Sensamagic
From Xenharmonic Reference
Sensamagic (b13 & b17), sometimes known in a tritave-equivalent context as Bohlen-Pierce-Stearns (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two 9/7s with 5/3; this means that the comma 245/243 is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of Meantone, relating the two simplest prime harmonics after the equave with a medium accuracy.
Sensamagic can be used as a temperament with octaves by one of several approaches:
- simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)
- equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in Sensi (19 & 27)) or 49/25 (resulting in an obscure Porcupine extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones)
- adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)
This page will focus on tritave and rank-3 Sensamagic.
TODO: complete page
Interval chain
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 440.7 | 9/7 |
| 2 | 881.3 | 5/3 |
| 3 | 1322.0 | 15/7 |
| 4 | 1762.7 | 25/9 |
| 5 | 301.4 | 25/21 |
| 6 | 742.0 | 75/49, 125/81 |
| 7 | 1182.7 | |
| 8 | 1623.4 | |
| 9 | 162.1 | |
| 10 | 602.7 | |
| 11 | 1043.4 | |
| 12 | 1484.1 |
* in 3.5.7-subgroup CWE tuning, tritave reduced. Intervals may be additionally octave-reduced in rank-3 sensamagic.
