86400edo: Difference between revisions
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→Tempered commas: consistency limit is 5 so... |
apparently no and rewrite |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|86400}} | |||
== Theory == | == Theory == | ||
86400 is a | 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 === | === Table of selected intervals === | ||
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[[Category:Equal divisions of the octave|#####]]<!-- 5-digit number --> | |||
[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number --> | |||
Revision as of 18:14, 25 December 2022
| ← 86399edo | 86400edo | 86401edo → |
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 |