Extraclassical tonality: Difference between revisions
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* Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees. | * Any pair of [[List of root-3rd-P5 triads in JI|JI medials]] with a latitude around ±25 degrees. | ||
* In terms of [[fractional monzo]]s, the arto and tendo thirds may be tuned as {{nowrap|1\2edf ± 1\2ed(9/8)}}. | * In terms of [[fractional monzo]]s, the arto and tendo thirds may be tuned as {{nowrap|1\2edf ± 1\2ed(9/8)}}. | ||
The following table lists EDFs up to 31 (and corresponding EDOs up to 53) that have arto and tendo thirds (which are defined broadly as a latitude of 22.5 to 30 degrees, which is moderately extended from the "canonical" arto and tendo latitude range of 24 to 28 degrees). | |||
{| class="wikitable" | |||
|+ | |||
!Fifth | |||
!Edos | |||
!Arto third | |||
!Tendo third | |||
!Notes | |||
|- | |||
|3 | |||
|5, 10, 15, 16, 20, 21, 25, 26, 30, 31, 36 | |||
|5: 240c | |||
|5: 480c | |||
|Widest range; corresponds to slendric. Diatonic thirds in multiples of 5edo. Same intervals are shared with multiples of 3edf up to 21, so they are grouped here. 5edo fendo. (8edo's thirds aren't here cuz they're technically neogothic!) | |||
|- | |||
|'''8''' | |||
|13, 14, 27, 28 | |||
|14: 257c | |||
13: 277c | |||
|14: 428c | |||
13: 462c | |||
|Narrowest range, 13edo fendo. Same intervals are shared with 16edf, so it is grouped here. Diatonic thirds found in 27edo. | |||
|- | |||
|'''11''' | |||
|18, 19, 37, 38 | |||
|19: 253c | |||
|19: 442c | |||
|Same intervals are shared with 22edf, so it is grouped here. 19edo saj and sin thirds. 18edo fendo. | |||
|- | |||
|'''14''' | |||
|24, 47*, 48 | |||
|24: 250c | |||
|24: 450c | |||
|Same intervals are shared with 28edf, so it is grouped here. | |||
|- | |||
|17 | |||
|29 | |||
|29: 248c | |||
|29: 455c | |||
|29edo saj and sin thirds. | |||
|- | |||
|'''19''' | |||
|32, 33 | |||
|32: 263c | |||
33: 254c | |||
|32: 450c | |||
33: 436c | |||
|32edo diatonic. | |||
|- | |||
|20 | |||
|34, 35 | |||
|34: 247c | |||
|34: 459c | |||
| | |||
|- | |||
|23 | |||
|39, 40 | |||
|39: 246c | |||
|39: 462c | |||
| | |||
|- | |||
|24 | |||
|41 | |||
|41: 234c, 263c | |||
|41: 439c, 468c | |||
|Intersection of the 3 and 8 categories; first tuning with 2 pairs. Slendric in 41edo. 41edo saj and sin chords. | |||
|- | |||
|'''25''' | |||
|42, 43 | |||
|43: 251c | |||
|43: 447c | |||
| | |||
|- | |||
|26 | |||
|44, 45 | |||
|44: 245c | |||
45: 240c | |||
|44: 464c | |||
45: 453c | |||
| | |||
|- | |||
|27 | |||
|46, 47 | |||
|46: 235c, 261c | |||
47: 230c, 255c | |||
|46: 444c, 470c | |||
47: 434c, 460c | |||
|Slendric in 46 and 47edo, 47edo sharp fifth generates both thirds in arto/tendo range | |||
|- | |||
|29 | |||
|49, 50 | |||
|50: 240c | |||
|50: 456c | |||
| | |||
|- | |||
|30 | |||
|51, 52 | |||
|51: 235c, 259c | |||
|51: 447c, 470c | |||
|Slendric in 51 and 52edo. | |||
|- | |||
|31 | |||
|53 | |||
|53: 249c | |||
|53: 453c | |||
|Very close to 13-limit intervals | |||
|} | |||
[[Category:19edo]] | [[Category:19edo]] | ||
[[Category:24edo]] | [[Category:24edo]] | ||