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Intervals

Two sounds, one ratio. The simpler the ratio, the more order appears both to the ear and in the figure; listen to just and equal-tempered intervals side by side.

RatioUnison1:1 · 0 centsMinor second16:15 · 112 centsMajor second9:8 · 204 centsMinor third6:5 · 316 centsMajor third5:4 · 386 centsPerfect fourth4:3 · 498 centsAugmented fourth45:32 · 590 centsPerfect fifth3:2 · 702 centsMinor sixth8:5 · 814 centsMajor sixth5:3 · 884 centsMajor seventh15:8 · 1,088 centsOctaves2:1 · 1,200 centsTwo orins (≈ 3:2)Real instruments rarely land on an exact ratio.

Perfect fifth · 220 Hz · 330 Hz

At an exact ratio the figure closes and stands still.

Ratio: 3:2
Just: 701.96 cents
Equal: 700 cents
Difference: −1.96 cents

Complexity: log₂(6) = 2.58

Top: harmonics of the lower sound; bottom: of the upper sound. Solid line: coinciding harmonics (2); dashed line: rough near-misses (0).

Settings

TimbrePure toneBowlDrone

TuningJustEqual

PlayingTogetherOne after the other

Shift±0 centsShifting passes a gate: no pair of partials may meet 4-40 Hz apart.

1859

Lissajous figures were used to compare tuning forks for the 1859 French pitch standard: when light was reflected off two forks together, the figure stood still at an exact ratio and turned if the pitch was off.

A history of tuning: from 415 to 443 Intervals and ratios: why does 3:2 sound consonant?

Frekans Studio is not a medical device and does not diagnose or treat any condition. Content is for relaxation, focus and personal exploration. Every item shows its level of evidence.

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