301edo
Theory
301edo is a strong 7-limit system, and distinctly consistent through the 17-odd-limit. The equal temperament tempers out 32805/32768 in the 5-limit, 2401/2400 in the 7-limit, 3025/3024, 5632/5625, 8019/8000 in the 11-limit, 729/728, 847/845, 1001/1000, 1716/1715, 2200/2197 in the 13-limit, and 561/560, 833/832, 1089/1088, 1156/1155, 1275/1274 and 1701/1700 in the 17-limit. Since it tempers out both 32805/32768 and 2401/2400, it supports the sesquiquartififths temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.29 | +0.40 | -0.06 | -1.15 | +0.67 | -1.30 | +1.49 | +1.63 | -1.01 | -0.85 |
| Relative (%) | +0.0 | -7.4 | +10.0 | -1.4 | -28.9 | +16.8 | -32.6 | +37.4 | +40.8 | -25.2 | -21.3 | |
| Steps (reduced) |
301 (0) |
477 (176) |
699 (97) |
845 (243) |
1041 (138) |
1114 (211) |
1230 (26) |
1279 (75) |
1362 (158) |
1462 (258) |
1491 (287) | |
Subsets and supersets
Since 301 factors into 7 × 43, 301edo has 7edo and 43edo as its subsets. This is related to the proposal of the deaf French mathematician and acoustician Joseph Sauveur to divide the octave in 43 parts called merides, and those into seven more parts called heptamerides. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.
301edo also tempers out [168 -43 -43⟩ and 5250987/5242880, so it supports the meridic temperament.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-477 301⟩ | [⟨301 477]] | +0.0927 | 0.0927 | 2.33 |- | 2.3.5 | 32805/32768, [3 45 -32⟩ | [⟨301 477 699]] | +0.0048 | 0.1456 | 3.65 |- | 2.3.5.7 | 2401/2400, 32805/32768, 1959552/1953125 | [⟨301 477 699 845]] | +0.0085 | 0.1262 | 3.17 |- | 2.3.5.7.11 | 2401/2400, 3025/3024, 5632/5625, 8019/8000 | [⟨301 477 699 845 1041]] | +0.0734 | 0.1720 | 4.31 |- | 2.3.5.7.11.13 | 729/728, 847/845, 1001/1000, 1716/1715, 3025/3024 | [⟨301 477 699 845 1041 1114]] | +0.0310 | 0.1834 | 4.60 |- | 2.3.5.7.11.13.17 | 561/560, 729/728, 833/832, 847/845, 1001/1000, 1089/1088 | [⟨301 477 699 845 1041 1114 1230]] | +0.0721 | 0.1973 | 4.95 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 25\301
| 99.67
| 18/17
| Quintaschis
|-
| 1
| 44\301
| 175.42
| 448/405
| Sesquiquartififths / sesquart (301e)
|-
| 1
| 68\301
| 271.10
| 90/77
| Quasiorwell
|-
| 1
| 76\301
| 302.99
| 25/21
| Quinmite
|-
| 1
| 125\301
| 498.34
| 4/3
| Helmholtz
|-
| 7
| 125\301
(4\301)
| 498.34
(15.95)
| 4/3
(245/243)
| Septant
|-
| 43
| 125\301
(1\301)
| 498.34
(3.99)
| 4/3
(540/539)
| Meridic
Template:Rank-2 end
Template:Orf