Intervals of BP: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This page lists the first 42 intervals of the [[Bohlen–Pierce]] scale in both its [[just intonation]] (JI) version and its [[Equal-step tuning|equal-tempered]] (ET) version, [[13edt]].
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-28 07:52:53 UTC</tt>.<br>
: The original revision id was <tt>165960433</tt>.<br>
: The revision comment was: <tt>fourth octave completed</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This page gives the intervals of the equal tempered [[BP|Bohlen-Pierce]] scale -- the 13th root of 3, along with some nearby just ratios for comparison.


||~ degree ||~ cents value ||~ nearby frequency ratios ||~ cents value ||~ difference between BP interval &amp; just interval ||
In the "nearby JI intervals, octave-reduced" columns, the intervals from the original just BP scale are in bold. Errors are sorted by ascending absolute value.
||||||~ first octave and first tritave... ||  ||  ||
|| 0 || 0 || 1/1 || 0 || 0 ||
|| 1 || 146.3 || 12/11
13/12
27/25 || 150.6
138.6
133.2 || -4.3
7.7
13.1 ||
|| 2 || 292.6 || 32/27
13/11
19/16
25/21 || 294.1
289.2
297.5
301.8 || -1.5
3.4
-4.9
-9.2 ||
|| 3 || 438.9 || 9/7 || 435.1 || 3.8 ||
|| 4 || 585.2 || 7/5
45/32 || 582.5
590.2 || 2.7
-5.0 ||
|| 5 || 731.5 || 32/21
26/17
75/49
49/32
20/13 || 729.2
735.6
736.9
737.7
745.8 || 2.3
-4.1
-5.4
-6.2
-14.3 ||
|| 6 || 877.8 || 5/3 || 884.4 || -6.6 ||
|| 7 || 1024.1 || 38/21
29/16
9/5
20/11 || 1026.7
1029.6
1017.6
1035.0 || -2.6
-5.5
6.5
-10.9 ||
|| 8 || 1170.4 || 49/25 || 1165.0 || 5.4 ||
||||||~ second octave... ||  ||  ||
|| 9 || 116.7 || 15/14
16/15
14/13 || 119.4
111.7
128.3 || -2.7
5.0
-11.6 ||
|| 10 || 263.0 || 7/6
22/19 || 266.9
253.8 || -3.9
9.2 ||
|| 11 || 409.3 || 19/15
81/64
24/19
14/11
63/50 || 409.2
407.8
404.4
417.5
400.1 || .1
1.5
4.9
-8.2
9.2 ||
|| 12 || 555.7 || 11/8
18/13
26/19
25/18 || 551.3
563.4
543.0
568.7 || 4.4
-7.7
12.7
-13.0 ||
||||||~ second tritave... ||  ||  ||
|| 13 || 702.0 || 3/2 || 702.0 || 0 ||
|| 14 || 848.3 || 18/11
13/8 || 852.6
840.5 || -4.3
7.8 ||
|| 15 || 994.6 || 16/9 || 996.1 || -1.5 ||
|| 16 || 1140.9 || 27/14 || 1137.0 || 3.9 ||
||||||~ third octave... ||  ||  ||
|| 17 || 87.2 || 20/19
21/20
19/18
22/21 || 88.8
84.5
93.6
80.5 || -1.6
2.7
-6.4
6.7 ||
|| 18 || 233.5 || 8/7
15/13 || 231.2
247.7 || 2.3
-14.2 ||
|| 19 || 379.8 || 5/4
26/21 || 386.3
369.7 || -6.5
10.1 ||
|| 20 || 526.1 || 19/14
27/20
15/11 || 528.7
519.6
537.0 || -2.6
6.5
-10.9 ||
|| 21 || 672.4 || 28/19
25/17
22/15 || 671.3
667.7
663.0 || 1.1
4.7
9.4 ||
|| 22 || 818.7 || 8/5
21/13 || 813.7
830.3 || 5.0
-11.6 ||
|| 23 || 965.0 || 7/4
26/15 || 968.8
952.3 || -3.8
12.7 ||
|| 24 || 1111.3 || 19/10
40/21
36/19
21/11 || 1111.2
1115.5
1106.4
1119.5 || 0.1
-4.2
4.9
-8.2 ||
||||||~ fourth octave... ||  ||  ||
|| 25 || 57.6 || 33/32 || 53.3 || 4.3 ||
||||||~ third tritave... ||  ||  ||
|| 26 || 203.9 || 9/8 || 203.9 || 0 ||
|| 27 || 350.2 ||  ||  ||  ||
|| 28 || 496.5 ||  ||  ||  ||
|| 29 || 642.8 ||  ||  ||  ||
|| 30 || 789.1 ||  ||  ||  ||
|| 31 || 935.4 ||  ||  ||  ||
|| 32 || 1081.7 ||  ||  ||  ||
||||||= **fifth octave...** ||  ||  ||
|| 33 || 28.0 ||  ||  ||  ||
||  ||  ||  ||  ||  ||
||  ||  ||  ||  ||  ||
||  ||  ||  ||  ||  ||
||  ||  ||  ||  ||  ||
||  ||  ||  ||  ||  ||</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Intervals of BP&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This page gives the intervals of the equal tempered &lt;a class="wiki_link" href="/BP"&gt;Bohlen-Pierce&lt;/a&gt; scale -- the 13th root of 3, along with some nearby just ratios for comparison.&lt;br /&gt;
&lt;br /&gt;


{| class="wikitable"
|-
! rowspan="2" | Degree
! colspan="2" | Just intonation
! colspan="2" | Equal-tempered
! colspan="3" | Nearby JI intervals, [[Octave reduction|octave-reduced]]
|-
! Ratio
! [[Cent]]s
! [[Hekt]]s
! Cents
! Ratio
! Cents
! Error in 13edt (¢)
|-
| 0
| 1/1
| 0
| 0
| 0
| 1/1
| 0
| 0
|-
| 1
| 27/25
| 133.238
| 100
| 146.304
| 12/11<br />13/12<br />'''27/25'''
| 150.6<br />138.6<br />'''133.2'''
| −4.3<br />+7.7<br />'''+13.1'''
|-
| 2
| 25/21
| 301.847
| 200
| 292.608
| 32/27<br />13/11<br />19/16<br />'''25/21'''
| 294.1<br />289.2<br />297.5<br />'''301.8'''
| −1.5<br />+3.4<br />−4.9<br />'''−9.2'''
|-
| 3
| 9/7
| 435.084
| 300
| 438.913
| '''9/7'''
| '''435.1'''
| '''+3.8'''
|-
| 4
| 7/5
| 582.512
| 400
| 585.217
| '''7/5'''<br />45/32
| '''582.5'''<br />590.2
| '''+2.7'''<br />−5.0
|-
| 5
| 75/49
| 736.931
| 500
| 731.521
| 32/21<br />26/17<br />'''75/49'''<br />49/32<br />20/13
| 729.2<br />735.6<br />'''736.9'''<br />737.7<br />745.8
| +2.3<br />−4.1<br />'''−5.4'''<br />−6.2<br />−14.3
|-
| 6
| 5/3
| 884.359
| 600
| 877.825
| '''5/3'''
| '''884.4'''
| '''−6.5'''
|-
| 7
| 9/5
| 1017.596
| 700
| 1024.130
| 38/21<br />29/16<br />'''9/5'''<br />20/11
| 1026.7<br />1029.6<br />'''1017.6'''<br />1035.0
| −2.6<br />−5.5<br />'''+6.5'''<br />−10.9
|-
| 8
| 49/25
| 1165.024
| 800
| 1170.434
| '''49/25'''
| '''1165.0'''
| '''+5.4'''
|-
| 9
| 15/7
| 1319.443
| 900
| 1316.738
| '''15/14'''<br />16/15<br />14/13
| '''119.4'''<br />111.7<br />128.3
| '''−2.7'''<br />+5.0<br />−11.6
|-
| 10
| 7/3
| 1466.871
| 1000
| 1463.042
| '''7/6'''<br />22/19
| '''266.9'''<br />253.8
| '''−3.8'''<br />+9.2
|-
| 11
| 63/25
| 1600.108
| 1100
| 1609.347
| 19/15<br />81/64<br />24/19<br />14/11<br />'''63/50'''
| 409.2<br />407.8<br />404.4<br />417.5<br />'''400.1'''
| +0.1<br />+1.5<br />+4.9<br />−8.2<br />'''+9.2'''
|-
| 12
| 25/9
| 1768.717
| 1200
| 1755.651
| 11/8<br />18/13<br />26/19<br />'''25/18'''
| 551.3<br />563.4<br />543.0<br />'''568.7'''
| +4.4<br />−7.7<br />+12.7<br />'''−13.1'''
|-
| 13
| 3/1
| 1901.955
| 1300
| 1901.955
| '''3/2'''
| '''702.0'''
| '''0'''
|-
| 14
| 81/25
| 2035.193
| 1400
| 2048.259
| 18/11<br />13/8<br />'''81/50'''
| 852.6<br />840.5<br />'''835.2'''
| −4.3<br />+7.8<br />'''+13.1'''
|-
| 15
| 25/7
| 2203.802
| 1500
| 2194.563
| 16/9<br />'''25/14'''
| 996.1<br />'''1003.8'''
| −1.5<br />'''−9.2'''
|-
| 16
| 27/7
| 2337.039
| 1600
| 2340.868
| '''27/14'''
| '''1137.0'''
| '''+3.8'''
|-
| 17
| 21/5
| 2484.467
| 1700
| 2487.172
| 20/19<br />'''21/20'''<br />19/18<br />22/21
| 88.8<br />'''84.5'''<br />93.6<br />80.5
| −1.6<br />'''+2.7'''<br />−6.4<br />+6.7
|-
| 18
| 225/49
| 2638.886
| 1800
| 2633.476
| 8/7<br />'''225/196'''<br />15/13
| 231.2<br />'''238.9'''<br />247.7
| +2.3<br />'''−5.4'''<br />−14.2
|-
| 19
| 5/1
| 2786.314
| 1900
| 2779.780
| '''5/4'''<br />26/21
| '''386.3'''<br />369.7
| '''−6.5'''<br />+10.1
|-
| 20
| 27/5
| 2919.551
| 2000
| 2926.085
| 19/14<br />'''27/20'''<br />15/11
| 528.7<br />'''519.6'''<br />537.0
| −2.6<br />'''+6.5'''<br />−10.9
|-
| 21
| 147/25
| 3066.979
| 2100
| 3072.389
| 28/19<br />25/17<br />'''147/100'''<br />22/15
| 671.3<br />667.7<br />'''667.0'''<br />663.0
| +1.1<br />+4.7<br />'''+5.4'''<br />+9.4
|-
| 22
| 45/7
| 3221.398
| 2200
| 3218.693
| '''45/28'''<br />8/5<br />21/13
| '''821.4'''<br />813.7<br />830.3
| '''−2.7'''<br />+5.0<br />−11.6
|-
| 23
| 7/1
| 3368.826
| 2300
| 3364.997
| '''7/4'''<br />26/15
| '''968.8'''<br />952.3
| '''−3.8'''<br />+12.7
|-
| 24
| 189/25
| 3502.063
| 2400
| 3511.302
| 19/10<br />40/21<br />36/19<br />21/11<br />'''189/100'''
| 1111.2<br />1115.5<br />1106.4<br />1119.5<br />'''1102.1'''
| +0.1<br />−4.2<br />+4.9<br />−8.2<br />'''+9.2'''
|-
| 25
| 25/3
| 3670.672
| 2500
| 3657.606
| 33/32<br />'''25/24'''
| 53.3<br />'''70.7'''
| +4.3<br />'''−13.1'''
|-
| 26
| 9/1
| 3803.910
| 2600
| 3803.910
| '''9/8'''
| '''203.9'''
| '''0'''
|-
| 27
| 243/25
| 3937.148
| 2700
| 3950.214
| 11/9<br />27/22<br />'''243/200'''
| 347.4<br />354.5<br />337.1
| +2.8<br />−4.3<br />'''+13.1'''
|-
| 28
| 75/7
| 4105.757
| 2800
| 4096.518
| 4/3<br />'''75/56'''
| 498.0<br />'''505.8'''
| −1.5<br />'''−9.2'''
|-
| 29
| 81/7
| 4238.994
| 2900
| 4242.823
| '''81/56'''<br />36/25
| '''639.0'''<br />631.3
| '''+3.8'''<br />+11.5
|-
| 30
| 63/5
| 4386.422
| 3000
| 4389.127
| 30/19<br />'''63/40'''<br />128/81<br />19/12<br />11/7<br />100/63
| 790.8<br />'''786.4'''<br />792.2<br />795.6<br />782.5<br />799.9.
| −1.7<br />'''2.7'''<br />−3.1<br />−6.5<br />+6.6<br />−10.8
|-
| 31
| 675/49
| 4540.841
| 3100
| 4535.431
| 12/7<br />'''675/392'''<br />19/11
| 933.1<br />'''940.8'''<br />946.2
| +2.3<br />'''−5.4'''<br />+10.8
|-
| 32
| 15/1
| 4688.269
| 3200
| 4681.735
| 28/15<br />'''15/8'''<br />13/7
| 1080.6<br />'''1088.3'''<br />1071.7
| +1.1<br />'''−6.5'''<br />+10.0
|-
| 33
| 81/5
| 4821.506
| 3300
| 4828.040
| 64/63<br />'''81/80'''
| 27.3<br />'''21.5'''
| +0.7<br />'''+6.5'''
|-
| 34
| 441/25
| 4968.934
| 3400
| 4974.344
| 21/19<br />'''441/400'''<br />10/9<br />11/10
| 173.3<br />'''168.9'''<br />182.4<br />165.0
| +1.0<br />'''+5.4'''<br />−8.1<br />+9.3
|-
| 35
| 135/7
| 5123.353
| 3500
| 5120.648
| '''135/112'''<br />6/5
| '''323.4'''<br />315.6
| '''−2.7'''<br />+5.0
|-
| 36
| 21/1
| 5270.781
| 3600
| 5266.952
| 17/13<br />'''21/16'''<br />98/75<br />64/49<br />13/10
| 464.4<br />'''470.8'''<br />463.1<br />462.3<br />454.2<br />
| +2.5<br />'''−3.8'''<br />+3.9<br />+4.6<br />+12.7
|-
| 37
| 567/25
| 5404.018
| 3700
| 5413.257
| 64/45<br />10/7<br />567/400
| 609.8<br />617.5<br />'''604.0'''
| +3.5<br />−4.2<br />'''+9.2'''
|-
| 38
| 25/1
| 5572.627
| 3800
| 5559.561
| 14/9<br />'''25/16'''
| 764.9<br />'''772.6'''
| −5.3<br />'''−13.1'''
|-
| 39
| 27/1
| 5705.865
| 3900
| 5705.865
| '''27/16'''
| '''905.9'''
| '''0'''
|-
| 40
| 729/25
| 5839.103
| 4000
| 5852.169
| 11/6<br />'''729/400'''
| 1049.4<br />'''1039.1'''
| +2.8<br />'''+13.1'''
|-
| 41
| 225/7
| 6007.712
| 4100
| 5998.473
| 1/1<br />'''225/224'''
| 0.0<br />'''7.7'''
| −1.5<br />'''+9.2'''
|}


&lt;table class="wiki_table"&gt;
[[Category:Bohlen–Pierce]]
    &lt;tr&gt;
[[Category:Lists of intervals]]
        &lt;th&gt;degree&lt;br /&gt;
[[Category:Tables]]
&lt;/th&gt;
        &lt;th&gt;cents value&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;nearby frequency ratios&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents value&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;difference between BP interval &amp;amp; just interval&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;first octave and first tritave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;146.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12/11&lt;br /&gt;
13/12&lt;br /&gt;
27/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;150.6&lt;br /&gt;
138.6&lt;br /&gt;
133.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-4.3&lt;br /&gt;
7.7&lt;br /&gt;
13.1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;292.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;32/27&lt;br /&gt;
13/11&lt;br /&gt;
19/16&lt;br /&gt;
25/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;294.1&lt;br /&gt;
289.2&lt;br /&gt;
297.5&lt;br /&gt;
301.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-1.5&lt;br /&gt;
3.4&lt;br /&gt;
-4.9&lt;br /&gt;
-9.2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;438.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;435.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;585.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/5&lt;br /&gt;
45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;582.5&lt;br /&gt;
590.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.7&lt;br /&gt;
-5.0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;731.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;32/21&lt;br /&gt;
26/17&lt;br /&gt;
75/49&lt;br /&gt;
49/32&lt;br /&gt;
20/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;729.2&lt;br /&gt;
735.6&lt;br /&gt;
736.9&lt;br /&gt;
737.7&lt;br /&gt;
745.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.3&lt;br /&gt;
-4.1&lt;br /&gt;
-5.4&lt;br /&gt;
-6.2&lt;br /&gt;
-14.3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;877.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6.6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1024.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;38/21&lt;br /&gt;
29/16&lt;br /&gt;
9/5&lt;br /&gt;
20/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1026.7&lt;br /&gt;
1029.6&lt;br /&gt;
1017.6&lt;br /&gt;
1035.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2.6&lt;br /&gt;
-5.5&lt;br /&gt;
6.5&lt;br /&gt;
-10.9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1170.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1165.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;second octave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;116.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/14&lt;br /&gt;
16/15&lt;br /&gt;
14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;119.4&lt;br /&gt;
111.7&lt;br /&gt;
128.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2.7&lt;br /&gt;
5.0&lt;br /&gt;
-11.6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;263.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/6&lt;br /&gt;
22/19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;266.9&lt;br /&gt;
253.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3.9&lt;br /&gt;
9.2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;409.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/15&lt;br /&gt;
81/64&lt;br /&gt;
24/19&lt;br /&gt;
14/11&lt;br /&gt;
63/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;409.2&lt;br /&gt;
407.8&lt;br /&gt;
404.4&lt;br /&gt;
417.5&lt;br /&gt;
400.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;.1&lt;br /&gt;
1.5&lt;br /&gt;
4.9&lt;br /&gt;
-8.2&lt;br /&gt;
9.2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;555.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/8&lt;br /&gt;
18/13&lt;br /&gt;
26/19&lt;br /&gt;
25/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551.3&lt;br /&gt;
563.4&lt;br /&gt;
543.0&lt;br /&gt;
568.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.4&lt;br /&gt;
-7.7&lt;br /&gt;
12.7&lt;br /&gt;
-13.0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;second tritave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;848.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/11&lt;br /&gt;
13/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;852.6&lt;br /&gt;
840.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-4.3&lt;br /&gt;
7.8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;994.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-1.5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1140.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1137.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3.9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;third octave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;87.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;20/19&lt;br /&gt;
21/20&lt;br /&gt;
19/18&lt;br /&gt;
22/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;88.8&lt;br /&gt;
84.5&lt;br /&gt;
93.6&lt;br /&gt;
80.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-1.6&lt;br /&gt;
2.7&lt;br /&gt;
-6.4&lt;br /&gt;
6.7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;233.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/7&lt;br /&gt;
15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;231.2&lt;br /&gt;
247.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.3&lt;br /&gt;
-14.2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;379.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4&lt;br /&gt;
26/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.3&lt;br /&gt;
369.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6.5&lt;br /&gt;
10.1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;526.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/14&lt;br /&gt;
27/20&lt;br /&gt;
15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;528.7&lt;br /&gt;
519.6&lt;br /&gt;
537.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2.6&lt;br /&gt;
6.5&lt;br /&gt;
-10.9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28/19&lt;br /&gt;
25/17&lt;br /&gt;
22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;671.3&lt;br /&gt;
667.7&lt;br /&gt;
663.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1.1&lt;br /&gt;
4.7&lt;br /&gt;
9.4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;818.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
21/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;813.7&lt;br /&gt;
830.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.0&lt;br /&gt;
-11.6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;965.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
26/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.8&lt;br /&gt;
952.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3.8&lt;br /&gt;
12.7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1111.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/10&lt;br /&gt;
40/21&lt;br /&gt;
36/19&lt;br /&gt;
21/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1111.2&lt;br /&gt;
1115.5&lt;br /&gt;
1106.4&lt;br /&gt;
1119.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.1&lt;br /&gt;
-4.2&lt;br /&gt;
4.9&lt;br /&gt;
-8.2&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;fourth octave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;57.6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;33/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53.3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4.3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;th colspan="3"&gt;third tritave...&lt;br /&gt;
&lt;/th&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;350.2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;496.5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;642.8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;789.1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;935.4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1081.7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td colspan="3" style="text-align: center;"&gt;&lt;strong&gt;fifth octave...&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;28.0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 15:44, 31 July 2025

This page lists the first 42 intervals of the Bohlen–Pierce scale in both its just intonation (JI) version and its equal-tempered (ET) version, 13edt.

In the "nearby JI intervals, octave-reduced" columns, the intervals from the original just BP scale are in bold. Errors are sorted by ascending absolute value.

Degree Just intonation Equal-tempered Nearby JI intervals, octave-reduced
Ratio Cents Hekts Cents Ratio Cents Error in 13edt (¢)
0 1/1 0 0 0 1/1 0 0
1 27/25 133.238 100 146.304 12/11
13/12
27/25 		150.6
138.6
133.2 		−4.3
+7.7
+13.1
2 25/21 301.847 200 292.608 32/27
13/11
19/16
25/21 		294.1
289.2
297.5
301.8 		−1.5
+3.4
−4.9
−9.2
3 9/7 435.084 300 438.913 9/7 435.1 +3.8
4 7/5 582.512 400 585.217 7/5
45/32 		582.5
590.2 		+2.7
−5.0
5 75/49 736.931 500 731.521 32/21
26/17
75/49
49/32
20/13 		729.2
735.6
736.9
737.7
745.8 		+2.3
−4.1
−5.4
−6.2
−14.3
6 5/3 884.359 600 877.825 5/3 884.4 −6.5
7 9/5 1017.596 700 1024.130 38/21
29/16
9/5
20/11 		1026.7
1029.6
1017.6
1035.0 		−2.6
−5.5
+6.5
−10.9
8 49/25 1165.024 800 1170.434 49/25 1165.0 +5.4
9 15/7 1319.443 900 1316.738 15/14
16/15
14/13 		119.4
111.7
128.3 		−2.7
+5.0
−11.6
10 7/3 1466.871 1000 1463.042 7/6
22/19 		266.9
253.8 		−3.8
+9.2
11 63/25 1600.108 1100 1609.347 19/15
81/64
24/19
14/11
63/50 		409.2
407.8
404.4
417.5
400.1 		+0.1
+1.5
+4.9
−8.2
+9.2
12 25/9 1768.717 1200 1755.651 11/8
18/13
26/19
25/18 		551.3
563.4
543.0
568.7 		+4.4
−7.7
+12.7
−13.1
13 3/1 1901.955 1300 1901.955 3/2 702.0 0
14 81/25 2035.193 1400 2048.259 18/11
13/8
81/50 		852.6
840.5
835.2 		−4.3
+7.8
+13.1
15 25/7 2203.802 1500 2194.563 16/9
25/14 		996.1
1003.8 		−1.5
−9.2
16 27/7 2337.039 1600 2340.868 27/14 1137.0 +3.8
17 21/5 2484.467 1700 2487.172 20/19
21/20
19/18
22/21 		88.8
84.5
93.6
80.5 		−1.6
+2.7
−6.4
+6.7
18 225/49 2638.886 1800 2633.476 8/7
225/196
15/13 		231.2
238.9
247.7 		+2.3
−5.4
−14.2
19 5/1 2786.314 1900 2779.780 5/4
26/21 		386.3
369.7 		−6.5
+10.1
20 27/5 2919.551 2000 2926.085 19/14
27/20
15/11 		528.7
519.6
537.0 		−2.6
+6.5
−10.9
21 147/25 3066.979 2100 3072.389 28/19
25/17
147/100
22/15 		671.3
667.7
667.0
663.0 		+1.1
+4.7
+5.4
+9.4
22 45/7 3221.398 2200 3218.693 45/28
8/5
21/13 		821.4
813.7
830.3 		−2.7
+5.0
−11.6
23 7/1 3368.826 2300 3364.997 7/4
26/15 		968.8
952.3 		−3.8
+12.7
24 189/25 3502.063 2400 3511.302 19/10
40/21
36/19
21/11
189/100 		1111.2
1115.5
1106.4
1119.5
1102.1 		+0.1
−4.2
+4.9
−8.2
+9.2
25 25/3 3670.672 2500 3657.606 33/32
25/24 		53.3
70.7 		+4.3
−13.1
26 9/1 3803.910 2600 3803.910 9/8 203.9 0
27 243/25 3937.148 2700 3950.214 11/9
27/22
243/200 		347.4
354.5
337.1 		+2.8
−4.3
+13.1
28 75/7 4105.757 2800 4096.518 4/3
75/56 		498.0
505.8 		−1.5
−9.2
29 81/7 4238.994 2900 4242.823 81/56
36/25 		639.0
631.3 		+3.8
+11.5
30 63/5 4386.422 3000 4389.127 30/19
63/40
128/81
19/12
11/7
100/63 		790.8
786.4
792.2
795.6
782.5
799.9. 		−1.7
2.7
−3.1
−6.5
+6.6
−10.8
31 675/49 4540.841 3100 4535.431 12/7
675/392
19/11 		933.1
940.8
946.2 		+2.3
−5.4
+10.8
32 15/1 4688.269 3200 4681.735 28/15
15/8
13/7 		1080.6
1088.3
1071.7 		+1.1
−6.5
+10.0
33 81/5 4821.506 3300 4828.040 64/63
81/80 		27.3
21.5 		+0.7
+6.5
34 441/25 4968.934 3400 4974.344 21/19
441/400
10/9
11/10 		173.3
168.9
182.4
165.0 		+1.0
+5.4
−8.1
+9.3
35 135/7 5123.353 3500 5120.648 135/112
6/5 		323.4
315.6 		−2.7
+5.0
36 21/1 5270.781 3600 5266.952 17/13
21/16
98/75
64/49
13/10 		464.4
470.8
463.1
462.3
454.2
 +2.5
−3.8
+3.9
+4.6
+12.7
37 567/25 5404.018 3700 5413.257 64/45
10/7
567/400 		609.8
617.5
604.0 		+3.5
−4.2
+9.2
38 25/1 5572.627 3800 5559.561 14/9
25/16 		764.9
772.6 		−5.3
−13.1
39 27/1 5705.865 3900 5705.865 27/16 905.9 0
40 729/25 5839.103 4000 5852.169 11/6
729/400 		1049.4
1039.1 		+2.8
+13.1
41 225/7 6007.712 4100 5998.473 1/1
225/224 		0.0
7.7 		−1.5
+9.2
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