BPS
Bohlen-Pierce-Stearns (BPS) is a temperament in the 3.5.7 subgroup generated by a sharp ~9/7 (or equivalently a flat ~7/3), tempering out the sensamagic comma, 245/243 so that a stack of two generators represents 5/3 in addition to 81/49, which generates a MOS scale of 4L 5s against the tritave, known as the Bohlen-Pierce Lambda scale. The "canonical" tuning for the generator is 3\13edt, representing the equal-tempered Bohlen-Pierce scale, but a range of other tunings are valid, including 4\17edt, 7\30edt, and 10\43edt.
As the generator of the Bohlen-Pierce scale, and the simplest decently accurate temperament of the 3.5.7 subgroup, this temperament fulfills a niche similar to meantone of the 2.3.5 subgroup, allowing for the tetrad 3:5:7:9 to serve as the theory's primary consonant tetrad.
For technical data, see Sensamagic clan#BPS.
Extensions
Several extensions of this temperament are possible to incorporate additional harmonics.
Interval chains
| # | Cents* | Approximate Ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 440.6 | 9/7, 35/27 |
| 2 | 881.1 | 5/3, 81/49 |
| 3 | 1321.7 | 15/7, 175/81 |
| 4 | 1762.2 | 25/9, 135/49 |
| 5 | 300.8 | 25/21, 405/343, 875/729 |
| 6 | 741.4 | 75/49, 125/81 |
Tuning spectrum
| Edt Generator |
Eigenmonzo (Unchanged-interval) |
Generator (¢) |
Comments |
|---|---|---|---|
| 5\22 | 432.263 | ||
| 7/3 | 435.084 | 0-comma | |
| 14\61 | 436.514 | ||
| 3645/2401 | 437.449 | 1/6-comma | |
| 23\100 | 437.450 | ||
| 49/45 | 438.632 | 1/4-comma | |
| 3\13 | 438.913 | ||
| 7/5 | 439.814 | 1/3-comma | |
| 25\108 | 440.267 | ||
| 440.340 | DR 3:5:7, close to 10/27-comma | ||
| 22\95 | 440.453 | ||
| 19\82 | 440.697 | ||
| 25/21 | 440.760 | 2/5-comma | |
| 16\69 | 441.033 | ||
| 13\56 | 441.525 | ||
| 5/3 | 442.179 | 1/2-comma | |
| 10\43 | 442.315 | ||
| 17\73 | 442.921 | ||
| 7\30 | 443.790 | ||
| 175/81 | 444.544 | 2/3-comma | |
| 18\77 | 444.613 | ||
| 11\47 | 445.138 | ||
| 4\17 | 447.519 | ||
| 35/27 | 449.275 | Full comma |
Other tunings
- DKW (3.5.7): ~3 = 1\1, ~9/7 = 440.554