Twelve TheoryMath + Music Playground

Explore interactive music theory and music by numbers through Free Play, Math Mode, Chord Game, Circle Counting, the Triad Chart, Chord Progressions, Church Modes, the Counterpoint Game, WTC, Dodecachordon, Harmonic Cone, the Harmonics Quiz, Frequency Chart, Harmonic Wave, Waveforms, Harmonic Polygons, Tuning String, Sheet Music, Musical Circles, and Ear Training.

Interactive module

Harmonic polygons

Equal-Hz edges reveal why harmonic intervals shrink as frequency rises.

Starting octave
A2
A2 · 108.00 Hz per edge

H1 is one unit (dot); H2 is two joined units (line). Regular polygons begin at H3.

H1Fundamental unit
108.00 Hz1 × 108.00 = 108.00 Hz
H2Two-unit line
216.00 Hz2 × 108.00 = 216.00 Hz
H3Triangle
324.00 Hz3 × 108.00 = 324.00 Hz
H4Square
432.00 Hz4 × 108.00 = 432.00 Hz
H5Pentagon
540.00 Hz5 × 108.00 = 540.00 Hz
H6Hexagon
648.00 Hz6 × 108.00 = 648.00 Hz
H7Heptagon
756.00 Hz7 × 108.00 = 756.00 Hz
H8Octagon
864.00 Hz8 × 108.00 = 864.00 Hz
Harmonic 1Fundamental unit · A2108.00 HzPerimeter = 1 × 108.00 HzMatches the nearest equal-tempered note

Hold a shape to hear its harmonic.

1–8 play harmonics · O / P change octave

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