User:Aura/Aura's introduction to 159edo: Difference between revisions

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== 5-limit diatonic music ==

Although 159edo inherits [[53edo]]'s close approximations of both the [[5-limit]] Zarlino scale and the [[3-limit]] [[diatonic]] MOS, these are not the only scales that one can use for fixed-pitch diatonic music. In fact, both of them are less than optimal for traditional Western classical music in this system, seeing as for the most part, each of the traditional diatonic modes has its own optimized scale in the 5-limit~~, with only Lydian and Locrian actually sharing the traditional Zarlino scale for their optimized 5-limit scale~~. The reason for this is that in non-meantone 5-limit systems such as 159edo, one inevitably has to deal with the ~40/27 wolf fifth and the ~27/20 wolf fourth, and there's only two ideal positions in the scale for those intervals to be situated in fixed-pitch diatonic music. For major modes, the ~27/20 wolf fourth is ideally situated between the ~5/4 major third and the ~27/16 major sixth, while for the minor modes and the diatonic blighted mode Locrian, the ~40/27 wolf fifth is ideally situated between the ~6/5 minor third and the ~16/9 minor seventh. Not only that, but it also pays to distinguish the Pythagorean major and minor thirds from their Ptolemaic counterparts as both types of major and minor third have distinct roles to play in the 5-limit diatonic music of the multiples of 53edo- and that includes 159edo itself~~. For the rest of this section, I'll be listing the optimized scales for 5-limit diatonic music as well as the necessary chords used by these systems~~.

Although 159edo inherits [[53edo]]'s close approximations of both the [[5-limit]] Zarlino scale and the [[3-limit]] [[diatonic]] MOS, these are not the only scales that one can use for fixed-pitch diatonic music. In fact, both of them are less than optimal for many facets of traditional Western classical music in this system, seeing as for the most part, each of the traditional diatonic modes has its own optimized scale in the 5-limit. The reason for this is that in non-meantone 5-limit systems such as 159edo, one inevitably has to deal with the ~[[40/27]] wolf fifth and the ~[[27/20]] wolf fourth, and there's only two ideal positions in the scale for those intervals to be situated in fixed-pitch diatonic music. For major modes, the ~27/20 wolf fourth is ideally situated between the ~[[5/4]] major third and the ~[[27/16]] major sixth, while for the minor modes and the diatonic blighted mode Locrian, the ~40/27 wolf fifth is ideally situated between the ~[[6/5]] minor third and the ~[[16/9]] minor seventh. Not only that, but it also pays to distinguish the Pythagorean major and minor thirds from their Ptolemaic counterparts as both types of major and minor third have distinct roles to play in the 5-limit diatonic music of the multiples of 53edo- and that includes 159edo itself.

=== Chords and Scales ===

For purposes of this section we shall assume the tonic to be D-natural as in the chart above.

For purposes of this section we shall assume the tonic to be D-natural as in the interval chart above.

==== Ionian and Major ====

This mode- along the corresponding tonality- is optimized for 5-limit using a variation on the Didymian diatonic scale.

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 == 5-limit diatonic music ==
-Although 159edo inherits [[53edo]]'s close approximations of both the [[5-limit]] Zarlino scale and the [[3-limit]] [[diatonic]] MOS, these are not the only scales that one can use for fixed-pitch diatonic music.  In fact, both of them are less than optimal for traditional Western classical music in this system, seeing as for the most part, each of the traditional diatonic modes has its own optimized scale in the 5-limit, with only Lydian and Locrian actually sharing the traditional Zarlino scale for their optimized 5-limit scale.  The reason for this is that in non-meantone 5-limit systems such as 159edo, one inevitably has to deal with the ~40/27 wolf fifth and the ~27/20 wolf fourth, and there's only two ideal positions in the scale for those intervals to be situated in fixed-pitch diatonic music. For major modes, the ~27/20 wolf fourth is ideally situated between the ~5/4 major third and the ~27/16 major sixth, while for the minor modes and the diatonic blighted mode Locrian, the ~40/27 wolf fifth is ideally situated between the ~6/5 minor third and the ~16/9 minor seventh.  Not only that, but it also pays to distinguish the Pythagorean major and minor thirds from their Ptolemaic counterparts as both types of major and minor third have distinct roles to play in the 5-limit diatonic music of the multiples of 53edo- and that includes 159edo itself.  For the rest of this section, I'll be listing the optimized scales for 5-limit diatonic music as well as the necessary chords used by these systems.
+Although 159edo inherits [[53edo]]'s close approximations of both the [[5-limit]] Zarlino scale and the [[3-limit]] [[diatonic]] MOS, these are not the only scales that one can use for fixed-pitch diatonic music.  In fact, both of them are less than optimal for many facets of traditional Western classical music in this system, seeing as for the most part, each of the traditional diatonic modes has its own optimized scale in the 5-limit.  The reason for this is that in non-meantone 5-limit systems such as 159edo, one inevitably has to deal with the ~[[40/27]] wolf fifth and the ~[[27/20]] wolf fourth, and there's only two ideal positions in the scale for those intervals to be situated in fixed-pitch diatonic music. For major modes, the ~27/20 wolf fourth is ideally situated between the ~[[5/4]] major third and the ~[[27/16]] major sixth, while for the minor modes and the diatonic blighted mode Locrian, the ~40/27 wolf fifth is ideally situated between the ~[[6/5]] minor third and the ~[[16/9]] minor seventh.  Not only that, but it also pays to distinguish the Pythagorean major and minor thirds from their Ptolemaic counterparts as both types of major and minor third have distinct roles to play in the 5-limit diatonic music of the multiples of 53edo- and that includes 159edo itself.
 === Chords and Scales ===
-For purposes of this section we shall assume the tonic to be D-natural as in the chart above.
+For purposes of this section we shall assume the tonic to be D-natural as in the interval chart above.
 ==== Ionian and Major ====
+This mode- along the corresponding tonality- is optimized for 5-limit using a variation on the Didymian diatonic scale.