User:Aura/Aura's Diatonic Scales: Difference between revisions

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== Introduction ==

Just about every non-microtonal musician these days is acquainted with the 12edo ~~diatonic~~ scale. Some may also know the ~~diatonic~~ modes- Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. However in higher EDOs, as well as in Just Intonation, things are a little different. To start with, there are two well-known tunings for diatonic scales: the Pythagorean Diatonic Scale, and Ptolemy's Intense Diatonic Scale, but the Pythagorean Diatonic Scale is ~~ill-suited for modulation~~, while the selections of notes in Ptolemy's Intense Diatonic Scale is ill-suited for building chords and chord progressions using just the notes in those scales. In both cases, it has been one sort of wolf-fifth or other that has caused problems due to the wolf fifth having a sound other than that of the 3/2 Perfect 5th. For the longest time, these wolf fifths were considered unusable, which is part of what led to the dominance of 12edo in the first place. However, I've found that the 40/27 grave fifth and intervals that approximate it ''are'' in fact usable in chord progressions- assuming that they are positioned correctly within a given just diatonic scale, and I have adopted my own version of a Just Diatonic Scale accordingly. Furthermore, I've found that in retuning the traditional ~~diatonic~~ modes in accordance with their differences from standard Major and Minor, the traditional ~~diatonic~~ modes cease to qualify as modes of the same ~~diatonic~~ scale, and instead give rise to several different ~~diatonic~~ scales of their own, complete with their own modes.

Just about every non-microtonal musician these days is acquainted with the 12edo [[5L 2s|Diatonic]] scale. Some may also know the Diatonic modes- Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. However in higher EDOs, as well as in Just Intonation, things are a little different. To start with, there are two well-known tunings for diatonic scales: the Pythagorean Diatonic Scale, and Ptolemy's Intense Diatonic Scale, but the Pythagorean Diatonic Scale is dissonant, while the selections of notes in Ptolemy's Intense Diatonic Scale is ill-suited for building chords and chord progressions using just the notes in those scales. In both cases, it has been one sort of wolf-fifth or other that has caused problems due to the wolf fifth having a sound other than that of the 3/2 Perfect 5th. For the longest time, these wolf fifths were considered unusable, which is part of what led to the dominance of 12edo in the first place. However, I've found that the 40/27 grave fifth and intervals that approximate it ''are'' in fact usable in chord progressions- assuming that they are positioned correctly within a given just diatonic scale, and I have adopted my own version of a Just Diatonic Scale accordingly. Furthermore, I've found that in retuning the traditional Diatonic modes in accordance with their differences from standard Major and Minor, the traditional Diatonic modes cease to qualify as modes of the same Diatonic scale, and instead give rise to several different Diatonic scales of their own, complete with their own modes.

As a final note, I prefer all the notes of my scales to be related to the ~~tonic~~ by ratios which have a power of 2 in either the numerator or the denominator, and this leads not only to 5/3 getting replaced by 27/16 as the ideal ratio for the Major Sixth scale degree above the Tonic- a change also made in light of my findings on the ideal location for the grave fifth and intervals that approximate it- but also to the substitution of 77/64 for 6/5 for the Minor Third scale degree in cases where I'm not restricted to using just the 3-limit and the 5-limit for defining notes in the diatonic scale. I shall use this page for detailing my findings, as well as to document the modes of the now-separated ~~diatonic~~ scales.

As a final note, I prefer all the notes of my scales to be related to the Tonic by ratios which have a power of 2 in either the numerator or the denominator, and this leads not only to 5/3 getting replaced by 27/16 as the ideal ratio for the Major Sixth scale degree above the Tonic- a change also made in light of my findings on the ideal location for the grave fifth and intervals that approximate it- but also to the substitution of 77/64 for 6/5 for the Minor Third scale degree in cases where I'm not restricted to using just the 3-limit and the 5-limit for defining notes in the diatonic scale. I shall use this page for detailing my findings, as well as to document the modes of the now-separated Diatonic scales.

== Why 27/16 instead of 5/3? ==

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== Diatonic Scales ==

All of the chief ~~diatonic~~ scales listed here are named for their most useful mode.

All of the chief Diatonic scales listed here are named for their most useful mode.

=== Ionian ===

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 == Introduction ==
-Just about every non-microtonal musician these days is acquainted with the 12edo diatonic scale.  Some may also know the diatonic modes- Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian.  However in higher EDOs, as well as in Just Intonation, things are a little different.  To start with, there are two well-known tunings for diatonic scales: the Pythagorean Diatonic Scale, and Ptolemy's Intense Diatonic Scale, but the Pythagorean Diatonic Scale is ill-suited for modulation, while the selections of notes in Ptolemy's Intense Diatonic Scale is ill-suited for building chords and chord progressions using just the notes in those scales.  In both cases, it has been one sort of wolf-fifth or other that has caused problems due to the wolf fifth having a sound other than that of the 3/2 Perfect 5th.  For the longest time, these wolf fifths were considered unusable, which is part of what led to the dominance of 12edo in the first place.  However, I've found that the 40/27 grave fifth and intervals that approximate it ''are'' in fact usable in chord progressions- assuming that they are positioned correctly within a given just diatonic scale, and I have adopted my own version of a Just Diatonic Scale accordingly.  Furthermore, I've found that in retuning the traditional diatonic modes in accordance with their differences from standard Major and Minor, the traditional diatonic modes cease to qualify as modes of the same diatonic scale, and instead give rise to several different diatonic scales of their own, complete with their own modes.
+Just about every non-microtonal musician these days is acquainted with the 12edo [[5L 2s|Diatonic]] scale.  Some may also know the Diatonic modes- Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian.  However in higher EDOs, as well as in Just Intonation, things are a little different.  To start with, there are two well-known tunings for diatonic scales: the Pythagorean Diatonic Scale, and Ptolemy's Intense Diatonic Scale, but the Pythagorean Diatonic Scale is dissonant, while the selections of notes in Ptolemy's Intense Diatonic Scale is ill-suited for building chords and chord progressions using just the notes in those scales.  In both cases, it has been one sort of wolf-fifth or other that has caused problems due to the wolf fifth having a sound other than that of the 3/2 Perfect 5th.  For the longest time, these wolf fifths were considered unusable, which is part of what led to the dominance of 12edo in the first place.  However, I've found that the 40/27 grave fifth and intervals that approximate it ''are'' in fact usable in chord progressions- assuming that they are positioned correctly within a given just diatonic scale, and I have adopted my own version of a Just Diatonic Scale accordingly.  Furthermore, I've found that in retuning the traditional Diatonic modes in accordance with their differences from standard Major and Minor, the traditional Diatonic modes cease to qualify as modes of the same Diatonic scale, and instead give rise to several different Diatonic scales of their own, complete with their own modes.
-As a final note, I prefer all the notes of my scales to be related to the tonic by ratios which have a power of 2 in either the numerator or the denominator, and this leads not only to 5/3 getting replaced by 27/16 as the ideal ratio for the Major Sixth scale degree above the Tonic- a change also made in light of my findings on the ideal location for the grave fifth and intervals that approximate it- but also to the substitution of 77/64 for 6/5 for the Minor Third scale degree in cases where I'm not restricted to using just the 3-limit and the 5-limit for defining notes in the diatonic scale.  I shall use this page for detailing my findings, as well as to document the modes of the now-separated diatonic scales.
+As a final note, I prefer all the notes of my scales to be related to the Tonic by ratios which have a power of 2 in either the numerator or the denominator, and this leads not only to 5/3 getting replaced by 27/16 as the ideal ratio for the Major Sixth scale degree above the Tonic- a change also made in light of my findings on the ideal location for the grave fifth and intervals that approximate it- but also to the substitution of 77/64 for 6/5 for the Minor Third scale degree in cases where I'm not restricted to using just the 3-limit and the 5-limit for defining notes in the diatonic scale.  I shall use this page for detailing my findings, as well as to document the modes of the now-separated Diatonic scales.
 == Why 27/16 instead of 5/3? ==
@@ Line 15: / Line 15: @@
 == Diatonic Scales ==
-All of the chief diatonic scales listed here are named for their most useful mode.
+All of the chief Diatonic scales listed here are named for their most useful mode.
 === Ionian ===