In music, 23 equal temperament, called 23-TET, 23-
EDO
Edo ( ja, , , "bay-entrance" or "estuary"), also romanized as Jedo, Yedo or Yeddo, is the former name of Tokyo.
Edo, formerly a ''jōkamachi'' (castle town) centered on Edo Castle located in Musashi Province, became the ''de facto'' capital of ...
("Equal Division of the Octave"), or 23-ET, is the
tempered scale derived by dividing the octave into 23 equal steps (equal frequency ratios). Each step represents a frequency ratio of , or 52.174 cents. This system is the largest EDO that has an error of at least 20 cents for the 3rd (3:2), 5th (5:4), 7th (7:4), and 11th (11:8) harmonics. The lack of approximation to simple intervals makes the scale notable among those
seeking to break free from conventional harmony rules.
History and use
23-EDO was advocated by ethnomusicologist
Erich von Hornbostel
Erich Moritz von Hornbostel (25 February 1877 – 28 November 1935) was an Austrian ethnomusicologist and scholar of music. He is remembered for his pioneering work in the field of ethnomusicology, and for the Sachs–Hornbostel system of music ...
in the 1920s, as the result of "a cycle of 'blown' (compressed) fifths"
of about 678 cents that may have resulted from "overblowing" a bamboo pipe. Today, tens of songs have been composed in this system.
Notation
There are two ways to notate the 23-tone system with the traditional letter names and system of sharps and flats, called ''melodic notation'' and ''harmonic notation''.
Harmonic notation preserves harmonic structures and interval arithmetic, but sharp and flat have reversed meanings. Because it preserves harmonic structures, 12-EDO music can be reinterpreted as 23-EDO harmonic notation, so it is also called conversion notation.
An example of these harmonic structures is the Circle of Fifths below (shown in 12-EDO, harmonic notation, and melodic notation.)
Melodic notation preserves the meaning of sharp and flat, but harmonic structures and interval arithmetic no longer work.
Interval size
Scale diagram
Modes
See also
*
Musical temperament
In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the p ...
*
Equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, ...
References
{{Musical tuning
Equal temperaments
Microtonality