Ledzo notation - Revision history

ArrowHead294 at 18:32, 11 February 2025

2025-02-11T18:32:14Z

← Older revision		Revision as of 18:32, 11 February 2025
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	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.

	{{~~Notation navbox~~}}		{{Navbox notation}}

ArrowHead294 at 18:31, 11 February 2025

2025-02-11T18:31:07Z

← Older revision		Revision as of 18:31, 11 February 2025
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	== Regular temperaments ==		== Regular temperaments ==
	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.


	{{Notation navbox}}		{{Notation navbox}}

	~~[[Category:Notation]]~~

BudjarnLambeth: add link plus {{Notation navbox}}

2024-12-03T00:01:40Z

add link plus {{Notation navbox}}

← Older revision		Revision as of 00:01, 3 December 2024
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	'''Ledzo notation''' is a JI and regular temperament notation proposed as an '''alternative to color notation''' by '''Vector Graphics'''. It aims to solve these '''observed problems''' with color notation:		'''Ledzo notation''' is a JI and regular temperament notation proposed as an '''alternative to [[color notation]]''' by '''Vector Graphics'''. It aims to solve these '''observed problems''' with color notation:

	* The association of intervals to "colors" in color notation is extraneous, unnecessary, and possibly counterintuitive for people with intuitive associations between colors and numbers/ratios/intervals/		* The association of intervals to "colors" in color notation is extraneous, unnecessary, and possibly counterintuitive for people with intuitive associations between colors and numbers/ratios/intervals/
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	== Regular temperaments ==		== Regular temperaments ==
	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.


			{{Notation navbox}}

	[[Category:Notation]]		[[Category:Notation]]

BudjarnLambeth: Categorised uncategorised page

2024-09-11T03:09:59Z

Categorised uncategorised page

← Older revision		Revision as of 03:09, 11 September 2024
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	== Regular temperaments ==		== Regular temperaments ==
	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.

			[[Category:Notation]]

VectorGraphics: VectorGraphics moved page User:VectorGraphics/Ledzo notation to Ledzo notation: Page is complete enough

2024-07-16T19:30:22Z

VectorGraphics moved page User:VectorGraphics/Ledzo notation to Ledzo notation: Page is complete enough

← Older revision	Revision as of 19:30, 16 July 2024
(No difference)

VectorGraphics at 07:12, 16 July 2024

2024-07-16T07:12:39Z

← Older revision		Revision as of 07:12, 16 July 2024
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	Octave complements can be specified by flipping the signs of the entries for each prime, and adding 1 to the '''a''' entry. For example, the major third is -2ac, while the minor sixth is 3a-c.		Octave complements can be specified by flipping the signs of the entries for each prime, and adding 1 to the '''a''' entry. For example, the major third is -2ac, while the minor sixth is 3a-c.

	To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval. In the case of WBN, only the first step is taken, so intervals are only labeled "third", "sixth", etc. Additionally, WBN does not have a built-in system of interval arithmetic, so using interval arithmetic with WBN intervals becomes harder.		To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval. In the case of WBN, only the first step is taken, so intervals are only labeled "third", "sixth", etc. Additionally, WBN does not have a built-in system of interval arithmetic, so using interval arithmetic with ledzo+WBN intervals becomes harder.

	In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').		In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').

VectorGraphics at 07:12, 16 July 2024

2024-07-16T07:12:22Z

← Older revision		Revision as of 07:12, 16 July 2024
Line 39:		Line 39:
	Octave complements can be specified by flipping the signs of the entries for each prime, and adding 1 to the '''a''' entry. For example, the major third is -2ac, while the minor sixth is 3a-c.		Octave complements can be specified by flipping the signs of the entries for each prime, and adding 1 to the '''a''' entry. For example, the major third is -2ac, while the minor sixth is 3a-c.

	To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval.		To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval. In the case of WBN, only the first step is taken, so intervals are only labeled "third", "sixth", etc. Additionally, WBN does not have a built-in system of interval arithmetic, so using interval arithmetic with WBN intervals becomes harder.

	In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').		In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').

VectorGraphics at 08:21, 14 July 2024

2024-07-14T08:21:19Z

← Older revision		Revision as of 08:21, 14 July 2024
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	== [[Interval arithmetic]] ==		== [[Interval arithmetic]] ==
	Ledzo notation supports a form of interval arithmetic natively, since intervals are stacked just by adding their monzos together. For example, a major third plus a minor third is a perfect fifth, and that's represented as follows: [-2 0 1⟩ * [1 1 -1⟩ = [-1 1 0⟩. This translates intuitively into the ledzo: -2ac + ab-c = -ab~~, analogously for the octave complements: -c + -bc = -b~~ (note that concatenation here does not mean multiplication in the logarithmic scale this is using, positive entries have a hidden plus sign that is not written!)		Ledzo notation supports a form of interval arithmetic natively, since intervals are stacked just by adding their monzos together. For example, a major third plus a minor third is a perfect fifth, and that's represented as follows: [-2 0 1⟩ * [1 1 -1⟩ = [-1 1 0⟩. This translates intuitively into the ledzo: -2ac + ab-c = -ab (note that concatenation here does not mean multiplication in the logarithmic scale this is using, positive entries have a hidden plus sign that is not written!)

	== Regular temperaments ==		== Regular temperaments ==
	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.

VectorGraphics at 08:19, 14 July 2024

2024-07-14T08:19:35Z

← Older revision		Revision as of 08:19, 14 July 2024
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	(And if you are using a prime higher than 101, either something's '''seriously gone wrong''' or this notation probably '''won't be useful''' for your use case anyway.)		(And if you are using a prime higher than 101, either something's '''seriously gone wrong''' or this notation probably '''won't be useful''' for your use case anyway.)

	Intervals with no '''a''' specified are assumed to be octave-reduced, you can specify '''0a''' if the distinction is significant. Due to this, octave complements can be specified by flipping the signs of the entries for each prime. For example, the major third is '''c''', while the minor sixth is '''-c'''.		'''LEGACY:''' <s>Intervals with no '''a''' specified are assumed to be octave-reduced, you can specify '''0a''' if the distinction is significant. Due to this, octave complements can be specified by flipping the signs of the entries for each prime. For example, the major third is '''c''', while the minor sixth is '''-c'''.</s>

			Reduction of intervals is no longer assumed.

			Octave complements can be specified by flipping the signs of the entries for each prime, and adding 1 to the '''a''' entry. For example, the major third is -2ac, while the minor sixth is 3a-c.

	To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval.		To provide a sense of the interval's size, ledzo notation can be paired with [[User:VectorGraphics/Walker brightness notation\|'''WBN''']] or another system for specifying interval regions in order to give a sense of the size of the interval.

	In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').		In order to disambiguate from other notation systems, letters are always written '''lowercase''' (so that, say, '''a''', when written, isn't confused for the note '''A''').

			Additionally, if the ledzo for an interval is a single letter with no number or minus sign, it takes a 1 before it, so that when spoken, ledzos aren't confused for note names.

	== Examples ==		== Examples ==
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	\|[[2/1]]		\|[[2/1]]
	\|[1⟩		\|[1⟩
	\|a octave		\|1a octave
	\|-		\|-
	\|[[3/2]]		\|[[3/2]]
	\|[-1 1⟩		\|[-1 1⟩
	\|b fifth		\| -ab fifth
	\|-		\|-
	\|[[4/3]]		\|[[4/3]]
	\|[2 -1⟩		\|[2 -1⟩
	\| -b fourth		\| 2a-b fourth
	\|-		\|-
	\|[[5/4]]		\|[[5/4]]
	\|[-2 0 1⟩		\|[-2 0 1⟩
	\|c third		\| -2ac third
	\|-		\|-
	\|[[8/5]]		\|[[8/5]]
	\|[3 0 -1⟩		\|[3 0 -1⟩
	\| -c sixth		\| 3a-c sixth
	\|-		\|-
	\|[[6/5]]		\|[[6/5]]
	\|[1 1 -1⟩		\|[1 1 -1⟩
	\|b-c third		\|ab-c third
	\|-		\|-
	\|[[5/3]]		\|[[5/3]]
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	\|[[7/6]]		\|[[7/6]]
	\|[-1 -1 0 1⟩		\|[-1 -1 0 1⟩
	\| -bd third		\| -a-bd third
	\|-		\|-
	\|[[9/7]]		\|[[9/7]]
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	\|[[14/9]]		\|[[14/9]]
	\|[1 -2 0 1⟩		\|[1 -2 0 1⟩
	\| -2bd sixth		\| a-2bd sixth
	\|-		\|-
	\|[[7/5]]		\|[[7/5]]
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	\|[[10/7]]		\|[[10/7]]
	\|[1 0 1 -1⟩		\|[1 0 1 -1⟩
	\|c-d tritone		\|ac-d tritone
	\|-		\|-
	\|[[81/80]]		\|[[81/80]]
	\|[-4 4 -1⟩		\|[-4 4 -1⟩
	\|4b-c comma		\| -4a4b-c comma
	\|-		\|-
	\|[[64/63]]		\|[[64/63]]
	\|[6 -2 0 -1⟩		\|[6 -2 0 -1⟩
	\| -2b-d comma		\| 6a-2b-d comma
	\|-		\|-
	\|[[531441/524288]]		\|[[531441/524288]]
	\|[-19 12⟩		\|[-19 12⟩
	\|~~12b~~ comma		\| -19a12b comma
	\|-		\|-
	\|[[3/1]]		\|[[3/1]]
	\|[0 1⟩		\|[0 1⟩
	\|~~0ab~~ tritave		\|1b tritave
	\|}		\|}

	== [[Interval arithmetic]] ==		== [[Interval arithmetic]] ==
	Ledzo notation supports a form of interval arithmetic natively, since intervals are stacked just by adding their monzos together. For example, a major third plus a minor third is a perfect fifth, and that's represented as follows: [-2 0 1⟩ * [1 1 -1⟩ = [-1 1 0⟩. This translates intuitively into the ledzo: c + b-c = b, analogously for the octave complements: -c + -bc = -b (note that concatenation here does not mean multiplication in the logarithmic scale this is using, positive entries have a hidden plus sign that is not written!)		Ledzo notation supports a form of interval arithmetic natively, since intervals are stacked just by adding their monzos together. For example, a major third plus a minor third is a perfect fifth, and that's represented as follows: [-2 0 1⟩ * [1 1 -1⟩ = [-1 1 0⟩. This translates intuitively into the ledzo: -2ac + ab-c = -ab, analogously for the octave complements: -c + -bc = -b (note that concatenation here does not mean multiplication in the logarithmic scale this is using, positive entries have a hidden plus sign that is not written!)

	== Regular temperaments ==		== Regular temperaments ==
	[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.		[[Regular temperaments]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system\|tempered primes]] used in the temperament.

VectorGraphics at 02:49, 14 July 2024

2024-07-14T02:49:42Z

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