86400edo - Revision history

ArrowHead294 at 23:01, 20 February 2025

2025-02-20T23:01:33Z

← Older revision		Revision as of 23:01, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|86400~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 23:01, 20 February 2025

2025-02-20T23:01:17Z

← Older revision		Revision as of 23:01, 20 February 2025
Line 8:		Line 8:
	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 [[24edo\|quarter-tone]], one minute is 5/6 of a cent, and one second, one step size is 1/72 of a cent.		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 [[24edo\|quarter-tone]], one minute is 5/6 of a cent, and one second, one step size is 1/72 of a cent.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Selected intervals in clock notation		\|+ style="font-size: 105%;" \| Selected intervals in clock notation
	~~!Steps~~
	~~!Name~~
	~~!Clock notation~~
	~~!Associated JI~~
	\|-		\|-
	\|0		! Steps
	~~\|Unison~~		! Name
	~~\|00:00:00~~		! Clock notation
	~~\|1/1 exact~~		! Associated JI
	\|-		\|-
	\|60		\| 0
	\|~~Minute~~		\| Unison
	\|00:01:00		\| 00:00:00
	\|		\| 1/1 exact
	\|-		\|-
	\|72		\| 60
	\|~~Cent~~		\| Minute
	\|00:01:12		\| 00:01:00
	\|		\|
	\|-		\|-
	\|~~141~~		\| 72
	\|~~Schisma~~		\| Cent
	\|00:02:21		\| 00:01:12
	\|~~32805/32768~~		\|
	\|-		\|-
	\|~~1548~~		\| 141
	\|~~Syntonic comma~~		\| Schisma
	\|00:25:48		\| 00:02:21
	\|81/80		\| 32805/32768
	\|-		\|-
	\|~~1689~~		\| 1548
	\|~~Pythagorean~~ comma		\| Syntonic comma
	\|00:28:09		\| 00:25:48
	\|~~531441~~/~~524288~~		\| 81/80
	\|-		\|-
	\|~~3600~~		\| 1689
	\|~~Quarter-tone, Hour~~		\| Pythagorean comma
	\|01:00:00		\| 00:28:09
	\|		\| 531441/524288
	\|-		\|-
	\|~~7200~~		\| 3600
	\|~~Dodecaphonic semitone~~		\| Quarter-tone, Hour
	\|02:00:00		\| 01:00:00
	\|		\|
	\|-		\|-
	\|~~14682~~		\| 7200
	\|~~Just whole tone~~		\| Dodecaphonic semitone
	\|04:04:42		\| 02:00:00
	\|~~9/8~~		\|
	\|-		\|-
	\|~~50400~~		\| 14682
	\|~~Dodecaphonic perfect fifth~~		\| Just whole tone
	\|14:00:00		\| 04:04:42
	\|		\| 9/8
	\|-		\|-
	\|~~50541~~		\| 50400
	\|~~Just~~ perfect fifth		\| Dodecaphonic perfect fifth
	\|14:02:21		\| 14:00:00
	\|~~3/2~~		\|
	\|-		\|-
	\|86400		\| 50541
	\|Octave		\| Just perfect fifth
	\|24:00:00		\| 14:02:21
	\|2/1 exact		\| 3/2
			\|-
			\| 86400
			\| Octave
			\| 24:00:00
			\| 2/1 exact
	\|}		\|}

	[[Category:Equal divisions of the octave\|#####]]<!-- 5-digit number -->		[[Category:Equal divisions of the octave\|#####]]<!-- 5-digit number -->

BudjarnLambeth at 07:18, 9 July 2023

2023-07-09T07:18:30Z

← Older revision		Revision as of 07:18, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}~~
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|86400}}		{{EDO intro\|86400}}

BudjarnLambeth at 04:04, 9 July 2023

2023-07-09T04:04:43Z

← Older revision		Revision as of 04:04, 9 July 2023
Line 1:		Line 1:
			{{novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|86400}}		{{EDO intro\|86400}}

Eliora: apparently no and rewrite

2022-12-25T18:14:05Z

apparently no and rewrite

← Older revision		Revision as of 18:14, 25 December 2022
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~86400 ~~EDO''' divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.~~		{{EDO intro\|86400}}

	== Theory ==		== Theory ==
	86400 is a ~~significantly composite~~ number 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.		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 ===
Line 75:		Line 75:
	\|}		\|}

	~~== Tempered commas ==~~		[[Category:Equal divisions of the octave\|#####]]<!-- 5-digit number -->
	~~86400edo tempers out the [[Kirnberger's atom]] in the 5-limit.~~

	[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->

Eliora: /* Tempered commas */ consistency limit is 5 so...

2022-12-25T18:11:52Z

Tempered commas: consistency limit is 5 so...

← Older revision		Revision as of 18:11, 25 December 2022
Line 76:		Line 76:

	== Tempered commas ==		== Tempered commas ==
	86400edo tempers out the [[Kirnberger's atom]]~~, albeit inconsistently,~~ in the 5-limit.		86400edo tempers out the [[Kirnberger's atom]] in the 5-limit.

	[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->		[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->

Plumtree: Infobox ET added

2022-10-04T22:30:16Z

Infobox ET added

← Older revision		Revision as of 22:30, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''86400 EDO''' divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.		'''86400 EDO''' divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.

Fredg999 category edits: Categories

2022-07-04T01:45:55Z

Eliora: /* Tempered commas */

2022-04-26T19:11:15Z

Tempered commas

← Older revision		Revision as of 19:11, 26 April 2022
Line 75:		Line 75:

	== Tempered commas ==		== Tempered commas ==
	86400edo ~~seems to temper~~ out the [[Kirnberger's atom]] ~~directly since both the difference between 700 cents and 3/2~~, ~~and the schisma are equal to 2 minutes 21 seconds. However~~, ~~stacking 11 of~~ the ~~2:21 interval times leads to 1551, while 12 times to 1692, each differing 3 steps from their assigned commas~~.		86400edo tempers out the [[Kirnberger's atom]], albeit inconsistently, in the 5-limit.

Eliora: Created page with "86400 EDO divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amo..."

2022-01-17T16:25:14Z

Created page with "86400 EDO divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amo..."

New page

86400 EDO divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.

== Theory ==
86400 is a significantly composite number 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 [[24edo|quarter-tone]], one minute is 5/6 of a cent, and one second, one step size is 1/72 of a cent.
{| class="wikitable"
|+Selected intervals in clock notation
!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
|}

== Tempered commas ==
86400edo seems to temper out the [[Kirnberger's atom]] directly since both the difference between 700 cents and 3/2, and the schisma are equal to 2 minutes 21 seconds. However, stacking 11 of the 2:21 interval times leads to 1551, while 12 times to 1692, each differing 3 steps from their assigned commas.

← Older revision		Revision as of 01:45, 4 July 2022
Line 1:		Line 1:
	86400 EDO divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.		'''86400 EDO''' divides the octave into steps of 13.9 millicent, or alternately, exactly 1/72 of a cent each. It is notable because it is the equal division corresponding to the amount of seconds in a day.

	== Theory ==		== Theory ==
Line 76:		Line 76:
	== Tempered commas ==		== Tempered commas ==
	86400edo tempers out the [[Kirnberger's atom]], albeit inconsistently, in the 5-limit.		86400edo tempers out the [[Kirnberger's atom]], albeit inconsistently, in the 5-limit.

			[[Category:Equal divisions of the octave\|#####]] <!-- 5-digit number -->