79edo: Difference between revisions

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==Theory==

== Theory ==

79edo is only [[consistent]] to the [[5-odd-limit]], but it works well as a no-7 [[13-limit|13-]] or [[17-limit]] tuning with a strong flat tuning tendency. It is in fact consistent to the no-7 [[13-odd-limit]], even though it is a [[zeta valley edo]] (notably, it is the last one until [[5941edo]]).

=== 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]].

=== As a tuning of other temperaments ===

Using the [[patent val]], 79edo [[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 supports the [[sentinel]] temperament and the 2.11.13-subgroup [[bluebirds]] temperament, and provides the [[optimal patent val]] for both.

79edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not [[support]] [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the closest approximation. The closest 5/4 is actually reached by stacking a whopping 16 fifths up (a double-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-closest approximation of 5/4 and thus supports [[meantone]]. The 7-limit 79c val also supports [[superpine]], a [[weak extension]] of meantone that splits the perfect fourth into three [[35/32]]'s.

79edo also has an alternative fifth (albeit much less accurate) of 713.9 cents, which is quite similar to [[37edo]]'s fifth. This fifth allows for [[archy]] and [[oceanfront]] temperaments.

=== Subsets and supersets ===

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

=== 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.

== Intervals ==

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

== 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…]

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

=== Others ===

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

* [[180rotator]]'s 9-tone 33\79 scale: 7 13 7 6 7 13 7 6 7 6

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

== Instruments ==

=== Lumatone ===

* [[Lumatone mapping for 79edo]]

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~~.

=== Skip fretting ===

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

~~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.~~

; Harmonics

1/1: string 2 open

~~== Interval table ==~~

2/1: string 1 fret 14

~~{{Interval table}}~~

~~== Regular temperament properties ==~~

3/2: string 5 fret 21

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

~~{{todo|expand}}~~

~~== Scales ==~~

5/4: string 5 fret 18

~~'''Bluebirds'''~~

7/4: string 5 fret 2

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

11/8: string 4 fret 11

~~'''Meantone'''~~

13/8: string 5 fret 11

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

* [[Meantone]] Minor Hexatonic

** 197.802

** 303.297

** 501.099

** 698.901

** 1002.198

** 1200.000

~~'''Oceanfront'''~~

17/16: string 2 fret 1

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

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

~~'''Sentinel'''~~

19/16: string 5 fret 6

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

== Music ==

=== Modern renderings ===

; Rusino

* [https://www.youtube.com/shorts/EytZXtN3TNw ''Looping the Rooms''] (2025) — microtonal cover in 79edo by [[Bryan Deister]] (2026)

=== 21st century ===

; [[Bryan Deister]]

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

* [https://www.youtube.com/watch?v=Imi-Sz2Ab8M ''79edo groove''] (2026)

; [[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==
+== Theory ==
+edo is only [[consistent]] to the [[5-odd-limit]], but it works well as a no-7 [[13-limit|13-]] or [[17-limit]] tuning with a strong flat tuning tendency. It is in fact consistent to the no-7 [[13-odd-limit]], even though it is a [[zeta valley edo]] (notably, it is the last one until [[5941edo]]).
+=== 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]].
+=== As a tuning of other temperaments ===
+Using the [[patent val]], 79edo [[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 supports the [[sentinel]] temperament and the 2.11.13-subgroup [[bluebirds]] temperament, and provides the [[optimal patent val]] for both.
+edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not [[support]] [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the closest approximation. The closest 5/4 is actually reached by stacking a whopping 16 fifths up (a double-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-closest approximation of 5/4 and thus supports [[meantone]]. The 7-limit 79c val also supports [[superpine]], a [[weak extension]] of meantone that splits the perfect fourth into three [[35/32]]'s.
+edo also has an alternative fifth (albeit much less accurate) of 713.9 cents, which is quite similar to [[37edo]]'s fifth. This fifth allows for [[archy]] and [[oceanfront]] temperaments.
+=== Subsets and supersets ===
+edo is the 22nd prime edo, past [[73edo]] and before [[83edo]].
+=== 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.
+== Intervals ==
+{{Interval table}}
-is the 22nd prime EDO number.
+== 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…]
-=== Decaononic whole tone ===
+=== Others ===
+* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)
+* [[180rotator]]'s 9-tone 33\79 scale: 7 13 7 6 7 13 7 6 7 6
-edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].
+== Instruments ==
+=== Lumatone ===
+* [[Lumatone mapping for 79edo]]
-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.
+=== Skip fretting ===
+'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.
-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.
+; Harmonics
+/1: string 2 open
-== Interval table ==
+/1: string 1 fret 14
-{{Interval table}}
-== Regular temperament properties ==
+/2: string 5 fret 21
-edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments#Oceanfront|oceanfront]], [[meantone]] and [[sentinel]].
-{{todo|expand}}
-== Scales ==
+/4: string 5 fret 18
-'''Bluebirds'''
+/4: string 5 fret 2
-* Bluebirds[6, 7, 13, 33...] [[MOS]]es
+/8: string 4 fret 11
-'''Meantone'''
+/8: string 5 fret 11
-* Meantone[7, 12, 19, 31...] MOSes
-* [[Meantone]] Minor Hexatonic
-** 197.802
-** 303.297
-** 501.099
-** 698.901
-** 1002.198
-** 1200.000
-'''Oceanfront'''
+/16: string 2 fret 1
-* Oceanfront[7, 12, 17, 22, 27...] MOSes
-** Subsets of the above: see [[Oceanfront scales]**
-'''Sentinel'''
+/16: string 5 fret 6
-* Sentinel[5, 8, 11, 14, 17, 31...] MOSes
 == Music ==
+=== Modern renderings ===
+; Rusino
+* [https://www.youtube.com/shorts/EytZXtN3TNw ''Looping the Rooms''] (2025) — microtonal cover in 79edo by [[Bryan Deister]] (2026)
+=== 21st century ===
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)
+* [https://www.youtube.com/watch?v=Imi-Sz2Ab8M ''79edo groove''] (2026)
 ; [[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 }}

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