Subharmonics 11–22: Difference between revisions
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Created page with "{{Infobox IFDO|steps=11}} '''11ifdo''' (inverse-arithmetic frequency division of the octave), or '''11udo''' (utonal division of the octave), if the attempt is made to use it as an actual tuning system, would divide the octave into sixteen inverse-arithmetically equal parts. It is a superset of 10ifdo and a subset of 12ifdo, its inverse is 11afdo. As a scale it may also be known as mode 11 of the subharmonic series or the Under-11 sca..." |
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{{Infobox | {{Infobox subharmonics|11}} | ||
{{Subharmonics intro|11}} | |||
It does not contain a perfect fourth or perfect fifth directly above its root, giving it an ungrounded 'floating' feeling similar to the [[ | 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 == | == Intervals == | ||
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== Scales == | == Scales == | ||
* Undersea cave{{idio}}: 22/20-22/16-22/14-22/12-22/11 | * Undersea cave{{idio}}: 22/20-22/16-22/14-22/12-22/10-22/8-22/7-4/1 | ||
* [[Octave-reduced]] undersea cave{{idio}}: 22/20-22/16-22/14-22/12-22/11 | |||
{{todo|expand|inline=1}} | {{todo|expand|inline=1}} | ||
{{Navbox subharmonics}} | |||
Latest revision as of 00:50, 11 October 2026
| 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 |
| View • Talk • EditUndertone scales | |
|---|---|
| Small modes | 3 • 11 • 16 • 18 |
| Families | 3/: 3 • 18 |
| Related | Subharmonic series • Harmonic series • Overtone scale • Ringer scale |