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I am trying to understand some basics of the acoustic theory.

Can someone in their own simple words explain what are the differences between the waves on two different instruments playing the same note? Such as how does a wave from a G on a guitar differ from a G in the same octave/frequency on a piano?

Also what does the 'bass' effect increase or decrease do to any wave signal you give it?

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To develop a visual understanding of it, you need to see it. There are modular synthesizer softwares who have "oscilloscope" modules where you can see what the sound looks like. Look for that. :) Barring that, use Audacity (audacity.sourceforge.net) to look at and modify audio files. –  Lennart Regebro Apr 4 '11 at 19:14
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Key to this is the harmonics of the note. If you just play a 440Hz perfect sine wave it doesn't sound very exciting at all, but add in some of the harmonics and it starts to come alive.

If you add in the waveforms at 3x and 5x the fundamental, or at 2x the fundamental you will get a very different tonal effect. Varying the relative amplitude of these also alters the tone. Adding in frequencies which are not a multiple can lead to more atonality (think bells or cymbals)

If you translate the waveform into the frequency domain (ie look at the output of a frequency analyser which has your sounds fed into it) you can see how much these harmonics shape the sounds we hear.

Bass and Treble (or wah and other filters) just boost or cut a particular range of frequencies.

have a look at this wikipedia article for a great starting point, and also search for fourier transform to understand how the time and frequency domains are equivalent.

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Alsop: and the waveforms added in 3x or 5x the fundamental, are of lower, smaller amplitude than the fundamental right? And I assume that the 'fundamental' frequency refers to the note's frequency right (eg. A440)? –  Vass Apr 3 '11 at 20:36
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@Vass - generally much smaller amplitude, but it is amazing how big an effect on tone a set of high harmonics can make. –  Rory Alsop Apr 3 '11 at 20:37
    
Alsop: What are the 'harmonics'? Just the frequencies which are even multiples? –  Vass Apr 3 '11 at 20:48
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@Vass - even and odd multiples. As an example, if you have a 440Hz tone and you add in an 880 Hz tone, it still sounds like an A, but tonally very different. Add in a 1760Hz and it sounds different again. –  Rory Alsop Apr 4 '11 at 11:02
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up vote 3 down vote accepted

So, the fundamental difficulty to understand here is that each individual sound is made up of many many composite frequencies. When you play A440 on a guitar, it sounds different from A440 on a piano because the piano has vastly different upper frequency content. You said "the waves", but this is a little bit misleading: The waveform you see when you record guitar or piano is actually the sum of many many frequencies. The only way they are "the same" is that they have the same fundamental frequency -- that is, the lowest audible frequency of these two notes is the same, that is, 440 Hz.

As for how filtering a sound affects its content:

If you put a bass-cut on a sound, you're essentially lowering the volume of the low frequencies of the sound. If you put a bass boost, you're raising the volume.

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Questioning Bre: I just still have a bit of difficulty in developing a visual interpretation of what raising the volume looks like, and many frequencies and the fundamental frequency. –  Vass Mar 31 '11 at 17:26
    
If you want to talk about it in detail, message me on gtalk - tastemyhouse@gmail.com –  Alexander Questioning Bresee Mar 31 '11 at 21:22
    
I've heard that it's the "attack" that varies from instrument to instrument. Whether you play C4 on piano or guitar or violin, after the initial attack, the notes all look the same and have the same frequency. –  advs89 Mar 31 '11 at 21:48
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that is incorrect. Attack is only part of what makes two sounds different, and further more many instruments have very similar attack / decay characteristics -- the piano and the guitar being two with exponentially decay post attack. –  Alexander Questioning Bresee Apr 1 '11 at 22:42
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If you want some quick visualizations.. I suggest you look at the Freesound Project. Especially the tag 'notes'.. You can see how different notes look like and play them to see how they sound..

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