79edo: Difference between revisions

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== Theory ==

79edo works well as a no-7 13- or 17-limit tuning. It is in fact [[consistent]] in the no-7 [[15-odd-limit]].

79edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]].

Using the [[patent val]], 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.

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=== Miscellany ===

79edo adequately represents the [[Decaononic]] way of playing, as 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A [[maximal evenness]] variant of such a scale can be generated by naively stacking six [[12edo]] diatonic majors and one Lydian [[tetrachord]]{{clarify}}. Since the final tetrachord does not 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{{clarify}}. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.

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

== Intervals ==

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 [[Subgroup temperaments#Oceanfront|oceanfront]], [[meantone]] and [[sentinel]].

79edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].

== Scales ==

=== Mos scales ===

* Bluebirds[6, 7, 13, 20, 33…]

* Meantone[7, 12, 19, 31…]

* Oceanfront[7, 12, 17, 22, 27…]

** Subsets of the above: see [[oceanfront scales]]

* Sentinel[5, 8, 11, 14, 17, 31…]

~~'''Bluebirds'''~~

=== Others ===

* ~~Bluebirds~~[6, 7, 13, 33~~...] [[MOS]]es~~

* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)

== Instruments ==

=== Lumatone ===

* [[Lumatone mapping for 79edo]]

'''~~Meantone~~'''

=== Skip fretting ===

* Meantone[~~7, 12, 19, 31...~~] ~~MOSes~~

'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.

* [[~~Meantone~~]] ~~Minor Hexatonic~~

** 197.802

** 303.~~297~~

** 501.099

** 698.901

** 1002.198

** 1200.~~000~~

; Harmonics

1/1: string 2 open

~~'''Oceanfront'''~~

2/1: string 1 fret 14

* Oceanfront[7~~, 12, 17, 22, 27...] MOSes~~

** Subsets of the above: ~~see [[oceanfront scales]]~~

3/2: string 5 fret 21

5/4: string 5 fret 18

7/4: string 5 fret 2

11/8: string 4 fret 11

13/8: string 5 fret 11

17/16: string 2 fret 1

~~'''Sentinel'''~~

19/16: string 5 fret 6

* Sentinel[5~~, 8, 11, 14, 17, 31...] MOSes~~

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)

; [[User:Francium|Francium]]

* [https://www.youtube.com/watch?v=gAELEuSZra8 Gold]

* [https://www.youtube.com/watch?v=gAELEuSZra8 ''Gold''] (2022)

; Silence and Secrecy ([[Julian Malerman]])

* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni Saint Sebastian, By the Hands of Reni]

* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni ''Saint Sebastian, By the Hands of Reni''] (2014)

[[Category:Listen]]

~~{{Todo| cleanup }}~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|79}}
+{{ED intro}}
 == Theory ==
-edo works well as a no-7 13- or 17-limit tuning. It is in fact [[consistent]] in the no-7 [[15-odd-limit]].
+edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]].
 Using the [[patent val]], 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.
@@ Line 16: / Line 16: @@
 === Miscellany ===
+edo adequately represents the [[Decaononic]] way of playing, as 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. A [[maximal evenness]] variant of such a scale can be generated by naively stacking six [[12edo]] diatonic majors and one Lydian [[tetrachord]]{{clarify}}. Since the final tetrachord does not 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{{clarify}}. From a regular temperament theory perspective, these scales are a part of the [[bluebirds]] temperament.
-edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].
+== Intervals ==
-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 [[Subgroup temperaments#Oceanfront|oceanfront]], [[meantone]] and [[sentinel]].
+edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].
 {{todo|expand}}
 == Scales ==
+=== Mos scales ===
+* Bluebirds[6, 7, 13, 20, 33…]
+* Meantone[7, 12, 19, 31…]
+* Oceanfront[7, 12, 17, 22, 27…]
+** Subsets of the above: see [[oceanfront scales]]
+* Sentinel[5, 8, 11, 14, 17, 31…]
-'''Bluebirds'''
+=== Others ===
-* Bluebirds[6, 7, 13, 33...] [[MOS]]es
+* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)
+== Instruments ==
+=== Lumatone ===
+* [[Lumatone mapping for 79edo]]
-'''Meantone'''
+=== Skip fretting ===
-* Meantone[7, 12, 19, 31...] MOSes
+'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.
-* [[Meantone]] Minor Hexatonic
-** 197.802
-** 303.297
-** 501.099
-** 698.901
-** 1002.198
-** 1200.000
+; Harmonics
+/1: string 2 open
-'''Oceanfront'''
+/1: string 1 fret 14
-* Oceanfront[7, 12, 17, 22, 27...] MOSes
-** Subsets of the above: see [[oceanfront scales]]
+/2: string 5 fret 21
+/4: string 5 fret 18
+/4: string 5 fret 2
+/8: string 4 fret 11
+/8: string 5 fret 11
+/16: string 2 fret 1
-'''Sentinel'''
+/16: string 5 fret 6
-* Sentinel[5, 8, 11, 14, 17, 31...] MOSes
 == Music ==
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)
 ; [[User:Francium|Francium]]
-* [https://www.youtube.com/watch?v=gAELEuSZra8 Gold]
+* [https://www.youtube.com/watch?v=gAELEuSZra8 ''Gold''] (2022)
 ; Silence and Secrecy ([[Julian Malerman]])
-* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni Saint Sebastian, By the Hands of Reni]
+* [https://soundcloud.com/fever-carpets/saint-sebastian-by-the-hands-of-reni ''Saint Sebastian, By the Hands of Reni''] (2014)
 [[Category:Listen]]
-{{Todo| cleanup }}