23edo: Difference between revisions

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=~~~~23 tone equal temperament~~~~=

=23 tone equal temperament=

~~'''''~~23-~~tET'''''~~, or ~~'''''~~23-EDO~~'''''~~, is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3|5/3]], [[11/7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just_intonation_subgroup|just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit|17-limit]] [[46edo|46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime_numbers|prime]] edo, following [[19edo|19edo]] and coming before [[29edo|29edo]].

23-TET, or 23-EDO, is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3|5/3]], [[11/7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just_intonation_subgroup|just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit|17-limit]] [[46edo|46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime_numbers|prime]] edo, following [[19edo|19edo]] and coming before [[29edo|29edo]].

==Intervals==

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<ul><li>~~the~~ dots indicate which frets on a 23-edo guitar would have dots.<ul><li>~~based~~ on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>

<ul><li>The dots indicate which frets on a 23-edo guitar would have dots.<ul><li>Based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>

The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila|Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:

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=~~'''~~23 tone [[Equal_Modes|Equal Modes]]:~~'''~~=

=23 tone [[Equal_Modes|Equal Modes]]:=

{| class="wikitable"

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-=<span style="background-color: #ffffff; color: #00b7e3; font-family: 'Times New Roman',Times,serif; font-size: 113%;">23 tone equal temperament</span>=
+=23 tone equal temperament=
-'''''23-tET''''', or '''''23-EDO''''', is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3|5/3]], [[11/7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just_intonation_subgroup|just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit|17-limit]] [[46edo|46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime_numbers|prime]] edo, following [[19edo|19edo]] and coming before [[29edo|29edo]].
+<b>23-TET</b>, or <b>23-EDO</b>, is a tempered musical system which divides the [[Octave|octave]] into 23 equal parts of approximately 52.173913 cents, which is also called with the neologism Icositriphony ''(Icositrifonía)''. It has good approximations for [[5/3|5/3]], [[11/7|11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just_intonation_subgroup|just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit|17-limit]] [[46edo|46edo]], the larger 17-limit [[k*N_subgroups|2*23 subgroup]] 2.9.15.21.33.13.17 is obtained. This is the largest subgroup on which 23 has the same tuning and commas as does 17-limit·46edo, and may be regarded as a basis for analyzing the harmony of 23-EDO so far, as approximations to just intervals goes. 23edo is the 9th [[prime_numbers|prime]] edo, following [[19edo|19edo]] and coming before [[29edo|29edo]].
 ==<span style="font-size: 1.4em;">Intervals</span>==
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 |}
-<ul><li>the dots indicate which frets on a 23-edo guitar would have dots.<ul><li>based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>
+<ul><li>The dots indicate which frets on a 23-edo guitar would have dots.<ul><li>Based on treating 23-EDO as a 2.9.15.21.33.13.17 subgroup temperament; other approaches are possible.</li></ul></li></ul>
 The chart below shows some of the [[MOSScales|Moment of Symmetry (MOS)]] modes of [[Mavila|Mavila]] available in 23edo, mainly Pentatonic(5-note), anti-diatonic(7-note), 9- and 16-note MOSs. Here the outer ring represents individual step of 23edo itself, while the rings moving inward represent 16, 9, 7 and 5 note MOSs:
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 |}
-='''23 tone [[Equal_Modes|Equal Modes]]:'''=
+=23 tone [[Equal_Modes|Equal Modes]]:=
 {| class="wikitable"