4L 7s: Difference between revisions
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Hypohard kleistonic edos include [[15edo]], [[19edo]], and [[34edo]]. | 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 kleistonic tunings | The sizes of the generator, large step and small step of kleistonic are as follows in various hypohard kleistonic tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
|- | |- | ||
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=== Parahard === | === Parahard === | ||
Parahard tunings of kleistonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢. | Parahard tunings of kleistonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢. | ||
The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. | The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone. | ||
Parahard kleistonic edos include [[19edo]], [[32edo]], and [[42edo]]. | |||
The sizes of the generator, large step and small step of kleistonic are as follows in various parahard kleistonic tunings: | |||
{| class="wikitable right-2 right-3 right-4" | |||
|- | |||
! | |||
![[19edo]] (hard) | |||
![[23edo]] (superhard) | |||
! [[42edo]] (parahard) | |||
! Some JI approximations | |||
|- | |||
| generator (g) | |||
| 5\19, 315.79 | |||
| 6\23, 313.04 | |||
| 11\42, 314.29 | |||
| 6/5 | |||
|- | |||
| L (octave - 3g) | |||
| 3\19, 189.47 | |||
| 4\23, 208.70 | |||
| 7\42, 200.00 | |||
| 10/9, 9/8 | |||
|- | |||
| s (4g - octave) | |||
| 1\19, 63.16 | |||
| 1\23, 52.17 | |||
| 2\42, 57.14 | |||
| 28/27, 33/32 | |||
|} | |||
=== Hyperhard === | === Hyperhard === | ||
Hyperhard tunings of kleistonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. | Hyperhard tunings of kleistonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. | ||
The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. | The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. | ||
These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity. | These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity, where the small step is generally flat of a quarter tone. | ||
Hyperhard kleistonic edos include [[23edo]], [[31edo]], and 27edo. | Hyperhard kleistonic edos include [[23edo]], [[31edo]], and [[27edo]]. | ||
The sizes of the generator, large step and small step of kleistonic are as follows in various hyperhard kleistonic tunings | The sizes of the generator, large step and small step of kleistonic are as follows in various hyperhard kleistonic tunings: | ||
{| class="wikitable right-2 right-3 right-4" | {| class="wikitable right-2 right-3 right-4" | ||
|- | |- | ||
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| 1\31, 38.71 | | 1\31, 38.71 | ||
| 1\27, 44.44 | | 1\27, 44.44 | ||
| 36/35 | | 36/35, 45/44 | ||
|} | |} | ||