Pythagorean Scale
Most consonant intervals:
•
1:1 – unison
•
2:1 – octave
–
12 semitones
•
3:2 – perfect 5
th
–
7
semitones
•
4:3 – perfect 4
th
–
5
semitones
Pythagoras (born about 580 B.C.)
The Pythagorean system is an attempt to build a complete chromatic scale
from only two of the pure tones: the octave and the perfect fifth
...
32
243
,
16
81
,
8
27
,
4
9
,
2
3
,
1
...
2
3
,
2
3
,
2
3
,
2
3
,
2
3
,
1
5
4
3
2
The goal was to close circle
(Circle of fifths), i.e. to end up
with the same note as started.
Unfortunately, it is impossible.
;
7
.
129
2
3
12
≈
128
2
7
=
2
3
4
2
3
=
If octave has 12 semitones, then 7 octaves have 12x7 semitones.
If perfect
5
th
has 7 semitones, 12 perfect
5
th
have 7x12 semitones.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Questions:
•
How to construct a convenient scale?
•
How to set up an interval between notes?
What is known:
•
Perfect fifth plus perfect forth is an octave
•
Perfect fourth up is the same as octave up and then perfect fifth down
•
Perfect fifth up is the same as octave up and then perfect fourth down
•
So we can use octave and perfect fifth to construct perfect fourth
•
12 perfect 5
th
are approximately equal to 7 octaves
12 semitones! 7 notes!
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '09
 #, Semitone, Equal temperament, Perfect fifth, Just intonation, Pythagorean Scale

Click to edit the document details