Equal temperament, just intonation, and Pythagorean tuning

A chromatic tuner does not invent pitch from nowhere. It compares what you play to a target frequency. Most free online tuners use equal temperament (12-TET) — the same grid as a modern piano. Orchestral and chamber players also care about just intonation (pure intervals in a key) and Pythagorean tuning (pure fifths for melodic lines).

Knowing which system you are aiming for stops the needle from “lying”: a pure major third is about 14 cents flat of equal temperament. If your tuner only speaks 12-TET, that pure third will look “flat” even when the chord is ringing.

Equal temperament divides the octave into twelve equal steps (100 cents each). Every key sounds equally “in tune” and equally slightly compromised. Piano, harp, mallet percussion, fretted guitar, and most digital instruments live here.

Use equal temperament whenever you share pitch with a fixed-pitch instrument, a track, or a piano reduction. For band warm-ups with electronic keyboards and for checking open strings against a piano, 12-TET is the honest reference.

• Default on almost every free online chromatic tuner
• Best with piano, harp, mallets, and fixed-pitch media
• Plug-and-play: no tonic selection required
• All keys are equally usable; pure thirds beat slightly

Just intonation (JI) tunes notes to simple frequency ratios (5-limit is common for Western practice). Relative to a chosen tonic, the pure perfect fifth is 3:2 (~+2¢ vs equal), and the pure major third is 5:4 (~−14¢ vs equal). Chords stop “beating” when voices lock those ratios.

This is the killer practice mode for ensemble intonation: pick the key of the passage (e.g. D), then tune so thirds and fifths ring. Orchestral winds and strings use this instinctively in sustained harmony even when the chart is written in equal temperament.

• Pick a tonic (root) for the key or chord context
• Pure major thirds sit flat of the piano; pure fifths slightly sharp
• Ideal for chorales, long tones, and section balance
• Change tonic when the harmony or key center moves

Pythagorean tuning builds the scale from pure fifths (3:2). Leading tones and major thirds sit sharp of equal temperament; half steps often feel tighter. Many string players prefer this for solo, linear lines — expressive intonation without piano under them.

Use Pythagorean when you practice melodies, etudes, and solo excerpts (including late-Romantic and Mahler-style lines) and want leading tones that “pull.” It is not the same as just intonation for stacked chords: a Pythagorean major third is wide, not pure.

• Pure-fifth chain; sharp leading tones vs 12-TET
• Great for solo / melodic practice without piano
• Still needs a tonic for key-relative offsets
• Different goal from Just — melody vs pure harmony

Match the mode to the room, not to ideology. Switching mid-rehearsal is normal when the repertoire changes.

• Piano, track, frets, or mallets in the room → Equal
• Sustained chords, section tuning, pure thirds → Just + tonic
• Solo line, etude, sharp leading tones → Pythagorean + tonic
• Instrument key (Bb/Eb/F) is separate — that is transposition, not temperament

Cents still mean 1/100 of an equal-tempered semitone as a measuring stick. What changes is the target frequency for each note name. 0¢ means “on the temperament target,” not “sounds like a piano” if you chose Just or Pythagorean.

Note names usually still snap to the nearest chromatic pitch class so the display stays readable. The needle then measures how far you are from that note’s target under the active system.

The free online chromatic tuner in the browser is equal-temperament by default for quick checks. The freemium iPhone app adds Equal, Just, and Pythagorean modes on the Tuner screen — with a tonic picker for Just and Pythagorean — next to band transposition, drones, metronome, and HYKOM.

Settings on the app defines each mode in plain language so students and private teachers can choose without a theory lecture.