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

Line 31:

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

While most microtonalists are keenly aware of the power of small rational intervals between notes, they don't seem to be as aware of some of the implications of such power- namely the implication that when such intervals exist between the wrong two notes in the scale, they can ~~destroy a sense of tonality~~. Think of it like this- frequency resonance between structures and the wind can wreak havoc, as was the case with [[Wikipedia:Tacoma Narrows Bridge (1940)|the original Tacoma Narrows Bridge]]. ~~Since Tonality~~ is based on frequency ~~resonance~~, it stands to reason that ~~tonality is~~ subject to that same phenomenon when certain resonances exist between the wrong two notes- from what I'm hearing from others, this "resonance in the wrong place" can lead to a sense of disorientation, and while this can indeed be exploited musically, there are times when such a sense of disorientation is not good, because it doesn't fit what one is trying to convey through the music.

While most microtonalists are keenly aware of the power of small rational intervals between notes, they don't seem to be as aware of some of the implications of such power- namely the implication that when such intervals exist between the wrong two notes in the scale, they can undermine tonal stability. Think of it like this- frequency resonance between structures and the wind can wreak havoc, as was the case with [[Wikipedia:Tacoma Narrows Bridge (1940)|the original Tacoma Narrows Bridge]]. Even though tonality is largely based on musical context, this context in part shaped by low-complexity frequency resonances. Thus, it stands to reason that tonal systems are subject to that same phenomenon when certain resonances exist between the wrong two notes- from what I'm hearing from others, this "resonance in the wrong place" can lead to a sense of disorientation, and while this can indeed be exploited musically, there are times when such a sense of disorientation is not good, because it doesn't fit what one is trying to convey through the music.

Take for example the 5/3 Major 6th- 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 3/2 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.

Take for example the 5/3 Major 6th- 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 3/2 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 difference-tone-based 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]]

@@ Line 31: / Line 31: @@
 == Why 27/16 instead of 5/3? ==
-While most microtonalists are keenly aware of the power of small rational intervals between notes, they don't seem to be as aware of some of the implications of such power- namely the implication that when such intervals exist between the wrong two notes in the scale, they can destroy a sense of tonality.  Think of it like this- frequency resonance between structures and the wind can wreak havoc, as was the case with [[Wikipedia:Tacoma Narrows Bridge (1940)|the original Tacoma Narrows Bridge]].   Since Tonality is based on frequency resonance, it stands to reason that tonality is subject to that same phenomenon when certain resonances exist between the wrong two notes- from what I'm hearing from others, this "resonance in the wrong place" can lead to a sense of disorientation, and while this can indeed be exploited musically, there are times when such a sense of disorientation is not good, because it doesn't fit what one is trying to convey through the music.
+While most microtonalists are keenly aware of the power of small rational intervals between notes, they don't seem to be as aware of some of the implications of such power- namely the implication that when such intervals exist between the wrong two notes in the scale, they can undermine tonal stability.  Think of it like this- frequency resonance between structures and the wind can wreak havoc, as was the case with [[Wikipedia:Tacoma Narrows Bridge (1940)|the original Tacoma Narrows Bridge]].   Even though tonality is largely based on musical context, this context in part shaped by low-complexity frequency resonances.  Thus, it stands to reason that tonal systems are subject to that same phenomenon when certain resonances exist between the wrong two notes- from what I'm hearing from others, this "resonance in the wrong place" can lead to a sense of disorientation, and while this can indeed be exploited musically, there are times when such a sense of disorientation is not good, because it doesn't fit what one is trying to convey through the music.
-Take for example the 5/3 Major 6th- 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 3/2 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.
+Take for example the 5/3 Major 6th- 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 3/2 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 difference-tone-based 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]]