Didymic chords: Difference between revisions

Septimal meantone chords: improve readability. Note the dominant seventh chord doesn't really require septimal meantone. Review the rest and leave only those that require septimal meantone
Readability and note the 5-limit pentad is a pentic scale
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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 with steps of 9/8-4/3-9/8-6/5.
* 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.


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, 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.
* 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.
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== External links ==
== External links ==
* [https://youtu.be/TYhPAbsIqA8 Adam Neely - Benedetti's Puzzle (mathematically impossible music)], a video explanation of the chord
* [https://youtu.be/TYhPAbsIqA8 Adam Neely - Benedetti's Puzzle (mathematically impossible music)], a video explanation of the chord in terms of a [[comma pump]]


[[Category:9-odd-limit]]
[[Category:9-odd-limit]]