4-9 Just Scale

What is the just scale?

The just scale is based on the overtone series and is developed from the major triad. However, the scale does not transfer between pitches. This means that the tuning for a C major scale is different then a D major scale under the just temperament.

How was the scale formed?

1. Start by forming a major triad:

do	mi	sol
f	(5/4)f	(3/2)f
4	5	6

2. Now, form major triads from sol going up and from do going down:

		do	mi	sol
		f	(5/4)f	(3/2)f
fa'	la'	do		sol	ti	re'
(2/3)f	(5/6)f	f		(3/2)f	(15/8)f	(9/4)f
4	5	6		4	5	6

3. Next, put the notes into a singe octave:

    (2/3)f becomes (4/3)f (ascends 1 octave)
    (5/6)f becomes (10/6)f (ascends 1 octave)
    f stays f
    (5/4)f stays (5/4)f
    (3/2)f stays (3/2)f
    (15/8)f stays (15/8)f
    (9/4)f becomes (9/8)f (descends 1 octave)

4. Finally, put the frequencies into ascending order:

f	(9/8)f	(5/4)f	(4/3)f	(3/2)f	(10/6)f	(15/8)f	2f
do	re	mi	fa	sol	la	ti	do

Continue: #REDIRECT 4-10 Tempered Scale

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