1edo: Difference between revisions
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i'm not sure telicity is really notable here, but feel free to revert if it is |
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'''1 equal divisions of the octave''' (abbreviated '''1edo'''), or '''1-tone equal temperament''' ('''1tet'''), '''1 equal temperament''' ('''1et)''' when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave. | '''1 equal divisions of the octave''' (abbreviated '''1edo'''), or '''1-tone equal temperament''' ('''1tet'''), '''1 equal temperament''' ('''1et)''' when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave. | ||
== Theory == | == Theory == | ||
One note repeated in octaves is an example of a [[trivial temperament]]; | One note repeated in octaves is an example of a [[trivial temperament]]; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. However, in terms of JI representation, it is simply the [[2-limit]] with all other primes tempered to some amount of octaves. | ||
The first piece of ''Musica ricercata'' by {{w|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. | The first piece of ''Musica ricercata'' by {{w|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. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|1}} | {{Harmonics in equal|1|columns=15}} | ||
== Music == | == Music == | ||
Revision as of 03:48, 6 January 2025
| ← 0edo | 1edo | 2edo → |
1 equal divisions of the octave (abbreviated 1edo), or 1-tone equal temperament (1tet), 1 equal temperament (1et) when viewed under a regular temperament perspective, is the tuning system that contains a single pitch and pitches octaves above and below that pitch. Each step of 1edo represents a frequency ratio of 2/1, or exactly the octave.
Theory
One note repeated in octaves is an example of a trivial temperament; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every edo. However, in terms of JI representation, it is simply the 2-limit with all other primes tempered to some amount of octaves.
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
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +498 | -386 | +231 | -204 | -551 | +359 | +112 | -105 | -298 | -471 | +572 | +427 | +294 | +170 | +55 |
| Relative (%) | +41.5 | -32.2 | +19.3 | -17.0 | -45.9 | +30.0 | +9.3 | -8.7 | -24.8 | -39.2 | +47.6 | +35.6 | +24.5 | +14.2 | +4.6 | |
| Step | 2 | 2 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 5 | 5 | 5 | |
Music
- See also: Category:1edo tracks
- Octaves Only (2023)
- PolyTech (2023)
- E (2022)
- One Note To Tell A Story (2022) – Newgrounds | YouTube
- "Cohesion", from Edolian (2020)
- Singularity (2024)
- "Neainaz Antithetica, Theme", from STAFFcirc vol. 7 (2021) – SoundCloud | Bandcamp