99693edo: Difference between revisions

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Undo revision 175551 by MisterShafXen (talk). It was a readability hell
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Mark as novelty. Adopt template: EDO intro. -redundant categories. Misc. cleanup
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{{Novelty}}
{{Infobox ET}}
{{Infobox ET}}
{{todo|improve synopsis}}
{{EDO intro}}
'''99693 equal divisions of the octave''' ('''99693edo''') is the tuning that divides the [[octave]] into 99693 equal steps of about 0.012 [[cent|cents]]. It is notable for being the [[edo]] below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).


== Theory ==
99693edo is notable for being the [[edo]] below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).
{{todo|complete section}}
 
=== Prime harmonics ===
{{Harmonics in equal|99693|columns=15|prec=3}}
{{Harmonics in equal|99693|columns=15|prec=3}}
[[Category:99693edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->

Revision as of 16:25, 10 January 2025

This page presents a novelty topic.

It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex.

Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

← 99692edo 99693edo 99694edo →
Prime factorization 32 × 11 × 19 × 53
Step size 0.012037 ¢ 
Fifth 58317\99693 (701.959 ¢) (→ 19439\33231)
Semitones (A1:m2) 9447:7494 (113.7 ¢ : 90.2 ¢)
Dual sharp fifth 58317\99693 (701.959 ¢) (→ 19439\33231)
Dual flat fifth 58316\99693 (701.947 ¢)
Dual major 2nd 16940\99693 (203.906 ¢) (→ 1540\9063)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

99693edo is notable for being the edo below 100000 with the lowest maximum error, using direct approximation for each harmonic, for the first 547 harmonics (547 being the 100th prime number).

Prime harmonics

Approximation of odd harmonics in 99693edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
Error Absolute (¢) +0.004 +0.000 +0.004 -0.004 -0.001 +0.001 +0.004 -0.005 +0.004 -0.004 -0.006 +0.001 +0.000 +0.004 +0.004
Relative (%) +33.3 +2.2 +36.6 -33.3 -11.6 +6.3 +35.6 -43.3 +36.2 -30.1 -46.2 +4.5 +0.0 +30.1 +30.7
Steps
(reduced) 		158010
(58317) 		231480
(32094) 		279874
(80488) 		316019
(16940) 		344881
(45802) 		368908
(69829) 		389490
(90411) 		407491
(8719) 		423489
(24717) 		437883
(39111) 		450967
(52195) 		462960
(64188) 		474029
(75257) 		484307
(85535) 		493899
(95127)
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