665edo: Difference between revisions
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+RTT table and rank-2 temperaments |
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{{Infobox ET | {{Infobox ET | ||
| Prime factorization = | | Prime factorization = 5 × 7 × 19 | ||
| Step size = 1.80451¢ | | Step size = 1.80451¢ | ||
| Fifth = 389\665 (701.95¢) | | Fifth = 389\665 (701.95¢) | ||
| Line 19: | Line 19: | ||
=== Miscellaneous properties === | === Miscellaneous properties === | ||
A [[maximal evenness]] scale deriving from the 118 & 665 temperament, known as [[vavoom]], can also theoretically serve as a calendar leap week cycle corresponding to a year length of 365d 5h 48m 37+17/19s, about 7 seconds shorter than the average length of the tropical year today. Given the excellence of both 118 and 665 in 5-limit, this is a great point of intersection of solar calendar leap rules and just intonation-based temperaments. | A [[maximal evenness]] scale deriving from the 118 & 665 temperament, known as [[vavoom]], can also theoretically serve as a calendar leap week cycle corresponding to a year length of 365d 5h 48m 37+17/19s, about 7 seconds shorter than the average length of the tropical year today. Given the excellence of both 118 and 665 in 5-limit, this is a great point of intersection of solar calendar leap rules and just intonation-based temperaments. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal 8ve<br>stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| -1054 665 }} | |||
| [{{val| 665 1054 }}] | |||
| +0.0000 | |||
| 0.0000 | |||
| 0.00 | |||
|- | |||
| 2.3.5 | |||
| {{monzo| -14 -19 19 }}, {{monzo| 54 -37 2 }} | |||
| [{{val| 665 1054 1544 }}] | |||
| +0.0213 | |||
| 0.0301 | |||
| 1.67 | |||
|- | |||
| 2.3.5.7 | |||
| 4375/4374, 703125/702464, {{monzo| 36 -5 0 -10 }} | |||
| [{{val| 665 1054 1544 1867 }}] | |||
| -0.0015 | |||
| 0.0474 | |||
| 2.63 | |||
|- | |||
| 2.3.5.7.11 | |||
| 4000/3993, 4375/4374, 117649/117612, 131072/130977 | |||
| [{{val| 665 1054 1544 1867 2301 }}] | |||
| -0.0511 | |||
| 0.1078 | |||
| 5.97 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 1575/1573, 2080/2079, 4096/4095, 4375/4374, 31250/31213 | |||
| [{{val| 665 1054 1544 1867 2301 2461 }}] | |||
| -0.0594 | |||
| 0.1002 | |||
| 5.55 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per Octave | |||
! Generator<br>(Reduced) | |||
! Cents<br>(Reduced) | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 62\665 | |||
| 111.88 | |||
| 16/15 | |||
| [[Vavoom]] | |||
|- | |||
| 1 | |||
| 138\665 | |||
| 249.02 | |||
| {{monzo| -26 18 -1 }} | |||
| [[Monzismic]] | |||
|- | |||
| 7 | |||
| 288\665<br>(3\665) | |||
| 519.70<br>(5.41) | |||
| 27/20<br>(325/324) | |||
| [[Brahmagupta]] | |||
|- | |||
| 19 | |||
| 276\665<br>(4\665) | |||
| 498.05<br>(7.21) | |||
| 4/3<br>(225//224) | |||
| [[Enneadecal]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||