HT selection (was fortepiano wire)

Avery Todd atodd@UH.EDU
Wed, 27 Nov 2002 10:44:37 -0600


Ron,

How do the ones you post below compare to the EBVT offsets you posted
a while ago? Just curious.

Avery

>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   0.0
>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   3.0
>C#  -.4
>D   1.0
>D#  1.8
>E  -1.2
>F   2.8
>F# -1.6
>G   2.0
>G#   .8
>A   0.0
>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   3.0
>G#  1.2
>A   0.0
>A#  3.75
>B  -2.25
>
>Good luck, and feel free to ask more questions!
>
>
>Ron Koval
>Concordia University

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