One more 12-tone tuning . . .

[Richard Moody]

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> From: Paul H. Erlich <PErlich@acadian-asset.com>
> Date: Wednesday, September 01, 1999 1:44 PM
> 
> . . . or rather two varieties of one, should be mentioned. It was discovered
> by Dave Keenan and has six nearly just 7-limit tetrads, i.e., three 4:5:6:7
> chords and three 1/7:1/6:1/5:1/4 chords. 
> 
> In the second version, the same chords have a maximum deviation under 2
> cents! It is tuned with the following deviations from 12-tET:
> 
> C    0.0
> Db  15.6
> D    0.1
> D# -31.2
> E  -15.6
> F    0.0
> F# -15.6
> G    0.0
> Ab  15.6
> A  -15.6
> A# -31.2
> B  -15.6
> 
> But that introduces a wolf fifth D-A, and the minor thirds D-F and F#-A are
> as in 12-equal, so you lose the nice diatonic scales of the meantone
> temperament.

Running the numbers above through my "Beat Sheet"  (spread sheet to calculate beats
from cents) shows 4 wolf Fifths between A3 and A4  from 8 to 18 bps, two beating
flat instead of sharp.  There are 7 Thirds under 2.5 bps but they are all narrow. 
Others are aboove 30 bps.  The minor thirds are 4 under 1bps and the rest range from
16-45 bps.  Almost fast enough for the beat frequencies to have their own tones. 
Perhaps they do in the next octave.  ---ric