Didymic chords

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 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, 27/20 acute fourth, a 40/27 grave fifth, or, an 81/64 major third.

The chord can be extended to a pentad known as the meantone add2/6 pentad:

• 1-9/8-5/4-3/2-5/3, with steps 9/8-9/8-6/5-9/8-6/5

Built on C, it is C-D-E-G-A.

Both chords are palindromic.

Septimal meantone chords

The dominant seventh chord is an essentially tempered chord in septimal meantone:

• 1-5/4-3/2-9/5, with steps 5/4-6/5-6/5-9/8

Built on G, it is G-B-D-F.

Its inversion is the half-diminished chord:

• 1-6/5-10/7-9/5, with steps 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 9/8-9/8-9/8-10/7
• 1-9/8-5/4-14/9, with steps 9/8-9/8-5/4-9/7
• 1-5/4-7/5-14/9, with steps 5/4-9/8-9/8-9/7
• 1-9/8-7/5-14/9, with steps 9/8-5/4-9/8-9/7

External links

• Adam Neely - Benedetti's Puzzle (mathematically impossible music), a video explanation of the chord