Trying to Figure Out Well Temperament, Help!

[arnold1@mindspring.com]

     Since you sent me this message earlier, I have been trying to
figure out how to tune this temperament.  There are some things I
do not understand, which I note in the following part of your
message which I have copied to this one, plus I have come up with
a "version" of my own that I would like you to look at and suggest
changes in; it isn't quite right.

Your version:
1. c1-c0 Descending octave from middle c.
2. c1-f0 Descending pure fifth from middle c. Verify pure fourth
c0-f0.
 3. f0-BbDescendin pure fifth.
4. Bb-bb Transposition by ascending octave. Verify pure fourth f0-
bb0.
 5. bb0-eb0 Descending pure fifth. Verify pure fourth Bb-eb0.
 6. eb0-eb1 Transposition by ascending octave. Verify pure fourth
bb0-eb1.
 7. eb1-ab0 Descending pure fifth. Verify pure fourth eb0-ab0.
 8. g#0-c#0 Descending pure fifth.
9. c#0-c#1 Transposition by ascending octave. Verify pure fourth
g#0-c#1. (Wasn't this done in Step 1?)

 10. c#1-f#0Descending pure fifth, Verify pure fourth c#0-f#0.
(Again, wasn't this done earlier?)

 11. f#0-BWell-tempered fifth. Within the B-major triad the third
B-d#0must beat six times
faster than the fifth B-f#0. (I do not understand this one at all.
There is no such thing as an f0-b fifth.)

12. B-b0 Transposition by ascending octave.
13. b0-e0 Descending pure fifth. Verify pure fourth B-e0.
14. e0-e1 Transposition by ascending octave. Verify pure fourth b0-
e1. 15. c1-g0Well-tempered fifth. flattened. must beat from below
at the same rate as the third c0-e0 beats within the C-major triad.
Beats slightly faster-virtually at the same pace- as the
well-tempered fifth B-f#0 a semitone below. (I thought you had
tuned the c0 g0 fifth earlier. C1-g0 is a fourth.  Obviously, I
don't understand something.

16. g0-d1Well-tempered fifth. Flattened to beat 3/2-times faster
than c0-g0.
17. d1-d0 Transposition by descending octave.
18. d0-a0Well-tempered fifth. Beats hardly faster-virtually at the
same rate- as c0-g0 a whole tone below.
19. a0-e1Check:This must be a well tempered fifth, e1 must not be
changed. Compare beat-rate with g0-d1 a whole tone below.
Play c-e-g and listen to this well-tempered C-major triad which
opens the door to perfoming music in all 24 keys, both
major and minor.

The following is what I figured out.  It is not quite in the same
order as yours, because of the few things I didn't understand.
Also, I changed the names of the notes to be a little more what I
am use to calling them.  Would this work at all?  I did it this way
because I gathered that one is tuning fifths and octives, and
checking them with fourths.  I used the + sign when I am tuning the
note on the top, and the - sign when I am tuning the note on the
bottom.  C1 is middle c, c0 is an octive below it, and there are b
flat and b below c0.

 c1 with fork
 c1-c0 octive
 c1-f0 pure fifth, test c0+f0 forth
f0-b flat (below c0) pure fifth
b flat+b flat0 octive, test f0+b flat pure fourth
b flat0-e flat0 pure fifth, test -b flat+e flat0 fourth
e flat0+e flat 1 octive, test with f0 pure fourth
e flat1-g sharp0 fifth, test with e flat1 fourth
g sharp0-c sharp fifth
c sharp0+c sharp1 octive
c0+g0 fifth, test with g0+c1 fourth
g0+d1 fifth, flattened to beat 3/2 times faster than c0+g0
d1-d0 octive, test d0+g0 fourth
d0+a0 tempered fifth, test a0+d1 fourth
a0+e1 tempered fifth,
e1-e0 octive
c sharp1-f sharp0 fifth
f sharp0-b (below c0) fifth
-b+b0 octive

Finally, let me ask you, who might appreciate this type
temperament?  I would think that classical music as late as
Beethoven, or Chopin would sound great, but how about by the time
one gets to such impressionists as Debussy, and Ravel?  How about,
shall we say, modern popular music, or popular church hymns?  (I am
trying to determine whose piano not to tune this way.)  This is
very interesting to me, and I would like to catch on to it, but I
fear that some would find it quite foreign.  I am trying to cut
down on the number of pianos I might have to retune for free
because they didn't like it.  Thank you very much.








Arnold Schmidt, Raleigh, NC, arnold1@mindspring.com

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