Error in Stretch Methods

I have developed what I believe to be a very accurate method of producing consistent stretch that creates pure P11/P12/P22 and even P19 if we are tuning a Small Scale piano. (Small Scale pianos are pianos whose F3F43 and A3A4 octaves can be tuned to a pure 4:2 and a pure 6:3 simultaneously.) But this beat speed window method can't be used in the extremes because the beats are too fast (treble) or too slow (bass), so I use a different, less accurate/precise method. For the treble I just listen to the P8 (octave), P12 (octave plus fifth) and P22 (triple octave) below and try to get them to sound as clean as possible. For the bass, I listen to what Virgil Smith called, "The Natural Beat". There's no good science to prove that when playing a bass octave, there is a beat produced at the fundamental of the bottom note if the octave is not clean, but that's what Virgil said he did, and that's what I do. If this method is not as accurate or precise as the beat speed window method, I still think it is appropriate because the error is so small. For example, consider the Railsback curve, shown below, that shows the sharp treble and flat bass of a piano tuned by a "fine tuner". Now, let's consider that the green line represents the "perfect" stretch, or at least the P12/P22 stretch produced by my beat speed windows. Now let's consider that my stretch method in the extremes, is not as accurate. Once I begin using that method, there will be error. However, if I was to use an inaccurate method from the beginning, like just listening to octaves, the error would start closer to the center, and the accumulated error would be huge once we would get to the extremes. Looking at the above curve reminds me of what my tunings used to sound like before I started using beat speed windows for stretch. I could never get the treble and bass to sound clean enough for my ear.

About the author 

Mark Cerisano, RPT, B.Sc.(Mech.Eng.)

Instructor and Founder, howtotunepianos.com

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