Magic Music Clacton — musical sound explained | magicmusicclacton.com
An interval is the distance between two pitches, and the consonant intervals are the ones whose frequencies form simple whole-number ratios.
When two tones sound together, their pressure waves add. If the frequencies stand in a simple ratio, the combined waveform repeats quickly and regularly: with a 2:1 ratio the pattern resets every cycle of the lower note, with 3:2 every two cycles. The ear reads this rapid regularity as smoothness — the sensation called consonance.
The octave, 2:1, is the most consonant interval: the upper tone coincides with every second cycle of the lower so completely that the two nearly merge. Next come the perfect fifth at 3:2 and the perfect fourth at 4:3, the structural pillars of scales worldwide. The major third (5:4) and minor third (6:5) add the sweetness that makes triads possible.
| Interval | Ratio | Cents (just) | Equal-tempered |
|---|---|---|---|
| Octave | 2:1 | 1,200 | 1,200 |
| Perfect fifth | 3:2 | ≈ 702 | 700 |
| Perfect fourth | 4:3 | ≈ 498 | 500 |
| Major third | 5:4 | ≈ 386 | 400 |
| Minor third | 6:5 | ≈ 316 | 300 |
| Major sixth | 5:3 | ≈ 884 | 900 |
On narrow screens, swipe or scroll the plate sideways.
Complicated ratios — 45:32, the tritone, is the classic case — produce wave patterns that repeat only over long stretches, and the result sounds restless or tense. Dissonance is not a defect: it is the engine that makes harmony move, but it is defined by the same arithmetic as consonance.
Because pitch is logarithmic, interval sizes are added rather than multiplied when measured in cents: 1200 cents to the octave, 100 to the equal-tempered semitone. A pure fifth measures about 702 cents, a pure major third about 386 — each a few cents from its tempered counterpart, and each difference audible as a slow beating.
Ratios also explain why purely tuned instruments clash across keys: a chain of pure fifths and thirds cannot close back on the starting note. That impossibility, quantified as the Pythagorean and syntonic commas, is the entire reason tuning systems exist.
Further reading