Xenharmonic Wiki

79edo: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled
18,215 edits
→Music: Add Bryan Deister's ''microtonal improvisation in 79edo'' (2025)
 
(20 intermediate revisions by 7 users not shown)
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|79}}
{{ED intro}}


==Theory==
== Theory ==
{{Harmonics in equal|79}}
79edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] in the no-7 [[13-odd-limit]].  
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]].  
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.  


79 is the 22nd prime EDO number.
The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].  


=== Decaononic whole tone ===
=== Odd harmonics ===
 
{{Harmonics in equal|79}}
79edo adequately represents the [[Decaononic]] way of playing, where a tone is considered to be [[10/9]] instead of [[9/8]].


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


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.
=== 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.


== Interval table ==
== Intervals ==
{{Interval table}}
{{Interval table}}


== Regular temperament properties ==
== Regular temperament properties ==
79edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments#Oceanfront|oceanfront]] and [[sentinel]].
79edo supports the [[bluebirds]] temperament. It also supports [[Subgroup temperaments #Oceanfront|oceanfront]], [[meantone]], and [[sentinel]].
{{todo|expand}}
{{todo|expand}}


== Scales ==
== Scales ==
=== Bluebirds ===
=== Mos scales ===
* [[Bluebirds]][7] - also [[glacial]]
* Bluebirds[6, 7, 13, 20, 33…]
* Bluebirds[46]
* Meantone[7, 12, 19, 31…]
=== Meantone ===
* Oceanfront[7, 12, 17, 22, 27…]
* [[Meantone]] Minor Hexatonic
** Subsets of the above: see [[oceanfront scales]]
** 197.802
* Sentinel[5, 8, 11, 14, 17, 31…]
** 303.297
 
** 501.099
=== Others ===
** 698.901
* [[Meantone]] Minor Hexatonic: 13 7 13 13 20 13 ((13, 20, 33, 46, 66, 79)\79)
** 1002.198
 
** 1200.000
== Instruments ==
=== Oceanfront ===
=== Lumatone ===
* [[Subgroup temperaments#Oceanfront|Oceanfront]][7]
* [[Lumatone mapping for 79edo]]
* Oceanfront[12]
 
** 197.468
=== Skip fretting ===
** 227.848
'''Skip fretting system 79 7 19''' is a [[skip fretting]] system for [[79edo]]. All examples are for 5-string bass.
** 258.228
 
** 455.696
; Harmonics
** 486.076
1/1: string 2 open
** 683.544
 
** 713.924
2/1: string 1 fret 14
** 744.304
 
** 941.772
3/2: string 5 fret 21
** 972.152
 
** 1169.620
5/4: string 5 fret 18
** 1200.000
 
* Oceanfront[17]
7/4: string 5 fret 2
* Oceanfront[22]
 
* Oceanfront[27, 32, 37, 42]
11/8: string 4 fret 11
* [[POTE oceanfront scales]] (these aren't in 79edo, but the tuning is almost identical to 79edo, so they can be easily retuned to 79edo)
 
13/8: string 5 fret 11
 
17/16: string 2 fret 1
 
19/16: string 5 fret 6


== Music ==
== Music ==
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=qj6tmkMvQMU ''microtonal improvisation in 79edo''] (2025)
; [[User:Francium|Francium]]
; [[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]])
; 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:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Prime EDO]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/79edo"