98304edo - Revision history

ArrowHead294 at 22:37, 20 February 2025

2025-02-20T22:37:57Z

Fredg999: /* External links */ Misc. edits

2024-07-07T22:46:33Z

External links: Misc. edits

← Older revision		Revision as of 22:46, 7 July 2024
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/13mu.aspx ~~Tonalsoft Encyclopedia \| ''~~13mu / tridekamu'']		* [http://tonalsoft.com/enc/number/13mu.aspx 13mu / tridekamu] on [[Tonalsoft Encyclopedia]]

FloraC: /* Theory */ fix grammar

2023-11-07T08:21:06Z

Theory: fix grammar

← Older revision		Revision as of 08:21, 7 November 2023
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	=== As a tuning standard ===		=== As a tuning standard ===
	A step of 98304edo is known as '''tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.		A step of 98304edo is known as a '''tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: /* Selected intervals */ formatting

2023-11-07T08:05:58Z

Selected intervals: formatting

← Older revision		Revision as of 08:05, 7 November 2023
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	== Selected intervals ==		== Selected intervals ==
	{\| class="wikitable"		{\| class="wikitable right-1 right-2 center-3 right-4 right-5"
	\|-		\|-
	! rowspan="2"\| #		! rowspan="2"\| #

FloraC: Move the 13mu info to the theory section

2023-11-07T08:04:58Z

Move the 13mu info to the theory section

Show changes

BudjarnLambeth at 07:18, 9 July 2023

2023-07-09T07:18:41Z

← Older revision		Revision as of 07:18, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.		{{EDO intro\|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

BudjarnLambeth at 04:04, 9 July 2023

2023-07-09T04:04:15Z

← Older revision		Revision as of 04:04, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.		{{EDO intro\|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

FloraC: Cleanup

2023-02-20T07:21:26Z

Cleanup

← Older revision		Revision as of 07:21, 20 February 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''98304EDO''' is the [[~~EDO\|~~equal division of the octave]] into~~ 98304 ~~parts of exact 0.01220703125 cents each, which is to say 2<sup>(1/98304)</sup> as a frequency ratio.~~ Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.		{{EDO intro\|98304}} Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

	==~~Intervals~~==		== Theory ==
	~~98304EDO~~ is [[consistent]] to the [[19-odd~~-limit\|19~~-limit]], tempering out \|45 2 -28 6~~>~~, \|-54 15 -16 24~~>~~, and \|-29 135 -18 -51~~>~~ in the 7-limit; \|-4 15 -14 7 -2~~>~~, \|-3 28 2 -9 -6~~>~~, \|-50 0 -2 17 2~~>~~, and \|30 10 8 -2 -17~~>~~ in the 11-limit; 123201/123200, 32427005625/32426652544, 278924131584/278916015625, 37744795080531/37744172597248, and 156905298045000/156904157228819 in the 13-limit; 2000033/2000000, 154002541/154001250, 303464448/303460625, 338676338/338671875, 791249550/791243563, and 176846618624/176846076825 in the 17-limit; 89376/89375, 104976/104975, 709632/709631, 5836831/5836800, 494190983/494190000, 1206902781/1206878450, and 21867094832/21867015625 in the 19-limit.		98304edo is [[consistent]] to the [[19-odd-limit]], tempering out {{monzo\| 45 2 -28 6 }}, {{monzo\| -54 15 -16 24 }}, and {{monzo\| -29 135 -18 -51 }} in the 7-limit; {{monzo\| -4 15 -14 7 -2 }}, {{monzo\| -3 28 2 -9 -6 }}, {{monzo\| -50 0 -2 17 2 }}, and {{monzo\| 30 10 8 -2 -17}} in the 11-limit; 123201/123200, 32427005625/32426652544, 278924131584/278916015625, 37744795080531/37744172597248, and 156905298045000/156904157228819 in the 13-limit; 2000033/2000000, 154002541/154001250, 303464448/303460625, 338676338/338671875, 791249550/791243563, and 176846618624/176846076825 in the 17-limit; 89376/89375, 104976/104975, 709632/709631, 5836831/5836800, 494190983/494190000, 1206902781/1206878450, and 21867094832/21867015625 in the 19-limit.

			=== Prime harmonics ===
			{{Harmonics in equal\|98304}}

			== Selected intervals ==
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! rowspan="2"\| ~~98304EDO <br>steps~~		! rowspan="2"\| #
	! rowspan="2"\| ~~cents <br>value~~		! rowspan="2"\| Cents
	! colspan="2"\| JI ~~interval~~		! colspan="2"\| JI Interval
	! rowspan="2"\| ~~error~~ <br>(cents)		! rowspan="2"\| Error <br>(cents)
	\|-		\|-
	! \| ratio		! \| ratio
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	\|}		\|}

	==See also==		== See also ==
	*[[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units		* [[Equal-step tuning\|Equal multiplications]] of MIDI-resolution units
	**[[24edo]] (1mu tuning)		** [[24edo]] (1mu tuning)
	**[[48edo]] (2mu tuning)		** [[48edo]] (2mu tuning)
	**[[96edo]] (3mu tuning)		** [[96edo]] (3mu tuning)
	**[[192edo]] (4mu tuning)		** [[192edo]] (4mu tuning)
	**[[384edo]] (5mu tuning)		** [[384edo]] (5mu tuning)
	**[[768edo]] (6mu tuning)		** [[768edo]] (6mu tuning)
	**[[1536edo]] (7mu tuning)		** [[1536edo]] (7mu tuning)
	**[[3072edo]] (8mu tuning)		** [[3072edo]] (8mu tuning)
	**[[6144edo]] (9mu tuning)		** [[6144edo]] (9mu tuning)
	**[[12288edo]] (10mu tuning)		** [[12288edo]] (10mu tuning)
	**[[24576edo]] (11mu tuning)		** [[24576edo]] (11mu tuning)
	**[[49152edo]] (12mu tuning)		** [[49152edo]] (12mu tuning)
	**[[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)

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

Plumtree: Infobox ET added

2022-10-04T22:30:37Z

Infobox ET added

← Older revision		Revision as of 22:30, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''98304EDO''' is the [[EDO\|equal division of the octave]] into 98304 parts of exact 0.01220703125 cents each, which is to say 2<sup>(1/98304)</sup> as a frequency ratio. Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.		'''98304EDO''' is the [[EDO\|equal division of the octave]] into 98304 parts of exact 0.01220703125 cents each, which is to say 2<sup>(1/98304)</sup> as a frequency ratio. Its adjacent step is known as '''Tridecamu''' (thirteenth MIDI-resolution unit, 13mu, 2<sup>13</sup> = 8192 equal divisions of the [[12edo]] semitone). The internal data structure of the 13mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down; all bits are used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

Fredg999 category edits: Sort key

2022-07-04T01:46:02Z

Sort key

← Older revision		Revision as of 01:46, 4 July 2022
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	**[[196608edo]] (14mu tuning)		**[[196608edo]] (14mu tuning)

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