标签： Music Theory

Music

Notes

Chords

When pitches are combined together, chords are made.

Triads include three diffent pitches. The most common chords are major triads, minor triads, augmented triads, diminished triads. Suspended second and suspended fourth also consist of three different notes, but because of the different intervals between notes and notes, we don’t name them with “triads”.

Seventh chords consist of four different notes. Dominant seventh, major seventh, minor seventh, diminished seventh, half-dimished seventh, augmented seventh, augmented-major seventh, minor-major seventh will be introduced here.

Of course there are ninth chords which consist of five notes or even eleventh chords, thirteenth chords, etc. Although sometimes people use them in popular songs, I will not do further introduction here.

The figure below shows these chords with root C.

Summary for Chords
Music

Notes

Scales

A scale is a series of pitches arranged in order of whole tone, semitone and other intervals. It can be simply understood as multiple notes that are arranged from low to high and from high to low according to a certain interval relationship, which is the scale.

There are many scales. Here I just introduce several basic scales: major scales, natural minor scales, harmonic minor scales, melodic minor scales, lonian scales, Dorian scales, Phrygian scales, Lydian scales, Mixolydian scales, Aeolian scales and Locrian scales.

Major Scales

A major scale is arranged with the rule: full, full, half, full, full, full, half. A C major scale contains: C, D, E, F, G, A, B.

Natural Minor Scale

A natural minor scale is arranged with the rule: full, half, full, full, half, full, full. An A natural minor scale contains: A, B, C, D, E, F, G.

Notice that major scales and natural minor scales have a relationship shown as the figure below:

The cirlce of fifths is useful for understanding major scales and natural minor scales.

Harmonic Minor Scale

A harmonic minor scale is nearly the same with the natural minor scale except lifting the sixth pitch in the scale. A harmonic minor scale is arranged with the rule: full, half, full, full, half, full, half. There is such a long distance between the fifth and sixth pitches in a harmonic minor scale, sometimes it might sound a little bit wierd.

Melodic Minor Scale

A harmonic minor scale is arranged with the rule: full, half, full, full, full, full, half. A melodic minor scale on C contains C, D, Eb, F, G, A, B.

lonian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian scales

Ionian Scale on C: C, D, E, F, G, A, B

Dorian Scale on D: D, E, F, G, A, B, C

Phrygian Scale on E: E, F, G, A, B, C, D

Lydian Scale on F: F, G, A, B, C, D, E

Mixolydian Scale on G: G, A, B, C, D, E, F

Aeolian Scale on A: A, B, C, D, E, F, G

Locrian Scale on B: B, C, D, E, F, G, A

Summary

The scales on C can be summarized as the photo below.

Summary for Scales

Music

Notes

Pitches, Frequencies and Intervals

Music is related to sound caused by vibration. In equal temperament, every pair of adjacent pitches is separated by the same interval. The pitches of an equal temperament can be produced by repeating a generating interval. Classical western music theory divides frequencies into 7 pitches, C, D, E, F, G, A, B. The human ear’s perception of pitch mainly depends on the frequency ratio, not the frequency difference. The equal temperament uses the diatonic scale. Johann Sebastian Bach stipulates that there are 12 pitches in an octave, and the relationship between pitches and frequencies is shown as follow:

Octave→
Note↓		0123456789
C16.352
(-48)		32.703
(-36)		65.406
(-24)		130.81
(-12)		261.63
(+0)		523.25
(+12)		1046.5
(+24)		2093.0
(+36)		4186.0
(+48)		8372.0
(+60)
C#/Db17.324
(-47)		34.648
(-35)		69.296
(-23)		138.59
(-11)		277.18
(+1)		554.37
(+13)		1108.7
(+25)		2217.5
(+37)		4434.9
(+49)		8869.8
(+61)
D18.354
(-46)		36.708
(-34)		73.416
(-22)		146.83
(-10)		293.66
(+2)		587.33
(+14)		1174.7
(+26)		2349.3
(+38)		4698.6
(+50)		9397.3
(+62)
D#/Eb19.445
(-45)		38.891
(-33)		77.782
(-21)		155.56
(-9)		311.13
(+3)		622.25
(+15)		1244.5
(+27)		2489.0
(+39)		4978.0
(+51)		9956.1
(+63)
E20.602
(-44)		41.203
(-32)		82.407
(-20)		164.81
(-8)		329.63
(+4)		659.26
(+16)		1318.5
(+28)		2637.0
(+40)		5274.0
(+52)		10548
(+64)
F21.827
(-43)		43.654
(-31)		87.307
(-19)		174.61
(-7)		349.23
(+5)		698.46
(+17)		1396.9
(+29)		2793.8
(+41)		5587.7
(+53)		11175
(+65)
F#/Gb23.125
(-42)		46.249
(-30)		92.499
(-18)		185.00
(-6)		369.99
(+6)		739.99
(+18)		1480.0
(+30)		2960.0
(+42)		5919.9
(+54)		11840
(+66)
G24.500
(-41)		48.999
(-29)		97.999
(-17)		196.00
(-5)		392.00
(+7)		783.99
(+19)		1568.0
(+31)		3136.0
(+43)		6217.9
(+55)		12544
(+67)
G#/Ab25.957
(-40)		51.913
(-28)		103.83
(-16)		207.65
(-4)		415.30
(+8)		830.61
(+20)		1661.2
(+32)		3322.4
(+44)		6644.9
(+56)		13290
(+68)
A27.500
(-39)		55.000
(-27)		110.00
(-15)		220.00
(-3)		440.00
(+9)		880.00
(+21)		1760.0
(+33)		3520.0
(+45)		7040.0
(+57)		14080
(+69)
A#/Bb29.135
(-38)		58.270
(-26)		116.54
(-14)		233.08
(-2)		466.16
(+10)		932.33
(+22)		1864.7
(+34)		3729.3
(+46)		7458.6
(+58)		14917
(+70)
B30.868
(-37)		61.735
(-25)		123.47
(-13)		246.94
(-1)		493.88
(+11)		987.77
(+23)		1975.5
(+35)		3951.1
(+47)		7902.1
(+59)		15804
(+71)
Relationship between Pitches and Frequencies

The relationship between frequencies and their corresponding pitches have changed a lot. Nowadays, standard pitch is defined as A4=440 Hz.

Pitch interval is the difference between two pitches perceived by humans.

In the mid-range of human hearing, human perception of intervals between notes of different pitches is roughly logarithmic; in the high-frequency range, it does not conform to the logarithmic rule. This characteristic of human hearing is determined by the physiological structure of the human auditory system. That is to say, for the three tones with frequencies of 200Hz/400Hz/800Hz, two of the intervals are roughly equal; while for the three tones with frequencies of 200Hz/400Hz/600Hz, humans will hear these two intervals different.

For two tones with a double frequency difference, such as 440Hz/880Hz, the interval between them is set to octave.

The most common temperament used today is equal temperament. The relationship of frequency ratio and pitches of the equal temperament is shown as follow:

IntervalsEqual Temperament
C:C1.0000
D:C1.1225
E:C1.2599
F:C1.3348
G:C1.4983
A:C1.6818
B:C1.8877
C’:C2.0000
Equal Temperament

For the 12 pitches in an octave, the name of intervals and their frequency ratio is shown as follow:

Number of SemitonesPitch IntervalFrequency Ratio
0Perfect Unison1:1
1Minor Second16:15
2Major Second9:8
3Minor Third6:5
4Major Third5:4
5Perfect Fourth4:3
6Augmented Fourth45:32
6Diminished Fifth64:45
7Perfect Fifth3:2
8Minor Sixth8:5
9Major Sixth5:3
10Minor Seventh16:9
11Major Seventh15:8
12Perfect Octave2:1
Names of Pitch Intervals