Omnidiatonic

Omnidiatonic (also known as interdia and archylino) is a 7-note maximum-variety-3 scale with the step signature 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). In terms of Greek scales, this can be seen as Archytas' diatonic.

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)	[math]\displaystyle{ \displaystyle \frac{1}{2} \lt G_\text{1} \lt \frac{3}{5} }[/math]
RH inner generator (G2R = M + s)	[math]\displaystyle{ \displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 4 G_\text{1} - 2 \text{ for }\frac{1}{2} \lt G_\text{1} \le \frac{4}{7} }[/math] [math]\displaystyle{ \displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 2 - 3 G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5} }[/math]
LH inner generator (G2L = L + M)	[math]\displaystyle{ \displaystyle 2 - 3 G_\text{1} \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for } \frac{1}{2} \lt G_\text{1} \le \frac{4}{7} }[/math] [math]\displaystyle{ \displaystyle 4 G_\text{1} - 2 \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5} }[/math]
Large step (L = 1 - G1 - G2R)	[math]\displaystyle{ \displaystyle \frac{1}{7} \lt L \lt \frac{1}{2} }[/math]
Middle step (M = 2G1 - 1)	[math]\displaystyle{ \displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt L \text{ for } \frac{1}{7} \lt L \le \frac{1}{5} }[/math] [math]\displaystyle{ \displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2} }[/math]
Small step (s = 1 - G1 - G2L)	[math]\displaystyle{ \displaystyle \frac{1}{2} (1 - 5 L) \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} \lt L \le \frac{1}{5} }[/math] [math]\displaystyle{ \displaystyle 0 \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2} }[/math]

Tuning	L	M	s	Comments
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

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