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 |
|
Todo: complete table
add audio examples |
Modes
Interval values given in cents.
Yellow indicates intervals in the subminor and minor third interval regions.
Purple indicates intervals in the major and supermajor third interval regions.
Blue indicates intervals in the perfect fourth interval region.
Red indicates intervals in the perfect fifth interval region.
Green indicates intervals in the subminor seventh ('barbershop seventh') interval region.
(Interval region boundaries are subjective and approximate. See interval region for discussion.)
| 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:
