23edo: Difference between revisions

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== Theory ==

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]], [[11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]] [[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]] and coming before [[29edo]].

23-TET, or 23-EDO, is a tempered musical system which divides the [[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]], [[11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]] [[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]] and coming before [[29edo]].

23-EDO was proposed by ethnomusicologist [http://en.wikipedia.org/wiki/Erich_von_Hornbostel Erich von Hornbostel] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.

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Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.

{| class="wikitable center-all left-9"

{| class="wikitable center-all left-9 right-2"

|-

! [[Degree]] <ref>The dots indicate which frets on a 23-edo guitar would have dots.</ref>

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|-

| 5

| 260.87

| 260.870

| 7/6, 15/13, 29/25

| A2, d3

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|-

| 6

| 313.~~0435~~

| 313.043

| 6/5

| m3

Line 207:

|-

| 17

| 886.~~9565~~

| 886.957

| 5/3

| M6

Line 217:

|-

| 18

| 939.13

| 939.130

| 12/7, 26/15, 50/29

| A6, d7

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|-

| 23··

| 1200

| 1200.000

| 2/1

| P8

Line 660:

[[Category:Twentuning]]

~~[[Category:Todo:unify precision]]~~

[[Category:Todo:improve synopsis]]

@@ Line 8: / Line 8: @@
 == Theory ==
-<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]], [[11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]] [[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]] and coming before [[29edo]].
+<b>23-TET</b>, or <b>23-EDO</b>, is a tempered musical system which divides the [[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]], [[11/7]], 13 and 17, allowing it to represent the 2.5/3.11/7.13.17 [[just intonation subgroup]]. If to this subgroup is added the commas of [[17-limit]] [[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]] and coming before [[29edo]].
 -EDO was proposed by ethnomusicologist [http://en.wikipedia.org/wiki/Erich_von_Hornbostel Erich von Hornbostel] as the result of continuing a circle of "blown" fifths of ~678-cent fifths that (he argued) resulted from "overblowing" a bamboo pipe.
@@ Line 26: / Line 26: @@
 Armodue notation is a nonatonic notation that uses the numbers 1-9 as note names.
-{| class="wikitable center-all left-9"
+{| class="wikitable center-all left-9 right-2"
 |-
 ! [[Degree]] <ref>The dots indicate which frets on a 23-edo guitar would have dots.</ref>
@@ Line 87: / Line 87: @@
 |-
 | 5
-| 260.87
+| 260.870
 | 7/6, 15/13, 29/25
 | A2, d3
@@ Line 97: / Line 97: @@
 |-
 | 6
-| 313.0435
+| 313.043
 | 6/5
 | m3
@@ Line 207: / Line 207: @@
 |-
 | 17
-| 886.9565
+| 886.957
 | 5/3
 | M6
@@ Line 217: / Line 217: @@
 |-
 | 18
-| 939.13
+| 939.130
 | 12/7, 26/15, 50/29
 | A6, d7
@@ Line 267: / Line 267: @@
 |-
 | 23··
-| 1200
+| 1200.000
 | 2/1
 | P8
@@ Line 660: / Line 660: @@
 [[Category:Twentuning]]
-[[Category:Todo:unify precision]]
 [[Category:Todo:improve synopsis]]