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Tetrads of meantone

🔗Gene Ward Smith <gwsmith@svpal.org>

4/26/2005 2:02:13 PM

Tetrads of meantone

Here are tetrads of meantone along with 7-limit interpretations.
It would be interesting to know more about when and by whom some of
these were used in common practice harmony.

Dominant seventh C-E-G-Bb 1-5/4-3/2-16/9 = 1-5/4-3/2-9/5

German sixth C-E-G-A# 1-5/4-3/2-7/4 major/otonal tetrad

Swiss sixth C-D#-G-A# 1-7/6-3/2-7/4

French sixth C-E-F#-A# 1-5/4-10/7-7/4

Added sixth C-E-G-A 1-5/4-3/2-5/3

Tristan/half-diminished C-Eb-G-Bbb 1-6/5-3/2-12/7 minor/utonal tetrad

"Mozart tetrad" C-Fb-G-Bb 1-9/7-3/2-9/5 supermajor tetrad

"Subminor tetrad" C-D#-G-A 1-7/6-3/2-5/3 subminor tetrad

Incomplete dominant 9th/minor added sixth C-Eb-G-A 1-6/5-3/2-5/3

Diminished seventh C-Eb-Gb-Bbb, C-Eb-Gb-A, C-Eb-F#--A, C-D#--F#-A

Major seventh C-E-G-B 1-5/4-3/2-15/8

Minor seventh C-Eb-G-Bb 1-6/5-3/2-9/5

"Meanpop sixth" C-Eb-G-A# 1-6/5-3/2-7/4, the (7/4)/(6/5) = 35/24
interval is a meanpop 16/11.