What are the ratios of Just Intonation?

Asked by: Matt Boyce

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. An interval tuned in this way is said to be pure, and is called a just interval.

How do you calculate just intonation?

You can find the frequencies of the notes in the rest of the octaves by adding a multiplication or division by 2 in the calculation. For each additional octave upwards or downwards respectively.

What is 5 limit just intonation?

Five-limit tuning

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.

Is just intonation microtonal?

just intonation – microtonal musical tuning system and scale.

Is just intonation Pythagorean?

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.

How many notes are in just intonation?

To produce a twelve-tone scale, one of them is arbitrarily discarded. The twelve remaining notes are repeated by increasing or decreasing their frequencies by a power of 2 (the size of one or more octaves) to build scales with multiple octaves (such as the keyboard of a piano).

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

What ratio is a major 3rd?

A major third in just intonation corresponds to a pitch ratio of 5:4 or 386.31 cents; in equal temperament, a major third is equal to four semitones, a ratio of 21/3:1 or 400 cents, 13.69 cents wider than the 5:4 ratio. The older concept of a ditone made a dissonantly wide major third with the ratio 81:64.

How many cents is 1 octave?


Musical intervals are often expressed in cents, a unit of pitch based upon the equal tempered octave such that one equal tempered semitone is equal to 100 cents. An octave is then 1200¢ and the other equal tempered intervals can be obtained by adding semitones: If f1 = Hz and f2 = Hz then the interval is cents.

What is the ratio of a tritone?

The tritone in the 12-tone equal tempered scale divides the ‘octave’ precisely in half, and thus has a size of exactly 600 cents or 6.00 Semitones. Mathematically, since the “octave” is the ratio 2:1, this tritone is the square-root of 2, also written 2(1/2).

Is just intonation the harmonic series?

It states that just intonation is a method of tuning based on the intervals of the harmonic series. In the West, some of the oldest extant sources that give detailed accounts of rational or integer number ratios in music are the Division of the Canon by Euclid (fl.

Should I tune to equal or just temperament?

For the purposes of this chart, it is assumed that C4 = 261.63 Hz is used for both (this gives A4 = 440 Hz for the equal tempered scale).

Just vs Equal Temperament (and related topics)

Interval Ratio to Fundamental Just Scale Ratio to Fundamental Equal Temperament
Major Seventh 15/8 = 1.8750 1.88775

Does 3 4 5 make right triangles?

Yes, 3-4-5 makes a right triangle. Putting those numbers into the Pythagorean theorem and solving proves that they make a right triangle.

Does 9 12 15 form a right triangle?

Which set of sides could make a right triangle? Explanation: By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

Does 5 12 and 13 form a right triangle?

Yes, 5 12 and 13 make a right triangle. They are referred to as Pythagorean triplets, where 5 squared and 12 squared equal 13 squared, which is the application of the Pythagorean theorem.

Can a 6 8 10 make a right triangle?

When the side lengths of a triangle are in the ratio 3: 4: 5, then it is a right triangle. These sides are 6: 8: 10, then the triangle is a right one.

Does 1 2 3 make right triangles?

Thus, 1,2,3 is not a Pythagorean triple and sides of such lengths cannot form a right triangle.

Does 7 24 and 25 form a right triangle?

Yes, 7, 24, 25 is a Pythagorean Triple and sides of a right triangle.