Scale

1
Scale

• Array of certain discrete frequencies chosen for
  musical purposes
• Note An individual frequency of the scale

2
Consonance
A combination of two or more tones of different
frequencies that is generally agreed to have a
pleasing sound
Ratio of Consonant Frequency
11, 12, 23, 34
3
Interval
When the frequency ratio is 21,
octave
When the frequency ratio is 32,
fifth
When the frequency ratio is 43,
fourth
Interval separation of two notes in the scale
4
Interval
5
Physical meaning of Interval
Ratio of frequencies independent of differences
of frequencies
Fifth 32 Fourth 43 Octave 21
6
Scales
Pentatonic scales
Pythagorean scale
Just scale
Equal temperament scale
7
2f
f
2f
f
Pentatonic scale or Five tone scale
8
Pythagorean Scales
An octave is fourth plus a fifth going up a
forth leads to the same letter as going down a
fifth and vice versa.
All notes on the scale can be reached by going up
or down 12 successive fifths or 12 successive
fourths.
9
Circle of Fifths
F
C
Gb
Db
B
Cb
G
Ab
Fb
E
Eb
Bbb
D
A
Ebb
Bb
D
A
Abb
F
G
C
E
C
10
Pythagorean Scale
Pythagorean diatonic scale
Interval 98
Pythagorean whole tone
Interval 256243
Pythagorean diatonic semitone
11
Pythagorean Scale
Advantages
Emphasis on perfect fifths and fourths ? Many
concert violinists tend to favor Pythagorean
tuning in their performance
Disadvantages
Poor tuning of thirds
12
Just Scale
The scale based on the major triad, a group of
three notes that sound particularly harmonious
(CEG)
The frequency ratios of the notes in the major
triad 456
21 octave 32 perfect fifth 43 perfect
fourth 53 major sixth 54 major third 85
minor sixth 65 minor third
13
Equal Temperament
?Most convenient temperament ?All semitones are
the same
An octave 12 equal semitones Whole tone twice
the size of the semitones
2
1
One semitone
Fifth
Fourth
14
Cents
I (cents) interval in cents R a frequency ratio
One cent 1/100 of a semitone in equal temperament
Octave 1200 cents Fifth Fourth Major
third Major sixth
700 cents
500 cents
400 cents
900 cents
15
Just
Pythagorean
Tempered
Ratio
Cents
Cents
Ratio
Cents
Note
1200 1224 1086 1110 996 1020 906 732 816 702 588 6
12 498 522 384 408 294 318 204 90 114 0
C B Cb B Bb A A Ab G G Gb F F E Fb E Eb D D
Db C C
1200 1200 1100 1100 1000 1000 900 800 800 700 600
600 500 500 400 400 300 300 200 100 100 0
2.000 1.953 1.920 1.875 1.800 1.758 1.667 1.600 1.
563 1.500 1.440 1.406 1.333 1.302 1.280 1.250 1.20
0 1.172 1.125 1.037 1.042 1
1200 1159 1129 1088 1018 977 884 814 773 702 631 5
90 498 457 427 386 316 275 204 112 71 0
2.000 2.027 1.873 1.898 1.778 1.802 1.688 1.58 1.6
02 1.500 1.405 1.424 1.333 1.352 1.249 1.266 1.185
1.201 1.125 1.054 1.068 1.000
16
(No Transcript)