The Tuning of Lou Harrison's Tandy's Tango

from the Mode CD Por Gitaro: Suites for Tuned Guitars performed by John Schneider

Notes by Bill Alves

Although Harrison appreciated the crystaline sonorities of just intonation, he understood that some musical intentions were best expressed with the use of temperament. (For the difference between just intonation and temperament, see my introduction here, as well as this page.) The second tuning published by Johann Kirnberger, an eighteenth-century composer and student of J. S. Bach's, offers an interesting middle ground: only one pitch in the tuning (the A) is tempered. Because all the dissonance of the "wolf" interval is borne only by a single compromised pitch, it probably was not widely used even in the eighteenth century. However, Harrison appreciated the fact that he could have both a large number of just intervals as well as what he called "gutsy fifths" when the tempered A is involved. Since his composition of his Piano Concerto (1985), which uses Kirnberger II tuning, he often kept his home piano (once owned by Henry Cowell) in this tuning. When choreographer Tandy Beal asked him for a piano piece, he wrote this one with a sensitive ear for how its harmonies would work in this tuning, using the "gutsy fifths" at key points of dissonance. Of course, when this piece is performed in equal temperament, this dimension of the work vanishes, so John Schneider replicated this tuning in his version for guitar. Here is Harrison's own diagram explaining the Kirnberger II temperament:

Here is the same tuning with further information:

PitchC Db D Eb E F F# G Ab A Bb B
Ratio from 1/11/1 256/243 9/8 32/27 5/4 4/3 45/32 3/2 128/81 [tempered] 16/9 15/8
Cents from 1/10 90.2 203.9 294.1 386.3 498 590.2 702 792.2 895.2 996.1 1088.3
Frequency262.4 276.4 295.2 310.9 327.9 349.8 368.9 393.5 414.6 440 466.4 491.9
Ratio between pitches256/243 2187/2048 256/243 135/128 16/15 135/128 16/15 256/243 * * 135/128
Cents between pitches90.2 113.7 90.2 92.2 111.7 92.2 111.7 90.2 103 100.9 92.2

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