1193edo: Difference between revisions

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== Theory ==

1193edo is [[consistent]] to the [[11-odd-limit]]. ~~The~~ equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit; [[3025/3024]], [[41503/41472]], 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and [[117440512/117406179]] in the 11-limit~~. It supports the [[gross]] temperament~~.

1193edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 144 -22 -47 }} (gross comma) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[41503/41472]], 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and [[117440512/117406179]] in the 11-limit.

=== Prime harmonics ===

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== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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| {{monzo| 1891 -1193 }}

| {{mapping| 1193 1891 }}

| -0.0443

| −0.0443

| 0.0443

| 4.41

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| {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }}

| {{mapping| 1193 1891 2770 }}

| -0.0209

| −0.0209

| 0.0491

| 4.88

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| 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }}

| {{mapping| 1193 1891 2770 3349 }}

| -0.000028

| −0.000028

| 0.0558

| 5.55

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| 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244

| {{mapping| 1193 1891 2770 3349 4127 4415 }}

| -0.0121

| −0.0121

| 0.0617

| 6.14

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

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

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~

! Associated ratio*

! Temperaments

|-

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| [[Dodifo]]

|}

<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

== Music ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1193}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit; [[3025/3024]], [[41503/41472]], 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and [[117440512/117406179]] in the 11-limit. It supports the [[gross]] temperament.
+edo is [[consistent]] to the [[11-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 144 -22 -47 }} (gross comma) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[41503/41472]], 151263/151250, 17561600/17537553, 26214400/26198073, 95703125/95664294, and [[117440512/117406179]] in the 11-limit.
 === Prime harmonics ===
@@ Line 13: / Line 13: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 25: / Line 26: @@
 | {{monzo| 1891 -1193 }}
 | {{mapping| 1193 1891 }}
-| -0.0443
+| −0.0443
 | 0.0443
 | 4.41
@@ Line 32: / Line 33: @@
 | {{monzo| 10 -40 -23 }}, {{monzo| 77 -31 -12 }}
 | {{mapping| 1193 1891 2770 }}
-| -0.0209
+| −0.0209
 | 0.0491
 | 4.88
@@ Line 39: / Line 40: @@
 | 2401/2400, {{monzo| -13 -12 15 -1 }}, {{monzo| 41 -15 -5 -2 }}
 | {{mapping| 1193 1891 2770 3349 }}
-| -0.000028
+| −0.000028
 | 0.0558
 | 5.55
@@ Line 53: / Line 54: @@
 | 2401/2400, 3025/3024, 4096/4095, 78125/78078, 114345/114244
 | {{mapping| 1193 1891 2770 3349 4127 4415 }}
-| -0.0121
+| −0.0121
 | 0.0617
 | 6.14
@@ Line 67: / Line 68: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 92: / Line 94: @@
 | [[Dodifo]]
 |}
-<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
 == Music ==