# How does digital audio data capture 'texture'? (And not only pitch and volume)

I've been reading about digital audio. I now have a basic understanding of frequency and amplitude. To my understanding, frequency is the 'width' of a wave, and amplitude is the 'height' of a particular sample in time.

Frequency translates to pitch, and amplitude translates to gain/volume/not sure about the technical term.

But what I don't understand, is where does the 'texture' come from?

E.g. a guitar and a violin might each be recorded playing the same note in the exact same volume. But the audio recordings will sound completely different.

Please describe what exactly will be different in the digital data of the two recordings. What element in digital sound dictates 'texture'?

(Please try to explain in terms a person not from this field would be able to understand. I need a general, not a detailed understanding).

Simply... the 'texture' or complexity of the wave.

The addition & subtraction of a myriad simple sine waves of different frequencies & phases, overlaying each other.

Without going into any detail, I'll leave that to the guy who gets the 'tick' for his answer ;-)
... a drawing of an apple & a photograph of an apple are both recognisably an apple, yet may differ in a thousand ways.

If you take time as a constant - the sampling frequency of the data, then each data point is the addition/subtraction of all these waves at that exact point, expressed as pure 'volume' i.e., how far in or out a speaker coil will be pushed at that precise moment.
Running each of these tiny snapshots one after the other gives the eventual fluidity of motion which drives the air pressure changes we then perceive as sound.

• Let me ask a different question: there's a software audio library, where a wave is played by iterating over a long list of floating-point numbers. A specific list of these numbers is interpreted by a Wave Player to the sound of a smooth sine wave, while a different list would cause the Wave Player to create a harsh 'squarish' tone. Can you explain in general how a long list of floating-point numbers can express a sound wave? Sep 19, 2014 at 20:19
• Put another way, how do you express an audio wave, in a long one-dimensional list of numbers? Sep 19, 2014 at 20:22
• So amplitude - i.e the volume of each sample, also dictates the 'texture'? Sep 20, 2014 at 10:05
• And if so, than each nunber in that list represents the amplitude of a particular sample? (The frequency is governed by something else). Sep 20, 2014 at 10:07

Texture, AKA Timbre, comes from overtones, AKA harmonics.

When you play a note on any instrument (including your voice), the note has more than one frequency. The lowest frequency is called the fundamental frequency. It is the one we hear most and the one that determines what note it actually is.

The higher frequencies are what we call the overtone series. They are always the same intervals from the fundamental frequency. It is the amplitude of these overtone frequencies that gives each instrument a different texture.

I hope this helps and wasn't to complicated! You should read about harmonics, overtone series, additive synthesis and subtractive synthesis to help get a clearer picture!

• Good answer, though I object a bit to saying "more than one frequency". The fundamental definition of frequency is simply inverse of the period duration, i.e. the time you need to wait until the signal repeats. That's just one frequency for any proper tone-signal. When talking of harmonics, one is referring to the signal's Fourier transform, which decomposes it into sinuoid waves, which are very useful, but really also very particular. Our ears actually do something in between Fourier transform and auto-correlation analysis, but none of this is really needed for explaining sound differences. Sep 20, 2014 at 0:46
• What do you mean by "none of this is really needed for explaining sound differences?" Sep 20, 2014 at 21:37
• I mean it's entirely legit to explain "this waveform sounds different from that one" without ever mentioning harmonics and Fourier transform, simply by saying "A has some sharp spikes, whereas B is smooth everywhere". Of course that translates to "A has many harmonics whereas B is almost a sine", but that doesn't make it the only interpretation. Fourier transform just takes you from one basis of the Hilbert space to another. Sep 20, 2014 at 21:46
• Ah yes! I can start to see what you're saying, though I don't know exactly what the Hilbert Space is. Will read about it. Sep 20, 2014 at 21:56