2520edo: Difference between revisions

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{{EDO intro|2520}}
{{EDO intro|2520}}


2520edo is the 18th [[highly composite EDO]] and the least common multiple of numbers of 1 through 10 inclusive.  
2520edo is the 18th [[highly composite edo]] and the least common multiple of numbers of 1 through 10 inclusive.  


From a regular temperament perspective, it is a great 2.3.5.11.13 subgroup tuning where it tempers out [[6656/6655]].  
It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal GPV sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.


2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides the tuning for the [[ennealimmal temperament]] and the rank-3 [[ennealimmic]] temperament. 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. 2520e val is a member of the [[optimal GPV sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472, and coming after [[2361edo|2361e]] val and before the [[2679edo|2679e]] val.
=== Prime harmonics ===
=== Prime harmonics ===
{{harmonics in equal|2520}}
{{Harmonics in equal|2520}}
 
[[Category:Jacobin]]
[[Category:Jacobin]]

Revision as of 07:03, 13 March 2023

← 2519edo 2520edo 2521edo →
Prime factorization 23 × 32 × 5 × 7
Step size 0.47619 ¢ 
Fifth 1474\2520 (701.905 ¢) (→ 737\1260)
Semitones (A1:m2) 238:190 (113.3 ¢ : 90.48 ¢)
Consistency limit 5
Distinct consistency limit 5
Special properties

Template:EDO intro

2520edo is the 18th highly composite edo and the least common multiple of numbers of 1 through 10 inclusive.

It is a good 2.3.5.11.13 subgroup tuning where it tempers out 6656/6655. The 2520d val tempers out 2401/2400 and 4375/4374 and provides a tuning for the ennealimmal temperament and the rank-3 ennealimmic temperament. The 2520de val is a tuning for the hemiennealimmal temperament in the 11-limit. The 2520e val is a member of the optimal GPV sequence for the tribilo temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472.

Prime harmonics

Approximation of prime harmonics in 2520edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.050 -0.123 +0.222 +0.111 -0.051 -0.194 +0.106 -0.179 -0.053 +0.203
Relative (%) +0.0 -10.6 -25.9 +46.6 +23.2 -10.8 -40.6 +22.3 -37.6 -11.2 +42.5
Steps
(reduced) 		2520
(0) 		3994
(1474) 		5851
(811) 		7075
(2035) 		8718
(1158) 		9325
(1765) 		10300
(220) 		10705
(625) 		11399
(1319) 		12242
(2162) 		12485
(2405)
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