pianotech-digest V2002 #200

[Paul N. Bailey]

""Subject: Re: Jon's temperament adventure

''Paul:

''I'm not sure I understand this chart.  Does that mean that the narrowest
""fifth is the Ab-Eb at 1.8c.?

''David Love'''''

Yup, the chart got mangled just enough ya can't understand it unless you
know what it
means ....

So I tried to copy just the part about the fifths, and it still isn't
really clear, but

The column furthest left (with all the -1.5's (and -1.455's) and occasional
-3.5's (and
occasional -3.455's) tells how many cents narrow of just (exactly 3/2
ratio) the fifths
are.  The middle column tells the beats per second, and the right column is
the note names,
with an occasional number added to tell which octave you're in.

This temperament has 9 fifths about 1/2 cent smaller than ET fifths, and 3
fifths about 1 and
1/2 cents larger than ET fifths, and 9 times 1/2  =  3 times 3/2, so there
you are.
                
                
-1.5    0.9     f4
-1.5    0.8     e
-1.5    0.8     Eb
-3.455  1.8     d
-1.5    0.7     c#
-1.455  0.7     c4
-1.455  0.6     b3
-1.5    0.6     a#
-3.455  1.3     a
-1.5    0.5     g#
-3.455  1.2     g
-1.5    0.5     f#
-1.5    0.4     f
-1.5    0.4     e
-1.5    0.4     Eb
-3.5    0.9     d
-1.5    0.3     c#
-1.5    0.3     c3