Sensamagic: Difference between revisions
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'''Sensamagic''', sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''', is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s 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''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''', is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s 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: | 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" | * 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]]) or 49/25 (resulting in an obscure porcupine extension called "hedgehog" that splits the octave into two 7/5~10/7 tritones) | * equating the octave to a false octave found on the sensamagic generator chain, such as 125/63 (resulting in [[sensi]] (19 & 46)) 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 | * adding the octave as an additional generator, resulting in rank-3 sensamagic (41 & 19 & 27) | ||
This page will focus on tritave and rank-3 sensamagic. | This page will focus on tritave and rank-3 sensamagic. | ||
Revision as of 12:16, 5 March 2026
Sensamagic (b13 & b17), sometimes known in a tritave-equivalent context as Bohlen-Pierce-Stearns, 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 & 46)) 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)
This page will focus on tritave and rank-3 sensamagic.
TODO: complete page
