Omnidiatonic: Difference between revisions
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Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27. | Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27. | ||
== Modes == | |||
Omnidiatonic has 14 modes total, with 7 LH and 7 RH modes. | |||
{| class="wikitable" | |||
|+Omnidiatonic modes | |||
!Left handed | |||
!Right handed | |||
|- | |||
|LmsmLsm | |||
|LmsLmsm | |||
|- | |||
|LsmLmsm | |||
|LmsmLms | |||
|- | |||
|mLmsmLs | |||
|mLmsLms | |||
|- | |||
|mLsmLms | |||
|msLmsmL | |||
|- | |||
|msmLsmL | |||
|msmLmsL | |||
|- | |||
|smLmsmL | |||
|sLmsmLm | |||
|- | |||
|smLsmLm | |||
|smLmsLm | |||
|} | |||
== Tunings == | == Tunings == | ||
{| class="wikitable" | |||
|+Tuning range of omnidiatonic | |||
! | |||
! Tuning range (in [[octave]]s) | |||
|- | |||
! Outer generator <br>(''G''<sub>1</sub> = L + 2m + s) | |||
| <math>\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}</math> | |||
|- | |||
! RH inner generator <br>(''G''<sub>2R</sub> = m + s) | |||
| <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math> | |||
|- | |||
! LH inner generator <br>(''G''<sub>2L</sub> = L + m) | |||
| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math> | |||
|- | |||
! Large step <br>(L = 1 - ''G''<sub>1</sub> - ''G''<sub>2R</sub>) | |||
| <math>\displaystyle \frac{1}{7} < L < \frac{1}{2}</math> | |||
|- | |||
! Middle step <br>(m = 2''G''<sub>1</sub> - 1) | |||
| <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math> | |||
|- | |||
! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>) | |||
| <math>\displaystyle \frac{1}{2} (1 - 5 L) < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <br><math>\displaystyle 0 < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math> | |||
|} | |||
{|class="wikitable" | {|class="wikitable" | ||
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|} | |} | ||
== See also == | |||
* [[Nicetone]] – sister 3L 2m 2s scale | |||
* [[Antinicetone]] – sister 2L 2m 3s scale | |||
* [[5L 2s]] – LM-equalized version of omnidiatonic | |||
** [[5L 2s Muddles]] – other diatonic muddles | |||
* [[2L 5s]] – MS-equalized version of omnidiatonic | |||
* [[2L 3s]] – collapsed version of omnidiatonic | |||
[[Category:Rank-3 scales]] | [[Category:Rank-3 scales]] | ||
[[Category:7-tone scales]] | |||
[[Category:GO scales]] | |||