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How does just intonation work?

Author

William Jenkins

Published Mar 06, 2026

How does just intonation work?

Just intonation, in music, system of tuning in which the correct size of all the intervals of the scale is calculated by different additions and subtractions of pure natural thirds and fifths (the intervals that occur between the fourth and fifth, and second and third tones, respectively, of the natural harmonic series

Also asked, do singers sing in just intonation?

Singers will tune to whatever is around them. If that's instruments in 12-TET, that's what they'll tune to. If it's a choir, they will probably tend to harmonise in just intonation, and also follow each other if they tend to drift flat or sharp from any initial reference pitch.

One may also ask, is Pythagorean tuning just intonation? In Pythagorean tuning, which was wedded to Pythagorean philosophy and thus to an expression of ratios within the three-limit system, all the intervals of the scale had to be derived, as we saw in the last page, from perfect fifths, the 3:2 ratio. In Just intonation, we add the ratios that include the numbers 5 and 6.

Similarly one may ask, is just intonation better?

Some people describe harmonies in Just Intonation as being "full" or "rich", while others describe them as "bland" or "lifeless". However, most people would agree that JI harmonies are considerably smoother than tempered harmonies.

What instruments use just intonation?

The modern un-fretted bowed string instruments; the violin, viola, cello and bass, can and do play in just intonation and can modulate to any key center and maintain just intonation. Modern brass instruments without valves, such as the bugle, play in just intonation in one key only.

How can I improve my intonation for singing?

To free up your voice, simply breathe in, and then as you breathe out perform a vocalised sigh. You'll notice this sounds like a pitch sweeping downwards, but it will probably feel more natural than regular singing exercises. Try and make your sigh as vocalised as possible so it's close to actually singing.

What is intonation for singing?

In music, intonation is the pitch accuracy of a musician or musical instrument. Intonation may be flat, sharp, or both, successively or simultaneously. In vocal music, intonation also signifies the singing of an opening phrase.

Why is intonation important in singing?

Because the intonation choices that the vocal ensemble singer faces are quite complex, work on intonation issues is central to vocal ensemble practice, not only in terms of exact pitches, but also concerning aspects of voice technique, communication between singers and the balancing of voices.

Do orchestras use equal temperament?

Meanwhile, an orchestra is made of a bunch of instruments, some of which tune naturally by ear—strings, woodwinds, brass—but also instruments in fixed, equal temperament: harp, marimbas and xylophones, harpsichord and piano, etc.

Why is intonation important in music?

In music, intonation refers to pitch accuracy - that is, whether a tone is played 'in tune' or not. In order to play or sing in tune with proper intonation, it is vitally important to have a keen sense of pitch differentiation.

How do I tune my guitar to intonation?

Tune all the open strings to what you want to set them to at the 12th fret harmonic. Now fret those strings at the 12th fret. If they're sharp or flat, the intonation has to be adjusted. This is done by moving the bridge saddles either forward or backward depending if those fretted notes are sharp or flat.

Why is just intonation not used?

Just intonation frequencies are based on the harmonic series. However, if an instrument is tuned with the frequencies obtained in the above manner, the instrument only sounds good in one key. In other keys it sounds out of tune (because the frequency ratios for the intervals are not simple integer fractions like 3/2).

What is the difference between just intonation and equal temperament?

Just tuning is often used by ensembles (such as for choral or orchestra works) as the players match pitch with each other "by ear." The "equal tempered scale" was developed for keyboard instruments, such as the piano, so that they could be played equally well (or badly) in any key.

Who invented just intonation?

Harry Partch

How many cents is a chord?

The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each.

Centitone.

CentitonesCents
100 per whole tone200 per whole tone

What is 5 limit just intonation?

The 5-limit consists of all just intonation intervals whose numerators and denominators are both products of the primes 2, 3, and 5; these are sometimes called regular numbers. Some examples of 5-limit intervals are 5/4, 6/5, 10/9 and 81/80.

What is a pure fifth?

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones.

How many cents flat is a minor third?

294.13 cents

How many cents is a semitone?

100 cents

When was just intonation used?

Supposedly used in medieval monophonic music (melody only, without harmony) and considerably discussed by theorists, just intonation proved impractical for polyphonic (multipart) music and was replaced at least by the year 1500 by meantone temperament.

Is Pythagorean tuning the same as equal temperament?

In equal temperament, pairs of enharmonic notes such as A♭ and G♯ are thought of as being exactly the same note—however, as the above table indicates, in Pythagorean tuning they have different ratios with respect to D, which means they are at a different frequency.

What is Pythagorean tuning used for?

Pythagorean tuning provides uniformity but not the chords. Just tuning, based on the simpler ratios of the overtone series, provides the chords but suffers from inequality of intervals. Meantone tuning provides equal intervals but gives rise to several objectionable chords, even in simple music. All…

What is the defining characteristic of a just intonation tuning system?

In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. Any interval tuned in this way is called a just interval.

How do you calculate Pythagorean tuning?

From a C, we will build a major scale according to the Pythagorean tuning. We first calculate the fifth by multiplying the frequency of C by 3/2 (fifth size): To multiply a number by a fraction we multiply by the numerator (top number) and then divide by the denominator (bottom number). G = 261 x 3 / 2.

How does the Pythagorean theorem relate to music?

Pythagoras observed several ratios of sound wave frequencies and the corresponding intervals between them, including 4:3 (known to musicians as the interval of a perfect fourth, or two pitches that are five semitones apart from each other) and 3:2 (a perfect fifth, seven semitones apart).

What does Pythagoras say about music?

Pythagoras believed that the planets themselves, all heavenly bodies, rang out notes of vibration based on their orbit and distance to each other. We humans simply lack the ability to hear this music of the spheres. These mathematical ratios helped to define every system of intonation throughout history.

How many cents is a syntonic comma?

21.51 cents

Is a guitar equal tempered?

Guitars are tuned to 'equal temperament'. The basic way to understand this is that the 12 musical notes are evenly split up, which allows us to use straight frets on a guitar.

What does semitone mean?

A semitone (sometimes called a half tone or a half step) is the distance from a white key to a neighboring black key on the piano keyboard—for example, from G to G-sharp or from E to E-flat. Semitones are the smallest intervals that are used intentionally in almost any of the music you'll normally hear.

What is Justonic?

Short definition for those who just want to play: (go to technical definition) The Justonic system allows fixed tone or fretted instruments (keyboards and guitars) to play pure harmonic music which requires that all notes must be flexible, and they must be precisely retuned, on the fly, in real-time as you play.

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