I came across this thread in the Audiobus forum. Thanks for posting it Mike - it sounds great. The MuseScore developers are apparently adding the StaffPad interpretation engine into MuseScore as a free plugin. Also, there are some complaints that no new third party libraries have been released for StaffPad since its acquisition by Muse Group. Unfortunately the engraving is not so strong in StaffPad from what I have seen and heard from others, and there is a lot of frustration when using the pencil for more complicated passages. If those same vendors made customized versions of their libraries for Dorico for iPad, it would certainly make them sound much better, but without Dorico itself doing some kind of read-ahead to shape the phrase there would be a lot missing in terms of expressiveness. I would imagine it does some kind of read-ahead for interpretation like what NotePerformer does, coupled with special versions of the sample libraries that are configured for proper orchestral balance with the dynamic response curve tweaked to match the dynamic mappings that StaffPad uses. I have heard many demos just like this one and all are quite impressive, even the built in library is very good. In the same way, playing a major chord sort of implies a bass note a couple octaves below the root of the chord - if all the harmonics are there, then we expect it to be there.Yes, StaffPad is well known for its very strong playback. If you filter them out, the notes will sound about the same - we take most of our perceptual cues from the higher harmonics, and our brain just inserts the implied bass fundamental.
Interestingly, we don't really perceive the fundamental frequencies of the low notes in a piano much at all in the first place. Having a super long bass string instead of a short double-wound bass string probably behaves more like an ideal string (with harmonics that are closer to whole-number multiples of the fundamental), so it should sound like it has a more definite pitch and less like a gong. Piano tuners deal with this be stretching the octave, so that the piano sounds in tune even though it kind of isn't. They don't behave like ideal strings for various reasons, so the harmonics aren't exact multiples of the fundamental frequency. In a piano, the bass and treble strings have a lot of inharmonicity. The overtones are the harmonic series, not just octaves (1:2, 1:4, 1:8, etc.) but an octave and a fifth (1:3), two octaves and a third, (1:5), etc. I think the overall effect of stiffness would dominate this one, however.) (I have to admit that the zero-first-derivative boundary condition having no additional effect is coming from my intuitions about linearity of solutions to the wave equation, but maybe it still has some interesting effect. Of course, the pitch of the string also increases with tension, so there's a lot going on. Based on the stress/strain graphs I could find, Young's modulus of a guitar string increases with tension, increasing inharmonicity. In the wave equation, stiffness involves a factor with a coefficient proportional to Young's modulus. (Though, through time in a frequency-dependent way.) But, even when plucking a string, rather than having a sharp peak at the plectrum, it will necessarily be similarly smoothed out. So, this radius of curvature will be visible there. The boundary condition of a guitar string is that the displacement and first derivative of displacement of the string are zero at both ends. Stiffness causes there to basically be a radius of curvature in the string when you apply a force. My understanding is that this bridge effect is actually what is happening across the entire length of the string it's just that the boundary condition makes the effects of stiffness clearer.
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