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

Modes

Interval values given in cents.

	0	48.77	98.955	150.637	203.91	258.874	315.641	374.333	435.084	498.045	563.382	631.283	701.955	775.636	852.592	933.129	1017.596	1106.397	1200
0	0	48.77	98.955	150.637	203.91	258.874	315.641	374.333	435.084	498.045	563.382	631.283	701.955	775.636	852.592	933.129	1017.596	1106.397	0
48.77	1151.23	0	50.185	101.867	155.14	210.104	266.871	325.563	386.314	449.275	514.612	582.513	653.185	726.866	803.822	884.359	968.826	1057.627	1151.23
98.955	1101.045	1149.815	0	51.682	104.955	159.919	216.686	275.378	336.129	399.09	464.427	532.328	603	676.681	753.637	834.174	918.641	1007.442	1101.045
150.637	1049.363	1098.133	1148.318	0	53.273	108.237	165.004	223.696	284.447	347.408	412.745	480.646	551.318	624.999	701.955	782.492	866.959	955.76	1049.363
203.91	996.09	1044.86	1095.045	1146.727	0	54.964	111.731	170.423	231.174	294.135	359.472	427.373	498.045	571.726	648.682	729.219	813.686	902.487	996.09
258.874	941.126	989.896	1040.081	1091.763	1145.036	0	56.767	115.459	176.21	239.171	304.508	372.409	443.081	516.762	593.718	674.255	758.722	847.523	941.126
315.641	884.359	933.129	983.314	1034.996	1088.269	1143.233	0	58.692	119.443	182.404	247.741	315.642	386.314	459.995	536.951	617.488	701.955	790.756	884.359
374.333	825.667	874.437	924.622	976.304	1029.577	1084.541	1141.308	0	60.751	123.712	189.049	256.95	327.622	401.303	478.259	558.796	643.263	732.064	825.667
435.084	764.916	813.686	863.871	915.553	968.826	1023.79	1080.557	1139.249	0	62.961	128.298	196.199	266.871	340.552	417.508	498.045	582.512	671.313	764.916
498.045	701.955	750.725	800.91	852.592	905.865	960.829	1017.596	1076.288	1137.039	0	65.337	133.238	203.91	277.591	354.547	435.084	519.551	608.352	701.955
563.382	636.618	685.388	735.573	787.255	840.528	895.492	952.259	1010.951	1071.702	1134.663	0	67.901	138.573	212.254	289.21	369.747	454.214	543.015	636.618
631.283	568.717	617.487	667.672	719.354	772.627	827.591	884.358	943.05	1003.801	1066.762	1132.099	0	70.672	144.353	221.309	301.846	386.313	475.114	568.717
701.955	498.045	546.815	597	648.682	701.955	756.919	813.686	872.378	933.129	996.09	1061.427	1129.328	0	73.681	150.637	231.174	315.641	404.442	498.045
775.636	424.364	473.134	523.319	575.001	628.274	683.238	740.005	798.697	859.448	922.409	987.746	1055.647	1126.319	0	76.956	157.493	241.96	330.761	424.364
852.592	347.408	396.178	446.363	498.045	551.318	606.282	663.049	721.741	782.492	845.453	910.79	978.691	1049.363	1123.044	0	80.537	165.004	253.805	347.408
933.129	266.871	315.641	365.826	417.508	470.781	525.745	582.512	641.204	701.955	764.916	830.253	898.154	968.826	1042.507	1119.463	0	84.467	173.268	266.871
1017.596	182.404	231.174	281.359	333.041	386.314	441.278	498.045	556.737	617.488	680.449	745.786	813.687	884.359	958.04	1034.996	1115.533	0	88.801	182.404
1106.397	93.603	142.373	192.558	244.24	297.513	352.477	409.244	467.936	528.687	591.648	656.985	724.886	795.558	869.239	946.195	1026.732	1111.199	0	93.603
1200	0	48.77	98.955	150.637	203.91	258.874	315.641	374.333	435.084	498.045	563.382	631.283	701.955	775.636	852.592	933.129	1017.596	1106.397	0

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

Instruments

Lumatone mappings

Herman Miller, 7 Sep 2026

• LTN file: File:18ifdo.ltn
• Image file: