175edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The ''175 equal division'' divides the octave into 175 equal parts of 6.857 cents each. It tempers out 1029/1024 and 225/224, so that it [[support]]s 7-limit [[Miracle|miracle temperament]], and in fact provides an excellent alternative to [[72edo|72edo]] for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.
{{EDO intro|175}}


175edo tempers out [[1029/1024]] and [[225/224]], so that it [[support]]s 7-limit [[Miracle|miracle temperament]], and in fact provides an excellent alternative<sup>[why?]</sup> to [[72edo]] for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f val, {{val|175 277 406 491 605 '''647'''}} tempers out [[351/350]] just as 72 does, and provides a tuning for [[benediction]] temperament very close to the POTE tuning.
=== Harmonics ===
{{harmonics in equal|175}}
== Music ==
== Music ==
* [http://www.archive.org/details/RachmaninoffPlaysBlackjack http://www.archive.org/details/RachmaninoffPlaysBlackjack]
* [http://www.archive.org/details/RachmaninoffPlaysBlackjack http://www.archive.org/details/RachmaninoffPlaysBlackjack]
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[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Todo:clarify]]

Revision as of 18:02, 21 October 2023

← 174edo 175edo 176edo →
Prime factorization 52 × 7
Step size 6.85714 ¢ 
Fifth 102\175 (699.429 ¢)
Semitones (A1:m2) 14:15 (96 ¢ : 102.9 ¢)
Dual sharp fifth 103\175 (706.286 ¢)
Dual flat fifth 102\175 (699.429 ¢)
Dual major 2nd 30\175 (205.714 ¢) (→ 6\35)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

175edo tempers out 1029/1024 and 225/224, so that it supports 7-limit miracle temperament, and in fact provides an excellent alternative[why?] to 72edo for 7-limit miracle. In the 11-limit, it tempers out 243/242, 385/384, 441/440 and 540/439, and supports 11-limit miracle. In the 13-limit, 175f val, ⟨175 277 406 491 605 647] tempers out 351/350 just as 72 does, and provides a tuning for benediction temperament very close to the POTE tuning.

Harmonics

Approximation of odd harmonics in 175edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -2.53 -2.31 -1.97 +1.80 -2.75 +2.90 +2.02 -2.10 -2.66 +2.36 +2.58
Relative (%) -36.8 -33.7 -28.7 +26.3 -40.1 +42.3 +29.4 -30.6 -38.7 +34.4 +37.7
Steps
(reduced) 		277
(102) 		406
(56) 		491
(141) 		555
(30) 		605
(80) 		648
(123) 		684
(159) 		715
(15) 		743
(43) 		769
(69) 		792
(92)

Music

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