988edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
988edo is [[enfactoring|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. | 988edo is [[enfactoring|enfactored]] in the [[17-limit]], with the same tuning as [[494edo]], which is notable for being a [[zeta edo]]. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. A [[comma basis]] for 988edo in the 19-limit is {[[1156/1155]], [[1275/1274]], [[1445/1444]], [[1716/1715]], [[2080/2079]], [[2431/2430]], [[4096/4095]]}. An alternate mapping for 17 would be the 988g val, where it tempers out [[2025/2023]], 13013/13005, 15625/15606, 31213/31212. | ||
In addition, in the 988ccd val provides a tuning that is extremely close to the [[POTE tuning]] for [[quadritikleismic]] temperament in the 7-limit. | |||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
988edo has subset edos {{EDOs| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}. | Since 988 factors into {{factorization|988}}, 988edo has subset edos {{EDOs| 2, 4, 13, 19, 26, 38, 52, 76, 247, and 494 }}. | ||
One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb. | One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb. | ||
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Note: 17-limit temperaments supported by 494edo are not included. | Note: 17-limit temperaments supported by 494edo are not included. | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 4 | | 4 | ||
| 261\988<br>(14\988) | | 261\988<br />(14\988) | ||
| 317.004<br>(17.004) | | 317.004<br />(17.004) | ||
| 6/5<br>(126/125) | | 6/5<br />(126/125) | ||
| [[Quadritikleismic]] (988ccd) | | [[Quadritikleismic]] (988ccd) | ||
|- | |- | ||
| 19 | | 19 | ||
| 141\988<br>(37\988) | | 141\988<br />(37\988) | ||
| 171.255<br>(44.939) | | 171.255<br />(44.939) | ||
| 6545/5928<br>(?) | | 6545/5928<br />(?) | ||
| [[Kalium]] | | [[Kalium]] | ||
|- | |- | ||
| 52 | | 52 | ||
| 325\988<br>(2\988) | | 325\988<br />(2\988) | ||
| 394.736<br>(2.429) | | 394.736<br />(2.429) | ||
| 134560000/107132311<br>(?) | | 134560000/107132311<br />(?) | ||
| [[French deck]] | | [[French deck]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||
; [[birdshite stalactite]] | |||
* "clagworks" from ''clagworks / it's probably gout'' (2024) – [https://open.spotify.com/track/1Abk4KcVUHoRkKxYNSYm0F Spotify] | [https://birdshitestalactite.bandcamp.com/track/clagworks Bandcamp] | [https://www.youtube.com/watch?v=S0zS0rYtT2Y YouTube] | |||
; [[Eliora]] | ; [[Eliora]] | ||
* [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023) | * [https://www.youtube.com/watch?v=c7BW2xnQBb4 ''Alien ethnic motive in 13edo and 12rdo''] (2023) | ||
[[Category:Listen]] | |||