79edo: Difference between revisions

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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 [[Decaononic|way of playing]] where a tone is considered to be [[10/9]] instead of [[9/8]]. In [[12edo]] and meantones close to it used predominantly in Western music, when the difference between 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. 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. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.

=== Decaononic whole tone ===

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

In [[12edo]] and meantones close to it (used predominantly in Western music), when the difference between 10/9 and 9/8 is tempered out, what really happens is that only the 9/8 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.

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. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.

== Interval table ==

== Regular temperament properties ==

79edo supports the [[bluebirds]] temperament. It also supports [[oceanfront]].

== Scales ==

* Bluebirds[7] - also [[glacial]]

=== Bluebirds ===

* [[Bluebirds]][7] - also [[glacial]]

* Bluebirds[46]

* Minor Hexatonic

=== Meantone ===

* [[Meantone]] Minor Hexatonic

** 197.802

** 303.297

Line 21:

Line 33:

** 1002.198

** 1200.000

=== Oceanfront ===

* [[Oceanfront]][7]

* Oceanfront[12]

* * 197.468

* * 227.848

* * 258.228

* * 455.696

* * 486.076

* * 683.544

* * 713.924

* * 744.304

* * 941.772

* * 972.152

* * 1169.620

* * 1200.000

* Oceanfront[17]

* Oceanfront[22]

* Oceanfront[27, 32, 37, 42]

== Music ==

@@ Line 6: / Line 6: @@
 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 [[Decaononic|way of playing]] where a tone is considered to be [[10/9]] instead of [[9/8]]. In [[12edo]] and meantones close to it used predominantly in Western music, when the difference between 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. 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. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.
+=== Decaononic whole tone ===
+edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].
+In [[12edo]] and meantones close to it (used predominantly in Western music), when the difference between 10/9 and 9/8 is tempered out, what really happens is that only the 9/8 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.
+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. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.
 == Interval table ==
 {{Interval table}}
+== Regular temperament properties ==
+edo supports the [[bluebirds]] temperament. It also supports [[oceanfront]].
+{{todo|expand}}
 == Scales ==
-* Bluebirds[7] - also [[glacial]]
+=== Bluebirds ===
+* [[Bluebirds]][7] - also [[glacial]]
 * Bluebirds[46]
-* Minor Hexatonic
+=== Meantone ===
+* [[Meantone]] Minor Hexatonic
 ** 197.802
 ** 303.297
@@ Line 21: / Line 33: @@
 ** 1002.198
 ** 1200.000
+=== Oceanfront ===
+* [[Oceanfront]][7]
+* Oceanfront[12]
+* * 197.468
+* * 227.848
+* * 258.228
+* * 455.696
+* * 486.076
+* * 683.544
+* * 713.924
+* * 744.304
+* * 941.772
+* * 972.152
+* * 1169.620
+* * 1200.000
+* Oceanfront[17]
+* Oceanfront[22]
+* Oceanfront[27, 32, 37, 42]
 == Music ==