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Bohpier: Difference between revisions

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#redirect [[Sensamagic clan #Bohpier]]
'''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.
 
== Interval ==
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.
 
{| class="wikitable"
! rowspan="2" |Steps
! colspan="3" |Double dim.
! colspan="3" |Diminished
! colspan="3" |Minor
! colspan="3" |Major
! colspan="3" |Augmented
! colspan="3" |Double aug.
|-
! Gen.
! Cents*
! Ratios
! Gen.
! Cents*
! Ratios
! Gen.
! Cents*
! Ratios
! Gen.
! Cents*
! Ratios
! Gen.
! Cents*
! Ratios
! Gen.
! Cents*
! Ratios
|-
| text-align:"center" | 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
|
|}
<nowiki>*</nowiki> in 13-limit POTE tuning
 
== Tuning spectrum ==
Gencom: [2 12/11; 100/99 144/143 196/195 275/273]
 
Gencom map: [{{val| 1 0 0 0 2 2 }}, {{val| 0 13 19 23 12 14 }}]
 
{| class="wikitable center-1 right-2"
|-
! Eigenmonzo
! Neutral <br>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
|
|}
 
== Scale ==
* [[Bohpier8]]
* [[Bohpier9]]
* [[Bohpier17]]
* [[Bohpier25]]
* [[Bohpier33]]


[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Sensamagic clan]]
[[Category:Sensamagic clan]]
[[Category:Bohlen-Pierce]]
[[Category:Index of temperaments]]
Retrieved from "https://en.xen.wiki/w/Bohpier"