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8/7/2019 introduction to musical scales
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1.0 1.5 2.0
10
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0.2
0.4
0.6
0.8
1.0
0
0.2 0.4 0.6 0.8 1.00
0
0.2
0.4
0.6
0.8
1.0
d i ssonance
consonance
x critical bandwidth
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Frequency Difference f - f1
2
100
200
300
400
500
600
700
800
1000 2000 3000 4000 5000
Fifth
( 3/2
)
Whole T
one( 9/8
)
Mino
r Thir
d ( 6/5)
Center Frequency (Hz)
Critica
l Ban
d f CB
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0
1
2
3
4
5
6
250 300 350 400 450 500
1:1
5:64:5
3:4
2:3
3:5
1:2
dissonance
frequency in cps
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Pythagorean
Comma
C
G
D
A
E
F#
F
Bb
Eb
Ab
Db
Fifths up
Fifths down
Gb
B
}
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1 ( 2 )
98
23
1 6
2 7
F( 1)2
F( 1)
3
F( 1)
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3/2 9/8 27/16 81/64 243/1282/38/916/2764/81128/243
64/125
5/4
(per octave equivalence)
3/2 27/89/4 81/16 243/322/34/98/2716/8132/243
256/625
64/125
4/5
512/625
25/16
16/25
4/5
16/25
Intervalratio (5/4)
125/64
625/512625/256
125/64
25/16
5/4Intervalratio (3/2)
n
n
n n
Intervalratio (3/2) mod1 +1
Intervalratio (5/4) mod1 +1
(per octave equivalence)
Thirds
F i f t h s
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Thirds
F i f t h s
Thirds
F i f t h s
Thirds
F i f t h s
Thirds
F i f t h s
Thirds
F i f t h s
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0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
20
40
0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
5
10
15
0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
10
20
30
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0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
10
20
30
0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
5
10
0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
10
20
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1
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fifth
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third
0
5
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0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
2
4
6
0
1
2
3
4
5
6
7
fifth
0
1
2
3
4
5
6
7
third
0
2
4
6
8
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![Musical Scales: A Guitar Navigation Kit Ivan Radivojevic...The scales covered in this presentation fall into the following categories[1]: • Pentatonic (5 notes): Major, Minor, Dominant](https://img.dokumen.tips/doc/110x75/609eb396009c1f19ce24f3c7/musical-scales-a-guitar-navigation-kit-ivan-radivojevic-the-scales-covered.jpg)
