12 Undecimal Lou Harrison National Steel

For a general introduction to Just (Rational) Intonation and these presets, please visit Introduction to Just or Rational Intonation (JI).

About this tuning

12-tone 11-limit Rational Intonation scale, composed by Lou Harrison for the National Steel Guitar, as documented by Bill Alves. Commissioned by John Schneider, this tuning was also used by Ben Johnston in his remarkable late work The Tavern. The tuning is originally constructed with G as the central pitch (1/1 ratio), consisting of the following intervals: G 1/1, G♯ 33/32, A 9/8, B♭ 7/6, B 5/4, C 21/16, C♯ 11/8, D 3/2, E♭ 14/9, E 27/16, F 7/4, F♯ 15/8. In this scala file, the ratios have been recalculated with <C (septimally-lowered C) as the 1/1 to match the usual scala file format.

Legend of ASCII Notations

The following ASCII are used to write note names in rational intonation:

For EDO systems, the standard notation uses a degree and division, i.e. 1\31 for the first step of 31edo. If another interval is being divided, it may be placed in brackets or angle brackets afterwards, i.e. 1\11 (3/2) for Wendy Carlos beta.