Pinetone: Difference between revisions

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-==== Quartal Triads ====
+==== Quartal Chords ====
 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.
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 |sus ♯4 minor major
 |6:8:11
+|}
+-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.
+{| class="wikitable"
+|+3-step stacked pentads of the Pinetone diatonic on D
+!Root note
+!Notes
+!Meantone intervals
+!Porcupine intervals
+!Pinetone intervals
+!JI Intervals
+!JI chord approximated by triad
+|-
+!D
+|D-G-C-F-B
+|P4, P4, P4, A4
+|m4, M4, m4, M4
+|m4, Mm4, m4, M4
+|4/3, 27/20, 4/3, 11/8
+|30:40:54:72:99
+|-
+!E
+|E-A-D-G-C
+|P4, P4, P4, P4
+|M4, m4, m4, M4
+|Mm4, m4, m4, Mm4
+|27/20, 4/3, 4/3, 11/8
+|20:27:36:48:66
+|-
+!F
+|F-B-E-A-D
+|A4, P4, P4, P4
+|M4, m4, M4, m4
+|M4, m4, Mm4, m4
+|11/8, 4/3, 15/11, 4/3
+|24:33:44:60:80
+|-
+!G
+|G-C-F-B-E
+|P4, P4, A4, P4
+|M4, m4, M4, m4
+|Mm4, m4, M4, m4
+|27/20, 4/3, 11/8, 4/3
+|40:54:72:99:132
+|-
+!A
+|A-D-G-C-F
+|P4, P4, P4, P4
+|m4, m4, M4, m4
+|m4, m4, Mm4, m4
+|4/3, 4/3, 27/20, 4/3
+|45:60:80:108:144
+|-
+!B
+|B-E-A-D-G
+|P4, P4, P4, P4
+|m4, M4, m4, m4
+|m4, Mm4, m4, m4
+|4/3, 27/20, 4/3, 4/3
+|15:20:27:36:48
+|-
+!C
+|C-F-B-E-A
+|P4, A4, P4, P4
+|m4, M4, m4, M4
+|m4, M4, m4, Mm4
+|4/3, 11/8, 4/3, 15/11
+|18:24:33:44:60
 |}