Bohpier: Difference between revisions
Jump to navigation
Jump to search
Removed redirect to Sensamagic clan#Bohpier Tag: Removed redirect |
mNo edit summary |
||
| Line 1: | Line 1: | ||
'''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25 or 33 notes are available. | '''Bohpier temperament''' is a rank-two temperament for 7, 11, and 13 [[Harmonic limit|prime limits]]. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the [[245/243|sensamagic comma]] (245/243) and the gariboh comma (3125/3087). It is strongly related to [[Bohlen-Pierce]] scale, and from this it derives its name. Generator for the bohpier can be used either [[13edt|13ED3]], [[19ed5|19ED5]], or [[23ed7|23ED7]]. [[41edo|41EDO]] is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available. | ||
See [[Sensamagic clan #Bohpier]] for more technical data. | See [[Sensamagic clan #Bohpier]] for more technical data. | ||
== | == Intervals == | ||
Bohpier is considered as a [[cluster temperament]] with eight clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 50/49 ~ 55/54 ~ 56/55 ~ 66/65 ~ 78/77 all tempered together. | Bohpier is considered as a [[cluster temperament]] with eight clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 50/49 ~ 55/54 ~ 56/55 ~ 66/65 ~ 78/77 all tempered together. | ||
| Line 34: | Line 34: | ||
! Ratios | ! Ratios | ||
|- | |- | ||
| 1 | |||
| 17 | | 17 | ||
| 92.25 | | 92.25 | ||
| Line 280: | Line 280: | ||
|} | |} | ||
== | == Scales == | ||
* [[Bohpier8]] | * [[Bohpier8]] - [[1L 7s]] scale | ||
* [[Bohpier9]] | * [[Bohpier9]] - [[8L 1s]] scale | ||
* [[Bohpier17]] | * [[Bohpier17]] - [[8L 9s]] scale | ||
* [[Bohpier25]] | * [[Bohpier25]] - [[8L 17s]] scale | ||
* [[Bohpier33]] | * [[Bohpier33]] - [[8L 25s]] scale | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
Revision as of 20:59, 29 July 2021
Bohpier temperament is a rank-two temperament for 7, 11, and 13 prime limits. It tempers out 100/99, 144/143, 196/195, and 275/273 in the 13-limit, as well as the sensamagic comma (245/243) and the gariboh comma (3125/3087). It is strongly related to Bohlen-Pierce scale, and from this it derives its name. Generator for the bohpier can be used either 13ED3, 19ED5, or 23ED7. 41EDO is an excellent tuning for the bohpier, with generator 5\41, and MOS of 8, 9, 17, 25, or 33 notes are available.
See Sensamagic clan #Bohpier for more technical data.
Intervals
Bohpier is considered as a cluster temperament with eight clusters of notes in an octave. The chroma interval between adjacent notes in each cluster represents 40/39 ~ 50/49 ~ 55/54 ~ 56/55 ~ 66/65 ~ 78/77 all tempered together.
| Steps | Double dim. | Diminished | Minor | Major | Augmented | Double aug. | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Gen. | Cents* | Ratios | Gen. | Cents* | Ratios | Gen. | Cents* | Ratios | Gen. | Cents* | Ratios | Gen. | Cents* | Ratios | Gen. | Cents* | Ratios | |
| 1 | 17 | 92.25 | 9 | 119.42 | 15/14~14/13 | 1 | 146.60 | 13/12~12/11 | -7 | 173.78 | 11/10~10/9 | -15 | 200.96 | -23 | 228.14 | 8/7 | ||
| 2 | 18 | 238.85 | 15/13 | 10 | 266.03 | 7/6 | 2 | 293.21 | 13/11 | -6 | 320.38 | 6/5 | -14 | 347.56 | 11/9~16/13 | -22 | 374.74 | |
| 3 | 19 | 385.45 | 5/4 | 11 | 412.63 | 14/11 | 3 | 439.81 | 9/7 | -5 | 466.99 | 13/10 | -13 | 494.17 | 4/3 | -21 | 521.34 | |
| 4 | 20 | 532.05 | 15/11 | 12 | 559.23 | 11/8~18/13 | 4 | 586.41 | 7/5 | -4 | 613.59 | 10/7 | -12 | 640.77 | 13/9~16/11 | -20 | 667.95 | 22/15 |
| 5 | 21 | 678.66 | 13 | 705.83 | 3/2 | 5 | 733.01 | 20/13 | -3 | 760.19 | 14/9 | -11 | 787.37 | 11/7 | -19 | 814.55 | 8/5 | |
| 6 | 22 | 825.26 | 14 | 852.44 | 13/8~18/11 | 6 | 879.62 | 5/3 | -2 | 906.79 | 22/13 | -10 | 933.97 | 12/7 | -18 | 961.15 | 26/15 | |
| 7 | 23 | 971.86 | 7/4 | 15 | 999.04 | 7 | 1026.22 | 9/5~20/11 | -1 | 1053.40 | 11/6~24/13 | -9 | 1080.58 | 13/7~28/15 | -17 | 1107.75 | ||
* in 13-limit POTE tuning
Tuning spectrum
Gencom: [2 12/11; 100/99 144/143 196/195 275/273]
Gencom map: [⟨1 0 0 0 2 2], ⟨0 13 19 23 12 14]]
| Eigenmonzo | Neutral second |
Comments |
|---|---|---|
| 13/12 | 138.5727 | |
| 13/11 | 144.6049 | |
| 9/7 | 145.0280 | |
| 10/9 | 145.3709 | |
| 7/5 | 145.6280 | |
| 16/13 | 145.7520 | |
| 11/8 | 145.9432 | |
| 4/3 | 146.3042 | 9-odd-limit minimax |
| 8/7 | 146.4707 | |
| 16/15 | 146.5084 | |
| 15/14 | 146.6048 | |
| 11/9 | 146.6137 | 11-odd-limit minimax |
| 5/4 | 146.6481 | 5, 7, 13, and 15-odd-limit minimax |
| 7/6 | 146.6871 | |
| 15/11 | 146.8475 | |
| 18/13 | 146.9485 | |
| 14/11 | 147.0462 | |
| 15/13 | 147.0967 | |
| 6/5 | 147.3931 | |
| 14/13 | 147.5887 | |
| 11/10 | 147.8565 | |
| 13/10 | 149.1572 | |
| 12/11 | 150.6371 |