18ifdo
| ← 17ifdo 18ifdo 19ifdo → | |
|---|---|
| Prime factors | 2 3 |
| Fifth | 36 / 24 (701.9 cents) |
18ifdo (inverse-arithmetic frequency division of the octave), or 18udo (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 17ifdo and a subset of 19ifdo, its inverse is 18afdo. As a scale it may also be known as mode 18 of the subharmonic series or the Under-18 scale.
Directly above its root it contains copies of 6ifdo and 9ifdo, making it a comprehensive scale for under-3 harmony, the utonal version of over-3 primodality.
Above its root it contains a fairly even mix of 5-limit intervals familiar to 12edo listeners, and higher limit xenharmonic sonorities.
Coincidentally, 18ifdo has the property that its first step is similar in size to a 24edo-step, and its 18th step is similar in size to a 12edo-step.
Intervals
| # | Cents | Ratio | Interval name | Audio |
|---|---|---|---|---|
| 0 | 0.00 | 1/1 | perfect unison | |
| 1 | 48.770 | 36/35 | septimal quarter tone | |
| 2 | 98.955 | 18/17 | small septendecimal semitone, Arabic lute index finger | |
| 3 | 150.637 | 12/11 | small undecimal neutral second | |
| 4 | 203.910 | 9/8 | Pythagorean (whole) tone, major (whole) tone, octave-reduced 9th harmonic | |
| 5 | 258.874 | 36/31 | tricesimoprimal semifourth, tricesimoprimal subminor third | |
| 6 | 315.641 | 6/5 | classic minor third, just minor third | |
| 7 | 374.333 | 36/29 | vicesimononal major third | |
| 8 | 435.084 | 9/7 | supermajor third | |
| 9 | 498.045 | 4/3 | just perfect fourth, octave-reduced 3rd subharmonic | |
| 10 | 563.382 | 18/13 | tridecimal augmented fourth | |
| 11 | 631.283 | 36/25 | pental diminished fifth, classic diminshed fifth | |
| 12 | 701.955 | 3/2 | just perfect fifth, octave-reduced 3rd harmonic | |
| 13 | 775.636 | 36/23 | vicesimotertial augmented fifth | |
| 14 | 852.592 | 18/11 | undecimal neutral sixth | |
| 15 | 933.129 | 12/7 | septimal supermajor sixth | |
| 16 | 1017.596 | 9/5 | classic minor seventh, pental minor seventh | |
| 17 | 1106.397 | 36/19 | undevicesimal major seventh, Boethius' major seventh | |
| 18 | 1200.000 | 2/1 | octave |
Scales
- Fireflies[idiosyncratic term]: 36/30-36/24-36/21-36/20-36/18
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Todo: expand |