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<span style="display: block; text-align: right;">[[:de:Bohlen-Pierce Deutsch]]</span>
{{interwiki
|en = Bohlen-Pierce
|de = Bohlen-Pierce
}}
{{Wikipedia}}
[[File:vaisvil-BP-guitar-052-crop.jpg|thumb|x00px|Chris Vaisvil's BP electric guitar. [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar.]]]
[[File:Sword_BP_guitars.jpg|thumb|300px]]


The '''Bohlen-Pierce''' ('''BP''') scale is a [[nonoctave|nonoctave]] scale, a 13-part equal division of the perfect-twelfth ([[3/1|3/1]]) or [[Tritave|Tritave]] ('''13edt'''). Each step is about 146 ¢, making it a [[macrotonal|macrotonal]] scale. It is closely related to the rank two temperament [[Sensamagic_clan#Bohpier|bohpier]]. Bohlen-Pierce is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just_intonation_subgroups|subgroup]]. However, it (or at least 3.5.7-limit [[edt|13edt]]) can be extended to the 3.5.7.11/4 subgroup. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen-Pierce, from this extended perspective, may be found listed on the page [[Chords_of_bohpier|chords of bohpier]]. Bohlen-Pierce was discovered independently by [[Heinz_Bohlen|Heinz Bohlen]], [[John_Pierce|John Pierce]], [[Kees_van_Prooijen|Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.
The '''Bohlen–Pierce scale''' ('''BP''') is a 13-tone [[macrotonal]] [[nonoctave]] [[scale]] designed to emphasize odd-number intervals and chords, such as the 3:5:7:9 tetrad. It was first described as a 7-limit [[just intonation]] scale and as an [[equal-step tuning|equal temperament]], [[13edt|13 equal divisions of the tritave]]. The [[tritave]] (3/1) usually replaces the [[octave]] in the role of the [[equave]], such that intervals a tritave apart are considered [[equivalent]].


Chris Vaisvil's BP electric =&gt; [http://chrisvaisvil.com/the-bohlen-pierce-epiphone-roadie-guitar/ Music from this guitar]
It is closely related to the rank two temperament [[Sensamagic clan #Bohpier|bohpier]]. It is normally thought of (if not in these terms, then in fact) as a temperament defined on the 3.5.7 [[Just intonation subgroup|subgroup]]. However, it can be extended to the 3.5.7.11/4 subgroup, especially when considering 13edt instead of the JI version. This extension is controversial because of the presence of 2 in the denominator of 11/4, but the interval is present in the sense that 3^(12\13) provides an approximation to it. Chords of Bohlen–Pierce, from this extended perspective, may be found listed on the page [[chords of bohpier]].


<div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
Bohlen–Pierce was discovered independently by [[Heinz Bohlen]], [[John Pierce]], [[Kees van Prooijen]], and perhaps others, usually noticed for its good approximation of odd-number just ratios 3:5, 5:7, 3:7, etc.; but not necessarily 4:11, 5:6, 6:7, etc.
External image: http://chrisvaisvil.com/wp-content/uploads/2016/05/052-crop.jpg<br>
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[[Category:IMPORTDEBUG - Change External Images]]


<div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
== Theory ==
External image: http://www.ronsword.com/images/Sword_BP_guitars.jpg<br>
* [[Relationship between Bohlen–Pierce and octave-ful temperaments]]
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<div class='external-image-warning' style='background-color:#f8f9fa; border: 1px solid #eaecf0; padding-left: 0.5em; padding-right:0.5em; display:inline-block'>
=== Lambda scale ===
External image: http://ronsword.com/bpguitar.JPG<br>
{{Main|4L 5s (3/1-equivalent)}}
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[[Ron_Sword|Ron Sword]] and his 9-string 13-tone BP Touchstick/Guitar crossover instrument (aka: "''the Bohlen-Box''")
== Intervals ==
{{Main|Intervals of BP}}


=Triple Bohlen-Pierce=
== Variations ==
Proposed by [[Paul_Erlich|Paul Erlich]], is the Triple Bohlen-Pierce Scale, or 39th root of 3. It approximates additional odd harmonics and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen-Pierce scale interlocking three times with calm sounding quarter-tones, and for various JI modulations.
=== Triple Bohlen–Pierce ===
Proposed by [[Paul Erlich]] is [[39edt]], also known as the ''Triple Bohlen–Pierce scale''. It adds to 13edt accurate approximations to the 11th and 13th harmonics ([[11/9]] and [[13/9]]) and can be used in a variety of ways, for both just intonation chords and harmonies, as standard Bohlen–Pierce scale interlocking three times with calm-sounding quarter-tones, and for various JI modulations.


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== Regular temperament properties ==
External image: http://www.ronsword.com/images/3BP3.JPG<br>
{{Main| 13edt#Regular temperament properties }}
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(triple bohlen-pierce <span style="">39√3 Classical Guitar by Ron Sword</span>)
== Instruments ==
* [http://www.huygens-fokker.org/bpsite/instruments.html#anchor39641 Bohlen Pierce guitar]
* [[Clarinet#Bohlen-Pierce clarinets|Clarinets]]
* Metallophone
* Electronic Organ
* Stredici
* [http://bp.b0b.com/2016/01/tuning-a-kalimba-to-bp/ Kalimba] (Mbira)
* [http://bp.b0b.com/2012/11/sierra-pedal-steel/ Pedal Steel Guitar]


=Theory=
== Music ==
[http://www.huygens-fokker.org/bpsite/ Bohlen Pierce website]
{{Main| Bohlen–Pierce scale/Music }}
{{Catrel|Bohlen-Pierce tracks}}


[http://en.wikipedia.org/wiki/Bohlen-Pierce_scale Wikipedia Bohlen-Pierce scale]
== See also ==
* [[Catalog of 3.5.7 subgroup rank two temperaments]]
* [[Lumatone mapping for Bohlen–Pierce]]


[http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by Elaine Walker
== Further reading ==
* [[Sword, Ron]]. [https://ronsword.bigcartel.com/product/creative-applications-for-polyscales-and-scale-sequences ''Bohlen-Pierce Scales for Guitar: Includes Paul Erlich's Triple BP Scales. Notation methods, Chord-Scales, Melody Chords, Polyscales, and new Scales for the Bohlen-Pierce tuning'']. 2009. ([http://www.metatonalmusic.com/books.html Metatonal Music link])


Sword, Ronald. "Bohlen Pierce Scales for Guitar" IAAA Press, UK-USA. First Ed: May 2009.
== External links ==
* [http://www.huygens-fokker.org/bpsite/ The Bohlen-Pierce Site]
* [http://ziaspace.com/_academic/BP/ Bohlen-Pierce Scale Research] by [[Elaine Walker]]


[[Intervals_of_BP|Intervals of BP]]
[[Category:Bohlen–Pierce| ]] <!-- main article -->
 
[[Category:13-tone scales]]
=EDTs compatible with the BP nonatonic scale=
[[Category:Guitar]]
The Lambda MOS family of 4L+5s is well known for accurately representing the 3.5.7 subgroup when the generator is near the boundary of propriety, such as in the case of the Bohlen Pierce scale. Below is a list of the equal-temperaments which contain a 4L+5s scale using generators between 422.7 cents and 475.5 cents.
[[Category:Macrotonal]]
 
L=1 s=0 4 edt
 
L=1 s=1 9 edt (5flat40 7sharp18)
 
L=2 s=1 13 (5flat7 7flat3)
 
L=3 s=1 17 (5sharp10 7flat12)
 
L=3 s=2 22 (~14edo)
 
L=4 s=1 21
 
L=4 s=3 31
 
L=5 s=1 25
 
L=5 s=2 30 (~19edo) (5sharp3 7flat8)
 
L=5 s=3 35 (~22edo) (5flat14 7sharp0)
 
L=5 s=4 40
 
L=6 s=1 29
 
L=6 s=5 49 (~31EDO) (5sharp8 7sharp8) (Schism*)
 
L=7 s=1 33
 
L=7 s=2 38 (~24edo)
 
L=7 s=3 43 (~27edo) (5sharp0 7flat6)
 
L=7 s=4 48 (5flat13 7flat0)
 
L=7 s=5 53
 
L=7 s=6 58 5sharp1 7sharp10 (Schism*)
 
*Schism, by which I mean, the most accurate value for 5/3 and-or 7/3 is found outside the 4L+5s MOS.
 
[Also, the way I see it, as 4edt and 9edt are comparable to 5edo and 7edo, then the "counterparts" of Blackwood and Whitewood would be found in multiples therein and would be octatonic and octadecatonic, eg. 12edt and 27edt.]
 
{| class="wikitable"
|-
! colspan="7" | Generator
! | cents
! | L
! | s
! | notes
|-
| style="text-align:center;" | 1/4
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| colspan="2" style="text-align:center;" | 475.49
| style="text-align:center;" | 0
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8/33
| style="text-align:center;" | 461.08
| style="text-align:center;" | 403.445
| style="text-align:center;" | 57.635
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7/29
| style="text-align:center;" |
| style="text-align:center;" | 459.09
| style="text-align:center;" | 393.505
| style="text-align:center;" | 65.585
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13/54
| style="text-align:center;" | 457.88
| style="text-align:center;" | 387.435
| style="text-align:center;" | 70.455
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 6/25
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 456.47
| style="text-align:center;" | 380.39
| style="text-align:center;" | 76.08
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17/71
| style="text-align:center;" | 455.4
| style="text-align:center;" | 375.03
| style="text-align:center;" | 80.37
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11/46
| style="text-align:center;" |
| style="text-align:center;" | 454.815
| style="text-align:center;" | 372.12
| style="text-align:center;" | 82.695
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 16/67
| style="text-align:center;" | 454.2
| style="text-align:center;" | 369.03
| style="text-align:center;" | 85.17
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5/21
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 452.85
| style="text-align:center;" | 362.28
| style="text-align:center;" | 90.57
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19/80
| style="text-align:center;" | 451.71
| style="text-align:center;" | 356.62
| style="text-align:center;" | 94.91
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 14/59
| style="text-align:center;" |
| style="text-align:center;" | 451.31
| style="text-align:center;" | 354.6
| style="text-align:center;" | 96.7
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23/97
| style="text-align:center;" | 450.98
| style="text-align:center;" | 352.94
| style="text-align:center;" | 98.04
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 9/38
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 450.46
| style="text-align:center;" | 350.36
| style="text-align:center;" | 100.1
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 22/93
| style="text-align:center;" | 449.925
| style="text-align:center;" | 347.67
| style="text-align:center;" | 102.255
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13/55
| style="text-align:center;" |
| style="text-align:center;" | 449.55
| style="text-align:center;" | 345.81
| style="text-align:center;" | 103.74
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17/72
| style="text-align:center;" | 449.07
| style="text-align:center;" | 343.41
| style="text-align:center;" | 105.66
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 448.42
| style="text-align:center;" | 340.15
| style="text-align:center;" | 108.27
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 4/17
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 447.52
| style="text-align:center;" | 335.64
| style="text-align:center;" | 111.88
| style="text-align:center;" | Canonical BP scales are between here...
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19/81
| style="text-align:center;" | 446.14
| style="text-align:center;" | 328.73
| style="text-align:center;" | 117.41
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| style="text-align:center;" | <span style="display: block; text-align: center;">15/64</span>
| |
| style="text-align:center;" | 445.77
| style="text-align:center;" | 327.1
| style="text-align:center;" | 118.87
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 445.53
| style="text-align:center;" | 325.71
| style="text-align:center;" | 119.82
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 26/111
| style="text-align:center;" | 445.5
| style="text-align:center;" | 325.56
| style="text-align:center;" | 119.94
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11/47
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 445.14
| style="text-align:center;" | 323.74
| style="text-align:center;" | 121.4
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 29/124
| style="text-align:center;" | 444.81
| style="text-align:center;" | 322.105
| style="text-align:center;" | 122.705
| style="text-align:center;" | Golden BP is near here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 18/77
| style="text-align:center;" |
| style="text-align:center;" | 444.61
| style="text-align:center;" | 321.1
| style="text-align:center;" | 123.51
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25/107
| style="text-align:center;" | 444.38
| style="text-align:center;" | 319.955
| style="text-align:center;" | 120.425
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7/30
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 443.79
| style="text-align:center;" | 316.99
| style="text-align:center;" | 126.8
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 24/103
| style="text-align:center;" | 443.17
| style="text-align:center;" | 313.915
| style="text-align:center;" | 129.265
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17/73
| style="text-align:center;" |
| style="text-align:center;" | 442.92
| style="text-align:center;" | 312.65
| style="text-align:center;" | 130.27
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 27/116
| style="text-align:center;" | 442.7
| style="text-align:center;" | 311.53
| style="text-align:center;" | 131.17
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 10/43
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 442.315
| style="text-align:center;" | 309.62
| style="text-align:center;" | 132.695
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23/99
| style="text-align:center;" | 441.87
| style="text-align:center;" | 307.39
| style="text-align:center;" | 134.48
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13/56
| style="text-align:center;" |
| style="text-align:center;" | 441.525
| style="text-align:center;" | 305.67
| style="text-align:center;" | 135.845
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 16/69
| style="text-align:center;" | 441.03
| style="text-align:center;" | 303.21
| style="text-align:center;" | 137.82
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | 3/13
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 438.91
| style="text-align:center;" | 292.61
| style="text-align:center;" | 146.3
| style="text-align:center;" | ...and here
 
Boundary of propriety for Lambda scale
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17/74
| style="text-align:center;" | 436.935
| style="text-align:center;" | 282.72
| style="text-align:center;" | 154.215
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 14/61
| style="text-align:center;" |
| style="text-align:center;" | 436.515
| style="text-align:center;" | 280.61
| style="text-align:center;" | 155.905
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25/109
| style="text-align:center;" | 436.23
| style="text-align:center;" | 279.19
| style="text-align:center;" | 157.04
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11/48
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 435.845
| style="text-align:center;" | 277.37
| style="text-align:center;" | 158.495
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 30/131
| style="text-align:center;" | 435.56
| style="text-align:center;" | 275.86
| style="text-align:center;" | 159.7
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19/83
| style="text-align:center;" |
| style="text-align:center;" | 435.39
| style="text-align:center;" | 274.98
| style="text-align:center;" | 160.41
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 27/118
| style="text-align:center;" | 435.19
| style="text-align:center;" | 274.01
| style="text-align:center;" | 161.18
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8/35
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 434.73
| style="text-align:center;" | 271.71
| style="text-align:center;" | 163.02
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 29/127
| style="text-align:center;" | 434.305
| style="text-align:center;" | 269.57
| style="text-align:center;" | 164.735
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 21/92
| style="text-align:center;" |
| style="text-align:center;" | 434.14
| style="text-align:center;" | 268.755
| style="text-align:center;" | 165.385
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 34/149
| style="text-align:center;" | 434
| style="text-align:center;" | 268.06
| style="text-align:center;" | 165.94
| style="text-align:center;" | Golden Lambda scale is near here
 
18\7*30\11=7
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13/57
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 433.78
| style="text-align:center;" | 266.94
| style="text-align:center;" | 166.84
| style="text-align:center;" | <span style="display: block; text-align: center;">18\7*30\11=7</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31/136
| style="text-align:center;" | 433.53
| style="text-align:center;" | 265.71
| style="text-align:center;" | 167.62
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 18/79
| style="text-align:center;" |
| style="text-align:center;" | 433.36
| style="text-align:center;" | 264.83
| style="text-align:center;" | 168.53
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23/101
| style="text-align:center;" | 433.11
| style="text-align:center;" | 263.64
| style="text-align:center;" | 169.47
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5/22
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 432.26
| style="text-align:center;" | 259.36
| style="text-align:center;" | 172.905
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 22/97
| style="text-align:center;" | 431.37
| style="text-align:center;" | 254.9
| style="text-align:center;" | 176.47
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17/75
| style="text-align:center;" |
| style="text-align:center;" | 431.11
| style="text-align:center;" | 253.59
| style="text-align:center;" | 177.52
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 29/128
| style="text-align:center;" | 430.91
| style="text-align:center;" | 252.6
| style="text-align:center;" | 178.31
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 12/53
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 430.63
| style="text-align:center;" | 251.2
| style="text-align:center;" | 179.43
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 31/137
| style="text-align:center;" | 430.37
| style="text-align:center;" | 249.89
| style="text-align:center;" | 180.48
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 19/84
| style="text-align:center;" |
| style="text-align:center;" | 430.2
| style="text-align:center;" | 249.065
| style="text-align:center;" | 181.135
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 26/115
| style="text-align:center;" | 430.01
| style="text-align:center;" | 248.08
| style="text-align:center;" | 181.93
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7/31
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 429.47
| style="text-align:center;" | 245.41
| style="text-align:center;" | 184.06
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 23/102
| style="text-align:center;" | 428.87
| style="text-align:center;" | 242.41
| style="text-align:center;" | 186.46
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 16/71
| style="text-align:center;" |
| style="text-align:center;" | 428.61
| style="text-align:center;" | 241.09
| style="text-align:center;" | 187.59
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 25/111
| style="text-align:center;" | 428.37
| style="text-align:center;" | 239.89
| style="text-align:center;" | 188.48
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 9/40
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 427.94
| style="text-align:center;" | 237.74
| style="text-align:center;" | 190.2
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 20/89
| style="text-align:center;" | 427.41
| style="text-align:center;" | 235.07
| style="text-align:center;" | 192.34
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11/49
| style="text-align:center;" |
| style="text-align:center;" | 426.97
| style="text-align:center;" | 232.89
| style="text-align:center;" | 194.08
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13/58
| style="text-align:center;" | 426.3
| style="text-align:center;" | 229.55
| style="text-align:center;" | 196.75
| style="text-align:center;" |
|-
| style="text-align:center;" | 2/9
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 422.66
| colspan="2" style="text-align:center;" | 211.33
| style="text-align:center;" | Separatrix of Lambda and <span style="display: inline !important;">Anti-Lambda scales</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">13/59</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">419.075</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">225.66</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">193.41</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">11/50</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">418.43</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">228.235</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">190.2</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">20/91</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">418.015</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">229.91</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">188.105</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">9/41</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">417.5</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">231.95</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">185.56</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">25/114</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">417.095</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">233.57</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">183.52</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">16/73</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">416.87</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">234.49</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">182.38</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">23/105</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">416.62</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">235.48</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">181.14</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">7/32</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">416.05</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">237.74</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">178.31</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">26/119</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">415.55</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">239.74</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">175.81</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">19/87</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">415.37</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">240.48</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">174.89</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">31/143</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">415.215</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">241.09</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">174.12</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">12/55</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">414.97</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">242.07</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">172.905</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 29/133
| style="text-align:center;" | 414.71
| style="text-align:center;" | 243.11
| style="text-align:center;" | 171.605
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">17/78</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">414.53</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">243.84</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">170.69</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">22/101</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">414.29</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">244.81</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">169.48</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5/23
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">413.47</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">248.08</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">165.39</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">23/106</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">412.7</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">251.2</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">161.49</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">18/83</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">412.47</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">252.06</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">160.41</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">31/143</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">412.31</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">252.71</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">159.605</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">13/60</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">412.09</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">253.59</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">158.5</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">34/157</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">411.89</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">254.4</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">157.49</span>
| style="text-align:center;" | Golden Anti-Lambda scale is near here
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">21/97</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">411.76</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">254.9</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">156.86</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">29/134</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">411.625</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">255.49</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">156.13</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">8/37</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">411.23</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">257.02</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">154.21</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">27/125</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">410.82</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">258.67</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">152.16</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">19/88</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">410.65</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">259.36</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">151.29</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">30/139</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">410.49</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">259.98</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">150.51</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">11/51</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">410.23</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">261.05</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">149.17</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">25/116</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">409.9</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">262.34</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">147.565</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">14/65</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">409.75</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">263.35</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">146.3</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">17/79</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">409.28</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">264.83</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">144.45</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">3/14</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">407.56</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">271.71</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">135.85</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">Boundary of propriety for Anti-Lambda scale</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">16/75</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">405.75</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">278.95</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">126.8</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">13/61</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">405.345</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">280.62</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">124.72</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">23/108</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">405.05</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">281.77</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">123.275</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">10/47</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">404.7</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">283.29</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">121.4</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">27/127</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">404.35</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">284.54</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">119.81</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">17/80</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">404.165</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">285.29</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">118.87</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">24/113</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">403.955</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">286.135</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">117.82</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">7/33</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">403.445</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">288.175</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">115.27</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">25/118</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">402.955</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">290.13</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">112.83</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">18/85</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">402.77</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">290.89</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">111.88</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">29/137</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">402.6</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">291.54</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">111.06</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">11/52</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">402.35</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">292.61</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">109.73</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">26/123</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">402.05</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">293.8</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">108.24</span>
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 402.01
| style="text-align:center;" | 293.9
| style="text-align:center;" | 108.11
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">15/71</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">401.83</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">294.67</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">107.15</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">19/90</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">401.52</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">295.86</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">105.66</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 4\19
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">400.41</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">300.31</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">100.1</span>
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 399.69
| style="text-align:center;" | 303.185
| style="text-align:center;" | 96.51
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">17/81</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">399.18</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">305.25</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">93.92</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">13/62</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">398.8</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">306.77</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">92.03</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">22/105</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">398.515</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">307.94</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">90.57</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">9/43</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">398.08</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">309.62</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">88.46</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">23/110</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">397.68</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">311.23</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">86.45</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">14/67</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">397.42</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">312.26</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">85.16</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">19/91</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">397.11</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">313.51</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">83.6</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">5/24</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">396.24</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">316.99</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">79.25</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">16/77</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">395.21</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">321.11</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">74.1</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">11/53</span>
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">394.745</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">322.93</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">71.77</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">17/82</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">394.31</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">324.72</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">69.58</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">6/29</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">393.505</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">327.92</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">65.585</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">13/63</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">392.47</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">332.09</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">60.38</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7/34
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">391.58</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">335.64</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">55.94</span>
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | <span style="display: block; text-align: center;">8/39</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">390.145</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">341.38</span>
| style="text-align:center;" | <span style="display: block; text-align: center;">48.77</span>
| style="text-align:center;" |
|-
| style="text-align:center;" | <span style="display: block; text-align: center;">1/5</span>
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| colspan="2" style="text-align:center;" | <span style="display: block; text-align: center;">380.39</span>
| style="text-align:center;" | 0
| style="text-align:center;" |
|}
 
=Physical instruments tuned to the BP scale=
[http://www.swordguitars.com/Sword_Bohlen_Pierce_acoustic.JPG Bohlen Pierce guitar]
 
[[microtonal_clarinet#BPClarinets|Clarinets]]
 
Metallophone
 
Electronic Organ
 
Stredici
 
[http://bp.b0b.com/2016/01/tuning-a-kalimba-to-bp/ Kalimba] (Mbira)
 
[http://bp.b0b.com/2012/11/sierra-pedal-steel/ Pedal Steel Guitar]
 
=Compositions=
[https://soundcloud.com/overtoneshock/a-mean-little-voice-bohlen-pierce-or-13ed3 A Mean Little Voice] by Stephen Weigel
 
[http://chrisvaisvil.com/ask-for-it-over-the-ridge/ Ask For It] by [[Chris_Vaisvil|Chris Vaisvil]]
 
Links to available music written in BP at [http://www.huygens-fokker.org/bpsite/references2.html#anchor81501 above website].
 
<span style=""><span style="">[http://www.seraph.it/XenoTunes4_files/Bohl-en%20Roll.mp3 Bohl-en Roll]</span></span> by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/004e4fe53f09c06fd5e709a08d53d0d5-4.html blog entry])
 
<span style=""><span style="">[http://www.jeanpierrepoulin.com/mp3/BPguitares.mp3 Bohlen-Pierce electric guitar improvisation]</span></span> by [[Jean-Pierre_Poulin|Jean-Pierre Poulin]]
 
<span style=""><span style="">[http://www.ronsword.com/sounds/BP_stretched_chroma.mp3 Bohlen-Pierce "Stretched Chroma" Acoustic Improvisation]</span></span> by [[Ron_Sword|Ron Sword]]
 
<span style="">[http://www.kunstmusik.com/mp3/reminiscences.mp3 Reminiscences]</span> by [http://www.kunstmusik.com/2010/03/08/reminiscences/ Steven Yi]
 
<span style=""><span style="">[http://www.jeanpierrepoulin.com/mp3/Roll%27n%27Peace.mp3 Roll'n'Peace]</span></span> by [[Jean-Pierre_Poulin|Jean-Pierre Poulin]]
 
<span style=""><span style="">[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/01%20-%201.%20Bohlen-Pierce.mp3 Comets Over Flatland 1]</span></span> by [[Randy_Winchester|Randy Winchester]]
 
<span style=""><span style="">[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/02%20-%202.%20Bohlen-Pierce.mp3 Comets Over Flatland 2]</span></span> by [[Randy_Winchester|Randy Winchester]]
 
<span style=""><span style="">[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/03%20-%203.%20Bohlen-Pierce.mp3 Comets Over Flatland 3]</span></span> by [[Randy_Winchester|Randy Winchester]]
 
<span style=""><span style="">[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/04%20-%204.%20Bohlen-Pierce.mp3 Comets Over Flatland 4]</span></span> by [[Randy_Winchester|Randy Winchester]]
 
<span style=""><span style="">[http://micro.soonlabel.com/bohlen-pierce/daily20110915_BP_strings-Bohlen-Pierce-Island.mp3 Bohlen-Pierce Island audio]</span></span> by [[Chris_Vaisvil|Chris Vaisvil]]
 
<span style=""><span style="">[http://micro.soonlabel.com/bohlen-pierce/mesonic_atom_13th_root_of_3_BP_apx_X1.mp3 Mesonic Atom]</span></span> by [[Chris_Vaisvil|Chris Vaisvil]]
 
<span style=""><span style="">[http://micro.soonlabel.com/MOTU/Vaisvil-MOTU-8a-bending-the-rules-in-bohlen-pierce.mp3 Bending the Rules]</span></span> by [[Chris_Vaisvil|Chris Vaisvil]]
 
<span style="">[http://micro.soonlabel.com/gene_ward_smith/Others/Hansen/Bohlen-Pierce%20Canon.mp3 Bohlen-Pierce Canon]</span> by <span style="">[http://www.youtube.com/watch?v=sd1b9Lh8iFA Kjell Hansen]</span>.
 
[http://chrisvaisvil.com/bohlens-pierced-waltz/ Bohlen's Pierced Waltz] by [[Chris_Vaisvil|Chris Vaisvil]]
 
[http://chrisvaisvil.com/the-complex-plane-bp-guitar/ The Complex Plane ]by [[Chris_Vaisvil|Chris Vaisvil]]
 
==See also==
<ul><li>[[Catalog_of_3.5.7_subgroup_rank_two_temperaments|Catalog of 3.5.7 subgroup rank two temperaments]]</li></ul>      [[Category:bohlen-pierce]]
[[Category:bp]]
[[Category:edonoi]]
[[Category:edt]]
[[Category:equal]]
[[Category:guitar]]
[[Category:listen]]
[[Category:macrotonal]]
[[Category:scale]]
[[Category:theory]]
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