23ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 23 equal parts''' (23ED7) is related to the [[13edt|Bohlen-Pierce scale]], but with the 7/1 rather than the 3/1 being just. The step size is about 146.4707 cents, corresponding to 8.1928 [[EDO]]. It is almost identical to [[POTE generator]] for 7-limit [[bohpier|bohpier temperament]]. | '''[[Ed7|Division of the 7th harmonic]] into 23 equal parts''' (23ED7) is related to the [[13edt|Bohlen-Pierce scale]], but with the 7/1 rather than the 3/1 being just. The step size is about 146.4707 cents, corresponding to 8.1928 [[EDO]]. It is almost identical to [[POTE generator]] for 7-limit [[bohpier|bohpier temperament]]. | ||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 129: | Line 130: | ||
| | [[7/4|harmonic seventh]] plus two octaves | | | [[7/4|harmonic seventh]] plus two octaves | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal|23|7|1|intervals=prime}} | |||
{{Harmonics in equal|23|7|1|intervals=prime|collapsed=1|start=12}} | |||
== See also == | == See also == | ||
| Line 134: | Line 139: | ||
* [[19ed5|19ED5]]: relative ED5 | * [[19ed5|19ED5]]: relative ED5 | ||
{{stub}} | |||
[[Category:Ed7]] | [[Category:Ed7]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:Bohlen-Pierce]] | [[Category:Bohlen-Pierce]] | ||
[[Category:Bohpier]] | [[Category:Bohpier]] | ||
Revision as of 23:48, 22 December 2024
| ← 22ed7 | 23ed7 | 24ed7 → |
(convergent)
Division of the 7th harmonic into 23 equal parts (23ED7) is related to the Bohlen-Pierce scale, but with the 7/1 rather than the 3/1 being just. The step size is about 146.4707 cents, corresponding to 8.1928 EDO. It is almost identical to POTE generator for 7-limit bohpier temperament.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 146.4707 | 49/45 | |
| 2 | 292.9414 | 13/11 | |
| 3 | 439.4121 | 9/7 | |
| 4 | 585.8828 | 7/5 | |
| 5 | 732.3535 | 49/32 | |
| 6 | 878.8241 | 5/3 | |
| 7 | 1025.2948 | 9/5 | |
| 8 | 1171.7655 | 63/32 | |
| 9 | 1318.2362 | 15/7 | |
| 10 | 1464.7069 | 7/3 | |
| 11 | 1611.1776 | 28/11 | |
| 12 | 1757.6483 | 11/4 | |
| 13 | 1904.1190 | 3/1 | |
| 14 | 2050.5897 | 49/15 | |
| 15 | 2197.0604 | 32/9 | |
| 16 | 2343.5311 | 35/9 | |
| 17 | 2490.0018 | 21/5 | |
| 18 | 2636.4724 | 32/7 | |
| 19 | 2782.9431 | 5/1 | |
| 20 | 2929.4138 | 49/9 | |
| 21 | 3075.8845 | 77/13 | |
| 22 | 3222.3552 | 45/7 | |
| 23 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -28.2 | +2.2 | -3.4 | +0.0 | -50.1 | -46.4 | -71.4 | +29.0 | -8.9 | +29.3 | +60.3 |
| Relative (%) | -19.3 | +1.5 | -2.3 | +0.0 | -34.2 | -31.7 | -48.8 | +19.8 | -6.0 | +20.0 | +41.1 | |
| Steps (reduced) |
8 (8) |
13 (13) |
19 (19) |
23 (0) |
28 (5) |
30 (7) |
33 (10) |
35 (12) |
37 (14) |
40 (17) |
41 (18) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +46.9 | +15.6 | -66.8 | +72.1 | +10.6 | -28.6 | +60.2 | +44.2 | -56.2 | +42.2 | +51.9 |
| Relative (%) | +32.0 | +10.7 | -45.6 | +49.3 | +7.2 | -19.5 | +41.1 | +30.2 | -38.3 | +28.8 | +35.5 | |
| Steps (reduced) |
43 (20) |
44 (21) |
44 (21) |
46 (0) |
47 (1) |
48 (2) |
49 (3) |
50 (4) |
50 (4) |
51 (5) |
52 (6) | |
See also
|
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