|
|
| (28 intermediate revisions by 10 users not shown) |
| Line 1: |
Line 1: |
| '''Welcome to the Temperament Orphanage''' | | {{Technical data page}} |
| | |
| | '''Welcome to the temperament orphanage!''' |
|
| |
|
| These temperaments need to be adopted into a family. | | These temperaments need to be adopted into a family. |
| Line 7: |
Line 9: |
| Please give a short description of whatever temperament you leave here so that someone can help to match this temperament back to its rightful progenitors. | | Please give a short description of whatever temperament you leave here so that someone can help to match this temperament back to its rightful progenitors. |
|
| |
|
| == Absurdity == | | == Lafa (65 & 441) == |
| The 5-limit 7&84 temperament. So named because this is just an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the [[syntonic-chromatic equivalence continuum]], in this case where (81/80)<sup>5</sup> = 25/24.
| | This temperament was named by [[Petr Pařízek]] in 2011, referring to the characteristic that stacking 12 generators makes 6/1 – "l" for 12, "f" for 6<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. |
| | |
| Commas: 10460353203/10240000000
| |
| | |
| POTE generator: ~10/9 = 185.901 cents
| |
| | |
| Map: [<7 0 -17|, <0 1 3|]
| |
| | |
| EDOs: {{EDOs| 7, 70, 77, 84, 329 }}
| |
| | |
| Badness: 0.3412
| |
| | |
| [http://x31eq.com/cgi-bin/rt.cgi?ets=7_84&limit=5 The temperament finder - 5-limit Absurdity]
| |
| | |
| == Sevond ==
| |
| This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4.
| |
| | |
| Comma: 5000000/4782969
| |
| | |
| POTE generator: ~3/2 = 706.288 cents
| |
| | |
| Map: [<7 0 -6|, <0 1 2|]
| |
| | |
| EDOs: {{EDOs| 7, 42, 49, 56, 119 }}
| |
| | |
| Badness: 0.3393
| |
| | |
| === 7-limit ===
| |
| Adding 875/864 to the commas extends this to the 7-limit:
| |
| | |
| Commas: 875/864, 327680/321489
| |
| | |
| POTE generator: ~3/2 = 705.613 cents
| |
| | |
| Map: [<7 0 -6 53|, <0 1 2 -3|]
| |
| | |
| EDOs: {{EDOs| 7, 56, 63, 119 }}
| |
|
| |
|
| [http://x31eq.com/cgi-bin/rt.cgi?ets=7_49&limit=5 The temperament finder - 5-limit Sevond]
| | Subgroup: 2.3.5 |
|
| |
|
| == Seville ==
| | Comma list: {{monzo| 77 -31 -12 }} |
| This is similar to the above, but provides a less complex avenue to 5, but this time at the sake of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4.
| |
|
| |
|
| Comma: 78125/69984
| | Mapping: {{mapping| 1 11 -22 | 0 -12 31 }} |
|
| |
|
| POTE generator: ~3/2 = 706.410 cents
| | : Mapping generators: ~2, ~{{monzo| 33 -13 -5 }} |
|
| |
|
| Map: [<7 0 5|, <0 1 1|]
| | Optimal tuning (POTE): ~2 = 1\1, ~{{monzo| 33 -13 -5 }} = 941.4971 |
|
| |
|
| EDOs: {{EDOs| 7, 35b, 42c, 49c, 56cc, 119cccc }}
| | {{Optimal ET sequence|legend=1| 65, 246, 311, 376, 441, 2711, 3152, 3593, 4034, 4475, 4916, 5357 }} |
|
| |
|
| Badness: 0.4377 | | Badness: 0.184510 |
|
| |
|
| [http://x31eq.com/cgi-bin/rt.cgi?ets=7_49c&limit=5 The temperament finder - 5-limit Seville]
| | == Notes == |
|
| |
|
| [[Category:Temperament]] | | [[Category:Regular temperament theory]] |
| | [[Category:Temperament collections|*]] |