Preset group · Intervals
Intervals. The ratio between two tones, made visible.
An interval is the distance between two notes, and the oldest ones are written as simple ratios: the octave 2:1, the fifth 3:2, the fourth 4:3. A legend Nicomachus tells almost two thousand years ago says Pythagoras discovered them listening to the hammers in a forge. The legend doesn't hold up, but the ratios do.
This group is music's ear made visible: nine intervals, from unison to the tritone.
The formulas and the figures in the code.
The low tone is always 220 Hz (A3), in the left ear. The high one, in the right, is 220 × the interval's just ratio: unison 1:1, octave 2:1 (440 Hz), fifth 3:2 (330 Hz), fourth 4:3, major third 5:4, minor third 6:5, major sixth 5:3, major seventh 15:8.
The tritone is the exception: √2, the one that splits the octave right in half in equal temperament (311.1 Hz). It's the only irrational one in the group.
One line per preset.
- Unison 1:1
220 Hz
Unison 1:1: the same tone in both ears.
Physical figure (6, 2) · No layer
- Octave 2:1
220 Hz + 440 Hz
Octave 2:1: the same note, at double.
Physical figure (6, 2) · No layer
- Fifth 3:2
220 Hz + 330 Hz
Fifth 3:2: the most stable after the octave.
Physical figure (6, 2) · No layer
- Fourth 4:3
220 Hz + 293.3 Hz
Fourth 4:3: the fifth seen from above.
Physical figure (6, 2) · No layer
- Major third 5:4
220 Hz + 275 Hz
Major third 5:4: bright.
Physical figure (6, 2) · No layer
- Minor third 6:5
220 Hz + 264 Hz
Minor third 6:5: more inward.
Physical figure (6, 2) · No layer
- Major sixth 5:3
220 Hz + 366.7 Hz
Major sixth 5:3: open.
Physical figure (6, 2) · No layer
- Major seventh 15:8
220 Hz + 412.5 Hz
Major seventh 15:8: tense, it wants to resolve.
Physical figure (6, 2) · No layer
- Tritone √2
220 Hz + 311.1 Hz
Tritone √2: the octave split in half, the curve that doesn't close.
Physical figure (6, 2) · No layer
Tab. 01 · Plate figure calculated by the app's core (cym.core.js) for each frequency: a square plate driven at the center, f = 5.5·(n² + m²) Hz. Two modes = the plate answers with both.
The physical figure and the symbolic layer.
In XY, each simple ratio draws a Lissajous curve that closes: with 3:2, three lobes by two; the bigger the numbers, the more tangled. The tritone, √2, never closes. It's the mode that shows this group best.
In Chladni the plate follows both tones: the low one, 220 Hz, on mode (6, 2), and the high one, which changes with each interval (the fifth, a blend of modes (6, 4) and (8, 0)). No layers: what you see is the sound.
What people ask about this group.
Q1What is a musical interval?
The distance between two notes. The most consonant ones are written as simple ratios between their frequencies: the octave 2:1, the fifth 3:2, the fourth 4:3.
Q2Why do they all play over 220 Hz?
So that only the ratio changes. With the low tone fixed on A3, each preset shows one interval and nothing else.
Q3Why is the tritone √2?
Because it splits the octave into two equal halves in equal temperament: two tritones in a row make 2:1. √2 is irrational, so its curve in XY doesn't close.