**What is an Audio Waveform?**

As a matter of fact, a waveform is simply a graph that displays amplitude or level changes over time.* Amplitude* is measured in a bipolar manner, with positive and negative values; not to be confused with *level*, which can be the absolute value of *amplitude *changes or an average.

What makes this concept abstract is that waveforms typically contain tens of thousands of discrete changes within an unimaginably short period of time, crammed into a short block in a sequencer. As you probably already know, as you zoom in on a waveform, its contour becomes more and more visible.

**PCM and NYQUIST FREQUENCY**

A waveform is a digitized recreation of very dynamic voltage changes over time. Here is how they are typically generated….

The discrete changes in an input signal are rectified in an instant through a process called “Pulse Code Modulation” (PCM). Simply put, PCM assigns a *bit value* to each *sample* at whatever *sampling rate* you’re running. Furthermore, the higher the *bit depth*, the more values the computer has to chose from and the more accurate the rectification is.* Sampling Rate* for recording purposes is pretty standard – 44100 Hz, the *Nyquist Frequency* for audio. Here is why it is standard…

- The highest audible frequency for humans is 20,000 Hz.
- Every frequency has a positive half and a negative half (compression and rarefaction).
- So, as long as we sample (analyze and generate) rapidly enough to catch both the positive and negative portions of the highest (most rapidly oscillating) audible frequency – we can confidently rectify just about every audible frequency.
- This means at a sampling rate of 40000 Hz, we will catch both the positive and negative portions 20,000 Hz. However, since
*sine*waves are infinitely smooth and gradual, just one sample of each portion will not produce a very accurate waveform at very high and very low frequencies – but this gets pretty close. This is why the extra 4100 Hz in*Nyquist Frequency*exists. It accounts for any aliasing that may occur when sampling very low and very high frequencies.

Of course at this point you may be asking yourself “Why not just sample as frequently as possible? Why not just go to 50,000 Hz or 100,000 Hz?” The answer is negligence. We cannot hear the improvement past 44100 Hz. BUT THIS DOES NOT MEAN OTHER SAMPLE RATES ARE NOT USED. For example, when producing sound or music for film, the sample rate of the audio should match the video resolution rate – which is often over 90,000 Hz.

**SYNTHETIC WAVEFORMS**

Synthetic waveforms are MILES less complex than audio recorded from an acoustic or electrical source. This, frankly, is the beauty of them – they allow us to create sounds *from** scratch* without getting ahead of ourselves. After all, every frequency partial of a sound – harmonic or not – has the potential to send you down a path of unintentional, unfocused ideas that will do more harm than good in context. These are the four basic synthetic waveforms.

**Sine**

**Sine**

One harmonic, one frequency. So perfectly simple that it cannot technically exist acoustically or electrically. On the whole, even the most pure sounding oscillators and *self-resonating filters* have a little bit of noise in their output. Y*= Asinx *describes it mathematically.

**Square**

**Square**

Contains odd harmonics (odd whole number multiples of the fundamental). This means that if the fundamental frequency of a square wave is 200 Hz, it will also generate 600 Hz (3rd harmonic), 1000 Hz (5th harmonic), 1400 Hz (7th harmonic) and so on…..

**Triangle**

**Triangle**

In short. triangle is like a square wave in that it contains odd harmonics, except the harmonic content is lower in amplitude than in a square wave. Meaning, the harmonics have less influence on the overall shape of the wave.

**Sawtooth **

**Sawtooth**

Contains all harmonics. This means that this is the most complex of the four basic synthetic waveforms – but still nowhere close to as complex as real sound. In addition, ff the fundamental of a sawtooth is 100 Hz, that means it also contains 200 Hz, 300 Hz, 400 Hz ….etc. Each harmonic is a little lower in amplitude in comparison to the previous one.

To conclude, IT IS IMPORTANT TO REALIZE that triangle, square, and sawtooth waves **ARE MADE UP OF SINE WAVES** – AS IS EVERY SOUND IN THE UNIVERSE. In essence, one can synthesize a somewhat accurate square wave by adding odd multiples of the fundamental frequency to a *sine *wave. In the audio below, I have done just that! Listen to the sine wave gradually form into a* square *wave as I sweep in odd harmonics. The synthesized square wave plays in isolation at the end. I have isolated each partial on a different track and, in doing so, created a crude “spectrum” analysis of the sound.

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