4-8 Pythagorean Scale

What is the Pythagorean Scale?

The pythagorean scale is a mathematical scale developed from the musical fifth. The scale has intervals divided into tones and hemitones.

How was the scale formed?

1) Begin by putting the fifths in ascending order:

1	(3/2)	(3/2)^2	(3/2)^3	(3/2)^4	(3/2)^5
1	3/2	9//4	27/8	81/16	243/32

2) Now bring these notes into the same octave:

    1 stays 1
    3/2 stays 3/2
    9/4 turns into 9/8 (descends 1 octave)
    27/8 turns into 27/16 (descends 1 octave)
    81/16 turns into 81/64 (descends 2 octaves)
    243/32 turns into 243/128 (descends 2 octaves)

3) Next, arrange the notes into ascending order:

1

9/8

81/64

3/2

27/16

243/128

2

4) We can now see that the musical forth is missing. We can obtain this interval by descending from the beginning point a musical fifth and then moving up one complete octave.

5) Now we have all the notes forming the Pythagorean Scale:

1	9/8	81/64	4/3	3/2	27/16	243/128	2
do	re	mi	fa	sol	la	ti	do

Continue: #REDIRECT 4-9 Just Scale

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