo Schulter]] in 2002 in honor of the [[harmonia|harmoniai]] of [[Kathleen Schlesinger]].

[[Category:Harmonismic]]

@@ Line 7: / Line 7: @@
 == Temperaments ==
-Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 × 14/11 (→[[182/121]]) on the lower end and 11/9 × 16/13 (→[[176/117]]) on the higher end, and this interval is not mapped to 3/2. However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[Subgroup_temperaments#Parapyth_.28Rank_3.29|parapyth]].
+Tempering out this comma in the full 13-limit gives the rank-5 '''harmonismic temperament'''. Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 × 14/11 (→[[182/121]]) on the lower end and 11/9 × 16/13 (→[[176/117]]) on the higher end, and this interval is not mapped to 3/2. However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[parapyth]].
+== Etymology ==
+The harmonisma was named by [[Margo Schulter]] in 2002 in honor of the [[harmonia|harmoniai]] of [[Kathleen Schlesinger]].
 [[Category:Harmonismic]]