Subharmonics 11–22

Subharmonics 11–22

Prime factorization	11 (prime)
Dual sharp fifth	22/14 (782.492c)
Dual flat fifth	22/15 (663.049c)

The subharmonics 11–22 are a scale that consists of subharmonics 11 through 22 of the subharmonic series. Above the root they form the ratios 22/22, 22/21, …, 22/11 and repeat at the octave. Used as a tuning system, it is also called 11ifdo. The inverse consists of harmonics 11–22.

It does not contain a perfect fourth or perfect fifth directly above its root, giving it an ungrounded 'floating' feeling similar to the 12edo whole tone scale (6edo), but with a similar step size to the chromatic scale of 12edo, and with very xenharmonic new harmonies available. Composers who find 11edo and 13edo appealing are likely to enjoy this scale for similar reasons.

Intervals

#	Cents	Ratio	Interval name	Audio
0	0.000	1/1	perfect unison
1	80.537	22/21	undecimal minor semitone
2	165.004	11/10	large undecimal neutral second
3	253.805	22/19	undevicesimal semifourth, godzilla semifourth
4	347.408	11/9	undecimal neutral third
5	446.363	22/17	septendecimal supermajor third
6	551.318	11/8	undecimal super-fourth, octave-reduced 11th harmonic
7	663.049	22/15	undecimal diminished fifth
8	782.492	11/7	undecimal subminor sixth, undecimal augmented fifth
9	910.790	22/13	tridecimal major sixth
10	1049.363	11/6	undecimal neutral seventh
11	1200.000	2/1	octave

Scales

• Undersea cave^{[idiosyncratic term]}: 22/20-22/16-22/14-22/12-22/10-22/8-22/7-4/1
• Octave-reduced undersea cave^{[idiosyncratic term]}: 22/20-22/16-22/14-22/12-22/11

Todo: expand