This table demonstrates some of the logic behind the Lambda scale. It shows the 17-limit just intonation (JI) intervals that are closest to the equally tempered Bohlen Pierce scale. Notice that there are no close JI intervals for the F#, H#, and A# notes. Also, melody fragments in the D E F G range are virtually equal tempered with respect to one another.
The original JI scale has accidentals that are beyond the 17 limit: C# is 25/21, F# is 75/49, H# is 49/25, and A# is 63/25. Using those ratios would bring the accidentals within 10 cents of the ET notes, but the ear gravitates towards ratios with lower denominators. In any case, it’s good to avoid H# because of its proximity to the octave. 49/25 can’t compete with 2/1. Same with A# against a strong C – most listeners will hear it as a too-sharp 10th.
| Bohlen Pierce ET to JI intervals best match, 17 limit |
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| ET cents | JI | JI cents | diff | ||
| 0 | 0.0 | 1/1 | 0.0 | +0.0 | C |
| 1 | 146.3 | 12/11 | 150.6 | +4.3 | |
| 2 | 292.6 | 13/11 | 289.2 | -3.4 | D |
| 3 | 438.9 | 9/7 | 435.1 | -3.8 | E |
| 4 | 585.2 | 7/5 | 582.5 | -2.7 | F |
| 5 | 731.5 | 17/11 | 753.6 | +22.1 | |
| 6 | 887.8 | 5/3 | 884.4 | -3.4 | G |
| 7 | 1024.1 | 9/5 | 1017.6 | -6.5 | H |
| 8 | 1170.4 | 2/1 | 1200.0 | +29.6 | |
| 9 | 1316.7 | 15/7 | 1319.4 | +2.7 | J |
| 10 | 1463.0 | 7/3 | 1466.9 | +3.9 | A |
| 11 | 1609.3 | 5/2 | 1586.3 | -23.0 | |
| 12 | 1755.7 | 11/4 | 1751.3 | -4.4 | B |
| 13 | 1902.0 | 3/1 | 1902.0 | +0.0 | C |
