5L 3s: Difference between revisions
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The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]). | The only notable harmonic entropy minimum is Vulture/[[Hemifamity_temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region does not approximate low-complexity JI harmony well, but can be melodically interesting due to the distorted diatonic scale structure (see also [[oneirotonic]]). | ||
=== Tridec (21&29, 2.7/5.11/5.13/5) === | === Tridec (21&29, 2.7/5.11/5.13/5) === | ||
=== | === A-Team (13&18, 4:5:9:21) === | ||
=== | Sortable table of intervals in the Dylathian mode and their A-Team interpretations: | ||
{| class="wikitable right-2 right-3 right-4 sortable" | |||
|- | |||
! Degree | |||
! Size in 13edo | |||
! Size in 18edo | |||
! Size in 31edo | |||
! Note name on L | |||
! class="unsortable"| Approximate ratios<ref>The harmonics over 1/1 are in bold. The ratio interpretations that are not valid for 18edo are italicized.</ref> | |||
! #Gens up | |||
|- | |||
| 1 | |||
| 0\13, 0.00 | |||
| 0\18, 0.00 | |||
| 0\31, 0.00 | |||
| L | |||
| '''1/1''' | |||
| 0 | |||
|- | |||
| 2 | |||
| 2\13, 184.62 | |||
| 3\18, 200.00 | |||
| 5\31, 193.55 | |||
| M | |||
| '''9/8''', 10/9 | |||
| +3 | |||
|- | |||
| 3 | |||
| 4\13, 369.23 | |||
| 6\18, 400.00 | |||
| 10\31, 387.10 | |||
| N | |||
| '''5/4''' | |||
| +6 | |||
|- | |||
| 4 | |||
| 5\13, 461.54 | |||
| 7\18, 466.67 | |||
| 12\31, 464.52 | |||
| O | |||
| '''21/16''', ''13/10'' | |||
| +1 | |||
|- | |||
| 5 | |||
| 7\13, 646.15 | |||
| 10\18, 666.66 | |||
| 17\31, 658.06 | |||
| P | |||
| ''13/9'', ''16/11'' | |||
| +4 | |||
|- | |||
| 6 | |||
| 9\13, 830.77 | |||
| 13\18, 866.66 | |||
| 22\31, 851.61 | |||
| Q | |||
| '''''13/8''''', ''18/11'' | |||
| +7 | |||
|- | |||
| 7 | |||
| 10\13, 923.08 | |||
| 14\18, 933.33 | |||
| 24\31, 929.03 | |||
| J | |||
| 12/7 | |||
| +2 | |||
|- | |||
| 8 | |||
| 12\13, 1107.69 | |||
| 17\18, 1133.33 | |||
| 29\31, 1122.58 | |||
| K | |||
| | |||
| +5 | |||
|} | |||
<references/> | |||
=== Petrtri (13&21, 4:5:9:11:13:17) === | |||
==== Intervals ==== | |||
Sortable table of intervals in the Dylathian mode and their Petrtri interpretations: | |||
{| class="wikitable right-2 right-3 right-4 right-5 sortable" | |||
|- | |||
! Degree | |||
! Size in 13edo | |||
! Size in 21edo | |||
! Size in 34edo | |||
! Size in POTE tuning | |||
! Note name on L | |||
! class="unsortable"| Approximate ratios | |||
! #Gens up | |||
|- | |||
| 1 | |||
| 0\13, 0.00 | |||
| 0\21, 0.00 | |||
| 0\34, 0.00 | |||
| 0.00 | |||
| L | |||
| 1/1 | |||
| 0 | |||
|- | |||
| 2 | |||
| 2\13, 184.62 | |||
| 3\21, 171.43 | |||
| 5\34, 176.47 | |||
| 177.45 | |||
| M | |||
| 10/9, 11/10 | |||
| +3 | |||
|- | |||
| 3 | |||
| 4\13, 369.23 | |||
| 6\21, 342.86 | |||
| 10\34, 352.94 | |||
| 354.90 | |||
| N | |||
| 11/9, 16/13 | |||
| +6 | |||
|- | |||
| 4 | |||
| 5\13, 461.54 | |||
| 8\21, 457.14 | |||
| 13\34, 458.82 | |||
| 459.15 | |||
| O | |||
| 13/10, 17/13, 22/17 | |||
| +1 | |||
|- | |||
| 5 | |||
| 7\13, 646.15 | |||
| 11\21, 628.57 | |||
| 18\34, 635.294 | |||
| 636.60 | |||
| P | |||
| 13/9, 16/11 | |||
| +4 | |||
|- | |||
| 6 | |||
| 9\13, 830.77 | |||
| 14\21, 800.00 | |||
| 23\34, 811.77 | |||
| 814.05 | |||
| Q | |||
| 8/5 | |||
| +7 | |||
|- | |||
| 7 | |||
| 10\13, 923.08 | |||
| 16\21, 914.29 | |||
| 26\34, 917.65 | |||
| 918.30 | |||
| J | |||
| 17/10 | |||
| +2 | |||
|- | |||
| 8 | |||
| 12\13, 1107.69 | |||
| 19\21, 1085.71 | |||
| 31\34, 1094.12 | |||
| 1095.75 | |||
| K | |||
| 17/9, 32/17 | |||
| +5 | |||
|} | |||
=== Buzzard (48&53, 2.3.5.7) === | === Buzzard (48&53, 2.3.5.7) === |