Pythagorean scale

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The Pythagorean scale is made by stacking of fifth.

It was used throughout the middle ages.

The scale comes by multiplying the frequency with 3/2, and dividing with an extra 2 every time you come over an octave.

It can be proven that it is impossible to get a multiplier of a prime number to be equal to the multiplication of another prime number. (The two numbers are furthermore even and uneven)

The difference on B# and C is 531441/524288 or 1,013643265. This is called the the comma of Pythagoras.

Hear the comma of Pythagoras

 

 
Tone
Frequency relation
 Rel. Frequency
F
4/3
1,333333333
C
1/1
1
G
3/2
 1,5
D
9/8
 1,125
A
27/16
 1,6875
E
81/64
 1,265625
H
243/128
 1,8984375
F#
729/512
 1,423828125
Db
2187/2048
 1,067871094
Ab
6561/4096
 1,601806641
Eb
19683/32768
 1,20135498
Bb
59049/65536
 0,901016235
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