HT selection (was fortepiano wire)

[Ron Koval]

Jeff wrote:
<snip>
He and I discussed using a historical temperament for this recital.  But
the more we looked into it, the more it seemed like what the composers were 
looking for was closer to equal, so that's what we wound up going with.

I'm beginning to think that the HTs created more of a boundary for
creativity rather than the inspiration for it.  We've tried a couple and
the performers didn't like them at all.
<snip>

Don't give up!  It would help to know what you tried..... most of the 
"Historical" stuff is pretty strong for modern ears. (Toto, I don't think 
we're in Kansas anymore...)  If you have a good ETD, and are willing to try, 
here is a 'safe' route to key color.

I posted awhile back about stumbling onto a variable temperament during some 
spreadsheet trials.  It was developed keeping an eye to minimizing the 
offsets, and keeping a smooth progression through the major thirds, and the 
fifths.  I'll just post some offsets today that can get you started.

First step is the KV 1.9, (Koval Variable 1.9) an equal-temperament 
substitute, safe for all occasions.  The 1.9 relates to the maximum offset 
from equal temperament, which is the offset for C.  Start off by using this 
in practice rooms and for home tunings.  It may be surprising to hear how 
different this tuning will sound from ET with such small offsets!  Instead 
of all major thirds set at 13.7 cents from pure, the thirds will progress 
around the circle of fifths from 11 cents at C, to 16.3 cents at F#, and 
back to 11 cents at C.

C    1.9
C#   -.25
D    .63
D#   1.14
E   -.76
F   1.77
F#  -1.01
G   1.27
G#  .51
A   0
A#   1.58
B   -.95

Feel free to round-off the numbers as your ETD requires, these are 
spreadsheet calculations.

Next stop on this temperament journey will be the KV 3, for a little more 
difference from ET.  Still, nearly "under the radar" for most pianists, the 
thirds range from 9.5 cents to 17.8 cents.

C   3
C#  -.4
D   1
D#  1.8
E  -1.2
F   2.8
F# -1.6
G   2
G#  .8
A    0
A#  2.5
B  -1.5

Our final selection for today will be the KV 4.5, pretty much the strongest 
this temperament will expand to without getting inside-out fifths.  The 
thirds range from 7.4 cents to 19.9 cents.  This is pretty strong, yet still 
less than a Young's temperament with the full 21.5 cent third.

C  4.5
C# -.6
D  1.5
D# 2.7
E   -1.8
F  4.2
F# -2.4
G   3
G#  1.2
A   0
A#  3.75
B  -2.25

Good luck, and feel free to ask more questions!


Ron Koval
Concordia University






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