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subst edo intro, make it a bit "fancier"
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{{Infobox ET}}
{{Infobox ET}}
'''1 equal division of the octave''' ('''1edo''') is the [[tuning system]] that contains a single pitch and the [[octave]]s above and below that pitch.
{{#invoke:EDO_intro|edo_intro_frame
 
|EDO=1
}}
== Theory ==
== Theory ==
One note repeated in octaves is an example of a [[trivial temperament]]; it is even a system that demonstrates trivial examples of [[telicity]]. That said, it is actually useful in some cases from a musical standpoint, particularly as a subset of larger edos. However, in terms of JI representation, it is simply the [[2-limit]] with all other primes tempered to either the unison or octave.
One note repeated in octaves is an example of a [[trivial temperament]]; it is even a system that demonstrates trivial examples of [[telicity]]. That said, it is actually useful in some cases from a musical standpoint, particularly as a subset of larger edos. However, in terms of JI representation, it is simply the [[2-limit]] with all other primes tempered to either the unison or octave.

Revision as of 12:53, 11 February 2024

← 0edo 1edo 2edo →
Prime factorization n/a
Step size 1200 ¢ 
Fifth 1\1 (1200 ¢)
Semitones (A1:m2) 3:-2 (3600 ¢ : -2400 ¢)
Dual sharp fifth 1\1 (1200 ¢)
Dual flat fifth 0\1 (0 ¢)
Dual major 2nd 0\1 (0 ¢)
Consistency limit 3
Distinct consistency limit 1

Script error: No such module "EDO_intro".

Theory

One note repeated in octaves is an example of a trivial temperament; it is even a system that demonstrates trivial examples of telicity. That said, it is actually useful in some cases from a musical standpoint, particularly as a subset of larger edos. However, in terms of JI representation, it is simply the 2-limit with all other primes tempered to either the unison or octave.

The first piece of Musica ricercata by György Ligeti simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.

1edo is equivalent to 1afdo and 1ifdo.

Odd harmonics

Approximation of odd harmonics in 1edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +498 -386 +231 -204 -551 +359 +112 -105 -298 -471 +572
Relative (%) +41.5 -32.2 +19.3 -17.0 -45.9 +30.0 +9.3 -8.7 -24.8 -39.2 +47.6
Step 2 2 3 3 3 4 4 4 4 4 5

Music

See also: Category:1edo tracks
Blendy Wave
Francium
  • E (2022)
Frédéric Gagné
György Ligeti
Mandrake
NullPointerException Music
STC_1001

See also