11ifdo: Difference between revisions
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'''11ifdo''' ([[IFDO|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 scale. | '''11ifdo''' ([[IFDO|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 scale. | ||
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 11ifdo for similar reasons. | 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 11ifdo for similar reasons. | ||
== Intervals == | == Intervals == | ||
Latest revision as of 07:14, 26 August 2026
| ← 10ifdo 11ifdo 12ifdo → | |
|---|---|
| Prime factors | 11 |
| Fifth | 22 / 14 (782.4 cents) |
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 scale.
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 11ifdo 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]: 22/20-22/16-22/14-22/12-22/11
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Todo: expand |