Xenharmonic Wiki

Subharmonics 18–36: Difference between revisions

← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,830 edits
m →Modes: added major sixths and changed colour scheme to loosely reflect consonance
Sintel (talk | contribs)
autopatrolled, emailconfirmed
1,893 edits
No edit summary
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{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 134: Line 134:
{{todo|complete table|comment=add audio examples|inline=1}}
{{todo|complete table|comment=add audio examples|inline=1}}


```wikitext
== Modes ==
== Modes ==
Interval values given in [[cents]].
Interval values given in [[cents]].
Line 140: Line 139:
'''Orange''' indicates intervals in the subminor and minor third [[interval region]]s.
'''Orange''' indicates intervals in the subminor and minor third [[interval region]]s.


'''Yellow''' indicates intervals in the major and supermajor third interval regions.
'''Yellow''' indicates intervals in the major third region.


'''Teal''' indicates intervals in the perfect fourth interval 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.
'''Blue''' indicates intervals in the perfect fifth interval region.
Line 157: Line 158:
|-
|-
! 0
! 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 || style="background:#FDFFB6; font-weight:bold;" | 435.084 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 563.382 || 631.283 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 775.636 || 852.592 || 933.129 || 1017.596 || 1106.397 || 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
! 48.77
Line 163: Line 164:
|-
|-
! 98.955
! 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 || 532.328 || 603 || 676.681 || 753.637 || 834.174 || 918.641 || 1007.442 || 1101.045
| 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
! 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 || style="background:#FDFFB6; font-weight:bold;" | 412.745 || style="background:#9BF6FF; font-weight:bold;" | 480.646 || 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
| 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
! 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 || style="background:#FDFFB6; font-weight:bold;" | 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
| 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
! 258.874
Line 175: Line 176:
|-
|-
! 315.641
! 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 || 536.951 || 617.488 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 790.756 || style="background:#CAFFBF; font-weight:bold;" | 884.359
| 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
! 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 || 558.796 || 643.263 || 732.064 || 825.667
| 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
! 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 || style="background:#FDFFB6; font-weight:bold;" | 417.508 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 582.512 || 671.313 || 764.916
| 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
! 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 || style="background:#FDFFB6; font-weight:bold;" | 435.084 || style="background:#9BF6FF; font-weight:bold;" | 519.551 || 608.352 || style="background:#A0C4FF; font-weight:bold;" | 701.955
| 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
! 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 || 543.015 || 636.618
| 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
! 631.283
| 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 || 568.717
| 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
! 701.955
| style="background:#9BF6FF; font-weight:bold;" | 498.045 || 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
| 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
! 775.636
| style="background:#FDFFB6; font-weight:bold;" | 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 || style="background:#FDFFB6; font-weight:bold;" | 424.364
| 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
! 852.592
| 347.408 || style="background:#FDFFB6; font-weight:bold;" | 396.178 || 446.363 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 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
| 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
! 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 || style="background:#FDFFB6; font-weight:bold;" | 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
| 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
! 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 || 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
| 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
! 1106.397
Line 211: Line 212:
|-
|-
! 1200
! 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 || style="background:#FDFFB6; font-weight:bold;" | 435.084 || style="background:#9BF6FF; font-weight:bold;" | 498.045 || 563.382 || 631.283 || style="background:#A0C4FF; font-weight:bold;" | 701.955 || 775.636 || 852.592 || 933.129 || 1017.596 || 1106.397 || 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
|}
|}
```


== Scales ==
== Scales ==
Line 235: Line 235:


== Music ==
== 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]]
; [[Budjarn Lambeth]]
* [https://www.youtube.com/watch?v=zwMpZU5wo1A ''Four microtonal improvisations in 18ifdo''] (2026)
* [https://www.youtube.com/watch?v=zwMpZU5wo1A ''Four microtonal improvisations in 18ifdo''] (2026)


;; [[Claudi Meneghin]]
; [[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)
* [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)
{{Navbox subharmonics}}
Retrieved from "https://en.xen.wiki/w/Subharmonics_18–36"