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{{Infobox ET}}
{{Infobox ET}}
'''263EDO''' is the [[EDO|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. 263EDO is the 56th [[prime EDO]]. 263EDO is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]].
{{EDO intro|263}}
 
==Theory==
It tempers out 393216/390625 (Würschmidt comma) and |50 -33 1&gt; in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.  
263et tempers out 393216/390625 (Würschmidt comma) and |50 -33 1&gt; in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.  


Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.  
Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.  


Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.
Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.
 
===Prime harmonics===
{{Harmonics in equal|263}}
{{Harmonics in equal|263}}
===Subsets and supersets===
263edo is the 56th [[prime EDO]]. It is accurate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]].
==Regular temperament properties==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|417 -263}}
|{{val|263 417}}
| -0.2229
| 0.2229
| 4.89
|-
|2.3.5
|393216/390625, {{monzo|50 -33 1}}
|{{val|263 417 611}}
| -0.3666
| 0.2728
| 5.98
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
|1
|40\263
|182.51
|10/9
|[[Minortone]]
|-
|1
|85\263
|387.83
|5/4
|[[Würschmidt]]
|}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 20:43, 3 November 2023

← 262edo 263edo 264edo →
Prime factorization 263 (prime)
Step size 4.56274 ¢ 
Fifth 154\263 (702.662 ¢)
Semitones (A1:m2) 26:19 (118.6 ¢ : 86.69 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

Theory

263et tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit.

Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit.

Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.

Prime harmonics

Approximation of prime harmonics in 263edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.71 +1.52 -1.53 +0.77 -0.98 -0.01 -0.94 +1.38 +1.60 +0.21
Relative (%) +0.0 +15.5 +33.3 -33.4 +16.9 -21.6 -0.3 -20.5 +30.3 +35.1 +4.6
Steps
(reduced) 		263
(0) 		417
(154) 		611
(85) 		738
(212) 		910
(121) 		973
(184) 		1075
(23) 		1117
(65) 		1190
(138) 		1278
(226) 		1303
(251)

Subsets and supersets

263edo is the 56th prime EDO. It is accurate for the 17th harmonic, as the denominator of a convergent to log217, after 80 and before 343.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [417 -263⟩ ⟨263 417] -0.2229 0.2229 4.89
2.3.5 393216/390625, [50 -33 1⟩ ⟨263 417 611] -0.3666 0.2728 5.98

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 40\263 182.51 10/9 Minortone
1 85\263 387.83 5/4 Würschmidt
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