79edo: Difference between revisions

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~~=<span style="color: #790079; font-family: 'Times New Roman',Times,serif; font-size: 113%;">79 tone equal temperament</span>=~~

~~'''~~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~~.

== 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]]).

=Music=

=== Odd harmonics ===

[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~~)

=== 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 ==

== 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…]

=== 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 ==

=== Lumatone ===

* [[Lumatone mapping for 79edo]]

=== Skip fretting ===

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

; Harmonics

1/1: string 2 open

2/1: string 1 fret 14

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

19/16: string 5 fret 6

== 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''] (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''] (2014)

~~[[Category:Edo]]~~

~~[[Category:Prime edo]]~~

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-=<span style="color: #790079; font-family: 'Times New Roman',Times,serif; font-size: 113%;">79 tone equal temperament</span>=
+{{Infobox ET}}
+{{ED intro}}
-'''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.
+== 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]]).
-=Music=
+=== Odd harmonics ===
-[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)
+{{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.
+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}}
+== 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…]
+=== 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 ==
+=== Lumatone ===
+* [[Lumatone mapping for 79edo]]
+=== Skip fretting ===
+'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.
+; Harmonics
+/1: string 2 open
+/1: string 1 fret 14
+/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
+/16: string 5 fret 6
+== 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''] (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''] (2014)
-[[Category:Edo]]
-[[Category:Prime edo]]
 [[Category:Listen]]

79edo: Difference between revisions

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