The Tuning of Lou Harrison's Suite for National Steel Guitar

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

Notes by Bill Alves

The fingerboard of the Harrison National Steel Guitar
In 2001, San Francisco's Other Minds Festival commissioned Harrison to write his first piece for guitar since the Serenade, but to their surprise he decided to write for the unique timbre of a National steel-string guitar. Schneider commissioned a special just intonation version of the instrument from National Guitar and recorded the resulting piece Scenes from Nek Chand. This work for which the guitar was originally commissioned did not use all twelve pitches, but rather a mode formed from harmonics 6 through 11 based on the fundamental G. This gives D (harmonic 6), F (7), G (8), A (9), B (10), and C#(11).

It was left to Harrison's friend William Slye and myself to suggest the pitches which would fill out a twelve-pitch fretting. We chose pitches G#, Bb, C, E, Eb, and F# so that they would fill out a lattice (as shown in the diagram below) and so provide for closely related harmonies and keys for others who might wish to write for this instrument. Slye opted for the same set of harmonics starting on the pitch D. With the composer's encouragement, Schneider adapted Harrison's Jahla, Solo, Palace Music, Threnody to the Memory of Oliver Daniel, and Serenado por Gitaro for this unique instrument. (For the definition of cents and explanation of the following lattice diagram, see the note for the tuning of the Serenade.)

PitchG G# A Bb B C C# D Eb E F F#
Ratio from 1/11/1 33/32 9/8 7/6 5/4 21/16 11/8 3/2 14/9 27/16 7/4 15/8
Cents from 1/10 53.3 203.9 266.9 386.3 470.8 551.3 702 764.9 905.9 968.8 1088.3
Frequency392 404.2 441 457.3 490 514.5 539 588 609.8 661.5 686 735
Ratio between pitches33/32 12/11 28/27 15/14 21/20 22/21 12/11 28/27 243/224 28/27 15/14
Cents between pitches53.3 150.6 63 119.4 84.5 80.5 150.6 63 162.2 63 119.4

The lattice diagram for the National Steel Guitar tuning is slightly different from the others shown on this website because of the presence of four prime factors (aside from the octave, 2). The prime factor of 3 is shown in the left-to-right dimension (left for a 4/3 ratio, right for a 3/2 ratio). The prime factor of 5 is shown in the up-to-down dimension (up for a 5/4 ratio, down for a 8/5 ratio). The prime factor 7 is shown in the front-to-back dimension (back for a 7/4 ratio, forwards for an 8/7 ratio). Since we've run out of dimensions, the two pitches related by a ratio involving 11 are shown as lying between the others (back and up for an 11/8 ratio, forward and down for a 16/11 ratio).

Harrison originally specified a D diatonic just tuning for Solo, which this recording preserves, even though the C# has an unusual (but delicious) 11/6 relationship to the tonic D. In the score to Solo, Harrison wrote:

N.B. The tuning must be in "Just" D Major, otherwise
the tension of the 'false B Minor" will be lost,
& the "narrow escape" (tonally) in the climax
section will disappear, & thus the point of the
piece be lost

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