Yahoo Tuning Groups Ultimate Backup tuning LucyTuned 13 Tetrads as listed by Gene Wizard Smith

I've been playing with Gene Ward Smith's tetrads

You can hear how all 13 of them sound in order at:

http://www.lucytune.com/mp3/All13Chords.mp3

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.

Charles Lucy - lucy@harmonics.com
------------ Promoting global harmony through LucyTuning -------
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Gene and Charles,

Thanks to both of you, we now have yet another useful
and factual musical resource. More power to your arms!

Regards,
Yahya

-----Original Message-----
________________________________________________________________________
Date: Wed, 27 Apr 2005 02:38:46 +0100
From: Charles Lucy <lucy@...>
Subject: LucyTuned 13 Tetrads as listed by Gene Wizard Smith