Lesson 1
Sound
Before any of the theory, one physical fact and one fact about your ear. The physical fact is dull. The one about your ear is why music has the shape it does, and it is the reason your DAW numbers notes the way it does.
Sound is a pressure wave
A speaker cone pushes forward and squeezes the air in front of it. It pulls back and thins that air out. Repeat quickly and you have a travelling pattern of slightly-denser and slightly-thinner air, which arrives at your eardrum and pushes it about.
Two numbers describe the simplest version of that pattern. How many times per second the cycle repeats, measured in hertz, which you perceive as pitch. And how much the pressure swings each cycle, which you perceive as loudness. That is the whole of it. Everything else in this course is a consequence of those two quantities and the machinery that measures them.
Your ear does not measure frequency, it measures ratios
Here is where it stops being obvious. Play 100 Hz, then 200 Hz. The second sounds higher by a certain, very familiar amount: an octave. Now play 1000 Hz and 1100 Hz. You added exactly the same 100 Hz, but the second pair are barely different from each other, nothing like an octave apart.
What the ear responds to is not the difference between two frequencies but their ratio. 200 is to 100 as 2000 is to 1000, and both of those pairs sound like the same musical distance, because they are the same ratio. Equal musical steps are equal multiplications, not equal additions.
Which means pitch is logarithmic in frequency. Drag the slider below and switch between the two mappings. The gesture is identical; the result is not.
One slider, two ways of moving
The marks are octaves. Watch where they sit as you switch modes.
- Frequency
- 522.5 Hz
- Note
- C5
- MIDI note
- 71.98
- Octaves above 110 Hz
- 2.25
Every octave takes twice the hertz of the one below it, so the marks crowd to the left and a steady sweep races through the low notes and labours through the high ones.
Why your piano roll has evenly spaced rows
Look at the readout while you drag. In hertz mode the number races away; the MIDI note number, meanwhile, climbs at a steady rate no matter which mapping you use, because MIDI note numbers count in pitch rather than frequency.
That is the design decision behind every piano roll you have ever used. Rows are evenly spaced on screen because they are evenly spaced to your ear, even though the frequencies they represent double every twelve rows. A note an octave up is not a fixed number of hertz higher. It is exactly twice the frequency, every time, at every point on the keyboard.
The relationship is MIDI = 69 + 12 x log2(f / 440). The 440 is A above middle C, fixed by convention rather than by physics, and the 12 is the number of steps in an octave, which is also convention rather than physics. Lesson 5 is about where that twelve came from and what it cost. For now the useful part is the logarithm, which is not convention at all.