BPS: Difference between revisions

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'''Bohlen–Pierce–Stearns''' (BPS) is a [[non-octave]] [[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. This generates a [[MOS scale]] of [[4L 5s (3/1-equivalent)|4L 5s]] against the tritave, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13]]edt, representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17]]edt, [[30edt|7\30]]edt, and [[43edt|10\43]]edt.

'''Bohlen–Pierce–Stearns''' (BPS) is a [[non-octave]] [[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. This generates a [[MOS scale]] of [[4L 5s (3/1-equivalent)|4L 5s]] against the tritave, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13]]edt, representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17]]edt, [[30edt|7\30]]edt, and [[43edt|10\43]]edt.

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.

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	'''Bohlen–Pierce–Stearns''' (BPS) is a [[non-octave]] [[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. This generates a [[MOS scale]] of [[4L 5s (3/1-equivalent)\|4L 5s]] against the tritave, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt\|3\13]]edt, representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt\|4\17]]edt, [[30edt\|7\30]]edt, and [[43edt\|10\43]]edt.		'''Bohlen–Pierce–Stearns''' (BPS) is a [[non-octave]] [[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. This generates a [[MOS scale]] of [[4L 5s (3/1-equivalent)\|4L 5s]] against the tritave, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt\|3\13]]edt, representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt\|4\17]]edt, [[30edt\|7\30]]edt, and [[43edt\|10\43]]edt.

	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.		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.