1547edo: Difference between revisions
rtt table |
|||
| Line 3: | Line 3: | ||
==Theory== | ==Theory== | ||
{{harmonics in equal|1547}} | {{harmonics in equal|1547}} | ||
1547edo is excellent in the 7-limit. | 1547edo is excellent in the 7-limit. It tempers out [[4375/4374]] and it is a member of the [[optimal GPV sequence]] for the rank-3 temperament associated with this comma. | ||
In the 5-limit, it supports [[gross]]. | In the 5-limit, it supports [[gross]]. | ||
| Line 13: | Line 13: | ||
1547's divisors are {{EDOs|1, 7, 13, 17, 91, 119, 221}}. | 1547's divisors are {{EDOs|1, 7, 13, 17, 91, 119, 221}}. | ||
==Regular temperament properties== | ==Regular temperament properties== | ||
===Rank-2 temperaments | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal 8ve | |||
Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|2452 -1547}} | |||
|[{{val|1547 2542}}] | |||
|<nowiki>-0.015</nowiki> | |||
|0.015 | |||
| | |||
|- | |||
|2.3.5 | |||
|<nowiki>-52 -17 34, 40 -56 21</nowiki> | |||
|[{{val|1547 2542 3592}}] | |||
|<nowiki>-0.008</nowiki> | |||
| | |||
| | |||
|- | |||
|2.3.5.7 | |||
|4375/4374, -1 4 11 -11, 46 -14 -3 -6 | |||
|[{{val|1547 2542 3592 4343}}] | |||
| -0.007 | |||
|0.014 | |||
| | |||
|- | |||
|2.3.5.7.11 | |||
|4375/4374, 151263/151250, 820125/819896, 2097152/2096325 | |||
|[{{val|1547 2542 3592 4343 5352}}] | |||
|<nowiki>-0.017</nowiki> | |||
|0.024 | |||
| | |||
|- | |||
|2.3.5.7.11.13 | |||
|4375/4374, 4096/4095, 10648/10647, 91125/91091, 105644/105625 | |||
|[{{val|1547 2542 3592 4343 5352 5725}}] | |||
|<nowiki>-0.029</nowiki> | |||
|0.034 | |||
| | |||
|} | |||
===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 | ||