27edf: Difference between revisions
Jump to navigation
Jump to search
m Infobox ET added |
m Repair misleading link, todo expand, add harmonics, collapsible table |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
'''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to | '''[[EDF|Division of the just perfect fifth]] into 27 equal parts''' (27EDF) is related to [[46edo|46 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the 6-[[integer-limit]], with discrepancy for the 7th harmonic. | ||
It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, [[323edo|323]], [[369edo|369]], [[415edo|415]], and [[692edo|692]] EDOs. | |||
Lookalikes: [[46edo]], [[73edt]] | Lookalikes: [[46edo]], [[73edt]] | ||
==Harmonics== | |||
{{Harmonics in equal|27|3|2|intervals=prime|columns=8}} | |||
{{Harmonics in equal|27|3|2|intervals=prime|columns=8|start=9}} | |||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable mw-collapsible" | ||
|+ Intervals of 27edf | |||
|- | |- | ||
! | degree | ! | degree | ||
| Line 152: | Line 159: | ||
|} | |} | ||
{{todo|expand}} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
Revision as of 06:01, 19 December 2024
| ← 26edf | 27edf | 28edf → |
Division of the just perfect fifth into 27 equal parts (27EDF) is related to 46 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 4.0767 cents compressed and the step size is about 25.9983 cents. Unlike 46edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.
It is related to the regular temperament which tempers out 4375/4374 and 2199023255552/2188322577315 in the 7-limit, which is supported by 46, 323, 369, 415, and 692 EDOs.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.1 | -4.1 | -4.5 | +11.0 | +8.4 | +5.2 | +8.7 | -1.8 |
| Relative (%) | -15.7 | -15.7 | -17.3 | +42.1 | +32.4 | +20.0 | +33.6 | -7.1 | |
| Steps (reduced) |
46 (19) |
73 (19) |
107 (26) |
130 (22) |
160 (25) |
171 (9) |
189 (0) |
196 (7) | |
| Harmonic | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.4 | -6.0 | +8.6 | -11.7 | -7.5 | -11.9 | -9.9 | -9.9 |
| Relative (%) | +20.7 | -22.9 | +33.0 | -45.2 | -28.7 | -45.9 | -38.2 | -38.3 | |
| Steps (reduced) |
209 (20) |
224 (8) |
229 (13) |
240 (24) |
247 (4) |
250 (7) |
256 (13) |
264 (21) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 25.9983 | ||
| 2 | 51.9967 | ||
| 3 | 77.9950 | ||
| 4 | 103.9933 | ||
| 5 | 129.9917 | 69/64 | |
| 6 | 155.9900 | ||
| 7 | 181.9883 | 10/9 | |
| 8 | 207.9867 | pseudo-9/8 | |
| 9 | 233.9850 | pseudo-8/7 | |
| 10 | 259.9833 | pseudo-7/6 | |
| 11 | 285.9817 | ||
| 12 | 311.9800 | pseudo-6/5 | |
| 13 | 337.9783 | 175/144 | |
| 14 | 363.9767 | 216/175 | |
| 15 | 389.9750 | pseudo-5/4 | |
| 16 | 415.9733 | ||
| 17 | 441.9717 | pseudo-9/7 | |
| 18 | 467.9700 | ||
| 19 | 493.9683 | pseudo-4/3 | |
| 20 | 519.9667 | 27/20 | |
| 21 | 545.9650 | ||
| 22 | 571.9633 | 32/23 | |
| 23 | 597.9617 | ||
| 24 | 623.9600 | ||
| 25 | 649.9583 | ||
| 26 | 675.9567 | ||
| 27 | 701.9550 | exact 3/2 | just perfect fifth |