Ledzo notation: Difference between revisions

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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/

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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.

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 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''').

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

@@ Line 1: / Line 1: @@
-'''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/
@@ 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.
-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 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''').
@@ Line 118: / Line 118: @@
 == [[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]] can be notated by taking a, b, c, etc to stand for the [[Majestazic system|tempered primes]] used in the temperament.
+{{Navbox notation}}