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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|179}}
{{ED intro}}


179edo doesn't approximate any odd harmonic up to 23 with less than 22% error on [[21/16]]. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.
== Theory ==
179edo does not approximate well any odd [[harmonic]] up to 23, best being [[21/16]] with 22% error. Nonetheless, it is [[consistent]] in the [[7-odd-limit]] and there are a number of temperaments to be considered.


179edo tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]].
The equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }} in the 5-limit, and [[support]]s [[parakleismic]] and its [[extension]]s, providing the [[optimal patent val]] for 11- and 13-limit [[Ragismic microtemperaments #parkleismic|parkleismic]] temperament. In the 7-limit it tempers out [[3136/3125]], [[4375/4374]] and [[10976/10935]], in the 11-limit [[176/175]] and 1375/1372 and in the 13-limit [[169/168]], [[325/324]], [[351/350]] and [[352/351]], providing the optimal patent val for 11- and 13-limit [[ulmo]] temperament. It is additionally the optimal patent val for 7-limit [[cohemimabila]].


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|179}}
{{Harmonics in equal|179}}
=== Subsets and supersets ===
=== Subsets and supersets ===
179edo is the 41st [[prime edo]].


179edo is the 41st [[prime edo]].
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 284 -179 }}
| {{Mapping| 179 284 }}
| −0.6169
| 0.6166
| 9.20
|-
| 2.3.5
| {{Monzo| 20 -17 3 }}, {{monzo| 28 -3 -10 }}
| {{Mapping| 179 284 416 }}
| −0.7718
| 0.5490
| 8.19
|-
| 2.3.5.7
| 3136/3125, 4375/4374, 65536/64827
| {{Mapping| 179 284 416 503 }}
| −0.8673
| 0.5034
| 7.51
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
| 1
| 35\179
| 234.64
| 8/7
| [[Rodan]] (179d)
|-
| 1
| 47\179
| 315.08
| 6/5
| [[Parakleismic]]
|-
| 1
| 71\179
| 475.98
| 21/16
| [[Subfourth]] (179ef)
|-
| 1
| 79\179
| 529.61
| 512/375
| [[Mabila]] (5-limit)
|}
<nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 
== Music ==
; [[Francium]]
* "in a hopeless situation" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/787NGqkI5FHjQcfEOu4y4w Spotify] | [https://francium223.bandcamp.com/track/in-a-hopeless-situation Bandcamp] | [https://www.youtube.com/watch?v=kGdWmP81jwc YouTube]


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Listen]]
[[Category:Prime EDO]]
Retrieved from "https://en.xen.wiki/w/179edo"