143edo: Difference between revisions

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Adopt template: EDO intro; +prime error table; -redundant categories; misc. cleanup
+one-liner overview
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro}}
{{EDO intro}}
143edo is only [[consistent]] to the [[5-odd-limit]], and the error of the [[harmonic]] [[3/1|3]] is quite large.


The 143b val provides a tuning almost identical with that of the [[POTE tuning]] for 7-limit [[meantone]].
The 143b val provides a tuning almost identical with that of the [[POTE tuning]] for 7-limit [[meantone]].

Revision as of 07:04, 21 May 2024

← 142edo 143edo 144edo →
Prime factorization 11 × 13
Step size 8.39161 ¢ 
Fifth 84\143 (704.895 ¢)
Semitones (A1:m2) 16:9 (134.3 ¢ : 75.52 ¢)
Dual sharp fifth 84\143 (704.895 ¢)
Dual flat fifth 83\143 (696.503 ¢)
Dual major 2nd 24\143 (201.399 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

143edo is only consistent to the 5-odd-limit, and the error of the harmonic 3 is quite large.

The 143b val provides a tuning almost identical with that of the POTE tuning for 7-limit meantone.

Odd harmonics

Approximation of odd harmonics in 143edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.94 -0.30 -3.79 -2.51 +2.53 -1.37 +2.64 +4.14 -3.81 -0.85 +1.10
Relative (%) +35.0 -3.6 -45.2 -29.9 +30.1 -16.3 +31.5 +49.3 -45.4 -10.1 +13.1
Steps
(reduced)
227
(84)
332
(46)
401
(115)
453
(24)
495
(66)
529
(100)
559
(130)
585
(13)
607
(35)
628
(56)
647
(75)

Subsets and supersets

As 143 is 11 × 13, 143edo allows the polymicrotonal juxtaposition of 11edo and 13edo:

13_against_11.gif

If the 11edo and 13edo subsets are analyzed as two scales that share the tonic and are then combined (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.