1edo: Difference between revisions
CompactStar (talk | contribs) This is insane but does let you see what primes are mapped to what |
Note -> pitch; prime harmonics -> odd harmonics; note on equivalency to 1afdo and 1ifdo; linking and style |
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'''1 equal division of the octave''' ('''1edo''') is the [[tuning system]] that contains a single | '''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. | ||
== 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]]; 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. | 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. | ||
=== | 1edo is equivalent to [[AFDO|1afdo]] and [[IFDO|1ifdo]]. | ||
=== Odd harmonics === | |||
{{Harmonics in equal|1}} | {{Harmonics in equal|1}} | ||
Revision as of 07:54, 14 January 2024
| ← 0edo | 1edo | 2edo → |
1 equal division of the octave (1edo) is the tuning system that contains a single pitch and the octaves above and below that pitch.
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
| 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
- Octaves Only (2023)
- PolyTech (2023)
- E (2022)
- Play "Do" (2021) (MuseScore.com)
- One Note To Tell A Story (2022) (YouTube)
- "Cohesion", from Edolian (2020)
- "Neainaz Antithetica, Theme", from STAFFcirc vol. 7 (2021) (Bandcamp)