Just intonation: Encyclopedia II - Just intonation - The diatonic scale in just intonation

Just intonation - The diatonic scale in just intonation

It is possible to tune the familiar diatonic scale or chromatic scale in just intonation, in many ways, all of which make certain chords purely tuned and as consonant as possible, and others considerably more dissonant and indeed seeming out-of-tune to modern ears (see below for more on this).

The prominent notes of a given scale are tuned so that the ratios of their frequencies are comprised of relatively small integers. For example, in the key of G major, the ratio of the frequencies of the notes G:D (perfect fifth) is 2:3, while that of G:C (perfect fourth) is 3:4.

All ratios that involve the prime numbers of 2, 3 and 5 can be built out of the following 3 basic intervals:

• s=16:15 Semitone
• t=10:9 Minor tone
• T=9:8 Major tone

from which we get:

• 6:5 = Ts (minor third)
• 5:4 = Tt (major third)
• 4:3 = Tts (perfect fourth)
• 3:2 = TTts (perfect fifth)
• 2:1 = TTTttss (octave)

It gives rise to the following scale in the key of G (this is only one possibility):

G A B C D E F# G
 T t s T t T  s

with ratios w.r.t. G of

A 9/8, B 5/4, C 4/3, D 3/2
E 5/3, F# 15/8 and G 2/1

Adapted from the Wikipedia article "The diatonic scale in just intonation", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki