# Omnidiatonic

Omnidiatonic (also known as interdia and archylino) is a 7-note max-variety-3 scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. 14edo is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by CompactStar and the name "interdia" was given by Xenllium, both of which refer to this scale being intermediate between the 5L 2s diatonic scale and the 2L 5s antidiatonic scale. The name "archylino" was given by Praveen Venkataramana, which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).

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.

Omnidiatonic modes
Left handed Right handed
LmsmLsm LmsLmsm
LsmLmsm LmsmLms
mLmsmLs mLmsLms
mLsmLms msLmsmL
msmLsmL msmLmsL
smLmsmL sLmsmLm
smLsmLm smLmsLm

## Tunings

Tuning range of omnidiatonic
Tuning range (in octaves)
Outer generator
(G1 = L + 2m + s)
$\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}$
RH inner generator
(G2R = m + s)
$\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}$
$\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}$
LH inner generator
(G2L = L + m)
$\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}$
$\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}$
Large step
(L = 1 - G1 - G2R)
$\displaystyle \frac{1}{7} < L < \frac{1}{2}$
Middle step
(m = 2G1 - 1)
$\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}$
$\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}$
Small step
(s = 1 - G1 - G2L)
$\displaystyle \frac{1}{2} (1 - 5 L) < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}$
$\displaystyle 0 < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}$
14edo 3 2 1
16edo 4 2 1 Also has antidiatonic MOS
18edo 5 2 1 Also has antidiatonic MOS
19edo 4 3 1 Also has diatonic MOS
20edo 6 2 1
21edo 4 3 2
5 3 1
22edo 7 2 1 Also has diatonic MOS
23edo 5 3 2