2814edo: Difference between revisions

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== Theory ==
== Theory ==
{{Harmonics in equal|2814}}
{{Harmonics in equal|2814}}
2814edo has all its harmonics below 1 standard deviation in the 17-limit and it is [[consistent]].  
2814edo has all its harmonics below 20% error in the 17-limit and it is as a corollary [[consistent]].  


In the 7-limit, it is contorted, with the same commas tempered out as [[1407edo]].
In the 7-limit, it is contorted, with the same commas tempered out as [[1407edo]].


In the 11-limit, it supports rank three [[Kalismic temperaments#Odin|Odin]] temperament.
In the 11-limit, it supports rank three [[Kalismic temperaments#Odin|Odin]] temperament.
It is also a tuning for the [[Double Bastille]] temperament in the 2.5.7.11.13 subgroup.

Revision as of 18:43, 15 December 2022

← 2813edo 2814edo 2815edo →
Prime factorization 2 × 3 × 7 × 67
Step size 0.426439 ¢ 
Fifth 1646\2814 (701.919 ¢) (→ 823\1407)
Semitones (A1:m2) 266:212 (113.4 ¢ : 90.41 ¢)
Consistency limit 17
Distinct consistency limit 17

Template:EDO intro

Theory

Approximation of prime harmonics in 2814edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.036 +0.040 +0.044 +0.068 -0.016 -0.051 +0.142 -0.129 -0.153 -0.046
Relative (%) +0.0 -8.4 +9.4 +10.3 +15.9 -3.7 -12.0 +33.2 -30.3 -35.9 -10.8
Steps
(reduced)
2814
(0)
4460
(1646)
6534
(906)
7900
(2272)
9735
(1293)
10413
(1971)
11502
(246)
11954
(698)
12729
(1473)
13670
(2414)
13941
(2685)

2814edo has all its harmonics below 20% error in the 17-limit and it is as a corollary consistent.

In the 7-limit, it is contorted, with the same commas tempered out as 1407edo.

In the 11-limit, it supports rank three Odin temperament.

It is also a tuning for the Double Bastille temperament in the 2.5.7.11.13 subgroup.