Introductory examples in Sagittal notation: Difference between revisions

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The second example shows the best approximation for the same chord in [[12edo|12edo]]. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols are necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventional notation.

In [[22edo|22edo]] (third example), the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note has to stay. The ~~diffference~~ between the approximations of Pythagorean and just major third is one 22edo step, which is the best approximation of the syntonic comma in 22edo (more than twice as large as the just syntonic comma, though).

In [[22edo|22edo]] (third example), the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note has to stay. The difference between the approximations of Pythagorean and just major third is one 22edo step, which is the best approximation of the syntonic comma in 22edo (more than twice as large as the just syntonic comma, though).

Another property of 22edo is that the undecimal comma is approximated by one step as well . i.e. undecimal and syntonic comma are the same in 22edo, which makes one of the symbols unnecessary again. Overall, only one additional symbol is needed for the notation of 22edo (or, more precisely, two - one up and one down), representing a modification by one 22edo step. The syntonic comma symbol has been defined as the recommended standard symbol for 22edo.

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=Equal temperaments (2): 11edo scale=

As second example, an [[11edo|11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound ~~llike~~ a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols of [[22edo|22edo]] are used. For the same reason, the recommended symbols for [[16edo|16edo]] are those of [[48edo|48edo]].

As second example, an [[11edo|11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound like a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols of [[22edo|22edo]] are used. For the same reason, the recommended symbols for [[16edo|16edo]] are those of [[48edo|48edo]].

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 The second example shows the best approximation for the same chord in [[12edo|12edo]]. Here, both the syntonic as the septimal comma are tempered out, so none of the additional symbols are necessary. The best approximation of the otonal tetrad is the same as the best approximation for a Pythagorean dominant seventh chord and can be written the same way. We see that Sagittal notation, when used for the western standard tuning, is identical to conventional notation.
-In [[22edo|22edo]] (third example), the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note has to stay. The diffference between the approximations of Pythagorean and just major third is one 22edo step, which is the best approximation of the syntonic comma in 22edo (more than twice as large as the just syntonic comma, though).
+In [[22edo|22edo]] (third example), the septimal comma is tempered out, but not the syntonic comma. Therefore the symbol at the Bb note can be omitted, but the symbol at the E note has to stay. The difference between the approximations of Pythagorean and just major third is one 22edo step, which is the best approximation of the syntonic comma in 22edo (more than twice as large as the just syntonic comma, though).
 Another property of 22edo is that the undecimal comma is approximated by one step as well . i.e. undecimal and syntonic comma are the same in 22edo, which makes one of the symbols unnecessary again. Overall, only one additional symbol is needed for the notation of 22edo (or, more precisely, two - one up and one down), representing a modification by one 22edo step. The syntonic comma symbol has been defined as the recommended standard symbol for 22edo.
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 =Equal temperaments (2): 11edo scale=
-As second example, an [[11edo|11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound llike a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols of [[22edo|22edo]] are used. For the same reason, the recommended symbols for [[16edo|16edo]] are those of [[48edo|48edo]].
+As second example, an [[11edo|11edo]] scale is shown below. The task of defining a standard notation presents another possible pitfall here: 11edo doesn't have a good approximation of the perfect fifth. Building the notation following guideline 2 on series of fifths doesn't make much sense in this case - it would lead to strange effects, even contradicting guideline 1 (the written note E would sound like a D, the written note Eb like an E). This problem can be avoided using the symbols of a finer division - in the current case of 11edo, the symbols of [[22edo|22edo]] are used. For the same reason, the recommended symbols for [[16edo|16edo]] are those of [[48edo|48edo]].
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