53 Tertial

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

About this tuning

53-tone 3-Limit Rational Intonation scale, consisting of 53 notes per octave derived by tuning a chain of 53 3/2 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: 26 are harmonics (above C) and 26 are subharmonics (below C). Jing Fang (78–37 BCE), a Chinese music theorist, observed that a sequence of 53 just fifths is very nearly equal to 31 octaves. Compare this tuning to the 55-quintal Euler Lattice tuning (5-Limit with 2 enharmonic proximities added) and to 53edo, which closely approximates both tertial and quintal intervals.

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.