I've been off the grid for the Holiday weekend and apparently have some clarifying to do so here it goes... There have been three attempts to the best of my knowledge to formulate inharmonicity; by Jim Hayes, Dave Roberts and Dr. Al Sanderson. Although imperfect, I believe the point was certainly to demonstrate the deviation of a specific partial, typically the fourth, from the mathematical ideal to a practical application as a result of stiffness, as defined by a function of the wire length, material and tension. Yes, this is only one indicator and is not independent. In analyzing or designing scales, we have the properties of a scale that we can manipulate, namely the wire material, core diameter, and length as well as the wrap material, type and diameter and the various wound string inharmonicity controls such as the bare length, steps and types of whippings. Then we have the results or qualities that are a result of these scale properties. Inharmonicity, tension, breaking %, Z, and hammer to string contact time are ones that have been traditionally examined, but do not by any means encompass the whole picture. As for inharmonicity, while it is my belief that there will be future improvements to this formula; for now it is still worthwhile that we continue to examine it rather than discard it altogether. As mentioned, managing inharmonicity is important for smoothing the transition over breaks, but I also think you can hear the results of the proper management of inharmonicity through reconciling beat rates within a tuning. I standby my statement that there are practical ranges for inharmonicity, although I hope that it is clear that this is indeed a by-product of other considerations. My order of priorities is tension, inharmonicity, acoustical power, than breaking % so long as it remains in a practical limit. I'll see if I can find out more about the scale of the "zero inharm bass strings" before invoking it again; but let's face it, it's better to get this stuff out into the light rather than suppressing it altogether. Finally, I do apologize if my reference to "string theory" in quantum mechanics was perceived as misdirection. I was just being punny. Jude Reveley, RPT Absolute Piano Restoration, LLC Lowell, Massachusetts (978) 323-4545
This PTG archive page provided courtesy of Moy Piano Service, LLC