fundamentals and overtones · 20 Hz – 20 kHz, logarithmic scale
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
The solid band is the fundamental range, the pale one the overtones. The scale is logarithmic: every octave takes the same width.
The lowest note of a bass guitar is 41 hertz. Neither a phone speaker nor a laptop speaker reproduces that frequency at all: they have nothing to produce it with. Yet the bass is audible on them, and the note is heard correctly.
The ear derives pitch not from the fundamental itself but from the pattern of overtones that are whole multiples of it: 82, 124, 165 hertz and onwards. The series remains, so the note remains. Schouten described this in 1940; it is known as residue pitch.
The practical consequence is not obvious: lifting 40 hertz on a bass will not make it audible on a small speaker, because those hertz were never there. What makes it audible is the region of its own overtones — the pale band on this sheet.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 9 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
analog, digital, and speaker wiring · pinouts and balanced signals
seven carriers over a century at one scale, and what each one brought first
two shapes, twelve chords each
eight instruments at one scale · what each is about and how it sounds