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) would divide the octave into eighteen 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	septimal 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

Todo: expand