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Subharmonics 18–36: Difference between revisions

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{{Infobox IFDO|steps=18}}
{{Infobox subharmonics|18}}
'''18ifdo''' ([[IFDO|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.
{{Subharmonics intro|18}}


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]].  
Directly above its root it contains copies of [[Subharmonics 6–12|subharmonics 6–12]] and [[Subharmonics 9–18|subharmonics 9–18]], 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.
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.
Coincidentally, this scale 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.
The first serious attempt made at documenting and using this scale 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 ==
== Intervals ==
Line 131: Line 131:
| octave
| octave
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}
{{todo|complete table|comment=add audio examples|inline=1}}
== Modes ==
Interval values given in [[cents]].
'''Orange''' indicates intervals in the subminor and minor third [[interval region]]s.
'''Yellow''' indicates intervals in the major third region.
'''Teal''' indicates intervals in the perfect fourth region.
'''Pink''' indicates intervals in the semiaugmented fourth (near 11/8) region.
'''Blue''' indicates intervals in the perfect fifth interval region.
'''Green''' indicates intervals in the major sixth interval region.
'''Red''' indicates intervals in the subminor seventh ('barbershop seventh') interval region.
''(Interval region boundaries are subjective and approximate. See [[interval region]] for discussion.)''
{| class="wikitable" style="text-align:center;"
|-
! !! 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 || style="background:#FFD6A5; font-weight:bold;" | 258.874 || style="background:#FFD6A5; font-weight:bold;" | 315.641 || style="background:#FDFFB6; font-weight:bold;" | 374.333 || 435.084 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || style="background:#FFC6FF; font-weight:bold;" | 563.382 || 631.283 || style="background:#A0C4FF; font-weight:bold;" | 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 || style="background:#FFD6A5; font-weight:bold;" | 266.871 || style="background:#FFD6A5; font-weight:bold;" | 325.563 || style="background:#FDFFB6; font-weight:bold;" | 386.314 || 449.275 || style="background:#9BF6FF; font-weight:bold;" | 514.612 || 582.513 || 653.185 || 726.866 || 803.822 || style="background:#CAFFBF; font-weight:bold;" | 884.359 || style="background:#FFADAD; font-weight:bold;" | 968.826 || 1057.627 || 1151.23
|-
! 98.955
| 1101.045 || 1149.815 || 0 || 51.682 || 104.955 || 159.919 || 216.686 || style="background:#FFD6A5; font-weight:bold;" | 275.378 || style="background:#FFD6A5; font-weight:bold;" | 336.129 || style="background:#FDFFB6; font-weight:bold;" | 399.09 || 464.427 || style="background:#FFC6FF; font-weight:bold;" | 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 || style="background:#FFD6A5; font-weight:bold;" | 284.447 || 347.408 || 412.745 || style="background:#9BF6FF; font-weight:bold;" | 480.646 || style="background:#FFC6FF; font-weight:bold;" | 551.318 || 624.999 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 782.492 || style="background:#CAFFBF; font-weight:bold;" | 866.959 || style="background:#FFADAD; font-weight:bold;" | 955.76 || 1049.363
|-
! 203.91
| style="background:#FFADAD; font-weight:bold;" | 996.09 || 1044.86 || 1095.045 || 1146.727 || 0 || 54.964 || 111.731 || 170.423 || 231.174 || style="background:#FFD6A5; font-weight:bold;" | 294.135 || 359.472 || 427.373 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 571.726 || 648.682 || 729.219 || 813.686 || style="background:#CAFFBF; font-weight:bold;" | 902.487 || style="background:#FFADAD; font-weight:bold;" | 996.09
|-
! 258.874
| 941.126 || style="background:#FFADAD; font-weight:bold;" | 989.896 || 1040.081 || 1091.763 || 1145.036 || 0 || 56.767 || 115.459 || 176.21 || 239.171 || style="background:#FFD6A5; font-weight:bold;" | 304.508 || style="background:#FDFFB6; font-weight:bold;" | 372.409 || 443.081 || style="background:#9BF6FF; font-weight:bold;" | 516.762 || 593.718 || 674.255 || 758.722 || 847.523 || 941.126
|-
! 315.641
| style="background:#CAFFBF; font-weight:bold;" | 884.359 || 933.129 || style="background:#FFADAD; font-weight:bold;" | 983.314 || 1034.996 || 1088.269 || 1143.233 || 0 || 58.692 || 119.443 || 182.404 || 247.741 || style="background:#FFD6A5; font-weight:bold;" | 315.642 || style="background:#FDFFB6; font-weight:bold;" | 386.314 || 459.995 || style="background:#FFC6FF; font-weight:bold;" | 536.951 || 617.488 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 790.756 || style="background:#CAFFBF; font-weight:bold;" | 884.359
|-
! 374.333
| 825.667 || style="background:#CAFFBF; font-weight:bold;" | 874.437 || 924.622 || style="background:#FFADAD; font-weight:bold;" | 976.304 || 1029.577 || 1084.541 || 1141.308 || 0 || 60.751 || 123.712 || 189.049 || style="background:#FFD6A5; font-weight:bold;" | 256.95 || style="background:#FFD6A5; font-weight:bold;" | 327.622 || style="background:#FDFFB6; font-weight:bold;" | 401.303 || style="background:#9BF6FF; font-weight:bold;" | 478.259 || style="background:#FFC6FF; font-weight:bold;" | 558.796 || 643.263 || 732.064 || 825.667
|-
! 435.084
| 764.916 || 813.686 || style="background:#CAFFBF; font-weight:bold;" | 863.871 || 915.553 || style="background:#FFADAD; font-weight:bold;" | 968.826 || 1023.79 || 1080.557 || 1139.249 || 0 || 62.961 || 128.298 || 196.199 || style="background:#FFD6A5; font-weight:bold;" | 266.871 || 340.552 || 417.508 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 582.512 || 671.313 || 764.916
|-
! 498.045
| style="background:#A0C4FF; font-weight:bold;" | 701.955 || 750.725 || 800.91 || 852.592 || style="background:#CAFFBF; font-weight:bold;" | 905.865 || style="background:#FFADAD; font-weight:bold;" | 960.829 || 1017.596 || 1076.288 || 1137.039 || 0 || 65.337 || 133.238 || 203.91 || style="background:#FFD6A5; font-weight:bold;" | 277.591 || 354.547 || 435.084 || style="background:#9BF6FF; font-weight:bold;" | 519.551 || 608.352 || style="background:#A0C4FF; font-weight:bold;" | 701.955
|-
! 563.382
| 636.618 || style="background:#A0C4FF; font-weight:bold;" | 685.388 || 735.573 || 787.255 || 840.528 || style="background:#CAFFBF; font-weight:bold;" | 895.492 || style="background:#FFADAD; font-weight:bold;" | 952.259 || 1010.951 || 1071.702 || 1134.663 || 0 || 67.901 || 138.573 || 212.254 || style="background:#FFD6A5; font-weight:bold;" | 289.21 || style="background:#FDFFB6; font-weight:bold;" | 369.747 || 454.214 || style="background:#FFC6FF; font-weight:bold;" | 543.015 || 636.618
|-
! 631.283
| style="background:#FFC6FF; font-weight:bold;" | 568.717 || 617.487 || 667.672 || style="background:#A0C4FF; font-weight:bold;" | 719.354 || 772.627 || 827.591 || style="background:#CAFFBF; font-weight:bold;" | 884.358 || 943.05 || 1003.801 || 1066.762 || 1132.099 || 0 || 70.672 || 144.353 || 221.309 || style="background:#FFD6A5; font-weight:bold;" | 301.846 || style="background:#FDFFB6; font-weight:bold;" | 386.313 || 475.114 || style="background:#FFC6FF; font-weight:bold;" | 568.717
|-
! 701.955
| style="background:#9BF6FF; font-weight:bold;" | 498.045 || style="background:#FFC6FF; font-weight:bold;" | 546.815 || 597 || 648.682 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 756.919 || 813.686 || style="background:#CAFFBF; font-weight:bold;" | 872.378 || 933.129 || style="background:#FFADAD; font-weight:bold;" | 996.09 || 1061.427 || 1129.328 || 0 || 73.681 || 150.637 || 231.174 || style="background:#FFD6A5; font-weight:bold;" | 315.641 || style="background:#FDFFB6; font-weight:bold;" | 404.442 || style="background:#9BF6FF; font-weight:bold;" | 498.045
|-
! 775.636
| 424.364 || 473.134 || 523.319 || 575.001 || 628.274 || style="background:#A0C4FF; font-weight:bold;" | 683.238 || 740.005 || 798.697 || style="background:#CAFFBF; font-weight:bold;" | 859.448 || 922.409 || style="background:#FFADAD; font-weight:bold;" | 987.746 || 1055.647 || 1126.319 || 0 || 76.956 || 157.493 || 241.96 || style="background:#FFD6A5; font-weight:bold;" | 330.761 || 424.364
|-
! 852.592
| 347.408 || style="background:#FDFFB6; font-weight:bold;" | 396.178 || 446.363 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || style="background:#FFC6FF; font-weight:bold;" | 551.318 || 606.282 || 663.049 || style="background:#A0C4FF; font-weight:bold;" | 721.741 || 782.492 || 845.453 || 910.79 || style="background:#FFADAD; font-weight:bold;" | 978.691 || 1049.363 || 1123.044 || 0 || 80.537 || 165.004 || style="background:#FFD6A5; font-weight:bold;" | 253.805 || 347.408
|-
! 933.129
| style="background:#FFD6A5; font-weight:bold;" | 266.871 || style="background:#FFD6A5; font-weight:bold;" | 315.641 || style="background:#FDFFB6; font-weight:bold;" | 365.826 || 417.508 || 470.781 || 525.745 || 582.512 || 641.204 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 764.916 || 830.253 || style="background:#CAFFBF; font-weight:bold;" | 898.154 || style="background:#FFADAD; font-weight:bold;" | 968.826 || 1042.507 || 1119.463 || 0 || 84.467 || 173.268 || style="background:#FFD6A5; font-weight:bold;" | 266.871
|-
! 1017.596
| 182.404 || 231.174 || style="background:#FFD6A5; font-weight:bold;" | 281.359 || style="background:#FFD6A5; font-weight:bold;" | 333.041 || style="background:#FDFFB6; font-weight:bold;" | 386.314 || 441.278 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || style="background:#FFC6FF; font-weight:bold;" | 556.737 || 617.488 || style="background:#A0C4FF; font-weight:bold;" | 680.449 || 745.786 || 813.687 || style="background:#CAFFBF; font-weight:bold;" | 884.359 || style="background:#FFADAD; font-weight:bold;" | 958.04 || 1034.996 || 1115.533 || 0 || 88.801 || 182.404
|-
! 1106.397
| 93.603 || 142.373 || 192.558 || 244.24 || style="background:#FFD6A5; font-weight:bold;" | 297.513 || 352.477 || style="background:#FDFFB6; font-weight:bold;" | 409.244 || 467.936 || 528.687 || 591.648 || 656.985 || 724.886 || 795.558 || style="background:#CAFFBF; font-weight:bold;" | 869.239 || 946.195 || 1026.732 || 1111.199 || 0 || 93.603
|-
! 1200
| 0 || 48.77 || 98.955 || 150.637 || 203.91 || style="background:#FFD6A5; font-weight:bold;" | 258.874 || style="background:#FFD6A5; font-weight:bold;" | 315.641 || style="background:#FDFFB6; font-weight:bold;" | 374.333 || 435.084 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || style="background:#FFC6FF; font-weight:bold;" | 563.382 || 631.283 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 775.636 || 852.592 || 933.129 || 1017.596 || 1106.397 || 0
|}
|}


== Scales ==
== 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
* [[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{{idio}}: 36/30-36/24-36/21-36/20-36/18
* Fireflies{{idio}}: 36/30-36/24-36/21-36/20-36/18
* Han-Kumoi: 36/32-36/27-36/24-36/23-36/18
* Minor Blues: 36/30-36/27-36/26-36/24-36/20-36/18
* Minor hexatonic: 36/32-36/30-36/27-36/24-36/20-36/18
* Minor hexatonic: 36/32-36/30-36/27-36/24-36/20-36/18
* Sharpened dorian (sounds metallic/futuristic): 36/32-36/30-36/27-36/24-36/21-36/20-36/18
* 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{{idio}} (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: [[File:Miller 18ifdo mapping.png]]
 
== Music ==
; [[Noah Jordan]]
* [https://m.youtube.com/watch?v=voic4mft41M ''FILMBOARD: Microtonal Study #1 - 18ifdo — Inverse-Arithmetic Frequency Division of the Octave''] (2026)
 
; [[Budjarn Lambeth]]
* [https://www.youtube.com/watch?v=zwMpZU5wo1A ''Four microtonal improvisations in 18ifdo''] (2026)


; [[Claudi Meneghin]]
* [https://www.youtube.com/shorts/e0da1CkFNZI ''A 2-in-1 canon in F for organ (short version), in 18-IFDO, for baroque oboe and bassoon''] (2026)


{{todo|expand|inline=1}}
{{Navbox subharmonics}}
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