4L 7s: Difference between revisions
m →Hypohard: Hanson is a synonym of (5-limit) kleismic |
Hypohard table |
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Hypohard tunings of kleistonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢. | Hypohard tunings of kleistonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢. | ||
This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic (aka [[Hanson]]) temperament and its extensions. | This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth ([[3/2]]), an octave above. This is the range associated with the eponymous Kleismic (aka [[Hanson]]) temperament and its extensions. | ||
Hypohard kleistonic edos include [[15edo]], [[19edo]], and [[34edo]]. | |||
The sizes of the generator, large step and small step of kleistonic are as follows in various hypohard smitonic tunings. | |||
{| class="wikitable right-2 right-3 right-4" | |||
|- | |||
! | |||
! [[15edo]] (basic) | |||
! [[19edo]] (hard) | |||
! [[34edo]] (semihard) | |||
! Some JI approximations | |||
|- | |||
| generator (g) | |||
| 4\15, 320.00 | |||
| 5\19, 315.79 | |||
| 9\34, 317.65 | |||
| 6/5 | |||
|- | |||
| L (octave - 3g) | |||
| 2\15, 160.00 | |||
| 3\19, 189.47 | |||
| 5\34, 176.47 | |||
| 10/9, 11/10 | |||
|- | |||
| s (4g - octave) | |||
| 1\15, 80.00 | |||
| 1\19, 63.16 | |||
| 2\34, 70.59 | |||
| 25/24 | |||
|} | |||
=== Parahard === | === Parahard === | ||