EQUAL TEMPERAMENT

how many cents each interval misses the pure one by, and why exactly that much

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.

Formats: A4 · A3 · A2
What you get: Print-ready PDFs, one per size, with every letterform converted to outlines — nothing to install, nothing to shift.
Subject: music · everyone · reference · music room

At the top each bar shows where the pure ratio sits relative to the equal step: up means the pure interval is higher, down that it is lower. The table sets both numbers beside the ratio itself. At the foot is the arithmetic the correction comes from.

THE ERROR IS SHARED OUT UNEVENLY, AND THAT WAS A CHOICE

Equal temperament is said to be “slightly out of tune”. It is out of tune very unevenly: the fifth misses by 1.955 cents and the major third by 13.69 — seven times as far.

That is no accident. The fifth’s miss is exactly a twelfth of the Pythagorean comma: the gap between twelve fifths and seven octaves was shared out evenly among the fifths so that the circle would close. The third took no part in that sharing, and so received nothing.

On the sheet

At the top each bar shows where the pure ratio sits relative to the equal step: up means the pure interval is higher, down that it is lower. The table sets both numbers beside the ratio itself. At the foot is the arithmetic the correction comes from.
Colour carries meaning, but meaning never rests on colour alone — the sheet reads in black and white.
Nothing about how it was made: the sheet carries only what the reader needs.

Printing

Three sizes in the archive: A4 — 210×297 mm, A3 — 297×420 mm, A2 — 420×594 mm.
All text is converted to outlines. No fonts to install, and nothing shifts on another machine.
White background and sparing fills — it prints on a home printer without draining the cartridge.
Margins of at least 10 mm: a home printer cannot print to the edge.
No stroke thinner than 0.3 mm, so nothing disappears in print.

Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 7 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.

EQUAL TEMPERAMENT

THE ERROR IS SHARED OUT UNEVENLY, AND THAT WAS A CHOICE

On the sheet

Printing

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