783edo: Difference between revisions

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== Theory ==

783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the 11-limit, making it a flexible and versatile tuning. It tempers out the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It ~~supports~~ [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments#Francium|francium]].

783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the [[11-odd-limit]], making it a flexible and versatile tuning. The equal temperament [[tempering out|tempers out]] the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It [[support]]s [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments #Francium|francium]].

=== Prime harmonics ===

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=== Subsets and supersets ===

Since 783 factors into ~~33 × 29~~, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}.

Since 783 factors into {{factorization|783}}, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}.

== Regular temperament properties ==

=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

! Periods per 8ve

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~

! Associated ratio*

! Temperaments

|-

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|-

| 9

| 206\783 (32\783)

| 206\783 (32\783)

| 315.709 (49.042)

| 315.709 (49.042)

| 6/5 (36/35)

| 6/5 (36/35)

| [[Ennealimmal]]

|-

| 29

| 325\783 (1\723)

| 325\783 (1\723)

| 498.084 (1.533)

| 498.084 (1.533)

| 4/3 (32805/32768)

| 4/3 (32805/32768)

| [[Copper]]

|-

| 87

| 308\783 (2\783)

| 308\783 (2\783)

| 472.031 (3.065)

| 472.031 (3.065)

| {{monzo| 35 1 -6 -3 -4 }} (?)

| {{monzo| 35 1 -6 -3 -4 }} (?)

| [[87th-octave temperaments#Francium|Francium]]

| [[87th-octave temperaments #Francium|Francium]]

|}

<nowiki>*~~</nowiki>~~ [[Normal lists|~~octave~~-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|783}}
+{{ED intro}}
 == Theory ==
-edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the 11-limit, making it a flexible and versatile tuning. It tempers out the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It supports [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments#Francium|francium]].
+edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the [[11-odd-limit]], making it a flexible and versatile tuning. The equal temperament [[tempering out|tempers out]] the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It [[support]]s [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments #Francium|francium]].
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 783 factors into 3<sup>3</sup> × 29, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}.
+Since 783 factors into {{factorization|783}}, 783edo has subset edos {{EDOs| 3, 9, 27, 29, 87, and 261 }}.
 == Regular temperament properties ==
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 45: / Line 47: @@
 |-
 | 9
-| 206\783<br>(32\783)
+| 206\783<br />(32\783)
-| 315.709<br>(49.042)
+| 315.709<br />(49.042)
-| 6/5<br>(36/35)
+| 6/5<br />(36/35)
 | [[Ennealimmal]]
 |-
 | 29
-| 325\783<br>(1\723)
+| 325\783<br />(1\723)
-| 498.084<br>(1.533)
+| 498.084<br />(1.533)
-| 4/3<br>(32805/32768)
+| 4/3<br />(32805/32768)
 | [[Copper]]
 |-
 | 87
-| 308\783<br>(2\783)
+| 308\783<br />(2\783)
-| 472.031<br>(3.065)
+| 472.031<br />(3.065)
-| {{monzo| 35 1 -6 -3 -4 }}<br>(?)
+| {{monzo| 35 1 -6 -3 -4 }}<br />(?)
-| [[87th-octave temperaments#Francium|Francium]]
+| [[87th-octave temperaments #Francium|Francium]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct