179edo: Difference between revisions

Eliora (talk | contribs)
No edit summary
Francium (talk | contribs)
+regular temperament properties
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|179}}
{{EDO intro|179}}
 
== Theory ==
179edo doesn't approximate well any odd harmonic up to 23, best being [[21/16]] with 22% error. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.
179edo doesn't approximate well any odd harmonic up to 23, best being [[21/16]] with 22% error. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.


Line 8: Line 8:
=== 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|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}}
|{{val|179 284}}
| -0.6169
| 0.6166
| 9.20
|-
|2.3.5
|{{monzo|20 -17 3}}, {{monzo|28 -3 -10}}
|{{val|179 284 416}}
| -0.7718
| 0.5490
| 8.19
|-
|2.3.5.7
|3136/3125, 4375/4374, 10976/10935
|{{val|179 284 416 503}}
| -0.8673
| 0.5034
| 7.51
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
|1
|35\179
|234.64
|8/7
|[[Rodan]]
|-
|1
|47\179
|315.08
|6/5
|[[Parakleismic]]
|-
|1
|79\167
|529.61
|512/375
|[[Mabila]]
|}


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
[[Category:Prime EDO]]