653edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,265 edits
mNo edit summary
Cleanup; linking; clarify the title row of the rank-2 temp table; -redundant categories
Line 3: Line 3:


== Theory ==
== Theory ==
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.
653edo is [[consistency|distinctly consistent]] to the [[21-odd-limit]], [[tempering out]] {{monzo| 39 -29 3 }} ([[tricot comma]]) and {{monzo| -20 -24 25 }} ([[counterhanson comma]]) in the 5-limit; [[2401/2400]], [[65625/65536]], and {{monzo| 7 -27 13 2 }} 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 ===
=== Prime harmonics ===
Line 24: Line 24:
| 2.3
| 2.3
| {{monzo| 1035 -653 }}
| {{monzo| 1035 -653 }}
| [{{val| 653 1035 }}]
| {{mapping| 653 1035 }}
| -0.0113
| -0.0113
| 0.0113
| 0.0113
Line 31: Line 31:
| 2.3.5
| 2.3.5
| {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}
| {{monzo| 39 -29 3 }}, {{monzo| -20 -24 25 }}
| [{{val| 653 1035 1516 }}]
| {{mapping| 653 1035 1516 }}
| +0.0503
| +0.0503
| 0.0875
| 0.0875
Line 38: Line 38:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }}
| 2401/2400, 65625/65536, {{monzo| 7 -27 13 2 }}
| [{{val| 653 1035 1516 1833 }}]
| {{mapping| 653 1035 1516 1833 }}
| +0.0709
| +0.0709
| 0.0838
| 0.0838
Line 45: Line 45:
| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617
| 2401/2400, 3025/3024, 65625/65536, 1953125/1948617
| [{{val| 653 1035 1516 1833 2259 }}]
| {{mapping| 653 1035 1516 1833 2259 }}
| +0.0576
| +0.0576
| 0.0795
| 0.0795
Line 52: Line 52:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536
| 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536
| [{{val| 653 1035 1516 1833 2259 2416 }}]
| {{mapping| 653 1035 1516 1833 2259 2416 }}
| +0.0801
| +0.0801
| 0.0882
| 0.0882
Line 59: Line 59:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976
| 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976
| [{{val| 653 1035 1516 1833 2259 2416 2669 }}]
| {{mapping| 653 1035 1516 1833 2259 2416 2669 }}
| +0.0759
| +0.0759
| 0.0823
| 0.0823
Line 66: Line 66:
| 2.3.5.7.11.13.17.19
| 2.3.5.7.11.13.17.19
| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400
| 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400
| [{{val| 653 1035 1516 1833 2259 2416 2669 2774 }}]
| {{mapping| 653 1035 1516 1833 2259 2416 2669 2774 }}
| +0.0608
| +0.0608
| 0.0867
| 0.0867
Line 76: Line 76:
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Periods<br>per 8ve
! Generator<br>(Reduced)
! Generator*
! Cents<br>(Reduced)
! Cents*
! Associated<br>Ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
|-
|-
Line 105: Line 105:
| [[Tricot]]
| [[Tricot]]
|}
|}
 
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]

Revision as of 06:23, 25 October 2023

← 652edo 653edo 654edo →
Prime factorization 653 (prime)
Step size 1.83767 ¢ 
Fifth 382\653 (701.991 ¢)
Semitones (A1:m2) 62:49 (113.9 ¢ : 90.05 ¢)
Consistency limit 21
Distinct consistency limit 21

Template:EDO intro

Theory

653edo is distinctly consistent to the 21-odd-limit, tempering out [39 -29 3⟩ (tricot comma) and [-20 -24 25⟩ (counterhanson comma) in the 5-limit; 2401/2400, 65625/65536, and [7 -27 13 2⟩ 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

Approximation of prime harmonics in 653edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.036 -0.403 -0.373 -0.016 -0.711 -0.208 +0.190 +0.210 -0.481 -0.166
Relative (%) +0.0 +1.9 -21.9 -20.3 -0.9 -38.7 -11.3 +10.3 +11.4 -26.2 -9.0
Steps
(reduced) 		653
(0) 		1035
(382) 		1516
(210) 		1833
(527) 		2259
(300) 		2416
(457) 		2669
(57) 		2774
(162) 		2954
(342) 		3172
(560) 		3235
(623)

Subsets and supersets

653edo is the 119th prime edo.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢) 		Tuning Error
Absolute (¢) Relative (%)
2.3 [1035 -653⟩ [⟨653 1035]] -0.0113 0.0113 0.61
2.3.5 [39 -29 3⟩, [-20 -24 25⟩ [⟨653 1035 1516]] +0.0503 0.0875 4.76
2.3.5.7 2401/2400, 65625/65536, [7 -27 13 2⟩ [⟨653 1035 1516 1833]] +0.0709 0.0838 4.56
2.3.5.7.11 2401/2400, 3025/3024, 65625/65536, 1953125/1948617 [⟨653 1035 1516 1833 2259]] +0.0576 0.0795 4.33
2.3.5.7.11.13 2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536 [⟨653 1035 1516 1833 2259 2416]] +0.0801 0.0882 4.80
2.3.5.7.11.13.17 1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976 [⟨653 1035 1516 1833 2259 2416 2669]] +0.0759 0.0823 4.48
2.3.5.7.11.13.17.19 1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400 [⟨653 1035 1516 1833 2259 2416 2669 2774]] +0.0608 0.0867 4.72

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
Ratio* 		Temperaments
1 21\653 38.59 45/44 Hemitert
1 42\653 77.18 256/245 Tertiaseptal
1 172/653 316.08 6/5 Counterhanson
1 308/653 566.00 81920/59049 Tricot

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

Retrieved from "https://en.xen.wiki/index.php?title=653edo&oldid=126396"