301edo: Difference between revisions
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{{EDO intro|301}} | |||
== Theory == | == Theory == | ||
301edo is a strong 7-limit system, and distinctly consistent through the [[17-odd-limit]]. It 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. | 301edo is a strong 7-limit system, and distinctly [[consistent]] through the [[17-odd-limit]]. It 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 [[support]]s the [[sesquiquartififths]] temperament. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|301}} | |||
=== Divisors === | |||
301 is a composite number, since 301 = 7 × 43. This is related to the proposal of the deaf French mathematician and acoustician [[Wikipedia: Joseph Sauveur|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. | 301 is a composite number, since 301 = 7 × 43. This is related to the proposal of the deaf French mathematician and acoustician [[Wikipedia: Joseph Sauveur|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 {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]]. | 301edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
Revision as of 07:47, 15 January 2023
| ← 300edo | 301edo | 302edo → |
Theory
301edo is a strong 7-limit system, and distinctly consistent through the 17-odd-limit. It 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) | |
Divisors
301 is a composite number, since 301 = 7 × 43. 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
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 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 |
Rank-2 temperaments
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 25\301 | 99.67 | 200/189 | 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 |