23edf: Difference between revisions
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'''23EDF''' is the [[EDF|equal division of the just perfect fifth]] into 23 parts of 30.5198 [[ | {{Infobox ET}} | ||
'''23EDF''' is the [[EDF|equal division of the just perfect fifth]] into 23 parts of 30.5198 [[cents]] each, corresponding to 39.3188 [[edo]] (similar to every third step of [[118edo]]). | |||
== | ==History== | ||
A proponent of 23edf is [[Petr Pařízek]]. The first to write about 23edf on this wiki was [[Todd Harrop]] in 2015. | |||
==Theory== | |||
23edf is close to [[39edo]] and/or [[62edt]], however, the respective [[octave]] and [[tritave|twelfth]] would need to be nearly 10 cents flat. | |||
Some intervals in table below, selected on the basis of single-use of | Some intervals in table below, selected on the basis of single-use of [[prime]]s (for most cases): | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 81: | Line 83: | ||
| style="text-align:center;" | –1.9¢ | | style="text-align:center;" | –1.9¢ | ||
|} | |} | ||
=== Harmonics === | |||
{{Harmonics in equal|23|3|2}} | |||
{{Harmonics in equal|23|3|2|start=12|collapsed=1}} | |||
== Intervals == | |||
{| class="wikitable mw-collapsible" | |||
|+ Intervals of 23edf | |||
|- | |||
!Step number | |||
!Size (cents) | |||
|- | |||
|1 | |||
|30.5198 | |||
|- | |||
|2 | |||
|61.0296 | |||
|- | |||
|3 | |||
|91.55935 | |||
|- | |||
|4 | |||
|122.0791 | |||
|- | |||
|5 | |||
|152.5989 | |||
|- | |||
|6 | |||
|183.1187 | |||
|- | |||
|7 | |||
|213.6385 | |||
|- | |||
|8 | |||
|244.1583 | |||
|- | |||
|9 | |||
|274.678 | |||
|- | |||
|10 | |||
|305.1978 | |||
|- | |||
|11 | |||
|335.7176 | |||
|- | |||
|12 | |||
|366.2374 | |||
|- | |||
|13 | |||
|396.7572 | |||
|- | |||
|14 | |||
|427.277 | |||
|- | |||
|15 | |||
|457.7967 | |||
|- | |||
|16 | |||
|488.3165 | |||
|- | |||
|17 | |||
|518.8363 | |||
|- | |||
|18 | |||
|549.3561 | |||
|- | |||
|19 | |||
|579.8759 | |||
|- | |||
|20 | |||
|610.39565 | |||
|- | |||
|21 | |||
|640.9154 | |||
|- | |||
|22 | |||
|671.4352 | |||
|- | |||
|23 | |||
|701.955 | |||
|- | |||
|24 | |||
|732.4748 | |||
|- | |||
|25 | |||
|762.9946 | |||
|- | |||
|26 | |||
|793.51435 | |||
|- | |||
|27 | |||
|824.0341 | |||
|- | |||
|28 | |||
|854.5539 | |||
|- | |||
|29 | |||
|885.0737 | |||
|- | |||
|30 | |||
|915.5935 | |||
|- | |||
|31 | |||
|946.1133 | |||
|- | |||
|32 | |||
|976.633 | |||
|- | |||
|33 | |||
|1007.1529 | |||
|- | |||
|34 | |||
|1037.6726 | |||
|- | |||
|35 | |||
|1068.1924 | |||
|- | |||
|36 | |||
|1098.7122 | |||
|- | |||
|37 | |||
|1129.232 | |||
|- | |||
|38 | |||
|1159.7517 | |||
|- | |||
|39 | |||
|1190.2715 | |||
|- | |||
|40 | |||
|1220.7913 | |||
|- | |||
|41 | |||
|1251.3111 | |||
|- | |||
|42 | |||
|1281.8309 | |||
|- | |||
|43 | |||
|1312.35065 | |||
|- | |||
|44 | |||
|1342.8704 | |||
|- | |||
|45 | |||
|1373.3902 | |||
|- | |||
|46 | |||
|1403.91 | |||
|} | |||
{{todo|inline=1|complete table|text=Add at least one more column, showing what the notes are named, what JI they approximate, or anything else interesting about them individually.}} | |||
{{todo|expand}} | |||
[[Category:nonoctave]] | [[Category:nonoctave]] | ||