12 Tertial-Septimal LMY WTP

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 tertial-septimal Rational Intonation scale, composed by La Monte Young for his work The Well-Tuned Piano (1964-73-81-present), as documented by Kyle Gann. The tuning has three chains of perfect fifthsPitches a fifth apart have a 2:3 frequency ratio (in just intonation) or a difference of 700 cents (in 12 tone equal temperament).Visit the link to learn more, tuned in the proportion 2:3 (assigned to the piano keys D♯-A♯-E♯; C-G-D-A-E; B-F♯-C♯-G♯). Each of these chains is tuned a 4:7 apart, with the middle chain matching the usual diatonic notes in tertial tuning (A 440 Hz). D♯ is tuned down to a D raised by one septimal commaA comma is a small difference in pitch between the same interval in different tuning systems.Visit the link to learn more, and B is tuned down to a B♭ lowered by a septimal comma.

Young's original ratios are calculated as overtones of the note assigned to the piano key D♯, but for this scala file C has been assigned to the ratio 1/1, following usual practice. Notice that the scale is not uniformly ascending: the pitch assigned to the piano key C♯ is lower than C, and the pitch assigned to the piano key G♯ is similarly lower than G.

Learning more

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.