1536edo - Revision history

ArrowHead294 at 22:44, 20 February 2025

2025-02-20T22:44:42Z

← Older revision		Revision as of 22:44, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1536~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	=== As a tuning standard ===		=== As a tuning standard ===
	A step of 1536edo is known as a ''[[heptamu]]'' (seventh MIDI-resolution unit, 7mu, 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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 1536edo is known as a ''[[heptamu]]'' (seventh MIDI-resolution unit, 7mu, {{nowrap\|2<sup>7</sup> {{=}} 128}} equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.

	=== Odd harmonics ===		=== Odd harmonics ===

Fredg999: /* External links */ Misc. edits

2024-07-05T04:22:02Z

External links: Misc. edits

← Older revision		Revision as of 04:22, 5 July 2024
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/number/7mu.aspx ~~Tonalsoft Encyclopedia \| ''~~7mu / heptamu'']		* [http://tonalsoft.com/enc/number/7mu.aspx 7mu / heptamu] on [[Tonalsoft Encyclopedia]]

FloraC: /* Theory */ fix grammar

2023-11-07T08:22:48Z

Theory: fix grammar

← Older revision		Revision as of 08:22, 7 November 2023
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	=== As a tuning standard ===		=== As a tuning standard ===
	A step of 1536edo is known as ''[[heptamu]]'' (seventh [[MIDI]]-resolution unit, ''7mu'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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 1536edo is known as a ''[[heptamu]]'' (seventh MIDI-resolution unit, 7mu, 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: +external link

2023-11-07T07:54:37Z

+external link

← Older revision		Revision as of 07:54, 7 November 2023
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	** [[98304edo]] (13mu tuning)		** [[98304edo]] (13mu tuning)
	** [[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)

			== External links ==
			* [http://tonalsoft.com/enc/number/7mu.aspx Tonalsoft Encyclopedia \| ''7mu / heptamu'']

FloraC: Move the 7mu info to the theory section

2023-11-07T07:40:31Z

Move the 7mu info to the theory section

← Older revision		Revision as of 07:40, 7 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1536}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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\|1536}}

	== Theory ==		== Theory ==
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	If we do use it for the 5-limit, then {{val\| 1536 '''2434''' '''3566''' }} (1536b [[val]]) and {{val\| 1536 '''2435''' '''3567''' }} (1536c val) are worth considering, but 1536b is [[enfactoring\|enfactored]] through the 17-limit (see [[768edo]]), leaving us with 1536c alone. It [[tempering out\|tempers out]] 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.		If we do use it for the 5-limit, then {{val\| 1536 '''2434''' '''3566''' }} (1536b [[val]]) and {{val\| 1536 '''2435''' '''3567''' }} (1536c val) are worth considering, but 1536b is [[enfactoring\|enfactored]] through the 17-limit (see [[768edo]]), leaving us with 1536c alone. It [[tempering out\|tempers out]] 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.

			=== As a tuning standard ===
			A step of 1536edo is known as ''[[heptamu]]'' (seventh [[MIDI]]-resolution unit, ''7mu'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Rework on theory (patent val not worth considering against 1536b and 1536c)

2023-10-30T14:18:12Z

Rework on theory (patent val not worth considering against 1536b and 1536c)

← Older revision		Revision as of 14:18, 30 October 2023
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	{{EDO intro\|1536}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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\|1536}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.

	1536edo is in[[consistent]] to the [[5-odd-limit]] and ~~higher limits~~, with ~~three mappings possible for 5-limit: {{val~~\| ~~1536 2435 3566 }} (~~[[~~patent val~~]]), {{val\| 1536 '''2434''' 3566 }} (1536b ~~val,~~ [[~~enfactoring\|enfactored]] through the 17-limit, see [[768edo~~]]), and {{val\| 1536 2435 '''3567''' }} (1536c val)~~. Using the patent val~~, ~~it tempers out {{monzo~~\| ~~71 -36 -6 }} and {{monzo\| -32 -34 37 }} in~~ the 5-limit; [[~~703125/702464~~]], [[~~4802000/4782969~~]]~~, and 54975581388800/54936068900769 in the 7-limit. Using the 1536c val, it tempers out~~ 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.		== Theory ==
			1536edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. Otherwise it is excellent in approximating harmonics [[7/1\|7]], [[9/1\|9]], [[13/1\|13]], and [[15/1\|15]], making it suitable for a 2.9.15.7.13 [[subgroup]] interpretation, with an optional addition of either [[11/1\|11]] or [[17/1\|17]].

			If we do use it for the 5-limit, then {{val\| 1536 '''2434''' '''3566''' }} (1536b [[val]]) and {{val\| 1536 '''2435''' '''3567''' }} (1536c val) are worth considering, but 1536b is [[enfactoring\|enfactored]] through the 17-limit (see [[768edo]]), leaving us with 1536c alone. It [[tempering out\|tempers out]] 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|1536}}

			=== Subsets and supersets ===
			Since 1536 factors into {{factorization\|1536}}, 1536edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, and 768 }}.

	== See also ==		== See also ==

FloraC: Adopt template: EDO intro; cleanup

2023-10-17T07:38:38Z

Adopt template: EDO intro; cleanup

← Older revision		Revision as of 07:38, 17 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''1536EDO''' is the [[~~EDO\|~~equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/~~1536~~</sup> as a frequency ratio.~~ Its adjacent step is known as ''[[~~Heptamu~~]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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\|1536}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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 ==~~		1536edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for 5-limit: {{val\| 1536 2435 3566 }} ([[patent val]]), {{val\| 1536 '''2434''' 3566 }} (1536b val, [[enfactoring\|enfactored]] through the 17-limit, see [[768edo]]), and {{val\| 1536 2435 '''3567''' }} (1536c val). Using the patent val, it tempers out {{monzo\| 71 -36 -6 }} and {{monzo\| -32 -34 37 }} in the 5-limit; [[703125/702464]], [[4802000/4782969]], and 54975581388800/54936068900769 in the 7-limit. Using the 1536c val, it tempers out 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.
	~~1536EDO~~ is ~~inconsistent~~ to the [[5-limit]] and higher ~~limit~~, with three mappings possible for 5-limit: {{val\| 1536 2435 3566 }} (patent val), {{val\| 1536 '''2434''' 3566 }} (1536b val, ~~contorted~~ through the 17-limit), and {{val\| 1536 2435 '''3567''' }} (1536c val). Using the patent val, it tempers out {{monzo\| 71 -36 -6 }} and {{monzo\| -32 -34 37 }} in the 5-limit; [[703125/702464]], [[4802000/4782969]], and 54975581388800/54936068900769 in the 7-limit. Using the 1536c val, it tempers out 6115295232/6103515625 ([[vishnuzma]]) and {{monzo\| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.

	== See also ==		== See also ==
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	** [[98304edo]] (13mu tuning)		** [[98304edo]] (13mu tuning)
	** [[196608edo]] (14mu tuning)		** [[196608edo]] (14mu tuning)

	~~[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->~~

BudjarnLambeth at 06:54, 9 July 2023

2023-07-09T06:54:50Z

← Older revision		Revision as of 06:54, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.		'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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 05:06, 9 July 2023

2023-07-09T05:06:22Z

← Older revision		Revision as of 05:06, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.		'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.

Plumtree: Infobox ET added

2022-10-04T22:10:34Z

Infobox ET added

← Older revision		Revision as of 22:10, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.		'''1536EDO''' is the [[EDO\|equal division of the octave]] into 1536 parts of exact 0.78125 cents each, which is to say 2<sup>1/1536</sup> as a frequency ratio. Its adjacent step is known as ''[[Heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu 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, and 6 other bits which are not 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.