# 030 — Temp Circle

## Problem Situation

Tuning temperaments distribute impurity differently across the twelve keys. In equal temperament, every key gets the same slightly-off intervals. In quarter-comma meantone, eight keys get pure major thirds but the remaining four are unplayable -- one fifth becomes a howling "wolf." In Werckmeister III, C major is purest and remote keys carry progressively more tension.

Musicians, organ tuners, and historically informed performers know this intellectually, but the *pattern* of impurity distribution is invisible. You have to play every key to discover which ones benefit and which suffer. Lookup tables give numbers without showing the shape. The result: people choose temperaments without seeing what they trade.

## What Was Built

A circle-of-fifths instrument where each key position shows two interval qualities -- fifth purity (inner ring) and major third purity (outer ring) -- as radial bars. Longer, more saturated bars mean more deviation from pure intervals. Red indicates harsh beating or wolf intervals. Thin white/green lines indicate near-pure intervals.

Five historical temperaments: Equal (~1584), Quarter-Comma Meantone (~1523), Werckmeister III (1691), Kirnberger III (1779), and Vallotti (~1754). Switching between them animates the redistribution of impurity around the circle.

Hover readout shows exact cent deviations, interval sizes, and contextual interpretation. Summary panel shows pure interval counts, average deviations, and extremes. Bottom bar chart shows third quality across all 12 keys in circle-of-fifths order.

## Why This Form

The circle of fifths IS the mathematical structure of temperament. Temperaments distribute the Pythagorean comma (~23.5 cents) around this circle by narrowing or widening specific fifths. The resulting impurity in thirds cascades from how those fifths stack. Making this distribution visible ON the circle is the native form -- not a chart, not a table, not an explanation.

## What Is Actually Interesting

Switching between temperaments is the core move. Equal temperament shows uniform bars everywhere -- the democratic compromise. Meantone shows a dramatic cliff: pure thirds on one side, a red catastrophe on the other. Werckmeister shows smooth graduation from purity to color. The contrast between these distributions is the invisible thing this instrument makes visible.

The instrument reveals WHY certain keys sound different in historical temperaments, and why Baroque composers wrote in certain keys -- not arbitrary preference, but because the temperament gave each key a different character.

## Iterations

- v1.0: Initial build with circle instrument, five temperaments, hover readout, summary stats, bar chart.
- v1.1: Added divider ring between fifth and third zones for visual clarity. Fixed Werckmeister III fifth placement (B-F# not A-E). Fixed Kirnberger III schisma fifth at A-E. Improved pure-interval indicators (thin arcs instead of filled bars).

## Next Step

Add audio: click a key to hear a sustained major triad in that temperament. The beating would become audible, not just visible. Pair visual impurity with sonic impurity.

## Art Direction

Default Night Lab dark editorial direction. Monochrome background, amber/rust for impurity, subtle green-white for purity. JetBrains Mono for labels and metadata. Geist for body text. Minimal surfaces. Canvas-rendered circle for precise radial geometry.

## Promotion Candidate Read

Maybe. The form-to-problem fit is mathematically native -- the circle of fifths IS the domain's structure, and switching temperaments reveals the invisible redistribution of impurity. The preset contrast (Equal's uniformity vs Meantone's cliff vs Werckmeister's gradient) is a genuine revelation for anyone who hasn't internalized temperament theory. But the instrument is diagnostic-only and the audience is specialized (musicians, tuners, music theory enthusiasts). Adding audio playback would transform it from a visual diagram into a true temperament exploration instrument.
