Chapter One: An Acoustics Primer

### 7. What are wave shapes and spectral content? | page 3

Early on, researchers were able to quickly visualize real-world sound in two important ways—either by taking a snapshot of the instantaneous amplitudes of a sound’s component frequencies at a single given point in time (called an** FFT** or **Fast Fourier Transform**) or by creating a sequential series of snapshots to give a picture of how a particular sound evolves over time. This form of FFT gives tremendous insight into how the various partials of an instrument evolve in the first few milliseconds of its attack.

Pictured below are two FFT's. The figure on the left plots the frequencies and strengths of an instantaneous moment of an oboe note in two dimensions. The second analysis on the right demonstrates the attack phase of an oboe note in 3 dimensions, frequency, amplitude plus time. It can be viewed as a collection of sequencial snapshots of the analysis on the right, strung together to show how the note spectrally evolves over time.

Notice in the 'snapshot' FFT that the 2nd partial has a greater amplitude than the fundamental and also that partials #9 and #13 are missing from the spectrum. Notice in the second FTT how the various partials develop over time and change relationships.