Joe, this is what you're saying, yes? The warbling remains a constant, regardless of the force applied, but soft blows make it less evident? That's been my understanding.

(My piano does often shudder when I play. In fact, I think it shudders at the mere thought of my sitting down to play.)

Hello Jake,

Your understanding is correct in the way that you described it:  The warbling remains constant, regardless of force applied to the copper-wound string, because the warbling is a function of pitch frequency.  Soft blows makes it seem less evident, simply because the softer blow is quieter.

Personally, all of these previous discussions highlighted the differences between physics and metaphysics, in that physics involves planned experimentation, while metaphysics involves navel-gazing and little else.

Cheers,

Joe

Joe, this is what you're saying, yes? The warbling remains a constant, regardless of the force applied, but soft blows make it less evident? That's been my understanding.

(My piano does often shudder when I play. In fact, I think it shudders at the mere thought of my sitting down to play.) 

An aside: The original subject of that thread was how to tune CHAS. I've stayed away from the entire argument over CHAS for several months, now. Reading through that thread, I'm surprised to see many people who were vehemently opposed to the temperament now discussing it placidly. Apparently the winds have shifted a bit as the discussion has moved away from discussing Alfredo's theory and towards the practical application of his temperament and tuning, seen as a variation of ET.

As a piano tuner, myself, who was born with absolute pitch, please allow me to chime in on this subject:

The nature of inharmonicity (defined as a vibrating string's naturally occurring overtones becoming pitched sharper than mathematically predicted -- because the very ends of the strings are constrained and not allowed to vibrate freely) has to do with the pitch(es) of the overtones that shift upward, rather than the volume(s) of the same overtones generated by the same string -- independently of how loudly or softly the string is played.  It is because the constrained ends don't vibrate as freely, that they "force" the string's vibrational nodes, and therefore their harmonics, to behave as though the string was shorter, i.e., the pitches of the highest audible harmonics have been shifted upward.  EDIT:  Upon reviewing this statement in my mind, I would agree that an extremely pounded string might be over excited to the point that the harmonics might change -- but I also suspect that such pounding would have to be SO extreme that it would break the string before any change in harmonics' pitches be detected by human hearing.  END EDIT

By definition, the copper-wound steel strings comprise the longer of any given piano's steel strings, which generates the lowest amount of inharmonicity for any given piano.  Now, combine this with the fact that the very ends of the copper-wound strings are much, much thinner because the copper winding does not extend to the very ends of the steel-exposed strings.

* * * * *

As a tuner who has worked on several hundreds of pianos over the past four+ decades, and multiple times of those same pianos because of repeat business, I tune the lowest strings to minimize the amount of destructive pitch interference (i.e., warbling) of the fundamental tones with their one- and two- and sometimes three-octave counterparts.   Aside: One good trick is to lift your left knee, such that it contacts the piano's case (just below the keyboard bed) while you are tuning the very lowest octave of any piano.  Why?  This is because your nervous system is able to "feel" vibrations when the fundamental pitch and second harmonic ... no longer "warbles" with it's next-octave partner.  When the piano's lowest octave is out of tune, the piano's case literally shudders. (This knee trick works only for the lowest octave, because the number of undulations is low, and the longest, heaviest copper-wound strings are the most energetic and move the piano the most.)* 

Incidentally, when tuning the octaves in the piano's midrange, a piano tuner's hand can feel the fast vibrations of strings that are not perfectly tuned with one another:  the handle of the tuning hammer/wrench is perceived as buzzing or lightly vibrating until such time that the tuning becomes correct.  I believe that many blind piano tuners, whose finger sensitivities are especially acute due to their ability to read Braille, will concur with this notion.

Cheers,

Joe

*  If you wish to hear a smaller version of the shuddering for yourself, simply listen to the way your piano shudders in the penultimate measure of J.S. Bach's Prelude #1 in C Major from Book I of the Well-Tempered Clavier.  (C2 clashes with the next-higher B2, in a diatonic interval of a major seventh.)

My thought is of course transparent--people sometimes want a  more "dramatic" attack on hard strikes in Pianoteq instruments. Could an increased iH on strong blows contribute to a more forceful-sounding attack? Or is some of that already going on?

EDIT: Kees, another long-time tuner who writes often in the PW forum, has weighed in to say that force does not affect iH, which was my understanding as well. We'll have to wait for Olek to reply. I don't think I misunderstood him. He wrote "It is explained that the iH of wound strings is modified depending of the force of the stroke. I play them lightly and pluck them (impact lightly with something hard) to hear less modified partial series." English is not his native language. I assume he means "It is understood that," or "It is expected that..." Not something he would say without reason, however. He's tuned for many decades and has a repair shop in Paris that works on a wide variety of old instruments.