4L 3s: Difference between revisions
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== Tuning ranges == | == Tuning ranges == | ||
=== Parasoft === | === Parasoft === | ||
[[Parasoft]] smitonic tunings have step ratios between | [[Parasoft]] smitonic tunings have step ratios between 4/3 and 3/2, which implies a generator sharper than 5\18 = 333.3¢ and flatter than 7\25 = 336.0¢. | ||
Parasoft smitonic can be considered "meantone smitonic". This is because these tunings share the following features with [[meantone]] diatonic tunings: | Parasoft smitonic can be considered "meantone smitonic". This is because these tunings share the following features with [[meantone]] diatonic tunings: | ||
| Line 137: | Line 137: | ||
! [[18edo]] | ! [[18edo]] | ||
! [[25edo]] | ! [[25edo]] | ||
! Optimal (2.9.5 [[POTE]]) tuning | ! Optimal (2.9.5 [[POTE]]) tuning | ||
|- | |- | ||
| generator (g) | | generator (g) | ||
| 5\18, 333. | | 5\18, 333.3 | ||
| 7\25, 336. | | 7\25, 336.0 | ||
| 335.84 | | 335.84 | ||
|- | |- | ||
| L (octave - 3g) | | L (octave - 3g) | ||
| 3\18, 200. | | 3\18, 200.0 | ||
| 4\25, 192. | | 4\25, 192.0 | ||
| 193.16 | | 193.16 | ||
|- | |- | ||
| s (4g - octave) | | s (4g - octave) | ||
| 2\18, 133. | | 2\18, 133.3 | ||
| 3\25, 144. | | 3\25, 144.0 | ||
| 143.36 | | 143.36 | ||
|} | |} | ||
==== Intervals ==== | |||
Sortable table of major and minor intervals in parasoft smitonic tunings: | |||
{| class="wikitable right-2 right-3 right-4 sortable " | |||
|- | |||
! class="unsortable"|Degree | |||
! [[18edo]] | |||
! [[25edo]] | |||
! class="unsortable"| Note name on J | |||
! class="unsortable"| Approximate ratios | |||
! #Gens up | |||
|- | |||
| unison | |||
| 0\18, 0.0 | |||
| 0\25, 0.0 | |||
| J | |||
| 1/1 | |||
| 0 | |||
|- | |||
| min. smi2nd | |||
| 2\18, 133.3 | |||
| 3\18, 144.0 | |||
| K@ | |||
| | |||
| +4 | |||
|- | |||
| maj. smi2nd | |||
| 3\18, 200.0 | |||
| 4\25, 192.0 | |||
| K | |||
| 9/8, 10/9 | |||
| -3 | |||
|- | |||
| perf. smi3rd | |||
| 5\18, 333.3 | |||
| 7\25, 336.0 | |||
| L | |||
| 17/14, 40/33 | |||
| +1 | |||
|- | |||
| aug. smi3rd | |||
| 4\13, 400.0 | |||
| 8\25, 384.4 | |||
| L& | |||
| 5/4 | |||
| -6 | |||
|- | |||
| min. smi4th | |||
| 7\18, 466.7 | |||
| 10\25, 480.0 | |||
| M@ | |||
| | |||
| +5 | |||
|- | |||
| maj. smi4th | |||
| 8\18, 533.3 | |||
| 11\25, 528.0 | |||
| M | |||
| 19/14, 34/25 | |||
| -2 | |||
|- | |||
| min. smi5th | |||
| 10\18, 666.7 | |||
| 14\25, 672.0 | |||
| N | |||
| 28/19, 25/17 | |||
| +2 | |||
|- | |||
| maj. smi5th | |||
| 11\18, 733.3 | |||
| 15\25, 720.0 | |||
| N& | |||
| | |||
| -5 | |||
|- | |||
| dim. smi6th | |||
| 12\18, 800.0 | |||
| 17\25, 816.0 | |||
| O@ | |||
| 8/5 | |||
| +6 | |||
|- | |||
| perf. smi6th | |||
| 13\18, 866.7 | |||
| 18\25, 864.0 | |||
| O | |||
| 28/17, 33/20 | |||
| -1 | |||
|- | |||
| min. smi7th | |||
| 15\18, 1000.0 | |||
| 21\25, 1008.0 | |||
| P | |||
| 16/9, 9/5 | |||
| +3 | |||
|- | |||
| maj. smi7th | |||
| 16\18, 1066.7 | |||
| 22\25, 1056.0 | |||
| P& | |||
| 12/7 | |||
| -4 | |||
|} | |||
=== Hyposoft === | === Hyposoft === | ||
[[Hyposoft]] tunings of smitonic have [[step ratio]]s between 3/2 and 2/1 which implies that the generator is a supraminor third sharper than 3\11 = 327.27¢ and flatter than 5\18 = 333.33¢. | [[Hyposoft]] tunings of smitonic have [[step ratio]]s between 3/2 and 2/1 which implies that the generator is a supraminor third sharper than 3\11 = 327.27¢ and flatter than 5\18 = 333.33¢. | ||