176edo
| ← 175edo | 176edo | 177edo → |
The 176 equal divisions of the octave (176edo), or the 176(-tone) equal temperament (176tet, 176et) when viewed from a regular temperament perspective, is the equal division of the octave into 176 parts of about 6.82 cents each, a size close to 243/242, the rastma.
Theory
176edo is consistent to the 11-odd-limit. The equal temperament tempers out 78732/78125 (sensipent comma) and [41 -20 -4⟩ (undim comma) in the 5-limit; 6144/6125, 10976/10935, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 6912/6875, 8019/8000, 9801/9800 and 16384/16335 in the 11-limit. Using the patent val, 351/350, 364/363, 2080/2079, 2197/2187, and 4096/4095 in the 13-limit.
It supports the bison temperament and the commatic temperament, and provides the optimal patent val for countermiracle in the 7- and 11-limit, and countermanna, one of the extensions, in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.32 | +2.32 | -0.64 | +0.95 | -1.89 | -2.68 | +2.49 | -1.00 | -0.03 | +0.42 |
| Relative (%) | +0.0 | +4.7 | +34.1 | -9.4 | +14.0 | -27.7 | -39.3 | +36.5 | -14.7 | -0.5 | +6.1 | |
| Steps (reduced) |
176 (0) |
279 (103) |
409 (57) |
494 (142) |
609 (81) |
651 (123) |
719 (15) |
748 (44) |
796 (92) |
855 (151) |
872 (168) | |
Subsets and supersets
Since 176 factors into 24 × 11, 176edo has subset edos 2, 4, 8, 11, 22, 44, and 88.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [279 -176⟩ | [⟨176 279]] | −0.100 | 0.100 | 1.47 |- | 2.3.5 | 78732/78125, [41 -20 -4⟩ | [⟨176 279 409]] | −0.400 | 0.432 | 6.34 |- | 2.3.5.7 | 6144/6125, 10976/10935, 50421/50000 | [⟨176 279 409 494]] | −0.243 | 0.463 | 6.79 |- | 2.3.5.7.11 | 441/440, 3388/3375, 6144/6125, 8019/8000 | [⟨176 279 409 494 609]] | −0.250 | 0.414 | 6.08 |- | 2.3.5.7.11.13 | 351/350, 364/363, 441/440, 2197/2187, 3146/3125 | [⟨176 279 409 494 609 651]] | −0.123 | 0.473 | 6.93 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 17\176
| 115.91
| 77/72
| Mercy / countermiracle / counterbenediction / countermanna
|-
| 1
| 35\176
| 238.64
| 147/128
| Tokko
|-
| 1
| 65\176
| 443.18
| 162/125
| Sensipent
|-
| 1
| 73\176
| 497.73
| 4/3
| Gary / cotoneum
|-
| 1
| 83\176
| 565.91
| 13/9
| Tricot / trident
|-
| 2
| 23\176
| 20.45
| 81/80
| Commatic
|-
| 2
| 23\176
| 156.82
| 35/32
| Bison
|-
| 4
| 73\176
(15\176)
| 497.73
(102.27)
| 4/3
(35/33)
| Undim
|-
| 8
| 73\176
(7\176)
| 497.73
(47.73)
| 4/3
(36/35)
| Twilight
|-
| 8
| 83\176
(5\176)
| 565.91
(34.09)
| 168/121
(55/54)
| Octowerck (176f) / octowerckis (176)
|-
| 11
| 73\176
(7\176)
| 497.73
(47.73)
| 4/3
(36/35)
| Hendecatonic
|-
| 22
| 73\176
(1\176)
| 497.73
(6.82)
| 4/3
(385/384)
| Icosidillic / major arcana
Template:Rank-2 end
Template:Orf