79edo: Difference between revisions

Line 2:

==Theory==

== Theory ==

79edo works well as a no-5 17-limit tuning, or as a dual-5 17-limit tuning.

As an equal temperament, it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.

79edo's fifth is slightly flat and very similar to the one of [[12edo]] – the major third is too sharp to be the closest approximation of [[5/4]] so 79edo actually does not qualify as [[meantone]] in the patent val.

=== Odd harmonics ===

~~79edo works well as a no-fives 17-limit tuning, or as a dual-5 17-limit tuning.~~

It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for [[Orwellismic_temperaments#Sentinel-11-limit|sentinel temperament]].

79 is the 22nd prime ~~EDO number~~.

=== Subsets and supersets ===

79edo is the 22nd prime edo, past [[73edo]] and before [[83edo]].

79edo's fifth is slightly flat and very similar to the one of [[12edo]]–the major third is too sharp to be the closest approximation of [[5/4]] so 79edo actually does not qualify as [[meantone]] in the patent val.

=== Miscellany ===

=== ~~Decaononic whole tone~~ ===

79edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].

@@ Line 2: / Line 2: @@
 {{EDO intro|79}}
-==Theory==
+== Theory ==
+edo works well as a no-5 17-limit tuning, or as a dual-5 17-limit tuning.
+As an equal temperament, it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.
+edo's fifth is slightly flat and very similar to the one of [[12edo]] – the major third is too sharp to be the closest approximation of [[5/4]] so 79edo actually does not qualify as [[meantone]] in the patent val.
+=== Odd harmonics ===
 {{Harmonics in equal|79}}
-edo works well as a no-fives 17-limit tuning, or as a dual-5 17-limit tuning.
-It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for [[Orwellismic_temperaments#Sentinel-11-limit|sentinel temperament]].
-is the 22nd prime EDO number.
+=== Subsets and supersets ===
+edo is the 22nd prime edo, past [[73edo]] and before [[83edo]].
-edo's fifth is slightly flat and very similar to the one of [[12edo]]–the major third is too sharp to be the closest approximation of [[5/4]] so 79edo actually does not qualify as [[meantone]] in the patent val.
+=== Miscellany ===
-=== Decaononic whole tone ===
 edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].