just

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 ...

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.

Just temperament refers to a musical scale or musical intervals which maintain exact integer ratios between pitches. For example, the ration 3:2 is said to be a "just" musical fifth and is sometimes called a "perfect fifth".

A TUNING of a SCALE in just intonation involves the usage of FREQUENCY ratios based on integer proportions as found in the HARMONIC SERIES, instead of, for instance, a division of the OCTAVE into exactly equal parts (as in the case of EQUAL TEMPERAMENT).

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. There are several reasons for this.

The name "meantone temperament" derives from the fact that all such temperaments have only one size of the tone, while just intonation produces a major tone and a minor one, differing by a syntonic comma.

Pythagorean tuning is a type of just intonation. You don't quite get simple ratios by stacking P5, but what you get is also decent -> major/minor thirds and sixths are a schisma away from simple ratios, so you get a few good intervals in a 12 notes gamut.

Hence we can say that the Pythagorean theorem only works for right triangles. Q. Pythagoras' theorem holds good for right-angled triangles.

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. It is a compromise tuning scheme.

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.

The difference between just intonation and equal temperament lies in the focus of each tuning system: ET is easier to use and has been widely adopted. However, its harmonies don't sound as good as JI's. JI sounds harmonically in tune but can be melodically flat.

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.