What is Just Intonation in detailed terms, and how can I notate it?

In music, just intonation or pure intonation is the attempt to tune all 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 may be called a just interval; when it is sounded, no beating is heard.

1. How do you explain just intonation?
2. Is just intonation Pythagorean?
3. What does just intonation sound like?
4. What is just and equal intonation?

How do you explain just intonation?

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 ...

Is just intonation Pythagorean?

Applying the first part of this concept, some scholars refer to Pythagorean tuning as "3-limit just intonation," since all intervals are derived either from fifths (3:2) or octaves (2:1), ratios involving 3 as the largest prime.

What does just intonation sound like?

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.

What is just and equal intonation?

JUST TUNING or JUST INTONATION. 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).