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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