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
|ET cents||JI||JI cents||diff|