79edo: Difference between revisions

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~~'''79edo''' divides the octave into 79 equal parts of 15.190 cents each.~~

==Theory==

== 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]].

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.

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

=== Odd harmonics ===

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 ~~temperament where a tone is considered to be~~ [[~~10/9~~]] ~~instead of~~ [[~~9/8~~]]. ~~In most temperaments, when~~ the ~~difference betweein 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. ~~Proposed name: decaononic~~, ~~from "~~10 ~~over~~ 9".

=== 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 ==

~~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. Proposed name: Auramagnesic, from 79 (gold)~~ and ~~12 (magnesium)~~.

== Regular temperament properties ==

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

== Scales ==

* ~~Decaononic~~[7] ~~- also~~ [[~~glacial~~]]

=== Mos scales ===

* ~~Auramagnesic~~[46]

* 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)

== 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 ==

* [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~~)

; [[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''] (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:Equal divisions of the octave|##]] ~~

~~[[Category:Prime EDO]]~~

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-'''79edo''' divides the octave into 79 equal parts of 15.190 cents each.
+{{Infobox ET}}
+{{ED intro}}
-==Theory==
+== 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]].
+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.
+The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].
+=== Odd harmonics ===
 {{Harmonics in equal|79}}
-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 temperament where a tone is considered to be [[10/9]] instead of [[9/8]]. In most temperaments, when the difference betweein 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. Proposed name: decaononic, from "10 over 9".
+=== 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}}
-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. Proposed name: Auramagnesic, from 79 (gold) and 12 (magnesium).
+== Regular temperament properties ==
+edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].
+{{todo|expand}}
 == Scales ==
-* Decaononic[7] - also [[glacial]]
+=== Mos scales ===
-* Auramagnesic[46]
+* 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)
+== 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 ==
-* [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)
+; [[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''] (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:Equal divisions of the octave|##]] <!-- 2-digit number -->
-[[Category:Prime EDO]]
 [[Category:Listen]]