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.

The first serious attempt made at documenting and using 18ifdo was made by the Monthly Tunings Facebook group (a smaller group within the larger Xenharmonic Alliance). They voted it as the monthly tuning for September 2026, and made the first attempts to explore this tuning.

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

• Akebono II: 36/34-36/27-36/24-36/23-36/18
• Equiheptatonic: 36/33-36/30-36/27-36/24-36/22-36/20-36/18
• Equipentatonic: 36/31-36/27-36/24-36/21-36/18
• Fireflies^{[idiosyncratic term]}: 36/30-36/24-36/21-36/20-36/18
• Han-Kumoi: 36/32-36/27-36/24-36/23-36/18
• Minor Blues: 36/30-36/27-36/26-36/24-36/20-36/19-36/18
• Minor hexatonic: 36/32-36/30-36/27-36/24-36/20-36/18
• Minor melodic pentatonic: 36/32-36/30-36/24-36/19-36/18
• Mixolydian pentatonic: 36/32-36/27-36/24-36/19-36/18
• Neutral 2 neutral 6 pentatonic (sounds cold/ancient): 36/33-36/27-36/24-36/22-36/18
• Sharpened Dorian^{[idiosyncratic term]} (sounds metallic/futuristic): 36/32-36/30-36/27-36/24-36/21-36/20-36/18

Todo: expand