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 |
Other tunings
- DKW (3.5.7): ~3 = 1\1, ~9/7 = 440.554
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