18355edo: Difference between revisions

Revision as of 10:47, 14 February 2023

Prime factorization

5 × 3671

Step size

0.0653773 ¢

Fifth

10737\18355 (701.956 ¢)

Semitones (A1:m2)

1739:1380 (113.7 ¢ : 90.22 ¢)

Consistency limit

15

Distinct consistency limit

15

Template:EDO intro It is an extremely strong 7-limit system, with a lower relative error than any division until 84814, and a lower TE logflat badness than any besides 171 and 3125.

Approximation of prime harmonics in 18355edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.0000	+0.0009	+0.0006	+0.0000	+0.0087	+0.0280	-0.0249	+0.0190	+0.0013	-0.0158	-0.0179
Error	Relative (%)	+0.0	+1.3	+1.0	+0.0	+13.3	+42.9	-38.0	+29.0	+2.0	-24.1	-27.3
Steps (reduced)		18355 (0)	29092 (10737)	42619 (5909)	51529 (14819)	63498 (8433)	67922 (12857)	75025 (1605)	77971 (4551)	83030 (9610)	89168 (15748)	90934 (17514)

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 {{Infobox ET}}
-The 18355 division divides the octave into 18355 equal parts of 0.065377 cents each. It is an extremely strong 7-limit division, with a lower [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any division until [[84814edo|84814]], and a lower [[Tenney-Euclidean_metrics#Logflat TE badness|TE logflat badness]] than any besides [[171edo|171]] and [[3125edo|3125]].
+{{EDO intro|18355}} It is an extremely strong 7-limit system, with a lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any division until [[84814edo|84814]], and a lower [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any besides [[171edo|171]] and [[3125edo|3125]].
-{{Primes in edo|18355|prec=4}}
+=== Prime harmonics ===
+{{Harmonics in equal|18355|prec=4}}
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->