Tuning & Temperament
Just Intonation, Beating and Why Intervals Sound in Tune
Pure intervals come from small whole-number ratios, and beating is what stops them sounding pure. What just intonation gives, and what it cannot fix.
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Glossary
Articles
Tuning & Temperament
Pythagorean Tuning: How Stacked Pure Fifths Build a Scale
Pythagorean tuning builds every interval from pure 3:2 fifths. Here is the seven-note scale it produces, its whole tones and semitones in cents, and the wolf fifth it leaves behind.
Tuning & Temperament
What Are Cents? The Unit That Measures Small Pitch Differences
A cent is one hundredth of an equal-tempered semitone. Here is the formula, what the common intervals measure in cents, and what a tuner is showing you.
Harmony
The ii V I Progression in Major, Minor and Jazz Styles
Why ii V I is the backbone of tonal music: voice leading, turnarounds, minor-key forms, and the jazz reharm toolkit.