79edo: Difference between revisions

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'''79edo''' divides the octave into 79 equal parts of 15.190 cents each. 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.

'''79edo''' divides the octave into 79 equal parts of 15.190 cents each.

=Music=

==Theory==

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.

79edo adequately represents the temperament where a tone is considered to be [[10/9]] instead of [[9/8]]. In most temperaments, when the difference betweein 10/9 and 9/8 is tempered out, what really happens is that the 9/8 only note is used, and 10/9 is raised to be equal to 9/8. 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. Proposed name: decaononic, from "10 over 9".

A maximum evenness variant of such scale can be generated by naively stacking 6 [[12edo]] diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. Proposed name: Auramagnesic, from 79 (gold) and 12 (magnesium).

==Scales==

Decaononic[7] - also [[glacial]]

Auramagnesic[46]

==Music==

[https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni Saint Sebastian, By the Hands of Reni] by Silence and Secrecy (Julian Malerman)

@@ Line 1: / Line 1: @@
-'''79edo''' divides the octave into 79 equal parts of 15.190 cents each. 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.
+'''79edo''' divides the octave into 79 equal parts of 15.190 cents each.
-=Music=
+==Theory==
+{{primes in edo|79}}
+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.
+edo adequately represents the temperament where a tone is considered to be [[10/9]] instead of [[9/8]]. In most temperaments, when the difference betweein 10/9 and 9/8 is tempered out, what really happens is that the 9/8 only note is used, and 10/9 is raised to be equal to 9/8. 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. Proposed name: decaononic, from "10 over 9".
+A maximum evenness variant of such scale can be generated by naively stacking 6 [[12edo]] diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. Proposed name: Auramagnesic, from 79 (gold) and 12 (magnesium).
+==Scales==
+Decaononic[7] - also [[glacial]]
+Auramagnesic[46]
+==Music==
 [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni Saint Sebastian, By the Hands of Reni] by Silence and Secrecy (Julian Malerman)