# 86400edo

← 86399edo | 86400edo | 86401edo → |

^{7}× 3^{3}× 5^{2}**86400 equal divisions of the octave** (abbreviated **86400edo** or **86400ed2**), also called **86400-tone equal temperament** (**86400tet**) or **86400 equal temperament** (**86400et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 86400 equal parts of about 0.014 ¢ each. Each step represents a frequency ratio of 2^{1/86400}, or the 86400th root of 2.

## Theory

86400 is a number notable for being the number of seconds in a day, and as such it has a lot of divisors, factoring into 2^7 x 3^3 x 5^2. While it isn't in the ranks of highly composite and superabundant, it's abundancy index is about 2.66.

### Table of selected intervals

86400edo carries an interval size measure notation proposed by Eliora in January 2022, called the clock notation. The notation involves writing interval size measures using hours, minutes, seconds derived from steps of 86400edo. The notation's purpose is to write down intervals in the small-unnoticeable range. This means that one hour is a quarter-tone, one minute is 5/6 of a cent, and one second, one step size is 1/72 of a cent.

Steps | Name | Clock notation | Associated JI |
---|---|---|---|

0 | Unison | 00:00:00 | 1/1 exact |

60 | Minute | 00:01:00 | |

72 | Cent | 00:01:12 | |

141 | Schisma | 00:02:21 | 32805/32768 |

1548 | Syntonic comma | 00:25:48 | 81/80 |

1689 | Pythagorean comma | 00:28:09 | 531441/524288 |

3600 | Quarter-tone, Hour | 01:00:00 | |

7200 | Dodecaphonic semitone | 02:00:00 | |

14682 | Just whole tone | 04:04:42 | 9/8 |

50400 | Dodecaphonic perfect fifth | 14:00:00 | |

50541 | Just perfect fifth | 14:02:21 | 3/2 |

86400 | Octave | 24:00:00 | 2/1 exact |