The Tuning of Lou Harrison's Sonata in Cm and Sonata in Am

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

Notes by Bill Alves


Schneider's guitar fretted for meantone temperament		 Harrison always had a particular love of European music of the Baroque period. In his youth, he connected it with the Spanish period of California's history and the austere glory of the region's missions he visited while growing up in the San Francisco area. In 1934, when 17 years old, he wrote the Sonata in c minor not for piano, but rather for the harpsichord (also known as the cembalo), the dominant keyboard of the Baroque. By 1943, he had completed a set of six (the customary number in the Baroque) cembalo sonatas, including the Sonata in a minor.

Although Harrison did not compose these sonatas with a particular tuning in mind, he was not unaware of the possibilities, as he studied and performed in Baroque tunings while he participated in the early music ensemble of San Francisco State College in the 1930s. Upon republishing these sonatas in 1990, Harrison wrote, "Nowadays, thank Heavens, serious harpsichordists are concerned with fine intonation for their instrument and are exploring the necessary historical tunings and temperaments for the 17th and 18th century European repertoire. I heartily applaud this most musical development...". Harrison goes on to suggest several temperaments that would be appropriate for these works.

For this recording, John Schneider has chosen a tuning known as one-sixth-comma meantone temperament. In contrast to a just intonation tuning, temperaments involve some kind of compromise or adjustment to absolutely rational frequency ratios in order to allow play acceptable triads in many keys. Meantone temperaments involve compromising the tuning of the perfect fifth (otherwise a 3/2 ratio) so that a series of them will still result in acceptable thirds. (More details can be found here.) Meantone temperament differs from today's standard equal temperament in that the thirds sound somewhat better, and the keys retain distinctive characteristics that dissipate in equal temperament's grayness.

Because temperaments no longer have all pure intervals, they cannot be shown in a lattice diagram. Here are the pitches used in this recording of these two sonatas:

PitchCC#DD#EFF#GG#AA#BC
Comma temperament +1/2 -2/3 +1/6 -1/3 -1/6 +2/3 -1/2 +1/3 -5/6 0 -7/6 -1/3 +1/2
Cents0 88.6 196.7 285.3 393.5 482.1 590.2 698.4 787.0 895.1 983.7 1091.9 1200
Cents between steps88.6 108.1 88.6 108.1 88.6 108.1 108.1 88.6 108.1 88.6 108.1 108.1
Frequency262.4 276.1 293.9 309.4 329.3 346.6 369.0 392.7 413.4 440.0 463.1 493.0 524.7

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