749edo: Difference between revisions

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Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories
Adopt template: Factorization; misc. cleanup
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{{EDO intro|749}}
{{EDO intro|749}}


The equal temperament tempers out the [[schisma]], 32805/32768, and provides the [[optimal patent val]] for the 5-limit [[schismatic|schismatic (helmholtz)]] temperament.
The equal temperament is most notable for [[tempering out]] the [[schisma]], 32805/32768, and provides the [[optimal patent val]] for the 5-limit [[schismatic|schismatic (helmholtz)]] temperament.


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 749 factors into 7 × 107, 749edo contains [[7edo]] and [[107edo]] as its subsets.  
Since 749 factors into {{factorization|749}}, 749edo contains [[7edo]] and [[107edo]] as subsets.  


[[Category:Schismatic]]
[[Category:Schismatic]]

Revision as of 12:17, 2 November 2023

← 748edo 749edo 750edo →
Prime factorization 7 × 107
Step size 1.60214 ¢ 
Fifth 438\749 (701.736 ¢)
Semitones (A1:m2) 70:57 (112.1 ¢ : 91.32 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

The equal temperament is most notable for tempering out the schisma, 32805/32768, and provides the optimal patent val for the 5-limit schismatic (helmholtz) temperament.

Prime harmonics

Approximation of prime harmonics in 749edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.219 -0.199 +0.466 -0.183 +0.594 +0.786 +0.484 -0.237 +0.596 +0.492
Relative (%) +0.0 -13.7 -12.4 +29.1 -11.4 +37.1 +49.0 +30.2 -14.8 +37.2 +30.7
Steps
(reduced)
749
(0)
1187
(438)
1739
(241)
2103
(605)
2591
(344)
2772
(525)
3062
(66)
3182
(186)
3388
(392)
3639
(643)
3711
(715)

Subsets and supersets

Since 749 factors into 7 × 107, 749edo contains 7edo and 107edo as subsets.