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

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

While the 5/3 Major 6th is the traditional Contramediant, the note at 5/3 away from the Tonic forms a wolf fifth with a Supertonic at 9/8 away from the Tonic. This is not a good position for a wolf fifth as the resulting Perfect 5th between the Contramediant and the Mediant can lend itself to the tonicization of the Contramediant ~~itself~~ where one might otherwise want a clear sense that "we're not done yet"- a weakness of Ptolemy's Intense Diatonic Scale, and a persistent weakness of the traditional 12edo major scale. Furthermore, the note at 5/3 away from the Tonic is harmonically disconnected from the Tonic due to not occurring as an interval distance from the Tonic in the Tonic's own harmonic series, or even the Tonic's own subharmonic series. Worse, since a note forming a 5/3 ratio with the Tonic occurs very early in the Serviant's harmonic series, this sort of configuration can very easily result in the tonicization of the Serviant due to a strong virtual fundamental effect that is present even when the Serviant itself is not a direct component of the chord as demonstrated in the audio file below- an even more devastating weaknesses of Ptolemy's Intense Diatonic Scale. Meanwhile, the first chord played in the same audio file uses 27/16 as the Contramediant, and thus has C3 as a virtual fundamental- this gives it a much more stable configuration relative to the Key of C major.

While the 5/3 Major 6th is the traditional Contramediant, the note at 5/3 away from the Tonic forms a wolf fifth with a Supertonic at 9/8 away from the Tonic. This is not a good position for a wolf fifth as the resulting Perfect 5th between the Contramediant and the Mediant can lend itself to the tonicization of the Contramediant where one might otherwise want a clear sense that "we're not done yet"- a weakness of Ptolemy's Intense Diatonic Scale, and a persistent weakness of the traditional 12edo major scale. Furthermore, the note at 5/3 away from the Tonic is harmonically disconnected from the Tonic due to not occurring as an interval distance from the Tonic in the Tonic's own harmonic series, or even the Tonic's own subharmonic series. Worse, since a note forming a 5/3 ratio with the Tonic occurs very early in the Serviant's harmonic series, this sort of configuration can very easily result in the tonicization of the Serviant due to a strong virtual fundamental effect that is present even when the Serviant itself is not a direct component of the chord as demonstrated in the audio file below- an even more devastating weaknesses of Ptolemy's Intense Diatonic Scale. Meanwhile, the first chord played in the same audio file uses 27/16 as the Contramediant, and thus has C3 as a virtual fundamental- this gives it a much more stable configuration relative to the Key of C major.

[[File:Interval_Test.mp3|thumb|none|First chord: CM6 as 1/1-5/4-3/2-27/16 <br> Second chord: CM6 as 1/1-5/4-3/2-5/3]]

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 == Why 27/16 instead of 5/3? ==
-While the 5/3 Major 6th is the traditional Contramediant, the note at 5/3 away from the Tonic forms a wolf fifth with a Supertonic at 9/8 away from the Tonic.  This is not a good position for a wolf fifth as the resulting Perfect 5th between the Contramediant and the Mediant can lend itself to the tonicization of the Contramediant itself where one might otherwise want a clear sense that "we're not done yet"- a weakness of Ptolemy's Intense Diatonic Scale, and a persistent weakness of the traditional 12edo major scale.  Furthermore, the note at 5/3 away from the Tonic is harmonically disconnected from the Tonic due to not occurring as an interval distance from the Tonic in the Tonic's own harmonic series, or even the Tonic's own subharmonic series.  Worse, since a note forming a 5/3 ratio with the Tonic occurs very early in the Serviant's harmonic series, this sort of configuration can very easily result in the tonicization of the Serviant due to a strong virtual fundamental effect that is present even when the Serviant itself is not a direct component of the chord as demonstrated in the audio file below- an even more devastating weaknesses of Ptolemy's Intense Diatonic Scale.  Meanwhile, the first chord played in the same audio file uses 27/16 as the Contramediant, and thus has C3 as a virtual fundamental- this gives it a much more stable configuration relative to the Key of C major.
+While the 5/3 Major 6th is the traditional Contramediant, the note at 5/3 away from the Tonic forms a wolf fifth with a Supertonic at 9/8 away from the Tonic.  This is not a good position for a wolf fifth as the resulting Perfect 5th between the Contramediant and the Mediant can lend itself to the tonicization of the Contramediant where one might otherwise want a clear sense that "we're not done yet"- a weakness of Ptolemy's Intense Diatonic Scale, and a persistent weakness of the traditional 12edo major scale.  Furthermore, the note at 5/3 away from the Tonic is harmonically disconnected from the Tonic due to not occurring as an interval distance from the Tonic in the Tonic's own harmonic series, or even the Tonic's own subharmonic series.  Worse, since a note forming a 5/3 ratio with the Tonic occurs very early in the Serviant's harmonic series, this sort of configuration can very easily result in the tonicization of the Serviant due to a strong virtual fundamental effect that is present even when the Serviant itself is not a direct component of the chord as demonstrated in the audio file below- an even more devastating weaknesses of Ptolemy's Intense Diatonic Scale.  Meanwhile, the first chord played in the same audio file uses 27/16 as the Contramediant, and thus has C3 as a virtual fundamental- this gives it a much more stable configuration relative to the Key of C major.
 [[File:Interval_Test.mp3|thumb|none|First chord: CM6 as 1/1-5/4-3/2-27/16 <br> Second chord: CM6 as 1/1-5/4-3/2-5/3]]