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{{Infobox ET}}
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 55 equal parts''' (55EDF) is related to [[94edo|94 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 0.2951 cents compressed and the step size is about 12.7628 cents. It is consistent to the [[23-odd-limit|24-integer-limit]].
'''[[EDF|Division of the just perfect fifth]] into 55 equal parts''' (55EDF) is related to [[94edo]], but with the 3/2 rather than the 2/1 being [[just]]. The octave is [[Octave shrinking|compressed]] by about 0.2951 [[cents]] and the step size is about 12.7628 cents.  


Lookalikes: [[94edo]], [[149edt]]
It is [[consistent]] to the 24-[[integer limit]] (''which is contained within, but is not the same as, the [[23-odd-limit]]''). Its lookalikes include [[94edo]] and [[149edt]].


[[Category:Edf]]
== Harmonics ==
[[Category:Edonoi]]
{{Harmonics in equal|55|3|2}}
{{Harmonics in equal|55|3|2|columns=12|collapsed=1|start=12}}
 
{{todo|expand}}

Latest revision as of 19:23, 1 August 2025

← 54edf 55edf 56edf →
Prime factorization 5 × 11
Step size 12.7628 ¢ 
Octave 94\55edf (1199.7 ¢)
(semiconvergent)
Twelfth 149\55edf (1901.66 ¢)
(semiconvergent)
Consistency limit 24
Distinct consistency limit 15

Division of the just perfect fifth into 55 equal parts (55EDF) is related to 94edo, but with the 3/2 rather than the 2/1 being just. The octave is compressed by about 0.2951 cents and the step size is about 12.7628 cents.

It is consistent to the 24-integer limit (which is contained within, but is not the same as, the 23-odd-limit). Its lookalikes include 94edo and 149edt.

Harmonics

Approximation of harmonics in 55edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -0.30 -0.30 -0.59 -4.02 -0.59 +0.56 -0.89 -0.59 -4.31 -3.40 -0.89
Relative (%) -2.3 -2.3 -4.6 -31.5 -4.6 +4.4 -6.9 -4.6 -33.8 -26.7 -6.9
Steps
(reduced)
94
(39)
149
(39)
188
(23)
218
(53)
243
(23)
264
(44)
282
(7)
298
(23)
312
(37)
325
(50)
337
(7)
Approximation of harmonics in 55edf
Harmonic 13 14 15 16 17 18 19 20 21 22 23 24
Error Absolute (¢) +0.93 +0.26 -4.31 -1.18 -4.03 -0.89 -5.15 -4.61 +0.26 -3.70 -4.08 -1.18
Relative (%) +7.3 +2.1 -33.8 -9.2 -31.6 -6.9 -40.3 -36.1 +2.1 -29.0 -31.9 -9.2
Steps
(reduced)
348
(18)
358
(28)
367
(37)
376
(46)
384
(54)
392
(7)
399
(14)
406
(21)
413
(28)
419
(34)
425
(40)
431
(46)