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23edo: Difference between revisions

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== Selected just intervals ==
== Selected just intervals ==
{| class="wikitable center-all"
{{Q-odd-limit intervals|23}}
|+Direct mapping (even if inconsistent)
|-
! Interval, complement
! Error (abs, [[Cent|¢]])
|-
| [[14/11]], [[11/7]]
| 0.117
|-
| [[6/5]], [[5/3]]
| 2.598
|-
| [[9/8]], [[16/9]]
| 4.786
|-
| '''[[16/13]], [[13/8]]'''
| '''5.745'''
|-
| [[12/11]], [[11/6]]
| 5.885
|-
| [[7/6]], [[12/7]]
| 6.001
|-
| [[16/15]], [[15/8]]
| 7.383
|-
| [[11/10]], [[20/11]]
| 8.482
|-
| [[7/5]], [[10/7]]
| 8.599
|-
| [[18/13]], [[13/9]]
| 10.531
|-
| [[15/13]], [[26/15]]
| 12.958
|}


== Notation ==
== Notation ==
23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 is not E. Chord names are different because C - E - G is not P1 - M3 - P5.
23edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 is not E. Chord names are different because C - E - G is not P1 - M3 - P5.


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Important [[mos]]ses include:
Important [[mos]]ses include:


* mavila 2L5s 4334333 (13\23, 1\1)
* Mavila 2L5s 4334333 (13\23, 1\1)
* mavila 7L2s 133313333 (13\23, 1\1)
* Mavila 7L2s 133313333 (13\23, 1\1)
* sephiroth 3L4s 2525252 (7\23, 1\1)
* Sephiroth 3L4s 2525252 (7\23, 1\1)
* [[semiquartal]] 5L4s 332323232 (5\23, 1\1)
* [[Semiquartal]] 5L4s 332323232 (5\23, 1\1)


The chart below shows some of the mos modes of [[mavila]] available in 23edo, mainly Pentatonic (5-note), antidiatonic (7-note), 9- and 16-note mosses. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note mosses:
The chart below shows some of the mos modes of [[mavila]] available in 23edo, mainly Pentatonic (5-note), antidiatonic (7-note), 9- and 16-note mosses. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note mosses:
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|-
|-
| 3 3 4 3 3 3 4
| 3 3 4 3 3 3 4
|[[2L 5s|2L 5s (mavila, anti-diatonic)]]
| [[2L 5s|2L 5s (mavila, anti-diatonic)]]
|-
|-
| 4 3 3 3 3 4 3
| 4 3 3 3 3 4 3
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| [[3L 7s|3L 7s (sephiroid)]]
| [[3L 7s|3L 7s (sephiroid)]]
|-
|-
|4 1 1 4 1 1 4 1 1 4 1
| 4 1 1 4 1 1 4 1 1 4 1
|[[4L 7s|4L 7s (kleistonic)]]
| [[4L 7s|4L 7s (kleistonic)]]
|-
|-
| 3 1 3 1 3 1 3 1 3 1 3
| 3 1 3 1 3 1 3 1 3 1 3
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|-
|-
| 3 1 1 3 1 3 1 1 3 1 3 1 1
| 3 1 1 3 1 3 1 1 3 1 3 1 1
|[[5L 8s|5L 8s (ateamtonic)]]
| [[5L 8s|5L 8s (ateamtonic)]]
|-
|-
|2 2 2 2 1 2 2 2 1 2 2 2 1
| 2 2 2 2 1 2 2 2 1 2 2 2 1
|[[10L 3s|10L 3s (luachoid)]]
| [[10L 3s|10L 3s (luachoid)]]
|-
|-
| 2 2 1 2 2 1 2 2 1 2 2 1 2 1
| 2 2 1 2 2 1 2 2 1 2 2 1 2 1
|[[9L 5s]] (Brittle [[Titanium]])
| [[9L 5s]] (Brittle [[Titanium]])
|-
|-
|2 1 2 2 1 2 2 1 2 2 1 2 2 1
| 2 1 2 2 1 2 2 1 2 2 1 2 2 1
|Palestine 14
| Palestine 14
|-
|-
|1 1 1 4 1 1 1 1 4 1 1 1 1 4
| 1 1 1 4 1 1 1 1 4 1 1 1 1 4
|[[3L 11s]]
| [[3L 11s]]
|-
|-
| 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1
| 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1
|[[4L 11s|4L 11s (mynoid)]]
| [[4L 11s|4L 11s (mynoid)]]
|-
|-
| 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
| 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
|[[8L 7s]]
| [[8L 7s]]
|-
|-
|2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 1
| 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 1
|[[7L 9s|7L 9s (mavila chromatic)]]
| [[7L 9s|7L 9s (mavila chromatic)]]
|-
|-
|2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
| 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1
| Palestine 17
| Palestine 17
|-
|-
|2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1
| 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1
| Pathological 5L 13s (ateamtonic[18])
| Pathological 5L 13s (ateamtonic[18])
|-
|-
| 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
| 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1
|Pathological [[4L 15s|<nowiki>4L 15s (mynoid[19]]</nowiki>]]
| Pathological [[4L 15s|<nowiki>4L 15s (mynoid[19]]</nowiki>]]
|}
|}


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<youtube>K4iO7k152og</youtube>
<youtube>K4iO7k152og</youtube>


===Lumatone===
=== Lumatone ===
See: [[Lumatone mapping for 23edo]]
See: [[Lumatone mapping for 23edo]]


Retrieved from "https://en.xen.wiki/w/23edo"