Roughness
How rough a chord sounds comes from its overtones rubbing against each other. Tune the notes a little differently and some keys get calmer while others turn sour. One number per chord, in every temperament the minichord knows.
Connect the minichord, or try the test chords below.
Play a chord
–roughness
This chord in every temperament
Choose a temperament to hear it: with the minichord connected, it switches too.
Chord by chord
Solid: as tuned now. Dashed: the same notes in equal temperament.Sweet and sour keys
Each triad against the same triad in equal temperament. A temperament is tied to the keys, not to the key signature, so it favours some chords over others.
Where the roughness comes from
Two tones swept apart by an octave. The dips are where overtones line up: the pure ratios. The dots are the intervals in your chord, as tuned now.
Test chords
These only draw; the minichord makes its own sound. Without a minichord, the temperament list above decides the tuning.
Tone
Try the pure tone: tuning barely matters without overtones to collide, which is why temperaments sound different on real instruments. The measure is William Sethares's model of sensory roughness.