BPS: Difference between revisions
m The formal name is *BPS*, not the three-word combo |
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{{Infobox | {{Infobox regtemp | ||
| Title = BPS | | Title = BPS | ||
| Subgroups = 3.5.7 | | Subgroups = 3.5.7 | ||
| Line 5: | Line 5: | ||
| Edo join 1 = b13 | Edo join 2 = b17 | | Edo join 1 = b13 | Edo join 2 = b17 | ||
| Mapping = 1; 2 -1 | | Mapping = 1; 2 -1 | ||
| | | Generators = 9/7 | ||
| | | Generators tuning = 440.7 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| MOS scales = [[4L 1s (3/1-equivalent)|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)|4L 5s <3/1>]] | | MOS scales = [[4L 1s (3/1-equivalent)|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)|4L 5s <3/1>]] | ||
| Color name = | | Color name = | ||
| Odd limit 1 = 7 | Mistuning 1 = 4.73 | Complexity 1 = 4 | | Odd limit 1 = 7 | Mistuning 1 = 4.73 | Complexity 1 = 4 | ||
| Odd limit 2 = | | Odd limit 2 = 3.5.7 49 | Mistuning 2 = 9.46 | Complexity 2 = 9 | ||
}} | }} | ||
{{Wikipedia|Bohlen–Pierce scale}} | {{Wikipedia|Bohlen–Pierce scale}} | ||
'''BPS''' (for ''Bohlen–Pierce–Stearns'') is a [[non-octave]] [[regular temperament|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 {{mos scalesig|4L 5s<3/1>|link=1}}, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13edt]], representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17edt]], [[30edt|7\30edt]], and [[43edt|10\43edt]]. | '''BPS''' (for ''Bohlen–Pierce–Stearns'') is a [[non-octave]] [[regular temperament|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 {{mos scalesig|4L 5s<3/1>|link=1}}, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13edt]], representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17edt]], [[30edt|7\30edt]], and [[43edt|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 3:5:7:9 tetrad to serve as BPS' primary consonance, similar to how the 4:5:6 triad serves as meantone's primary consonance. | 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 3:5:7 triad or 3:5:7:9 tetrad to serve as BPS' primary consonance, similar to how the 4:5:6 triad serves as meantone's primary consonance. | ||
For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-twos extensions are stored on the latter). | For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-twos extensions are stored on the latter). | ||