47edf: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''47EDF''' is the [[EDF|equal division of the just perfect fifth]] into 47 parts of 14.9352 [[cent|cents]] each, corresponding to 80.3470 [[edo]] (similar to every third step of [[241edo]]). It is related to the [[microtempering|microtemperament]] which tempers out |39 -39 -47 47> (1.82802 cents) in the 7-limit, which is supported by [[482edo|482]], [[643edo|643]], [[1125edo|1125]], [[1205edo|1205]], [[1848edo|1848]], [[2330edo|2330]], [[2973edo|2973]], [[3053edo|3053]], and [[4178edo|4178]] EDOs. | '''47EDF''' is the [[EDF|equal division of the just perfect fifth]] into 47 parts of 14.9352 [[cent|cents]] each, corresponding to 80.3470 [[edo]] (similar to every third step of [[241edo]]). | ||
It is related to the [[microtempering|microtemperament]] which tempers out |39 -39 -47 47> (1.82802 cents) in the 7-limit, which is supported by [[482edo|482]], [[643edo|643]], [[1125edo|1125]], [[1205edo|1205]], [[1848edo|1848]], [[2330edo|2330]], [[2973edo|2973]], [[3053edo|3053]], and [[4178edo|4178]] EDOs. | |||
==Related regular temperaments== | ==Related regular temperaments== | ||
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EDOs: {{EDOs|80, 161, 482, 562, 643, 723, 1125, 1205, 1366, 1848, 2330, 2973, 3053, 4178, 6026}} | EDOs: {{EDOs|80, 161, 482, 562, 643, 723, 1125, 1205, 1366, 1848, 2330, 2973, 3053, 4178, 6026}} | ||
== Harmonics == | |||
{{Harmonics in equal|47|3|2}} | |||
{{Harmonics in equal|47|3|2|title=contd.|start=12}} | |||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 04:35, 18 December 2024
| ← 46edf | 47edf | 48edf → |
47EDF is the equal division of the just perfect fifth into 47 parts of 14.9352 cents each, corresponding to 80.3470 edo (similar to every third step of 241edo).
It is related to the microtemperament which tempers out |39 -39 -47 47> (1.82802 cents) in the 7-limit, which is supported by 482, 643, 1125, 1205, 1848, 2330, 2973, 3053, and 4178 EDOs.
Related regular temperaments
7-limit 1205&1848&2330
Comma: |39 -39 -47 47>
POTE generators: ~5/4 = 386.3319, ~3796875/3764768 = 14.9354
Mapping: [<1 1 0 0|, <0 47 0 39|, <0 0 1 1|]
EDOs: 80, 161, 482, 562, 643, 723, 1125, 1205, 1366, 1848, 2330, 2973, 3053, 4178, 6026
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.18 | -5.18 | +4.57 | +6.57 | +4.57 | +6.53 | -0.61 | +4.57 | +1.39 | +0.67 | -0.61 |
| Relative (%) | -34.7 | -34.7 | +30.6 | +44.0 | +30.6 | +43.7 | -4.1 | +30.6 | +9.3 | +4.5 | -4.1 | |
| Steps (reduced) |
80 (33) |
127 (33) |
161 (20) |
187 (46) |
208 (20) |
226 (38) |
241 (6) |
255 (20) |
267 (32) |
278 (43) |
288 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.77 | +1.35 | +1.39 | -5.80 | -6.21 | -0.61 | -4.61 | -3.79 | +1.35 | -4.51 | -6.79 |
| Relative (%) | -31.9 | +9.0 | +9.3 | -38.8 | -41.6 | -4.1 | -30.8 | -25.4 | +9.0 | -30.2 | -45.5 | |
| Steps (reduced) |
297 (15) |
306 (24) |
314 (32) |
321 (39) |
328 (46) |
335 (6) |
341 (12) |
347 (18) |
353 (24) |
358 (29) |
363 (34) | |