55 Tertial-Quintal Sabat Euler Lattice

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

About this tuning

55-tone tertial-quintal Rational Intonation scale, based on the primary roots of major and minor triads in the "Harmonium for Ben Johnston" section of Marc Sabat's string quartet Euler Lattice Spirals Scenery. The tertial diatonic tones are each divided in the same symmetric pattern of 9 "commasA comma is a small difference in pitch between the same interval in different tuning systems.Visit the link to learn more." To divide the interval C 1/1 - D 9/8 add two notes above C: 81/80 and 25/24, then add two more notes one Syntonic Comma above each of these. Similarly, add two notes below D: 10/9 and 27/25; then, add two more notes a Syntonic Comma below each of these. To divide the diatonic limmas E-F and B-C, add two successive Syntonic Commas upward from the lower note and two commas downward from the higher note, reaching a point of enharmonic near-equivalence (these two "pairs" of proximal enharmonics extend the tuning from 53 to 55 notes per octave).

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.