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'''144edo''' is the [[EDO|equal division of the octave]] into 144 parts of 8.3333 cents each. It is closely related to [[72edo]], but the patent vals differ on the mapping for 13 and 17. It is contorted in the 11-limit, tempering out 225/224, 243/242, 385/384, 441/440, and 4000/3993. Using the patent val, it tempers out 847/845, 1188/1183, 1701/1690, 1875/1859, and 4225/4224 in the 13-limit; 273/272, 715/714, 833/832, 875/867, 891/884, and 1275/1274 in the 17-limit; 210/209, 325/323, 343/342, 363/361, 400/399, 513/512, 665/663 in the 19-limit.
{{Infobox ET}}
{{ED intro}}


[[Category:Edo]]
144edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>
 
== Theory ==
144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1|13]] and [[17/1|17]]. It is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit. It [[support]]s [[hemisecordite]], the {{nowrap|41 &amp; 103}} temperament, though [[103edo]] is better suited for this purpose.
 
Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It supports [[semihemisecordite]], the {{nowrap|62 &amp; 82f}} temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]], supporting 17-limit hemisecordite. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.
 
Besides all these, the 144eff val supports hemimiracle, the {{nowrap|41 &amp; 103e}} temperament. 144ee supports oracle, the {{nowrap|31 &amp; 113e}} temperament. 144cf supports necromanteion, the {{nowrap|31 &amp; 113cf}} temperament.
 
=== Prime harmonics ===
{{Harmonics in equal|144}}
 
=== Subsets and supersets ===
144edo is the square of world-dominant [[12edo]].
 
Since 144 factors into 2<sup>4</sup> × 3<sup>2</sup>, 144edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, and 72 }}.
 
=== Approximation to φ ===
144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it can produce extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps.
 
== 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]] (%)
|-
| 2.3.5.7.11.13
| 225/224, 243/242, 385/384, 847/845, 1875/1859
| {{mapping| 144 228 334 404 498 533 }}
| +0.560
| 0.595
| 7.13
|- style="border-top: double;"
| 2.3.5.7.11.13.17
| 225/224, 243/242, 273/272, 325/324, 847/845, 875/867
| {{mapping| 144 228 334 404 498 533 589 }} (144)
| +0.362
| 0.734
| 8.80
|- style="border-top: double;"
| 2.3.5.7.11.13.17
| 170/169, 225/224, 243/242, 289/288, 375/374, 385/384
| {{mapping| 144 228 334 404 498 533 588 }} (144g)
| +0.653
| 0.596
| 7.15
|}
 
=== 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
| 7\144
| 58.33
| 27/26
| [[Hemisecordite]] (144)
|-
| 2
| 7\144
| 58.33
| 27/26
| [[Semihemisecordite]] (144g)
|-
| 12
| 1\144
| 8.33
| 129/128
| [[Substitute harmonic#Dotcom|Dotcom]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Music ==
; [[Hideya]]
* [https://www.youtube.com/watch?v=p71oF-A9gF8 ''Like an endless uphill''] (2022)
 
== References ==
<references />
 
== External links ==
* [http://tonalsoft.com/enc/number/144edo.aspx 144-tone equal-temperament / 144-edo] on [[Tonalsoft Encyclopedia]]
 
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/144edo"