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I understand that a pitch is nothing but a frequency which is wave cycles per second. So if i sing(human voice) a note A(which is 440hz) then why does it sound different that my friend singing the same note? Sameways A sounds differnt on synth than any other other instrument. So sure there is something other than frequency which makes the difference. My aim here is to understand the technical difference so that i can understand it in my DAW.

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"The frequency" that defines the note is typically the fundamental of a whole sequence of tones emitted by the instrument. Most instrument never excite a pure tone. The harmonics of any instrument can be predicted by the physics of the instrument to a good degree using some simple models (more complex modeling if desired), or controlled measurements in a lab.

I would add to your question the following. Not only do different instruments sound different but the same instrument can sound different if it is attacked differently. Case in point, the guitar. Picking closer to the bridge produces a completely different tone compared to picking closer to the finger board. The short story is that the attack near the bridge excites more harmonics of the string. Pizzicato sound different from bowed strings. And the list goes on. There is a natural sound that the instrument makes based on the physics of the instrument and the quality of materials and craftsmanship. Beyond that the player is in control of the tone and can alter the tone by altering the attack. This is the physics of playing.

If you want to learn more about how harmonics are excited and contribute to the overall sound of an instrument I'd recommend anything by Fletcher and Rossing (anything music related), and Physics and the sound of music by Rigden.

On another note, even if you could produce a pure tone using some equipment our ears are non-linear and create aural harmonics that our brain perceives. So it is likely that no one has ever really experience a pure note.

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Put simply - it's more frequencies! Nearly all instruments, that includes our voices, produce harmonics or partials at the same time as the basic note. It's down mainly to the construction of the instrument along with its material, and often exactly how it's played.

So given that, and the fact that each instrument will produce different levels of different harmonics, the timbre or tone of the same note will differ.

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Because although a PITCH may be defined simply as a frequency, a musical note contains more than pitch. It will have an attack, abrupt or gradual. A sustain, long (a bowed violin note) or short (a xylophone hit) A release, again abrupt or gradual. And that's only a simplification of the 'envelope' aspect of a note!

The sustain portion of the note may have an easily-analysed waveform, a flute tends towards a sinewave, an oboe towards a square wave (and those are gross over-simplifications). But the (far more chaotic) attack has a lot to do with defining the 'sound' too - as witness a synthesis technique where the attack is sampled, the sustain synthesized. Although this might have originated from a need to conserve (then) expensive sample memory, it survives as a remarkably useful and controllable strategy.

So it's partly basic freqency (the perceived pitch), partly the attack, partly the volume envelope, partly the waveform of the sustain portion... and all these are subject to variation and modulation from note to note, and even within one note. You'll find plenty of waveform pictures for different instruments online, though they tend to concentrate on the sustain portion of a note, which might be the LEAST characteristic part of the instrument's 'sound.

So, it's complicated!

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