Not In C

This Bohlen-Pierce arrangement of Terry Riley’s “In C” was realized on the musical hardware described in Rehearsal Room. It was performed by 13 identical algorithmic musicians known collectively as The Technical Academy. A characteristic feature of the ensemble is an indiscriminate fader controlled by a Markov chain on each voice. This is the third recording of the completed algorithm.

 

The notes of Terry Riley’s original score were remapped to Bohlen-Pierce notes in a slightly modified A Moll I mode; the B note would have mapped to BP’s J, but it was changed to Jb simply because Jb sounded better.  Riley’s C D E F F# G A Bb B becomes A B C D E F G H Jb. The work is titled “Not In C” because it’s based on this different scale.

In Odd tone map

Source code written in Ruby can be viewed at github.com/b0blee/TechAcademy.

Rehearsal Room

Developing Ruby code to drive antique synths with MIDI pitch bend messages.  This is a Roland D-110 coupled to a Roland U-110.  Each MIDI channel can only play one note because MIDI pitch bend affects the whole channel.  The audio track is monotonous, but useful for ringing out the instruments.

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Best Just Intonation Intervals

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  
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

Lambdafamily

Tuning a Kalimba to BP

I acquired a nice little 17-key kalimba (thumb piano), and tuned it to BP with a Korg AT-1 chromatic tuner. It sounds real nice. Here’s a demo just fooling around with it:

 

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Kalimba BP notes

17-key Kalimba BP Notes
(highest to lowest)

BP note 12 EDO Tuning
H C -37
G Bb +17
Gb A -30
F G +24
E F# -22
D E -32
Db Eb -15
C Db +39
B C -7
Bb Bb +46
A A (440 Hz)
J Ab -47
Jb F# +7
H F -39
G Eb +14
Gb D -32
F C +22