Sound of Music
93
Sound of Music How It Works Session 4 Musical Scales: Foundations of Music OLLI at Illinois Spring 2020 D. H. Tracy Easley Blackwood Suite for Guitar in 15- note Equal Tuning, Op. 33 Jeffrey Kust, guitarist (1990) Prelude (Allegro)
Transcript of Sound of Music
Sound of MusicHow It Works
Session 4Musical Scales: Foundations of Music
OLLI at Illinois
Spring 2020
D. H. Tracy
Easley BlackwoodSuite for Guitar in 15-
note Equal Tuning, Op. 33Jeffrey Kust, guitarist
(1990)
Prelude (Allegro)
Sound of MusicHow It Works
Session 4Musical Scales: Foundations of Music
OLLI at Illinois
Spring 2020
D. H. Tracy
Course Outline
1. Building Blocks: Some basic concepts
2. Resonance: Building Sounds
3. Hearing and the Ear
4. Musical Scales
5. Musical Instruments
6. Singing and Musical Notation
7. Harmony and Dissonance; Chords
8. Combining the Elements of Music
2/18/20 Sound of Music 4 3
Sound Familiar?
• Listen carefully to 4 notes
– 2 are “real”, 2 are “bogus”
• In isolation, it makes little difference…
– but in the context of a musical piece it may matter
2/18/20 Sound of Music 4 4
Music is Made with Notes Having Different Frequencies
• But how are these frequencies chosen?
• Example using Fixed Frequencies…
• But what if we used random frequencies?– Each note frequency
chosen at random • (within a small range)
• Music can be made with non-fixed frequencies
2/18/20 Sound of Music 4 5
2/18/20 Sound of Music 4 6
1000
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500
400
300
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100
0
Freq
ue
ncy
(H
z)The Octave As the
Universal Frequency Interval
100 Hz
200 Hz
400 Hz
800 Hz
But these wereComplex Tones with 16 Harmonics….
2/18/20 Sound of Music 4 7
1000
900
800
700
600
500
400
300
200
100
0
Freq
ue
ncy
(H
z)
Higher Octaves Contain NO additional
frequencies!
100 Hz
200 Hz
400 Hz
800 Hz
The Octave As the Universal Frequency
Interval
2/18/20 Sound of Music 4 8
1000
900
800
700
600
500
400
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100
0
Freq
ue
ncy
(H
z)
100 Hz
200 Hz
The Octave As the Universal Frequency
Interval
200 Hz100 Hz +
10
9
8
7
6
5
4
3
2
1
• The Combination of f and its octave sounds good
• The Combination f + 2fsounds a lot like f alone
2/18/20 Sound of Music 4 10
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Freq
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(H
z)
200 Hz
The Octave As the Universal Frequency
Interval
200 Hz + 400 Hz
10
9
8
7
6
5
4
3
2
1
• Again, the Combination of fand its octave sound good
• The Combination f + 2fsounds somewhat like f alone
400 Hz
200 Hz + 380 Hz
2/18/20 Sound of Music 4 11
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Freq
ue
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(H
z)
200 Hz
The Octave As the Universal Frequency
Interval10
9
8
7
6
5
4
3
2
1
• The Combination of f and its not-quite-octave sounds terrible
380 Hz
2/18/20 Sound of Music 4 12
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Freq
ue
ncy
(H
z)
200 Hz
The Octave As the Universal Frequency
Interval10
9
8
7
6
5
4
3
2
1
200 Hz + 397 Hz
• If we are close to an Octave, we can hear the beats
397 Hz
2/18/20 Sound of Music 4 13
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Freq
ue
ncy
(H
z)
200 Hz
The Octave As the Universal Frequency
Interval
200 Hz + 397 Hz
• Without Harmonics,Nothing so special
about the Octave
397 Hz
What if we used simple tones?No Harmonics…
2/18/20 Sound of Music 4 15
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800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
The Octave As the Universal Frequency
Interval
200 Hz + 380 Hz
• Again, without Harmonics,Nothing really special
about the octave
380 Hz
What if we used simple tones?No Harmonics…
2/18/20 Sound of Music 4 16
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1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
The Octave As the Universal Frequency
Interval
• With real musical notes having harmonics,Octave Ratios are a very good thing• most musical instruments are rich in harmonics• including the human voice
• Virtually all formal musical traditions organize scales by Octaves
• We will therefore construct Scales based on Octave Ratios400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
2/18/20 Sound of Music 4 17
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
300
600
1200
2400
2/18/20 Sound of Music 4 18
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1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
2. How should they be distributed?- i.e., exactly what frequencies?
2/18/20 Sound of Music 4 19
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
2. How should they be distributed?- i.e., exactly what frequencies?
f = 40 Hz
f = 80 Hz
f = 20 Hz
f = 10 Hz
So here we’ve chosen n=10 notes per octave, equally
spaced by 40 Hz
2/18/20 Sound of Music 4 20
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
2. How should they be distributed?- i.e., exactly what frequencies?
f = 40 Hz
f = 80 Hz
f = 20 Hz
f = 10 Hz
So here we’ve chosen n=10 notes per octave, equally
spaced by 40 Hz
But we have a problem. The notes at the bottom are too
crowded to see, while there is empty space at the top.
We need a different frequency scale.
A monk* came up with an answer 1000 years ago…
2/18/20 Sound of Music 4 21
Log ofFrequency
*Guido of Arezzo 1025
Use a compressed Logarithmic
Frequency Scale
2/18/20 Sound of Music 4 22
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1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
2. How should they be distributed?- i.e., exactly what frequencies?
Then This…
2/18/20 Sound of Music 4 23
1600
800
400
200
100
50
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
• If we add a note in one Octave, we need to add it in all Octaves.
400 Hz
100 Hz
50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
2. How should they be distributed?- i.e., exactly what frequencies?
150
75
Becomes This…Much clearer and
easier to see.Each octave looks
the same!
2/18/20 Sound of Music 4 24
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Freq
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ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
400 Hz
100 Hz
50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?
150
75
• Enough to make interesting musicbut…
• Not too many, lest weo Over-complicate Instrumentso Confuse listenerso Burden Composers
▪ Actual scales use from 5 to 24 notes/octave
2/18/20 Sound of Music 4 25
1600
800
400
200
100
50
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
400 Hz
100 Hz
50 Hz
800 Hz
1600 Hz
300
600
1200
2400
Two Choices to Make:
1. How many notes per Octave?2. How should they be distributed?
- i.e., exactly what frequencies?
150
75
• We want to choose notes that play well together for melody and harmony
• Ideally, we’d like a smooth, regular distribution
▪ Better yet, so regular that we could anchor an octave at any note!
Our original choice seen here was a bad one!
2/18/20 Sound of Music 4 26
1600
800
400
200
100
50
Freq
ue
ncy
(H
z)
200 Hz
Constructing Scalesbased on Octaves
400 Hz
100 Hz
50 Hz
800 Hz
1600 Hz
300
600
1200
2400
150
75
Our Focus: “Mother Scale”
• 12 Notes Per Octave
• Equal Spacing (on Log Scale)
➢ Clean➢ Simple➢ Elegant
… but not musically ideal
2/18/20 Sound of Music 4 27
Freq
ue
ncy
f→
• 12 Notes Per Octave
• Equal Spacing (on Log Scale)
Octave
So What Is This Mother Scale?
▪ Equal Ratios of Adjacent Frequencies➢ Ratio = 1.05946…➢ Each note 6% Higher
100 Hz
105.9 Hz6% increase
141.42136
112.2 118.9
126.0 133.5
149.8 158.7
168.2
178.2 188.8
200 Hz 12
11
10
9
8
7
6
5
4
3
2
1
0
2/18/20 Sound of Music 4 28
Freq
ue
ncy
f→
• 12 Notes Per Octave
• Equal Spacing (on Log Scale)
Octave
So What Is This Mother Scale?
▪ Equal Ratios of Adjacent Frequencies➢ Ratio = 1.05946…➢ Each note 6% Higher
100 Hz
105.9 Hz6% increase
141.42136
112.2 118.9
126.0 133.5
149.8 158.7
168.2
178.2 188.8
200 Hz 12
11
10
9
8
7
6
5
4
3
2
1
0
Using the Calculator on your PC or phone…
2/18/20 Sound of Music 4 29
Freq
ue
ncy
f→
• 12 Notes Per Octave
• Equal Spacing (on Log Scale)
Octave
So What Is This Mother Scale?
12
11
10
9
8
7
6
5
4
3
2
1
0100 Hz
A Particular Example of such a12-tone Equal Tempered scale is…
…….
“The 12 Tone Chromatic Scale”
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
30
The Chromatic Scale
fMIDI
.
Piano
Sound of Music 42/18/20
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
31
The Chromatic Scale
f
.
Piano
Sound of Music 42/18/20
424039373533323028
626058
5553
504846
4341
383634
3129
64636159575654525149474544
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
32
The Chromatic Scale
fMIDIPiano
Sound of Music 42/18/20
MIDI* Data
* Musical Instrument Digital Interface
424039373533323028
626058
5553
504846
4341
383634
3129
64636159575654525149474544
We can label these notes by Piano key # or MIDI note code numbers, which are piano key+20
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
2/18/20 Sound of Music 4 33
The Chromatic Scale
fMIDIPitch Class
All the C notesbelong to
Pitch Class Zero
Similarly, all the D notes belong to Pitch Class 2
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
Sound of Music 4 35
The Chromatic Scale
fMIDIPitch Class Solfège
2/18/20
Note
Solfege syllables used for singer training, and also as the Names of Notes in France, Spain, Italy, Russia etc.
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
Sound of Music 4 36
The Chromatic Scale
fMIDIPitch Class Solfège
2/18/20
Note
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
Sound of Music 4 37
The Chromatic Scale
fMIDIPitch Class Solfège
2/18/20
Note
Note that many notes are left out of Julie Andrews’ Song…
Alternate Scales with n 12: “Microtonal Scales”
2/18/20 Sound of Music 4 38
Easley Blackwood, Jr.(1933- )
Former music professor at U. of Chicago
Cedille Records 1994
Compositions inn-Tone Equal
Temperament:13-tone
To24-tone Scales
(Synthesizerand
Modified Guitar)
Example:
Fanfare in 19-note Equal Tuning, Op. 28a(Blackwood, Polyfusion Synthesizer)
. . . . . . . . . . . . . . . . .
Di64
C#/D♭ 6 165 85 1108.7C 6 0 Do84 1046.5
6263 83 987.8
82 932.3TiB 5 11
A#/B♭ 5 10 LiLa
60A 5 961 81 880
G#/A♭ 5 8 Si80 830.6
5859 79 784.0
78 740.0SolG 5 7
F#/G♭ 5 6 FiFa
56F 5 557 77 698.5E 5 4 Mi76 659.3
5455 75 622.3
74 587.3RiD#/E♭ 5 3
D 5 2 ReDi
52C#/D♭ 5 153 73 554.4
C 5 0 Do72 523.3
5051 71 493.9
70 466.2TiB 4 11
A#/B♭ 4 10 LiLa
48A 4 949 69 440
G#/A♭ 4 8 Si68 415.3
4647 67 392.0
66 370.0SolG 4 7
F#/G♭ 4 6 FiFa
44F 4 545 65 349.2E 4 4 Mi64 329.6
4243 63 311.1
62 293.7RiD#/E♭ 4 3
D 4 2 ReDi
40C#/D♭ 4 141 61 277.2
C 4 0 Do60 261.6B 3 1139 59 246.9
38 A#/B♭ 3 10 Li58 233.1A 3 937 57 220
36 G#/A♭ 3 8 Si56 207.7G 3 735 55 196.0
34 F#/G♭ 3 6 Fi54 185.0F 3 533 53 174.6
32 E 3 4 Mi52 164.8D#/E♭ 3 331 51 155.6
30 D 3 2 Re50 146.8C#/D♭ 3 129 49 138.6
28 C 3 0 Do48 130.8B 2 1127 47 123.5
26 A#/B♭ 2 10 Li46 116.545 110 LaA 2 925
Ti
Di
Ri
Fa
Sol
La
Ti
12 Note Per Octave Equal Tempered Scale:
Sound of Music 4 39
The Chromatic Scale
fMIDIPitch Class Solfège
2/18/20
Note
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7Subscales of The Chromatic Scale
Sound of Music 4 40
fMIDI
2/18/20
Note ChromaticScale
• Most Western music genres do not use the whole Chromatic Scale➢ Instead, they use smaller Subscales
• Such Subscale music includes:➢ Almost all pre-1910 music
▪ Traditional▪ Classical▪ Liturgical
➢ Pop music➢ Rock➢ Country and Bluegrass
• Music using the Chromatic Scale includes:➢ Modern “atonal” music (post-1910)➢ Much Jazz
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7Subscales of The Chromatic Scale
Sound of Music 4 41
fMIDI
2/18/20
Note ChromaticScale
How many Subscales are there?
Examples for m = 3-note Subscales
All together, 55 Patterns like these for m=3
But each Pattern could be anchored at 12
different noteswithin an Octave
So there are 12 x 55 = 660 m=3 Subscales
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7Subscales of The Chromatic Scale
Sound of Music 4 42
fMIDI
2/18/20
Note ChromaticScale
m Notes
Patterns Keys Total Scales
1 1 12 12
2 11 12 132
3 55 12 660
4 165 12 1980
5 330 12 3960
6 462 12 5544
7 462 12 5544
8 330 12 3960
9 165 12 1980
10 55 12 660
11 11 12 132
12 1 12 12
Pentatonic
Heptatonic(Includes Diatonic)
Used for Jazz?
Traditional Country Music
Blues
ClassicalPopRock
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7The Pentatonic (5 note) Subscales of
The Chromatic Scale
Sound of Music 4 43
fMIDI
2/18/20
Note ChromaticScale
There are 330 m=5 Patterns…
Reasonable rules:1. Avoid gap of 4 or more2. Avoid adjacent gaps of 3
With these rules, there arejust 5 Patterns possible!
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 4 45
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
Reasonable rules:1. Avoid gap of 4 or more2. Avoid adjacent gaps of 3
With these rules, there arejust 5 Patterns possible!
There are 330 m=5 Patterns…
these
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 4 46
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
Reasonable rules:1. Avoid gap of 4 or more2. Avoid adjacent gaps of 3
With these rules, there arejust 5 Patterns possible!
There are 330 m=5 Patterns…
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 4 47
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
Reasonable rules:1. Avoid gap of 4 or more2. Avoid adjacent gaps of 3
With these rules, there arejust 5 Patterns possible!
There are 330 m=5 Patterns…
Take the basic pattern and wrap it into a circle..
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 4 48
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
Reasonable rules:1. Avoid gap of 4 or more2. Avoid adjacent gaps of 3
With these rules, there arejust 5 Patterns possible!
There are 330 m=5 Patterns…
1211
10
9
8
76
5
4
3
2
1
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 449
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
1211
10
9
8
76
5
4
3
2
1
The Pentatonic Scale Circle:5 Modes of the Minor
Pentatonic Scale
minor Pentatonic Scale
Major Pentatonic Scale Egyptian Pentatonic Scale
Blues Minor Pentatonic Scale
Blues Major Pentatonic Scale
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 450
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
1211
10
9
8
76
5
4
3
2
1
The Pentatonic Scale Circle:5 Modes of the Minor
Pentatonic Scale
minor Pentatonic Scale
Major Pentatonic Scale
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 451
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
1211
10
9
8
76
5
4
3
2
1
The Pentatonic Scale Circle:5 Modes of the Minor
Pentatonic Scale
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 452
fMIDI
2/18/20
Note ChromaticScale The Pentatonic (5 note) Subscales of
The Chromatic Scale
1211
10
9
8
76
5
4
3
2
1
The Pentatonic Scale Circle:5 Modes of the Minor
Pentatonic Scale
minor Pentatonic Scale
Major Pentatonic Scale
How can musicians remember
these scales?
3
2
3
2
2
2-2-3-2-3
2
3
2
2
3
3-2-2-3-2
Triple
Double
Triple
Double
Double
DDTDT
minor
Major
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 454
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
The Pentatonic (5 note) Subscales of The Chromatic Scale: 12 KeysThe Pentatonic
Major Scalein 12 Keys →
Pentatonic Scalein Key of
C Major
CMaj
Pentatonic Scalein Key of
Bb Major
B bMaj
BMaj
DMajD b
Maj
E bMaj
EMaj
FMaj
GMaj
AMaj
G bMaj
A bMaj
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 455
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
The Pentatonic (5 note) Subscales of The Chromatic Scale: 12 KeysThe Pentatonic
Major Scalein 12 Keys →
Pentatonic Scalein Key of
C Major
CMaj
Pentatonic Scalein Key of
Bb Major
B bMaj
BMaj
DMajD b
Maj
E bMaj
EMaj
FMaj
GMaj
AMaj
G bMaj
A bMaj
Curiosity:C Major Uses
only White Piano Keys
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 456
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
The PentatonicMinor Scale
also has 12 Keys →
Pentatonic Scalein Key of
C minor
Cminor
B bminor
Dminor
D bminor
Eminor
Fminor
Gminor
Aminor
G bminor
A bminor
Pentatonic Scalein Key ofB minor
Bminor
E bminor
The Pentatonic (5 note) Subscales of The Chromatic Scale: 12 Keys
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 457
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
The PentatonicMinor Scale
also has 12 Keys →
Pentatonic Scalein Key of
C minor
Cminor
B bminor
Dminor
D bminor
Eminor
Fminor
Gminor
Aminor
G bminor
A bminor
Pentatonic Scalein Key ofB minor
Bminor
E bminor
The Pentatonic (5 note) Subscales of The Chromatic Scale: 12 Keys
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 458
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
E minor
The Pentatonic (5 note) Subscalesof The Chromatic Scale: Relative Keys
GMajor
If these 2 scales share theexact same notes …
then what is the difference between them?
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 459
fMIDI
2/18/20
Note ChromaticScale
1211
10
9
8
76
5
4
3
2
1
minor Pentatonic Scale
Major Pentatonic Scale
minor
Major
E minor
The Pentatonic (5 note) Subscalesof The Chromatic Scale: Relative Keys
GMajor
If these 2 scales share theexact same notes …
then what is the difference between them?
The “anchor notes” are different.These are called the
Tonic NotesThey form the “Pitch Center” of
the musical piece
Old MacDonaldHad a Farm
in Pentatonic G Major
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
f68
f69
f70
f71
f72
f73
f74
f75
f76
f77
f78
f79
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
G#4 415.30Hz
A4 440.00Hz
A#4 466.16Hz
B4 493.88Hz
C5 523.25Hz
C#5 554.37Hz
D5 587.33Hz
D#5 622.25Hz
E5 659.26Hz
F5 698.46Hz
F#5 739.99Hz
G5 783.99Hz
Pentatonic
G MajorScale
2/18/20 Sound of Music 4 60
Old MacDonaldHad a Farm
in Pentatonic G Major
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
f68
f69
f70
f71
f72
f73
f74
f75
f76
f77
f78
f79
11
6
30
6
6
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
G#4 415.30Hz
A4 440.00Hz
A#4 466.16Hz
B4 493.88Hz
C5 523.25Hz
C#5 554.37Hz
D5 587.33Hz
D#5 622.25Hz
E5 659.26Hz
F5 698.46Hz
F#5 739.99Hz
G5 783.99Hz
Pentatonic
G MajorScale
2/18/20 Sound of Music 4 63
f43
f44
f45
f46
f47
f48
f49
f50
f51
f52
f53
f54
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
G2 98.00Hz
G#2 103.83Hz
A2 110.00Hz
A#2 116.54Hz
B2 123.47Hz
C3 130.81Hz
C#3 138.59Hz
D3 146.83Hz
D#3 155.56Hz
E3 164.81Hz
F3 174.61Hz
F#3 185.00Hz
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
Swing LowSweet Chariot
in Pentatonic G MajorPentatonic
G MajorScale
2/18/20 Sound of Music 4 64
f43
f44
f45
f46
f47
f48
f49
f50
f51
f52
f53
f54
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
6
7
49
3
20
14
3
G2 98.00Hz
G#2 103.83Hz
A2 110.00Hz
A#2 116.54Hz
B2 123.47Hz
C3 130.81Hz
C#3 138.59Hz
D3 146.83Hz
D#3 155.56Hz
E3 164.81Hz
F3 174.61Hz
F#3 185.00Hz
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
Pentatonic
G MajorScale
Tonal Center
Swing LowSweet Chariot
in Pentatonic G Major
2/18/20 Sound of Music 4 66
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7Subscales of The Chromatic Scale
Sound of Music 4 67
fMIDI
2/18/20
Note ChromaticScale
m Notes
Patterns Keys Total Scales
1 1 12 12
2 11 12 132
3 55 12 660
4 165 12 1980
5 330 12 3960
6 462 12 5544
7 462 12 5544
8 330 12 3960
9 165 12 1980
10 55 12 660
11 11 12 132
12 1 12 12
Pentatonic
Heptatonic(Includes Diatonic)
Used for Jazz?
Traditional Country Music
Blues
ClassicalPopRock
Only ~20 are useful
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7The Heptatonic (7 note) Subscales of
The Chromatic Scale
Sound of Music 4 68
fMIDI
2/18/20
Note ChromaticScale
There are 462 m=7 Patternsbelonging to 66 families
If we require reasonably uniformcoverage of the 12 notes of the
Chromatic Scale, only 3 mainPattern families emerge…
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 470
fMIDI
2/18/20
Note ChromaticScale
Major Diatonic
minor
Major
minor
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
“The” DiatonicFamily Pattern
Heptatonic Pattern Family #1:
“Diatonic”
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 471
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
Major Diatonic
minor
Major
minor
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
“The” DiatonicFamily Pattern
Diatonic Pattern
2
2
2
2
2
1
1
Heptatonic Pattern Family #1:
“Diatonic”
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
72
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“The” DiatonicFamily Patterns
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
73
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“The” DiatonicFamily Patterns
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
74
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
“Major” modes
“minor” modes
Rare (sounds terrible)
4th Step3rd Step
“Natural Major”
“Natural minor”
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
75
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Most Uniform Coverage of the Octave
“Major” modes
“minor” modes
Rare (sounds terrible)
4th Step3rd Step
“Natural Major”
“Natural minor”
These 7 Modes have names:
1. Ionian (a.k.a. Natural Major)
2. Dorian3. Phrygian4. Lydian5. Mixolydian6. Aeolian (a.k.a. Natural minor)
7. Locrian
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
76
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“Major” modes
“minor” modes
Rare (sounds terrible)
The Diatonic (7 note) Subscales of The Chromatic Scale: 12 Keys
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
77
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“Major” modes
“minor” modes
Rare (sounds terrible)
The Diatonic (7 note) Subscales of The Chromatic Scale: 12 Keys
“Tonics”
“Dominants”(5th Notes)
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
78
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“Major” modes
“minor” modes
Rare (sounds terrible)
The Diatonic (7 note) Subscales of The Chromatic Scale: 12 KeysThere are 12 Keys:
C Db D Eb E F Gb G A Bb B
for each of 7 Modes
for a total of 7x12 =
84 Diatonic Scales
Tonics
Dominants
Sound of Music 4
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
79
fMIDI
2/18/20
Note ChromaticScale
Diatonic Pattern
1211
10
9
8
76
5
4
3
2
1
minor
Major
minor
“Natural Major” mode
“Natural minor” mode
The Diatonic (7 note) Subscales of The Chromatic Scale:
The Principal Modes
These are the Biggies
Beethoven Sonata No. 8
in C minor (??)Pathetique
f36f37f38f39f40f41
f42
f43
f44
f45
f46
f47
f48
f49
f50
f51
f52
f53
f54
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
f68
f69
f70
f71
f72
f73
f74
f75
f76
C2 65.41HzC#2 69.30HzD2 73.42Hz
D#2 77.78HzE2 82.41HzF2 87.31Hz
F#2 92.50Hz
G2 98.00Hz
G#2 103.83Hz
A2 110.00Hz
A#2 116.54Hz
B2 123.47Hz
C3 130.81Hz
C#3 138.59Hz
D3 146.83Hz
D#3 155.56Hz
E3 164.81Hz
F3 174.61Hz
F#3 185.00Hz
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
G#4 415.30Hz
A4 440.00Hz
A#4 466.16Hz
B4 493.88Hz
C5 523.25Hz
C#5 554.37Hz
D5 587.33Hz
D#5 622.25Hz
E5 659.26Hz
C minorScale
2/18/20 Sound of Music 4 80
Beethoven Sonata No. 8in C minor(??)
Pathetique[first 60 sec]
f36f37f38f39f40f41
f42
f43
f44
f45
f46
f47
f48
f49
f50
f51
f52
f53
f54
f55
f56
f57
f58
f59
f60
f61
f62
f63
f64
f65
f66
f67
f68
f69
f70
f71
f72
f73
f74
f75
f76
2
4
5
6
8
4
10
15
36
9
22
17
1
18
10
11
1
23
1
3
9
10
1
14
5
3
1
4
1
C2 65.41HzC#2 69.30HzD2 73.42Hz
D#2 77.78HzE2 82.41HzF2 87.31Hz
F#2 92.50Hz
G2 98.00Hz
G#2 103.83Hz
A2 110.00Hz
A#2 116.54Hz
B2 123.47Hz
C3 130.81Hz
C#3 138.59Hz
D3 146.83Hz
D#3 155.56Hz
E3 164.81Hz
F3 174.61Hz
F#3 185.00Hz
G3 196.00Hz
G#3 207.65Hz
A3 220.00Hz
A#3 233.08Hz
B3 246.94Hz
C4 261.63Hz
C#4 277.18Hz
D4 293.66Hz
D#4 311.13Hz
E4 329.63Hz
F4 349.23Hz
F#4 369.99Hz
G4 392.00Hz
G#4 415.30Hz
A4 440.00Hz
A#4 466.16Hz
B4 493.88Hz
C5 523.25Hz
C#5 554.37Hz
D5 587.33Hz
D#5 622.25Hz
E5 659.26Hz
C minor
E flat minor
2/18/20 Sound of Music 4 82
1211
10
9
8
76
5
4
3
2
1
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 483
fMIDI
2/18/20
Note ChromaticScale
Major Diatonic
minor
Major
minor
The Harmonic Minor Scale Subscales of The Chromatic Scale:
Less Uniform Coverage of the Octave
Harmonic MinorFamily Pattern
HarmonicMinor
Pattern
Heptatonic Pattern Family #2:
“Harmonic Minor”
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 484
fMIDI
2/18/20
Note ChromaticScale
HarmonicMinor
Pattern
1211
10
9
8
76
5
4
3
2
1
Major Diatonic
minor
Major
minor
The Harmonic Minor Scale Subscales of The Chromatic Scale:
Less Uniform Coverage of the Octave
Harmonic MinorFamily Pattern
Heptatonic Pattern Family #2:
“Harmonic Minor”
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7
Sound of Music 485
fMIDI
2/18/20
Note ChromaticScale
MelodicMinor
Pattern
1211
10
9
8
76
5
4
3
2
1
Major Diatonic
minor
Major
minor
The Melodic Minor Scale Subscales of The Chromatic Scale:
Also Less Uniform Coverage of the Octave
Melodic MinorFamily Pattern
Heptatonic Pattern Family #3:
“Melodic Minor”
Only Change from Harmonic Minor
2/18/20 Sound of Music 4 86Sound of Music
After the Apocalypse…..What if you were called upon
to reconstruct modern music?
Important Subscales of the Chromatic Scale
2/18/20 Sound of Music 4
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
1211
10
9
8
76
5
4
3
2
1
Pentatonic
Scale
CB
A
D
E
FG
C#/Db
D#/Eb
F#/Gb
G#/Ab
A#/Bb 1211
10
9
8
76
5
4
3
2
1
Chromatic
Scale440 Hz
+6%*
122*
HarmonicMinorPattern
1211
10
9
8
76
5
4
3
2
1
MelodicMinorPattern
1211
10
9
8
76
5
4
3
2
1
m
M
Modes
Major
minor
5 Modes12 Keys
7 Modes12 Keys
75
12
87
Chords
• 2 or more notes played simultaneously
– Commonly 3 or 4 (Triads or Tetrads)
– Normally chosen to sound good together
• Require musical instrument capable of simultaneous notes
– e.g. Piano, Organ, Guitar, Harp
– NOT Singing Voice, Bowed Strings, Woodwinds, Brasses etc.
• Much more common in Western music than in other traditions
• Frequently occur in sequences called Progressions
2/18/20 Sound of Music 4 88
• Combination of 2 notesplayed together
• 3:2 Frequency Ratio
• Also called “Fifth Chord”
2/18/20 Sound of Music 4 89
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz300 Hz
The Power Chord
• Combination of 2 notesplayed together
• 3:2 Frequency Ratio
• Also called “Fifth Chord”or “Open Fifth”
• Combination of 2 notesplayed together
• 3:2 Frequency Ratio
• Also called “Fifth Chord”
2/18/20 Sound of Music 4 90
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz300 Hz
The Power Chord
Queens of the Stone AgeGo With The Flow, 2003
2/18/20 Sound of Music 4 91
87 Hz
131Hz
(F 2)
(C 3) 139 Hz (Db 3)
208 Hz (Ab 3)
117Hz (Bb 2)
175 Hz (F 3)
All these notes belong to the F minor Pentatonic Scale
(and also to Ab Major, and to corresponding Diatonic Scales)
• Combination of 2 notesplayed together
• 3:2 Frequency Ratio
• Also called “Fifth Chord”
2/18/20 Sound of Music 4 92
2000
1800
1600
1400
1200
1000
800
600
400
200
0
Freq
ue
ncy
(H
z)
200 Hz300 Hz
The Power Chord
The dirty little secret:In the scales we have studied so far there are no 3:2 frequency ratios!
2.0001.888
1.682
1.498
1.3351.260
1.122
1.000
Example:
Diatonic Major Scale (Equal Tempered)
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 95
fMIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1c. Skip 1
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 96
fMIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1c. Skip 1 There are 7 such
triads, each starting on a different
degree of the C Major Scale.
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 97
fMIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1c. Skip 1 But some of them
are identical.
There are only 3 different kinds.
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 98
fMIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1c. Skip 1
I
IV
V
ii
iii
vi
vii
They can be labelled like this in Roman
Numerals according to the root note
degree(i.e. which note of the Major Scale they start on)
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 99
fMIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1c. Skip 1
Major minor diminishedminor
Power Chord
3:2
5:4~6:5
𝟐 :1
I
IV
V
ii
iii
vi
vii
They have names as follows. The approximate frequencies relative
to the root note are shown.
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Common Triad Chords(Based on Diatonic Scales)
Sound of Music 4 101
MIDI
2/18/20
Note ChromaticScale
Diatonic
Pattern
1211
10
9
8
76
5
4
3
2
1
C Major
Rule:a. Pick any noteb. Skip 1b. Skip 1
Major minor diminishedminor
Power Chord
3:2
5:4~6:5
𝟐 :1
I
IV
V
ii
iii
vi
vii
1
2
3
5
4
f
1
2
3
4
1
2
3Spectrogram of Major Triad showing the 3 notes in ratio
of 1:1.25:1.5.
Some of their harmonics coincide, so they sound nice.
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Chord Progressions
Sound of Music 4 102
fMIDI
2/18/20
Note ChromaticScale
C Major
I
IV
V
ii
iii
vi
vii
IV
V
II
x x x x x x x x x x
x xx xx x x xx xB 3 59 246.960 261.6C 4
C#/D♭ 4 61 277.262 293.7D 4
D#/E♭ 4 63 311.164 329.6E 4
F 4 65 349.266 370.0F#/G♭ 4
G 4 67 392.068 415.3G#/A♭ 4
A 4 69 44070 466.2A#/B♭ 4
B 4 71 493.972 523.3C 5
C#/D♭ 5 73 554.474 587.3D 5
D#/E♭ 5 75 622.376 659.3E 5
F 5 77 698.578 740.0F#/G♭ 5
G 5 79 784.080 830.6G#/A♭ 5
A 5 81 88082 932.3A#/B♭ 5
B 5 83 987.884 1046.5C 6
C#/D♭ 6 85 1108.7 Chord Progressions
Sound of Music 4 103
fMIDI
2/18/20
Note ChromaticScale
C Major
IV
V
II
“The 12 Bar Blues”
I I I
IV
I I
V
IV
2/18/20 Sound of Music 4 104
OLLI Scale Experimenter Sound of Music 2020
Equal Tempered Chromatic 12 note Scale
Piano MIDI Frequency Chromatic Note Key# Code (Hz) Scale Name
. . . . . . . . . .A 225 45 110A#/B♭ 246 116.526
B 227 47 123.5C 348 130.828
C#/D♭ 329 49 138.6D 350 146.830
D#/E♭ 331 51 155.6E 352 164.832F 333 53 174.6
F#/G♭ 354 185.034G 335 55 196.0
G#/A♭ 356 207.736A 337 57 220
A#/B♭ 358 233.138B 339 59 246.9
60 261.640C#/D♭ 441 61 277.2
C 4
D 462 293.7D#/E♭ 4
4243 63 311.1
64 329.644F 445 65 349.2E 4
F#/G♭ 466 370.0G 4
4647 67 392.0
68 415.348A 449 69 440
G#/A♭ 4
A#/B♭ 470 466.2B 4
5051 71 493.9
72 523.352C#/D♭ 553 73 554.4
C 5
D 574 587.3D#/E♭ 5
5455 75 622.3
76 659.356F 557 77 698.5E 5
F#/G♭ 578 740.0G 5
5859 79 784.0
80 830.660A 561 81 880
G#/A♭ 5
A#/B♭ 582 932.3B 5
84 1046.5
6263 83 987.8
1108.7C 664
C#/D♭ 665 85
Diatonic Major
Diatonic Minor
Diatonic Scales
Major Minor
Pentatonic Scales
Minor Major Triad Chords
Tetrad Chords
Pentatonic Major
Pentatonic Minor
Scale Sliders
Course Outline
1. Building Blocks: Some basic concepts
2. Resonance: Building Sounds
3. Hearing and the Ear
4. Musical Scales
5. Musical Instruments
6. Singing and Musical Notation
7. Harmony and Dissonance; Chords
8. Combining the Elements of Music
2/18/20 Sound of Music 4 106
Ukrainian Bandura
2/18/20 Sound of Music 4 107
Chromatic Scale65 StringsWith retuning mechanism
