/sci/ - Science & Math

>>11126766
the change between initial and final velocity (acceleration) determines the color, the initial velocity determines the volume
the nail/flesh determines the size of the window of time during which this information is communicated from finger to key, ie determining the total amount of possible variation between V initial and V final. nails are harder and transfer most rapidly the vector information, where as flesh is softer and pliant and requires more time, widening the window, and allowing for greater variation. all of this can be combined, meaning the nail can produce a soft sound, and the flesh a hard one, if the pianist has control of his 3 variables,
>the third one being
altering the angle of attack
and so you have an unbelievably vast range of tonal colors and texture, far more than the 8 for which we have notation, probably in the order of 100s
>when your pianissimo has a bite
all 3 of these combine to allow the pianist access to to the entire range of the pianos tonal colors under any physical conditions. ie polyphony

>>11126766
I made this for another discussion but some of it is relevant to your question.

The sound waves produced by instruments can be expressed as sums of sine waves of varying frequencies, called a superposition of waves. You can change the timbre of the instrument by changing the relative strength of the sines being added, or changing their phase relative to each other.
When you pluck/strike a string you force the string into a particular shape which will have a particular superposition of sine waves, then when you let go those sine waves evolve independently according to the physics of the string and that produces the sound. By changing how the pluck you can change the initial superposition and so you get different sounds. My fav example is plucking a guitar string from the middle and then its end, the difference is obvious and you can hear how plucking at the end requires more high frequency waves.

>>11127820
thanks
I know that sound is a basically a Fourier transform, and I know about overtones and harmonics and resonance, but I'm understanding what you're saying is the timbre is a relation of intensities between the overtones present in the sound?

the guitar model is the significantly simpler model as you're changing directly the material striking the string, and you can change where in the string you strike. whats strange to me is that the piano hammers never change, nor their position, only the material depressing the key. and yet still, the timbre changes.

this seems to me that there exists a function which determines various discrete values of velocity at which the timbral characteristics are defined as either hard or soft, and there must be some gradation within these values, say 2-2.9 = hard, 3-3
5 = soft, 3.6-4 = hard

but what's strange is all of this information is contained within the single quantity of the instantaneous velocity of the hammer when it leaves the action and flies to the string???

somehow a hammer moving at 1m/s will produce a hard sound, at 2m/s a soft sound, and at 3m/s a hard sound (arbitrary values)
there's a quality (timbre) oscillation occurring between velocities, and via some combination of some other values (my intuition says it's the accelerations acting on the key as it's depressed) the timbre is determined regardless of volume, which is entirely a product of the velocity of the hammer. somehow both characteristics are a product of the velocity, and, I'm guessing, accelerations determine which set of velocities are available to the hammer, determining which set of sounds are produced, soft or hard

an alternative explanation is that the hammer is somehow vibrating, and is itself constituted by harmonizing sinewaves, and this is no mere kinematics equation dealing with velocity and acceleration. because I'm struggling to see how merely velocity can determine all of these qualities

What do you mean by "hardness" and "softness" of tone?

>>11128238
You know, like how much dick you give it

>>11128238
the timbre of the sound, thats why I asked my first question in the op, how is timbre expressed mathematically?

when I strike the key with my nail, it has a bite, a hardness, it's brighter
when I use my fleshy finger pad, it has a softness, its darker

color is hard to describe to nonmusicians, because they don't have any personal relationship with it, but timbre is a well defined physical property of sound, usually attributed to resonances with the instrument body, which is true, but make no mistake, it's intrinsic to the waveform of the string separate from the body

you cannot play a line legato (connected) without continuity of color across the phrase, all the notes need to be either hard or soft, or they will appear as separate to the listener, because they are, because their colors (timbre, hard/soft) are different

>>11128250
My guess is you are approaching this from the angle of classical physics as if it were an ideal situation. So in that way, you must realize the hammer striking the string is not an elastic collision. There are going to be vibrations throughout the entire striking mechanism that reach your hand and back to the string for an amount of time. I would think the timbre of the note is probably dependent on the interaction of the key and the way you strike it with the hammer and the way it bounces off the string before during attack. You have more or less answered your own question. I'm not sure if that's correct, but it seems feasible that tone color and timber are effects of dampening. Good thread, OP.

>>11128250
>how is timbre expressed mathematically
Like anon >>11127820 already said, timbre is the relationship between the fundamental frequency and its overtones.
>but timbre is a well defined physical property of sound, usually attributed to resonances with the instrument body, which is true, but make no mistake, it's intrinsic to the waveform of the string separate from the body
The string, the actuation mechanism and the instrument body all play a role in the timbre.
See this neat little simulation of a vibrating string, it lets you manipulate the string and shows your the amplitude of the overtones being generated.
http://www.falstad.com/loadedstring/