Didymic chords: Difference between revisions

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A '''didymic chord''' is an [[essentially tempered chord]] of 5-limit [[meantone]]. The basic form of a didymic chord is the meantone sus2/6 tetrad:

A '''didymic chord''' is an [[essentially tempered chord]] of 5-limit [[meantone]]. The basic form of a didymic chord is the palindromic meantone sus2/6 tetrad:

* 1–9/8–3/2–5/3 with steps of 9/8, 4/3, 9/8, 6/5.

Every interval is an element of the [[9-odd-limit]]. In diatonic, it can be notated as C–D–G–A when built on C. The tempered essence explains why the common chord progression vi–ii–V–I does not work outside meantone unless one accepts a [[27/16]] major sixth, a [[27/20]] acute fourth, or a [[40/27]] grave fifth.

Every interval is an element of the [[9-odd-limit]]. In diatonic, it can be notated as C–D–G–A when built on C. The tempered essence explains why the common chord progression vi–ii–V–I does not work outside meantone unless one accepts a [[27/16]] major sixth, a [[27/20]] acute fourth, or a [[40/27]] grave fifth. It makes for an interesting comparison with the [[archytas chords|archy sus4/7]] chord.

The chord can be extended to a pentad known as the meantone add2/6 pentad, which also happens to be the [[2L 3s|pentic]] scale [[meantone5|Meantone[5]]]:

The chord can be extended to a palindromic pentad known as the meantone add2/6 pentad, which also happens to be the [[2L 3s|pentic]] scale [[meantone5|Meantone[5]]]:

* 1–9/8–5/4–3/2–5/3 with steps of 9/8, 9/8, 6/5, 9/8, 6/5.

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Built on C, it is C–D–E–G–A.

~~Both chords are palindromic~~.

There is also a didymic tetrad involving [[prime interval|prime]] [[7/1|7]]:

* 1–9/8–9/7–10/7 with steps 9/8, 8/7, 9/8, 7/5.

== Dominant seventh chord ==

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-A '''didymic chord''' is an [[essentially tempered chord]] of 5-limit [[meantone]]. The basic form of a didymic chord is the meantone sus2/6 tetrad:
+A '''didymic chord''' is an [[essentially tempered chord]] of 5-limit [[meantone]]. The basic form of a didymic chord is the palindromic meantone sus2/6 tetrad:
 * 1–9/8–3/2–5/3 with steps of 9/8, 4/3, 9/8, 6/5.
-Every interval is an element of the [[9-odd-limit]]. In diatonic, it can be notated as C–D–G–A when built on C. The tempered essence explains why the common chord progression vi–ii–V–I does not work outside meantone unless one accepts a [[27/16]] major sixth, a [[27/20]] acute fourth, or a [[40/27]] grave fifth.
+Every interval is an element of the [[9-odd-limit]]. In diatonic, it can be notated as C–D–G–A when built on C. The tempered essence explains why the common chord progression vi–ii–V–I does not work outside meantone unless one accepts a [[27/16]] major sixth, a [[27/20]] acute fourth, or a [[40/27]] grave fifth. It makes for an interesting comparison with the [[archytas chords|archy sus4/7]] chord.
-The chord can be extended to a pentad known as the meantone add2/6 pentad, which also happens to be the [[2L 3s|pentic]] scale [[meantone5|Meantone[5]]]:
+The chord can be extended to a palindromic pentad known as the meantone add2/6 pentad, which also happens to be the [[2L 3s|pentic]] scale [[meantone5|Meantone[5]]]:
 * 1–9/8–5/4–3/2–5/3 with steps of 9/8, 9/8, 6/5, 9/8, 6/5.
@@ Line 11: / Line 11: @@
 Built on C, it is C–D–E–G–A.
-Both chords are palindromic.
+There is also a didymic tetrad involving [[prime interval|prime]] [[7/1|7]]:
+* 1–9/8–9/7–10/7 with steps 9/8, 8/7, 9/8, 7/5.
 == Dominant seventh chord ==