653edo: Difference between revisions

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== Theory ==

653edo is consistent to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

653edo is distinctly [[consistent]] to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

=== Prime harmonics ===

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=== Miscellaneous properties ===

653edo is the 119th [[prime ~~EDO~~]].

653edo is the 119th [[prime edo]].

== Regular temperament properties ==

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

| 2.3.5.7.11.13.17

| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 10985/10976~~, 11271/11264~~

| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976

| [{{val| 653 1035 1516 1833 2259 2416 2669 }}]

| +0.0759

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

|+Table of rank-2 temperaments by generator

! Periods per ~~Octave~~

! Periods per 8ve

! Generator (Reduced)

! Cents (Reduced)

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is consistent to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.
+edo is distinctly [[consistent]] to the [[21-odd-limit]], tempering out 68719476736000/68630377364883 ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], 65625/65536, and 7656250000000/7625597484987 in the 7-limit; [[3025/3024]], [[41503/41472]], 496125/495616, and 1953125/1948617 in the 11-limit; [[2080/2079]], 4459/4455, [[6656/6655]], [[10985/10976]], and 170625/170368 in the 13-limit; [[1225/1224]], 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; [[1445/1444]], [[1521/1520]], 1540/1539, [[1729/1728]], 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.
 === Prime harmonics ===
@@ Line 9: / Line 9: @@
 === Miscellaneous properties ===
-edo is the 119th [[prime EDO]].
+edo is the 119th [[prime edo]].
 == Regular temperament properties ==
@@ Line 16: / Line 16: @@
 ! rowspan="2" | [[Comma list|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 58: / Line 58: @@
 |-
 | 2.3.5.7.11.13.17
-| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 10985/10976, 11271/11264
+| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976
 | [{{val| 653 1035 1516 1833 2259 2416 2669 }}]
 | +0.0759
@@ Line 75: / Line 75: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per Octave
+! Periods<br>per 8ve
 ! Generator<br>(Reduced)
 ! Cents<br>(Reduced)