How cultures divide the octave.
12 equal steps is one answer. Not the answer. Javanese gamelans use 5 or 7 unequal steps tuned by ear across generations. Arabic maqam splits the semitone in half — 24 quarter-tones. Indian classical music recognizes 22 microtonal shrutis. Thai music divides the octave into 7 equal parts where nothing aligns with Western tuning. The Bohlen-Pierce scale abandons the octave entirely for a 3:1 tritave.
Each system reflects a different set of values — which intervals matter, how much variation enriches a melody, whether modulation or purity takes priority. Click any degree to hear it. Compare two systems to see where they agree and where they diverge.
What is a cent?
A cent is 1/1200 of an octave — a logarithmic unit that makes pitch differences comparable across registers. An equal-tempered semitone is 100 cents. A quarter-tone is 50 cents. Most trained ears can distinguish differences of about 5-10 cents. The circle visualization maps cents to angle — evenly-spaced systems make regular polygons, uneven systems show their asymmetry.
Why so many systems?
Simple frequency ratios (3:2, 5:4) produce consonant intervals, but they do not divide the octave evenly. Every tuning system is a negotiation between purity of intervals and freedom of modulation. 12-TET sacrifices interval purity for total modulatory freedom. Just Intonation does the opposite. Most non-Western systems optimize for different priorities entirely — gamelan tuning prioritizes the shimmering beats between paired instruments, not interval purity.
The deviation chart
The deviation chart shows how far each degree sits from the nearest 12-TET pitch. Green bars above zero mean sharper. Red bars below zero mean flatter. Just Intonation's thirds sit 14 cents flat of 12-TET — audibly different. Pythagorean thirds sit 8 cents sharp. Meantone restores pure thirds but creates a wolf fifth. These are not errors. They are choices.
Listening across systems
Use the comparison mode to overlay two systems on the circle. Play the ascending scale to hear the character of each system. The ear adapts quickly — after a few repetitions of a gamelan scale, 12-TET starts to sound grid-locked. After a few repetitions of 12-TET, gamelan starts to sound drifting. Neither is wrong. Context sets the reference.