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Equal Temperament vs Just Intonation Comparator

Compare equal temperament vs just intonation side by side. Pick a root note, a tuning reference, and an interval or chord to see each version's frequency, cents, the exact just-intonation ratio, the cents difference, and the beat rate — then play ET, JI, or both at once to hear the difference for yourself. This ET vs JI temperament comparison covers every common interval and three chord types.

Set Up the Comparison

Compare an Interval Compare a Chord

Root Note

261.63 Hz

Tuning Reference (A4 = Hz)

Interval

Chord

Tone Waveform

Playback

Idle

Side-by-Side Comparison

C Major 3rd (M3)

Loading comparison...

Note	ET Frequency	ET Cents	JI Frequency	JI Ratio	JI Cents	Cents Diff (JI − ET)	Beat Rate

Just Intonation vs Equal Temperament Reference Table

Cents values for the common 5-limit just-intonation intervals against their 12-tone equal-tempered equivalents. A positive difference means the just interval is sharper than equal temperament; a negative difference means it is flatter.

Interval	JI Ratio	ET Cents	JI Cents	Difference (JI − ET)
Unison	1:1	0	0.00	+0.00
Minor 2nd	16:15	100	111.73	+11.73
Major 2nd	9:8	200	203.91	+3.91
Minor 3rd	6:5	300	315.64	+15.64
Major 3rd	5:4	400	386.31	−13.69
Perfect 4th	4:3	500	498.04	−1.96
Tritone	45:32	600	590.22	−9.78
Perfect 5th	3:2	700	701.96	+1.96
Minor 6th	8:5	800	813.69	+13.69
Major 6th	5:3	900	884.36	−15.64
Minor 7th	16:9	1000	996.09	−3.91
Major 7th	15:8	1100	1088.27	−11.73
Octave	2:1	1200	1200.00	+0.00

How to Use the Comparator

Step 1: Choose Root and Reference

Pick a root note (C4 by default) and a tuning reference (A4 = 440 Hz by default, adjustable from 380 to 500 Hz). The root frequency updates instantly so you can see exactly which pitch you are starting from.

Step 2: Pick an Interval or Chord

Switch between interval mode (unison through octave) and chord mode (major, minor, dominant 7th). The table fills in the equal-tempered and just-intonation frequency, cents, exact ratio, cents difference, and beat rate for every note.

Step 3: Hear the Difference

Press Play ET or Play JI to hear each version on its own, then Play Both to hear them sounded together. When the two versions differ, you will hear a slow beating whose speed matches the beat rate shown in the table.

What is equal temperament?

Equal temperament (specifically 12-tone equal temperament, or 12-TET) divides the octave into twelve identical steps. Every semitone is exactly 2^1/12 times the pitch below it, so the frequency of any note is ref × 2^{(midi − 69) / 12} and any interval of n semitones has the ratio 2^n/12. The advantage is symmetry: every key and every transposition sounds equally usable, which is exactly why pianos, guitars, and almost all fixed-pitch instruments are tuned this way. The trade-off is that no interval except the octave is acoustically pure — the thirds in particular are noticeably off.

What is just intonation?

Just intonation builds intervals from small whole-number frequency ratios drawn from the harmonic series — a perfect fifth is exactly 3:2, a major third exactly 5:4, an octave exactly 2:1. These ratios produce pure, beatless intervals because the overtones of the two notes line up. The catch is that just intonation is only pure relative to one tonal center. Transpose to another key and the fixed ratios no longer line up, leaving some intervals badly out of tune. That is the fundamental reason fixed-pitch instruments adopted equal temperament instead.

Note Frequency

f = ref · 2^((midi − 69) / 12)

Every frequency in this tool is derived from your chosen reference. With A4 (MIDI 69) at 440 Hz, C4 (MIDI 60) works out to 261.63 Hz.

Cents from a Ratio

cents = 1200 · log2(ratio)

The just major third 5:4 equals 386.31 cents, about 13.69 cents flatter than the equal-tempered 400 cents. The just fifth 3:2 equals 701.96 cents, about 1.96 cents sharper than the equal-tempered 700 cents.

What is the beat rate?

When two tones of slightly different frequency sound together, you hear a periodic rise and fall in loudness called beating. The beat rate is approximately the absolute difference between the two frequencies: beat ≈ |f_ET − f_JI| Hz. For a C4 major third, the equal-tempered E4 is 329.63 Hz and the just E4 is 327.03 Hz, so playing both at once produces about 2.6 beats per second. The beating is exactly what your ear uses to tell "in tune" from "slightly off," and it is the most direct way to hear the difference between just and equal temperament. Beating between deliberately detuned tones is also the basis of binaural beats.

Which one is better?

Neither is universally better — they solve different problems, and this is an honest trade-off rather than a case of one being "in tune" and the other "out of tune." Equal temperament is the modern standard because it makes every key equally usable and lets music modulate freely; the cost is that its thirds and sixths are slightly impure (its major third is about 14 cents wide) while its fifths are nearly perfect (only about 2 cents narrow). Just intonation gives pure, beatless chords, but only relative to a single tonal center, so it is impractical for fixed-pitch instruments that need to play in many keys. Singers, string ensembles, and barbershop groups can lean toward just intonation in the moment because they adjust pitch continuously; a piano cannot. Use this just intonation comparator to hear both and decide for yourself what each costs and gains. You can dig into the underlying numbers with the just intonation calculator and the equal temperament chart.

Frequently Asked Questions

What is the difference between equal temperament and just intonation?

Equal temperament divides the octave into twelve identical semitones, each a ratio of 2 to the power 1/12, so every key sounds equally usable but no interval except the octave is acoustically pure. Just intonation builds intervals from small whole-number ratios such as 3:2 and 5:4, which produces pure, beatless intervals but only relative to one tonal center. This tool shows both versions of any interval or chord side by side so you can compare frequencies, cents, and beat rates.

Why does the equal-tempered major third sound slightly out of tune?

The just major third is the ratio 5:4, which equals 386.31 cents. The equal-tempered major third is 400 cents, about 13.69 cents wider. That difference is large enough to be clearly audible: when an equal-tempered major third is held as a sustained chord, the mismatch between the notes' overtones produces noticeable beating. It is the single most compromised interval in equal temperament.

Is the equal-tempered perfect fifth out of tune too?

Only very slightly. The just perfect fifth is 3:2, which equals 701.96 cents, while the equal-tempered fifth is 700 cents. The difference is about 1.96 cents, which is small enough that the equal-tempered fifth sounds nearly pure to most listeners. This is why equal temperament works so well in practice: it concentrates almost all of its compromise in the thirds and sixths, leaving the fifths and fourths nearly beatless.

What is the beat rate and how is it calculated?

When two tones of slightly different frequency play together, the combined sound rises and falls in loudness at a rate equal to the difference between the two frequencies. This tool estimates the beat rate as the absolute difference between the equal-tempered frequency and the just-intonation frequency of the same note. For example, a C4 major third gives an equal-tempered E4 of 329.63 Hz and a just E4 of 327.03 Hz, a beat rate of about 2.6 Hz, meaning roughly 2.6 pulses per second.

How do I hear the difference between just and equal temperament?

Select an interval or chord, then use the playback buttons. Play ET plays the equal-tempered version, Play JI plays the pure just-intonation version, and Play Both sounds them together. With Both, you hear a slow throbbing or beating whenever the two versions differ, and the speed of that beating matches the beat rate shown in the table. Thirds and sixths produce the most obvious beating; the unison and octave produce none because the two versions are identical.

Why is just intonation not used for pianos?

Just intonation is pure only relative to a single tonal center. Because its intervals are fixed whole-number ratios tied to one key, transposing to another key leaves some intervals badly out of tune. A piano has fixed pitches and must play in every key, so a single just-intonation tuning would sound beautiful in one key and unacceptable in others. Equal temperament spreads the compromise evenly so that every key is equally usable, which is the practical trade-off fixed-pitch instruments accept.

Does changing the A4 reference change the comparison?

It changes the absolute frequencies and the beat rates, but not the cents differences. Cents and ratios are relative measurements, so the just major third is always 13.69 cents flatter than equal temperament regardless of reference pitch. However, because the beat rate is an absolute frequency difference, raising the reference from 440 Hz to a higher value increases the beat rate proportionally, since the same cents gap spans more hertz at a higher pitch.

Which intervals are the same in both tunings?

The unison (1:1) and the octave (2:1) are identical in equal temperament and just intonation, so they show a zero cents difference and no beating. Every other interval differs. The fifths and fourths differ by only about 2 cents, the major and minor seconds and sevenths by a few cents to about 12 cents, and the thirds and sixths by the largest amounts, roughly 14 to 16 cents.

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