118edo: Difference between revisions
+table of rank-2 temperaments |
+RTT property table |
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In the 11-limit, it tempers out [[385/384]] and [[441/440]], and is an excellent tuning for [[portent]], the temperament tempering out both, and for the 11-limit version of guiron, which does also. | In the 11-limit, it tempers out [[385/384]] and [[441/440]], and is an excellent tuning for [[portent]], the temperament tempering out both, and for the 11-limit version of guiron, which does also. | ||
118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]]. | 118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]]. | ||
== Rank-2 temperaments == | === Prime harmonics === | ||
{{primes in edo|118|prec=2}} | |||
== 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| -187 118 }} | |||
| [{{val| 118 187 }}] | |||
| -0.119 | |||
| 0.082 | |||
| 0.81 | |||
|- | |||
| 2.3.5 | |||
| 32805/32768, 1224440064/1220703125 | |||
| [{{val| 118 187 274 }}] | |||
| +0.036 | |||
| 0.093 | |||
| 0.91 | |||
|- | |||
| 2.3.5.7 | |||
| 1029/1024, 3136/3125, 4375/4374 | |||
| [{{val| 118 187 274 331 }}] | |||
| +0.270 | |||
| 0.412 | |||
| 4.05 | |||
|- | |||
| 2.3.5.7.11 | |||
| 385/384, 441/440, 3136/3125, 4375/4374 | |||
| [{{val| 118 187 274 331 408 }}] | |||
| +0.341 | |||
| 0.370 | |||
| 3.89 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
| Line 25: | Line 68: | ||
| [[Vavoom]] | | [[Vavoom]] | ||
|- | |- | ||
|1 | | 1 | ||
| 19\118 | | 19\118 | ||
| 193.22 | | 193.22 | ||
| Line 55: | Line 98: | ||
| [[Tritriple]] | | [[Tritriple]] | ||
|- | |- | ||
|2 | | 2 | ||
| 2\118 | | 2\118 | ||
| 20.34 | | 20.34 | ||
| Line 67: | Line 110: | ||
| [[Kleischismic]] | | [[Kleischismic]] | ||
|- | |- | ||
|2 | | 2 | ||
| 7\118 | | 7\118 | ||
| 71.19 | | 71.19 | ||