350edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The '''350 equal division''' divides the octave into 350 equal parts of 3.429 cents each. It tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the [[Optimal_patent_val|optimal patent val]] for [[Ragismic_microtemperaments#Amity|amity temperament]]. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for hemiamity temperament.
{{EDO intro|350}}


350 is divisible by 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.
The equal temperament [[tempering out|tempers out]] 1600000/1594323, the [[amity comma]], in the 5-limit, and [[4375/4374]], [[5120/5103]] and [[6144/6125]] in the 7-limit, and it provides the [[optimal patent val]] for the 7-limit [[amity]] temperament. In the 11-limit it tempers out [[3025/3024]] and [[9801/9800]], and provides the optimal patent val for 11-limit [[hemiamity]].
 
=== Odd harmonics ===
{{Harmonics in equal|350}}
 
=== Subsets and supersets ===
Since 350 factors into {{factorization|350}}, 350edo has subset edos {{EDOs| 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175 }}.


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

Revision as of 06:49, 15 November 2023

← 349edo 350edo 351edo →
Prime factorization 2 × 52 × 7
Step size 3.42857 ¢ 
Fifth 205\350 (702.857 ¢) (→ 41\70)
Semitones (A1:m2) 35:25 (120 ¢ : 85.71 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

The equal temperament tempers out 1600000/1594323, the amity comma, in the 5-limit, and 4375/4374, 5120/5103 and 6144/6125 in the 7-limit, and it provides the optimal patent val for the 7-limit amity temperament. In the 11-limit it tempers out 3025/3024 and 9801/9800, and provides the optimal patent val for 11-limit hemiamity.

Odd harmonics

Approximation of odd harmonics in 350edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.90 +1.11 +1.46 -1.62 +0.68 -0.53 -1.41 +1.33 +0.77 -1.07 -0.85
Relative (%) +26.3 +32.5 +42.6 -47.4 +19.9 -15.4 -41.2 +38.8 +22.5 -31.1 -24.7
Steps
(reduced)
555
(205)
813
(113)
983
(283)
1109
(59)
1211
(161)
1295
(245)
1367
(317)
1431
(31)
1487
(87)
1537
(137)
1583
(183)

Subsets and supersets

Since 350 factors into 2 × 52 × 7, 350edo has subset edos 2, 5, 7, 10, 14, 25, 35, 50, 70 and 175.