Hi David, Ric. There's not really a link between inharmonicity and loudness. < Agreed. Choices have to be made (hopefully) when rescaling as to a balance between smooth tensions, inharmonicity and loudness (Z factor). Different manufacturers/scalers will choose different criteria to emphasize and different shaped curves to follow. Perfectly smooth curves in all areas are difficult, if not impossible, to achieve. Small jumps between sections are common though the goal of smooth tension, in my view, should trump other factors. < Agreed. Inharmonicity isn't something you really hear though it can, obviously, effect how a piano tunes. < Here I don't agree. A single note with too much inharmonicity will sound awful, being itself way false with itself. You hear that clearly on bass notes of small pianos. With too low inharmonicity, a single note would loose the "piano sound" characteristic, to get closer to the organ or flute sound, which is ugly in a piano. Changes in tension and overall tension levels have a definite impact on aural perception. < Sure, but in my world, more tension means less sustain and less inharmonicity (and a harder touch feel at the key). All of these could not be a good thing. I'm not sure yet about the loudness factor. I find inconsistencies in the numerical data and my perceptions. Soundboard and bridge design, of course, will interplay with scaling for overall impact and certain perceptual details. < Sure. But when I meant projection, I didn't mean loudness. You have pianos that sound very loud at 1 or 2 meters around them, but the loudness decreases rapidly with the distance. Others (I have a particular and amazing straight strung 1873 Bechstein in mind) seem to have some obscure acoustic feature that makes them carry their sound way farther effortless, a bit like some venues acoustics (I think of the Concertgebouw in Amsterdam, Netherlands, here) where at the very back of the place, you still hear the tongues in the throats of the singers. I believe this has to do with inharmonicity, not only with loudness. Harmonic sounds can (do) cancel each other. What do you think ? Stéphane Collin.
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