534edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
BudjarnLambeth (talk | contribs)
mNo edit summary
Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories
Line 1: Line 1:
{{Infobox ET}}
{{Infobox ET}}
The '''534 equal division''' divides the octave into 534 equal parts of 2.247 cents each. It tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the [[Optimal_patent_val|optimal patent val]] for 7-limit [[Breedsmic_temperaments#Harry|harry temperament]].
{{EDO intro|534}}
 
534edo is [[consistent]] to the [[7-odd-limit]], but the error of [[harmonic]] [[3/1|3]] is quite large. The [[patent val]] [[tempering out|tempers out]] [[2401/2400]] and [[19683/19600]] in the 7-limit and provides the [[optimal patent val]] for 7-limit [[harry]] temperament.
 
=== Odd harmonics ===
{{Harmonics in equal|534}}
 
=== Subsets and supersets ===
Since 534 factors into 2 × 3 × 89, 534edo has subset edos {{EDOs| 2, 3, 6, 89, 178, and 267 }}.  


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Harry]]
[[Category:Harry]]

Revision as of 11:20, 29 October 2023

← 533edo 534edo 535edo →
Prime factorization 2 × 3 × 89
Step size 2.24719 ¢ 
Fifth 312\534 (701.124 ¢) (→ 52\89)
Semitones (A1:m2) 48:42 (107.9 ¢ : 94.38 ¢)
Dual sharp fifth 313\534 (703.371 ¢)
Dual flat fifth 312\534 (701.124 ¢) (→ 52\89)
Dual major 2nd 91\534 (204.494 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

534edo is consistent to the 7-odd-limit, but the error of harmonic 3 is quite large. The patent val tempers out 2401/2400 and 19683/19600 in the 7-limit and provides the optimal patent val for 7-limit harry temperament.

Odd harmonics

Approximation of odd harmonics in 534edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.831 +0.203 -0.287 +0.584 -0.756 -0.078 -0.628 +0.663 -0.884 -1.118 +0.939
Relative (%) -37.0 +9.0 -12.8 +26.0 -33.6 -3.5 -28.0 +29.5 -39.3 -49.8 +41.8
Steps
(reduced)
846
(312)
1240
(172)
1499
(431)
1693
(91)
1847
(245)
1976
(374)
2086
(484)
2183
(47)
2268
(132)
2345
(209)
2416
(280)

Subsets and supersets

Since 534 factors into 2 × 3 × 89, 534edo has subset edos 2, 3, 6, 89, 178, and 267.