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 meantone sus2/6 tetrad: | ||
* 1-9/8-3/2-5/3 | * 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. | ||
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The chord can be extended to a pentad known as the meantone add2/6 pentad: | The chord can be extended to a pentad known as the meantone add2/6 pentad: | ||
* 1-9/8-5/4-3/2-5/3 | * 1-9/8-5/4-3/2-5/3 with steps of 9/8-9/8-6/5-9/8-6/5. | ||
Built on C, it is C-D-E-G-A. | Built on C, it is C-D-E-G-A. | ||
Both chords are palindromic. | Both chords are palindromic. | ||
== Septimal meantone chords == | == Septimal meantone chords == | ||
The dominant seventh chord is an essentially tempered chord in septimal meantone: | The dominant seventh chord is an essentially tempered chord in septimal meantone: | ||
* 1-5/4-3/2-9/5 with steps of 5/4-6/5-6/5-9/8. | |||
Built on G, it is G-B-D-F. | |||
Built on G, it is G-B-D-F. | |||
Its inversion is the half-diminished chord: | Its inversion is the half-diminished chord: | ||
* 1-6/5-10/7-9/5 with steps of 6/5-6/5-5/4-9/8. | |||
Built on B, it is B-D-F-A. | |||
Other tetrads of septimal meantone are | |||
* 1-9/8-5/4-7/5 with steps of 9/8-9/8-9/8-10/7; | |||
* 1-9/8-7/5-14/9 with steps of 9/8-5/4-9/8-9/7; | |||
* 1-9/8-5/4-14/9 with steps of 9/8-9/8-5/4-9/7, and its inverse | |||
* 1-5/4-7/5-14/9 with steps of 5/4-9/8-9/8-9/7. | |||
They can be extended to the following pentads, with two palindromic chords and two pairs of chords in inverse relationship: | |||
* 1-9/8-5/4-3/2-9/5 with steps of 9/8-9/8-6/5-6/5-9/8; | |||
* 1-9/8-5/4-7/5-14/9 with steps of 9/8-9/8-9/8-9/8-9/7; | |||
* 1-9/8-5/4-7/5-7/4 with steps of 9/8-9/8-9/8-5/4-8/7, and its inverse | |||
* 1-5/4-7/5-14/9-7/4 with steps of 5/4-9/8-9/8-9/8-8/7; | |||
* 1-9/8-5/4-14/9-7/4 with steps of 9/8-9/8-5/4-9/8-8/7, and its inverse | |||
* 1-9/8-7/5-14/9-7/4 with steps of 9/8-5/4-9/8-9/8-8/7. | |||
* 1-9/8-5/4-7/5 | Finally, there are a palindromic hexad, | ||
* 1-9/8-5/4-7/5-14/9-7/4 with steps of 9/8-9/8-9/8-9/8-9/8-8/7. | |||
== External links == | == External links == | ||
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[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Pentads]] | [[Category:Pentads]] | ||
[[Category:Hexads]] | |||
[[Category:Meantone]] | [[Category:Meantone]] | ||