# 1edo

← 0edo | 1edo | 2edo → |

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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 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; 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)