1547edo: Difference between revisions
mNo edit summary |
Cleanup; clarify the title row of the rank-2 temp table |
||
| Line 3: | Line 3: | ||
== Theory == | == Theory == | ||
1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It tempers out [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma. | 1547edo is [[consistent]] to the [[15-odd-limit]] and is excellent in the 7-limit. It [[Tempering out|tempers out]] [[4375/4374]] and it is a member of the [[optimal ET sequence]] for the rank-3 temperament associated with this comma. | ||
In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]]. | In the 5-limit, it supports [[gross]], which is a very high-accuracy temperament. The 118-tone [[maximal evenness]] scale produced by gross is [[concoctic]], since it uses 118\1547 as the generator. In addition, 1547edo tempers out the [[septendecima]] and thus supports the [[chlorine]] temperament in 5-limit and also in the 7-limit. 1547edo tempers out the 5-limit comma {{monzo| 236 -61 -60 }}, thus associating a stack of sixty [[15/8]]'s with [[4/3]], and sixty-one of them make [[5/4]]. | ||
| Line 14: | Line 14: | ||
{{Harmonics in equal|1547}} | {{Harmonics in equal|1547}} | ||
=== | === Subsets and supersets === | ||
1547 has subset edos {{EDOs| 7, 13, 17, 91, 119, and 221 }}. | 1547 has subset edos {{EDOs| 7, 13, 17, 91, 119, and 221 }}. | ||
| Line 30: | Line 30: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 2452 -1547 }} | | {{monzo| 2452 -1547 }} | ||
| | | {{mapping| 1547 2542 }} | ||
| -0.015 | | -0.015 | ||
| 0.015 | | 0.015 | ||
| Line 37: | Line 37: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| -52 -17 34 }}, {{monzo| 40 -56 21 }} | | {{monzo| -52 -17 34 }}, {{monzo| 40 -56 21 }} | ||
| | | {{mapping| 1547 2542 3592 }} | ||
| -0.008 | | -0.008 | ||
| 0.017 | | 0.017 | ||
| Line 44: | Line 44: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, {{monzo| -1 4 11 -11 }}, {{monzo| 46 -14 -3 -6 }} | | 4375/4374, {{monzo| -1 4 11 -11 }}, {{monzo| 46 -14 -3 -6 }} | ||
| | | {{mapping| 1547 2542 3592 4343 }} | ||
| -0.007 | | -0.007 | ||
| 0.014 | | 0.014 | ||
| Line 51: | Line 51: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 4375/4374, 117649/117612, 234375/234256, 2097152/2096325 | | 4375/4374, 117649/117612, 234375/234256, 2097152/2096325 | ||
| | | {{mapping| 1547 2542 3592 4343 5352 }} | ||
| -0.017 | | -0.017 | ||
| 0.024 | | 0.024 | ||
| Line 58: | Line 58: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683 | | 4096/4095, 4375/4374, 6656/6655, 78125/78078, 85750/85683 | ||
| | | {{mapping| 1547 2542 3592 4343 5352 5725 }} | ||
| -0.029 | | -0.029 | ||
| 0.034 | | 0.034 | ||
| Line 68: | Line 68: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
| Line 115: | Line 115: | ||
| [[Protactinium]] | | [[Protactinium]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||
; [[Eliora]] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=oac5JZ9FtB8 Prelude and Fugue in Two Elements | * [https://www.youtube.com/watch?v=oac5JZ9FtB8 ''Prelude and Fugue in Two Elements''] | ||
[[Category:Listen]] | [[Category:Listen]] | ||