There are some powerful arguments for using perfect 3:1. Because ET fifths (and twelfths) are contracted, but pianos need stretch, the perfect 3:1 brings these two factors into alignment -- the beating twelfths become beatless and the resulting stretch handles the inharmonicity of the octaves. All Baldassin's work is about aligning harmonics -- we generally hear the 3rd partial pretty strongly, and if it's perfect that can make for a very nice tuning. Look in the archives for P12. Jason <div>On 3/25/07, Andrew and Rebeca Anderson <<a href="mailto:anrebe@sbcglobal.net">anrebe@sbcglobal.net</a>> wrote:<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"> Ron Koval's One for All style for the Verituner got me to tinkering with my unit.  His style is a nice very clean (no stretch) tuning that works well on small instruments and is acceptable for most situations although you may want more stretch in concert halls. I got Rick Baldassin's book, "On Pitch", out and started tinkering with a tuning to use on the concert instruments I maintain (selecting style points in the compass related to usual scaling breaks).  The choice of octaves at each style point is limited on the Verituner by the area you are at on the piano.  From the mid-range up there is the choice of the 3:1 12th.  I'm curious how that compares a-la Baldassin's discussion style with other octaves.  This choice isn't mentioned in his book and I'm not sure that I understand it correctly. By the way doing this has made the tunings come out much more like my studied aural tunings and cleaned up the low tenor on the concert grands a lot.  The stock tuning styles have very few check points and a single octave choice per point resulting in very little octave choice being accessed by the computer. Any comments or explication welcome. Andrew Anderson </blockquote></div> -- =jason's cell 425 830 1561=