Pinetone: Difference between revisions
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Also of interest are the quartal triads of the Pinetone diatonic. We describe these as stacked 3-step intervals (fourths) of the scale, with major and minor designating the large and small 3-step intervals (fourths) respectively. This may seem an odd way to describe quartal chords, but it is consistent with the naming scheme I introduce for the Porcupine[7] 3-step (quartal) triads along side the quartal triads of the Pinetone diatonic. | Also of interest are the quartal triads of the Pinetone diatonic. We describe these as stacked 3-step intervals (fourths) of the scale, with major and minor designating the large and small 3-step intervals (fourths) respectively. This may seem an odd way to describe quartal chords, but it is consistent with the naming scheme I introduce for the Porcupine[7] 3-step (quartal) triads along side the quartal triads of the Pinetone diatonic. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Table 2.9. 3-step stacked triads of the Ptolemismic Pinetone diatonic | |+Table 2.9. 3-step stacked triads of the Ptolemismic Pinetone diatonic in D (dorian symmetric minor) | ||
!Root note | !Root note | ||
!Triad notes | !Triad notes | ||
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We can see that compared to tertian (2-step stacked) chords, quartal (3-step stacked) chords are much more evenly spread in the Pinetone diatonic. 3-step pentads ala the quartal voicings of modern jazz harmony may also be of interest. Two octaves are spanned by four 3-step intervals and a 2-step remainder. Given that Pinetone cannot be generated by 4/3 perfect fourths like Meantone can these pentads have much more variety in Pinetone than in Meantone. As in modern jazz, variety is found through utilizing all inversions of the pentad. The root position and 2nd inversion are shown, where the second inversion spans an octave with a symmetric pattern of two 3-step intervals on either side of a 2-step interval. Root position pentads on A and B (2nd inversion on G and A) cover the notes of the [[The Pinetone System#Pinetone pentatonic|Pinetone major and minor pentatonics]] respectively, introduced below. | We can see that compared to tertian (2-step stacked) chords, quartal (3-step stacked) chords are much more evenly spread in the Pinetone diatonic. 3-step pentads ala the quartal voicings of modern jazz harmony may also be of interest. Two octaves are spanned by four 3-step intervals and a 2-step remainder. Given that Pinetone cannot be generated by 4/3 perfect fourths like Meantone can these pentads have much more variety in Pinetone than in Meantone. As in modern jazz, variety is found through utilizing all inversions of the pentad. The root position and 2nd inversion are shown, where the second inversion spans an octave with a symmetric pattern of two 3-step intervals on either side of a 2-step interval. Root position pentads on A and B (2nd inversion on G and A) cover the notes of the [[The Pinetone System#Pinetone pentatonic|Pinetone major and minor pentatonics]] respectively, introduced below. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Table 2.10. 3-step stacked pentads of the Ptolemismic Pinetone diatonic | |+Table 2.10. 3-step stacked pentads of the Ptolemismic Pinetone diatonic in D | ||
!Root note | !Root note | ||
!Notes | !Notes | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+Table 2.11. 2nd inversion (symmetric) 3-step stacked pentads of the Ptolemismic Pinetone diatonic | |+Table 2.11. 2nd inversion (symmetric) 3-step stacked pentads of the Ptolemismic Pinetone diatonic in D | ||
!Root note | !Root note | ||
!Notes | !Notes | ||