In
music
Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
, 58 equal temperament (also called 58-ET or 58-
EDO
Edo (), also romanized as Jedo, Yedo or Yeddo, is the former name of Tokyo.
Edo, formerly a (castle town) centered on Edo Castle located in Musashi Province, became the '' de facto'' capital of Japan from 1603 as the seat of the Tokugawa shogu ...
) divides the octave into 58 equal parts of approximately 20.69
cents each. It is notable as the simplest equal division of the octave to faithfully represent the
17-limit,
and the first that distinguishes between all the elements of the 11-limit
tonality diamond
In music theory and musical tuning, tuning, a tonality diamond is a two-dimensional diagram of ratios in which one dimension is called the Otonality and Utonality, otonality and the other is called the utonality.Rasch, Rudolph (2000). "A Word or ...
. The next-smallest equal temperament to do both these things is
72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72 TET, 72 EDO, or 72 ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Each ste ...
.
Compared to
72-EDO, which is also consistent in the 17-limit, 58-EDO's approximations of most intervals are not quite as good (although still workable). One obvious exception is the perfect fifth (slightly better in 58-EDO), and another is the tridecimal minor third (11:13), which is significantly better in 58-EDO than in 72-EDO. The two systems temper out different commas; 72-EDO tempers out the comma 169:168, thus equating the 14:13 and 13:12 intervals. On the other hand, 58-EDO tempers out 144:143 instead of 169:168, so 14:13 and 13:12 are left distinct, but 13:12 and 12:11 are equated.
58-EDO, unlike 72-EDO, is not a
multiple of 12, so the only interval (up to octave equivalency) that it shares with 12-EDO is the 600-cent
tritone
In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be ...
(which functions as both 17:12 and 24:17). On the other hand, 58-EDO has fewer pitches than 72-EDO and is therefore simpler.
History and use
The medieval Italian music theorist
Marchetto da Padova
Marchetto da Padova (Marchettus of Padua; fl. 1305 – 1319) was an Italian music theorist and composer of the late medieval era. His innovations in notation of time-values were fundamental to the music of the Italian ars nova, as was his w ...
proposed a system that is approximately 29-EDO, which is a subset of 58-EDO, in 1318.
Interval size
See also
*
Harry Partch's 43-tone scale; 58-EDO is the smallest equal temperament that can reasonably approximate this scale
References
External links
Xenharmonic Wiki article on 58edo
{{Musical tuning
Equal temperaments
Microtonality