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Bohlen–Pierce scale
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==Intervals and scale diagrams== The following are the thirteen notes in the scale (cents rounded to nearest whole number): '''Justly tuned''' {| class="wikitable" |align=center bgcolor="#ffeeee"|'''Interval (cents)''' |bgcolor="#ffeeee"| |colspan=2 align=center bgcolor="#ffeeee"|133 |colspan=2 align=center bgcolor="#ffeeee"|169 |colspan=2 align=center bgcolor="#ffeeee"|133 |colspan=2 align=center bgcolor="#ffeeee"|148 |colspan=2 align=center bgcolor="#ffeeee"|154 |colspan=2 align=center bgcolor="#ffeeee"|147 |colspan=2 align=center bgcolor="#ffeeee"|134 |colspan=2 align=center bgcolor="#ffeeee"|147 |colspan=2 align=center bgcolor="#ffeeee"|154 |colspan=2 align=center bgcolor="#ffeeee"|148 |colspan=2 align=center bgcolor="#ffeeee"|133 |colspan=2 align=center bgcolor="#ffeeee"|169 |colspan=2 align=center bgcolor="#ffeeee"|133 |bgcolor="#ffeeee"| |- |align=center bgcolor="#fffbee"|'''Note name''' |colspan=2 align=center bgcolor="#fffbee"|C |colspan=2 align=center bgcolor="#fffbee"|D{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|D |colspan=2 align=center bgcolor="#fffbee"|E |colspan=2 align=center bgcolor="#fffbee"|F |colspan=2 align=center bgcolor="#fffbee"|G{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|G |colspan=2 align=center bgcolor="#fffbee"|H |colspan=2 align=center bgcolor="#fffbee"|J{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|J |colspan=2 align=center bgcolor="#fffbee"|A |colspan=2 align=center bgcolor="#fffbee"|B{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|B |colspan=2 align=center bgcolor="#fffbee"|C |- |align=center bgcolor="#eeeeff"|'''Note (cents)''' |colspan=2 align=center bgcolor="#eeeeff"|0 |colspan=2 align=center bgcolor="#eeeeff"|133 |colspan=2 align=center bgcolor="#eeeeff"|302 |colspan=2 align=center bgcolor="#eeeeff"|435 |colspan=2 align=center bgcolor="#eeeeff"|583 |colspan=2 align=center bgcolor="#eeeeff"|737 |colspan=2 align=center bgcolor="#eeeeff"|884 |colspan=2 align=center bgcolor="#eeeeff"|1018 |colspan=2 align=center bgcolor="#eeeeff"|1165 |colspan=2 align=center bgcolor="#eeeeff"|1319 |colspan=2 align=center bgcolor="#eeeeff"|1467 |colspan=2 align=center bgcolor="#eeeeff"|1600 |colspan=2 align=center bgcolor="#eeeeff"|1769 |colspan=2 align=center bgcolor="#eeeeff"|1902 |} '''Equal-tempered''' {| class="wikitable" |align=center bgcolor="#ffeeee"|'''Interval (cents)''' |bgcolor="#ffeeee"| |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |colspan=2 align=center bgcolor="#ffeeee"|146 |bgcolor="#ffeeee"| |- |align=center bgcolor="#fffbee"|'''Note name''' |colspan=2 align=center bgcolor="#fffbee"|C |colspan=2 align=center bgcolor="#fffbee"|C{{music|sharp}}/D{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|D |colspan=2 align=center bgcolor="#fffbee"|E |colspan=2 align=center bgcolor="#fffbee"|F |colspan=2 align=center bgcolor="#fffbee"|F{{music|sharp}}/G{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|G |colspan=2 align=center bgcolor="#fffbee"|H |colspan=2 align=center bgcolor="#fffbee"|H{{music|sharp}}/J{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|J |colspan=2 align=center bgcolor="#fffbee"|A |colspan=2 align=center bgcolor="#fffbee"|A{{music|sharp}}/B{{music|flat}} |colspan=2 align=center bgcolor="#fffbee"|B |colspan=2 align=center bgcolor="#fffbee"|C |- |align=center bgcolor="#eeeeff"|'''Note (cents)''' |colspan=2 align=center bgcolor="#eeeeff"|0 |colspan=2 align=center bgcolor="#eeeeff"|146 |colspan=2 align=center bgcolor="#eeeeff"|293 |colspan=2 align=center bgcolor="#eeeeff"|439 |colspan=2 align=center bgcolor="#eeeeff"|585 |colspan=2 align=center bgcolor="#eeeeff"|732 |colspan=2 align=center bgcolor="#eeeeff"|878 |colspan=2 align=center bgcolor="#eeeeff"|1024 |colspan=2 align=center bgcolor="#eeeeff"|1170 |colspan=2 align=center bgcolor="#eeeeff"|1317 |colspan=2 align=center bgcolor="#eeeeff"|1463 |colspan=2 align=center bgcolor="#eeeeff"|1609 |colspan=2 align=center bgcolor="#eeeeff"|1756 |colspan=2 align=center bgcolor="#eeeeff"|1902 |} {{Audio|BP ET lambda scale.ogg|play equal tempered Bohlen–Pierce scale}} {| frame="box" rules="all" cellpadding="4" style="text-align:center" align=center |- bgcolor=#DDDDFF !Steps !Name !EQ interval !Cents in EQ !Just intonation interval !Traditional name !Cents in just intonation !Difference |- | 0 | C | 3<sup>{{frac|0|13}}</sup> = 1.00 | {{0|000}}0.00 | {{0}}1:1{{0}} = 1.00 | Unison | {{0|000}}0.00 | {{0|−0}}0.00 |- | 1 | C♯/D♭ | 3<sup>{{frac|1|13}}</sup> = 1.09 | {{0}}146.30 | 27:25 = 1.08 | Great limma | {{0}}133.24 | {{0|−}}13.06 |- | 2 | D | 3<sup>{{frac|2|13}}</sup> = 1.18 | {{0}}292.61 | 25:21 = 1.19 | Quasi-tempered minor third | {{0}}301.85 | {{0}}−9.24 |- | 3 | E | 3<sup>{{frac|3|13}}</sup> = 1.29 | {{0}}438.91 | {{0}}9:7{{0}} = 1.29 | Septimal major third | {{0}}435.08 | {{0|−0}}3.83 |- | 4 | F | 3<sup>{{frac|4|13}}</sup> = 1.40 | {{0}}585.22 | {{0}}7:5{{0}} = 1.40 | Lesser septimal tritone | {{0}}582.51 | {{0|−0}}2.71 |- | 5 | F♯/G♭ | 3<sup>{{frac|5|13}}</sup> = 1.53 | {{0}}731.52 | 75:49 = 1.53 | BP fifth | {{0}}736.93 | {{0}}−5.41 |- | 6 | G | 3<sup>{{frac|6|13}}</sup> = 1.66 | {{0}}877.83 | {{0}}5:3{{0}} = 1.67 | Just major sixth | {{0}}884.36 | {{0}}−6.53 |- | 7 | H | 3<sup>{{frac|7|13}}</sup> = 1.81 | 1024.13 | {{0}}9:5{{0}} = 1.80 | Greater just minor seventh | 1017.60 | {{0|−0}}6.53 |- | 8 | H♯/J♭ | 3<sup>{{frac|8|13}}</sup> = 1.97 | 1170.44 | 49:25 = 1.96 | BP eighth | 1165.02 | {{0|−0}}5.42 |- | 9 | J | 3<sup>{{frac|9|13}}</sup> = 2.14 | 1316.74 | 15:7{{0}} = 2.14 | Septimal minor ninth | 1319.44 | {{0}}−2.70 |- | 10 | A | 3<sup>{{frac|10|13}}</sup> = 2.33 | 1463.05 | {{0}}7:3{{0}} = 2.33 | Septimal minimal tenth | 1466.87 | {{0}}−3.82 |- | 11 | A♯/B♭ | 3<sup>{{frac|11|13}}</sup> = 2.53 | 1609.35 | 63:25 = 2.52 | Quasi-tempered major tenth | 1600.11 | {{0|−0}}9.24 |- | 12 | B | 3<sup>{{frac|12|13}}</sup> = 2.76 | 1755.66 | 25:9{{0}} = 2.78 | Classic augmented eleventh | 1768.72 | −13.06 |- | 13 | C | 3<sup>{{frac|13|13}}</sup> = 3.00 | 1901.96 | {{0}}3:1{{0}} = 3.00 | Just twelfth, "tritave" | 1901.96 | {{0|−0}}0.00 |}
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