Sensamagic

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, 125/27
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