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

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 While large EDOs like [[159edo]] have a bit of a learning curve compared to smaller systems, the fact that this system sports not only consistency to the [[17-odd-limit]], but also both additional options for imitating the pitch-hue palettes of smaller tuning systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, and, the ability to perform sophisticated harmonic and melodic maneuvers that involve substituting intervals that are one or two steps away from the equivalents of traditional musical intervals in such a way as to fly under the radar of many listeners, all while having a step size that is above the average listener's melodic [[JND]], makes this system well worth the price of admission- particularly for those who can use or make synthesizers and other digital-system-based instruments.
-== 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.
 == Intervals and Notation ==
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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.
 === Chords and Scales ===