48edf: Difference between revisions

Latest revision as of 19:23, 1 August 2025

Division of the just perfect fifth into 48 equal parts (48EDF) is related to 82edo, but with the 3/2 rather than the 2/1 being just. The octave is compressed by about 0.8269 cents and the step size is about 14.6241 cents.

Unlike 82edo, it is only consistent up to the 4-integer-limit, with discrepancy for the 5th harmonic.

Lookalikes: 82edo, 130edt

Approximation of prime harmonics in 48edf
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-0.83	-0.83	+6.88	-5.29	+1.92	+5.19	-5.89	+6.28	-2.75	+5.42	+6.96
Error	Relative (%)	-5.7	-5.7	+47.1	-36.2	+13.1	+35.5	-40.3	+43.0	-18.8	+37.1	+47.6
Steps (reduced)		82 (34)	130 (34)	191 (47)	230 (38)	284 (44)	304 (16)	335 (47)	349 (13)	371 (35)	399 (15)	407 (23)

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-'''[[EDF|Division of the just perfect fifth]] into 48 equal parts''' (48EDF) is related to [[82edo|82 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 0.8269 cents compressed and the step size is about 14.6241 cents. Unlike 82edo, it is only consistent up to the [[3-odd-limit|4-integer-limit]], with discrepancy for the 5th harmonic.
+{{Infobox ET}}
+'''[[EDF|Division of the just perfect fifth]] into 48 equal parts''' (48EDF) is related to [[82edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The octave is [[Octave shrinking|compressed]] by about 0.8269 [[cents]] and the step size is about 14.6241 cents.
+Unlike 82edo, it is only consistent up to the 4-[[integer-limit]], with discrepancy for the 5th harmonic.
 Lookalikes: [[82edo]], [[130edt]]
-[[Category:Edf]]
+== Harmonics ==
-[[Category:Edonoi]]
+{{Harmonics in equal|48|3|2|intervals=prime}}
+{{stub}}