23edo: Difference between revisions

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<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]].

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 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

<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>

=Commas=

{| class="wikitable"

|-

! | Name 1

! | Name 2

| |<nowiki> | -7 3 1 </nowiki>&gt;

| style="text-align:right;" | 92.18

| style="text-align:center;" | Major Chroma

| style="text-align:center;" | Major Limma

| |<nowiki> | -6 -5 6 </nowiki>&gt;

| style="text-align:right;" | 8.11

| style="text-align:center;" | Kleisma

| style="text-align:center;" | Semicomma Majeur

| |<nowiki> | 2 2 -1 -1 </nowiki>&gt;

| style="text-align:right;" | 48.77

| style="text-align:center;" | Septimal Quarter Tone

| style="text-align:center;" |

| |<nowiki> | -9 1 2 1 </nowiki>&gt;

| style="text-align:right;" | 43.41

| style="text-align:center;" | Avicennma

| style="text-align:center;" | Avicenna's Enharmonic Diesis

| |<nowiki> | 5 -4 3 -2 </nowiki>&gt;

| style="text-align:right;" | 13.47

| style="text-align:center;" | Octagar

| style="text-align:center;" |

| |<nowiki> | 11 1 -3 -2 </nowiki>&gt;

| style="text-align:right;" | 5.36

| style="text-align:center;" | Porwell

| style="text-align:center;" |

| |<nowiki> | 2 -2 2 0 -1 </nowiki>&gt;

| style="text-align:right;" | 17.40

| style="text-align:center;" | Ptolemisma

| style="text-align:center;" |

| |<nowiki> | -3 2 -1 2 -1 </nowiki>&gt;

| style="text-align:right;" | 3.93

| style="text-align:center;" | Werckisma

| style="text-align:center;" |

|}

{| class="wikitable"

| |

|}

=Books=

This movie is a series of still shots Chris took during the process of making a 23 edo guitar in a stick like form. At the end the guitar is played without effects etc. and the open string tuning is sounded - which starts with a normal E and then adjusted to the 9th / 7th fret unison, like a typical 12edo guitar fashion.

[[Category:11/7]]

[[Category:23-tone]]