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 [[13-odd-limit]], even though it is a [[~~The Riemann zeta function and tuning#Valley edos|~~zeta valley edo]].

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]]).

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.

=== Odd harmonics ===

=== 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.

~~The 79c val~~ [[support]]s [[meantone]] ~~with a tuning~~ very close to [[1/7-~~comma~~ meantone|1/~~7-comma~~]].

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.

~~=== Odd harmonics ===~~

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.

~~{{Harmonics in equal|79}}~~

=== Subsets and supersets ===

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== Intervals ==

~~== Regular temperament properties ==~~

~~79edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]] and [[sentinel]]. Its alternate 79c val supports [[meantone]] in the 5-limit.~~

~~{{todo|expand}}~~

== Scales ==

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=== 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

== Instruments ==

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== 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]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]], even though it is a [[The Riemann zeta function and tuning#Valley edos|zeta valley edo]].
+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]]).
-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.
+=== Odd harmonics ===
+{{Harmonics in equal|79}}
+=== 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.
-The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].
+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.
-=== Odd harmonics ===
+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.
-{{Harmonics in equal|79}}
 === Subsets and supersets ===
@@ Line 20: / Line 23: @@
 == Intervals ==
 {{Interval table}}
-== Regular temperament properties ==
-edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]] and [[sentinel]]. Its alternate 79c val supports [[meantone]] in the 5-limit.
-{{todo|expand}}
 == Scales ==
@@ Line 35: / Line 34: @@
 === 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
 == Instruments ==
@@ Line 63: / Line 63: @@
 == 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]]

79edo: Difference between revisions

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