Just Intonation (Minor)
Pure minor thirds (6:5) and fifths in the home minor key.
Quick Facts
- Creator
- Renaissance tuning theory
- Historical Era
- Renaissance / Theory
- Formula Type
- just-ratios
- Key Advantage
- Pure minor thirds (6:5) and fifths in the home minor key.
- Key Limitation
- Key-locked: pure tuning degrades when modulating or mixing major and minor passages.
- Typical Use
- Theoretical study of minor-mode just tuning and a cappella minor-key vocal music.
Mathematical Basis
Just intonation uses simple whole-number frequency ratios (5:4 major third, 3:2 fifth, 6:5 minor third) to achieve maximum harmonic purity in the home key. Intervals are pure but fixed to one tonal center.
Sound Character
Just intonation produces exceptionally pure consonances in the home key: major thirds (5:4), perfect fifths (3:2), and minor thirds (6:5) are all beatless. The result is a choir-like blend where chords fuse into a unified sound. Modulation causes increasing dissonance as the key moves away from the tonal center.
Just Intonation (Minor) Frequency Table — All 12 Notes at A4=440Hz
| Note | Equal Temp. (Hz) | Just Intonation (Minor) (Hz) | Cents from Equal |
|---|---|---|---|
| C4 | 261.626 | 261.626 | 0.00 |
| Db4 | 277.183 | 275.311 | -11.73 |
| D4 | 293.665 | 294.329 | +3.91 |
| Eb4 | 311.127 | 313.950 | +15.64 |
| E4 | 329.628 | 327.032 | -13.69 |
| F4 | 349.228 | 349.624 | +1.96 |
| Gb4 | 369.994 | 367.910 | -9.78 |
| G4 | 391.995 | 392.439 | +1.96 |
| Ab4 | 415.305 | 411.570 | -15.64 |
| A4 | 440.000 | 436.043 | -15.64 |
| Bb4 | 466.164 | 470.927 | +17.60 |
| B4 | 493.883 | 490.548 | -11.73 |
Frequencies in Hz at A4=440Hz. Positive cents = sharper than equal temperament. Negative = flatter. Formula: f = f_equal × 2(cents/1200)
Historical Context
Just Intonation (Minor) originates from the Renaissance / Theory era, developed by Renaissance tuning theory. It was primarily used for Theoretical study of minor-mode just tuning and a cappella minor-key vocal music..
Just intonation was championed by Renaissance theorist Gioseffo Zarlino as the ideal for vocal polyphony. It remains the natural tuning of unaccompanied choirs and a cappella ensembles.
Who Uses Just Intonation (Minor) Today
Just intonation is used by a cappella choirs, barbershop quartets, and string quartets exploring pure intonation. It is the theoretical basis for understanding consonance and the physics of harmonic resonance.
Tune with Just Intonation (Minor) — Get Tunable.
Tunable supports Just Intonation (Minor) and 15 other tuning systems including equal temperament, Pythagorean, just intonation, and well temperaments. See exact Hz values in real-time as you play.