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HONR 204E > Final > Flashcards

Final Flashcards

1
Q

Unison

A

1 line space
0 half-steps is perfect
1 is augmented

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2
Q

Second

A 
2 line spaces
1 half-step is minor
2 is major
3 is augmented
M, M, m, M, M, M, M
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3
Q

Third

A

3 line spaces
3 half-steps is minor
4 is major
M, m, m, M, M, m, m

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4
Q

Fourth

A

4 lines
5 half-steps is perfect
6 is augmented
P, P, P, A, P, P, P

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5
Q

Fifth

A

5 lines
6 half-steps is diminished
7 is perfect
P, P, P, P, P, P, d

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6
Q

Sixth

A

6 lines
8 half-steps is minor
9 is major
M, M, m, M, M, m, m

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7
Q

Seventh

A

7 lines
10 half-steps is minor
11 is major
M, m, m, M, m, m, m

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8
Q

Octave

A

8 lines
11 half-steps is diminished
12 is perfect
13 is augmented

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9
Q

Equal tempered half-step

A

2^1/12 f

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10
Q

Pythagorean white notes

A

f, 9/8f, 81/64f, 4/3f, 3/2f, 27/16f, 243/128f, 2f

It does not close the circle of fifths. Thirteen notes instead of twelve

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11
Q

Just white notes

A

f, 9/8f, 5/4f, 4/3f, 3/2f, 5/3f, 15/8f, 2f

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12
Q

Sequence of fifths

A

C, G, D, A, E, B, F#, D♭, A♭, E♭, B♭, F, C

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13
Q

Counterpoint

A

A style of composition where a piece is composed of various independent voices and for which harmony is a result of these voices sounding together

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14
Q

Fugue

A

A canonic composition that is less rigid with statements of theme

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15
Q

Canon

A

It starts off with the theme, with other instruments or voices copying it

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16
Q

Ricercar

A

A precursor to the fugue

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17
Q

Three properties of tones

A

Pitch - the property of a sound that enables it to be ordered on a scale going from low to high
Loudness - intensity of a sound
Timbre - Quality/color of a sound

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18
Q

Notes

A

Notes are tones with onsets and offsets

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19
Q

Onset and offset

A

Onset is when the note begins and offset is when it ends

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20
Q

Sound

A

The physical object perceived by tones

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21
Q

Interval

A

Set of two pitches. Interval length is the distance in half-steps between them

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22
Q

Shepard tones

A

They create the illusion of infinitely rising or falling tones. The average frequency of Shepard tones remains the same

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23
Q

Chord

A

Three or more pitches sounded simultaneously or functioning as if they were sounded simultaneously.

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24
Q

Triad

A

A 3-chord built out of stacked thirds. A root pitch is transposed up a major or minor third. That second pitch is then transposed up a major or minor third

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25
Q

Augmented triad

A

A M-M triad. C+

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26
Q

Major triad

A

A M-m triad. C

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27
Q

Minor triad

A

A m-M triad. c

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28
Q

Diminished triad

A

A m-m triad. c°

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29
Q

Octave equivalence

A

Two pitches are octave equivalent to each other if they are related by transposition by a number of octaves.
P1 = P2 + 12n

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30
Q

Seventh chords

A

A 4-chord built out of stacked chords. A root pitch is transposed up three times by thirds.

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31
Q

Major 7th

A

M-m-M. Cmaj7

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32
Q

Dominant 7th

A

M-m-m. C7

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33
Q

Minor/major 7th

A

m-M-M. cmaj7

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34
Q

Minor 7th

A

m-M-m. c7

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35
Q

Half-diminished 7th

A

m-m-M. cØ7

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36
Q

Diminished 7th

A

m-m-m. c°7

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37
Q

Augmented/major 7th

A

M-M-m. C+maj7

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38
Q

Chord-type

A

Two chords are of the same type if one is a transposition of the other

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39
Q

Whole-tone scales

A

They are generated by taking whole steps. They have rotational and inversional symmetry

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40
Q

WT0

A

{0, 2, 4, 6, 8, 10}

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41
Q

WT1

A

{1, 3, 5, 7, 9, 11}

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42
Q

Octatonic scales

A

They are generated by alternating between whole and half-steps. They have rotational and inversional symmetry

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43
Q

Oct0,1

A

{0, 1, 3, 4, 6, 7, 9, 10}

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44
Q

Oct0,2

A

{0, 2, 3, 5, 6, 8, 9, 11}

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45
Q

Oct1,2

A

{1, 2, 4, 5, 7, 8, 10, 11}

46
Q

Petrushka chords

A

They are built out of a major triad and its transposition up by 6

47
Q

FTA

A

Any integer n > 1 can be written as a prime factorization

n = p1^n1 · p2^n2 ···· pr^nr

48
Q

Divisibility

A

m|n if there exists some q such that

n = mq

49
Q

Least common multiple

A

?

50
Q

Greatest common denominator

A

?

51
Q

Inverse elements

A

Any element g^-1 such that
g · g^-1 = e
It sends an element to the identity element.

52
Q

Identity element

A

Any element e ∈ G such that

e · g = g

53
Q

Homomorphism

A

Two groups G and H are homomorphic if φ sends the identity of G to the identity of H; and if φ respects the group operation of the groups

54
Q

Isomorphism

A

An isomorphism is a group homomorphism from G to H that is also invertible. It needs to be 1-1 and onto

55
Q

1-1

A

φ sends distinct elements to distinct elements

56
Q

Onto

A

φ “hits” all elements of Y

57
Q

Order of elements

A

The smallest positive integer n such that g^n = e.

It is how many times an element needs to be multiplied by itself to be the identity element

58
Q

Equivalence relations

A

x = y
x ≡ y mod m
x is isomorphic to y

59
Q

Quotient

A

Denoted X/~

It is the set of all equivalence classes of X

60
Q

Congruence modulo n

A

x is congruent to y if
n | (x - y).
Written x ≡ y mod n, which assets a relation. It is not formula

61
Q

_mod n

A

This is a number. Compute it

62
Q

Modular arithmetic

A

Integers x and y are congruent modulo m if
x = y + mq
for some q

63
Q

ℝ_>0

A

The set of all positive real numbers. Its group operation is multiplication.

64
Q

ℝ

A

The set of all real numbers. Its group operation is addition.

65
Q

ℤ

A

The set of all integers

66
Q

ℚ

A

The set of rational numbers

67
Q

C_n

A

C_n = {e=x^0, x^1, x^,2,…,x^n-1}.
Its group operation is
x^i · x^j = x^(x+j) mod n

68
Q

D_n

A 
D_n = {1, x, x^2, ... x^n-1, xy, (x^2)y, ..., (x^n-1)y}
Its group operation is 
x^n = 1 = y^2
x^i · x^j = x^(i + j) mod n
y · x^i = (x^n-i)y
69
Q

ℤ/nℤ

A 
For any integer r, [r]_n is the congruence class of all integers congruent to r modulo n.
Its group operation is
[r]_n + [s]_n = [r+s]_n
70
Q

S_n

A

The set of all invertible functions from the set {1, 2, …, n} to itself. Computation is done with cyclic notation

71
Q

Cyclic notation

A

(12)(34)(134) = (142)(3)

72
Q

Orbit

A

Denoted O_s. The orbit of a chord is its chord-type. It is the set of all transpositions by s

73
Q

Stabilizer

A

Denoted Stab_s. The set of elements that map s to itself

74
Q

Lagrange’s theorem

A 
#O_s = #G / #Stab_s
It answers how many chords of a given type there are.
75
Q

X_freq

A

The set of all possible frequencies. It is equal to ℝ_>0

76
Q

X_pitch

A

The set of all possible pitches. It is equal to ℝ

77
Q

X_pc

A

The set of pitch-classes. It is equal to {[P1]_12, …, [Pr]_12}

78
Q

T_freq

A

The set of all transpositions. It acts on X_freq via multiplication

79
Q

T_pitch

A

The set of all transpositions. It acts on X_pitch via addition

80
Q

Isomorphism from T_freq to T_pitch

A

Φ(x) sends T_freq to T_pitch.
Φ(x) = 12log_2 (x)
Ψ(x) sends T_pitch to T_freq
Ψ(x) = 2^(x/12)

81
Q

Pitch arithmetic

A

A pitch P is added to or subtracted from by n, where n is the number half-steps

82
Q

Pitch-class arithemtic

A

A pitch [P]_12 is added to by [n]_12, where n is the number of half-steps

83
Q

T_12

A 
The group of equal-tempered pitch-class transpositions.
T_12 = {t_0, t_1, ... t_11}.
Its group operation is
t_i ◦ t_j = t_t+j
84
Q

M_12

A

The group of equal-tempered transpositions and inversions.
M_12 = {e, t, t^2, …, t^11, ti, (t^2)i, …, (t^11)i}.
t^12 = i^2 = e
i(t^j) = (t^12-i)j

85
Q

Rigid motions

A

The transformation of a space that preserves distance

86
Q

Distance formula

A

In X_pitch, it is
d(P1, P2) = |P1 - P2|
In X_pc, it is the minimum length of the arcs between two points

87
Q

Transpositional symmetry

A

If a chord has any rotation t_j such that t_j (X) = X, then that chord has transpositional symmetry

88
Q

Inversional symmetry

A

If a chord has any inversion i_q0 such that i_q0 (X) = X, then that chord has inversional symmetry

89
Q

Musical Offering. Canon I. a 2 cancrizans

A

By J.S. Bach. It is a crab canon. Instrument one plays through from left to right, then back. Instrument two plays from right to left, then back

90
Q

Musica Ricercata No. 1

A

By György Ligeti. It is the first piece in Musica Ricercata. It only has two pitches. Each subsequent piece adds a pitch.

91
Q

Musica Ricercata No. 11

A

By György Ligeti. It is the last of Musica Ricercata. It has all twelve pitches. It is an homage to Girolamo Frescobaldi’s “Ricercata cromatico”

92
Q

I Fiori Musicali: Ricercar cromatico post il Credo

A

By Girolamo Frescobaldi. It uses most pitches in its subject. Musica Ricercata No. 11 is an homage to it

93
Q

Eleven Intrusions

A

By Harry Partch. He invented and composed with a just scale containing 43 distinct frequencies within the octave

94
Q

Serenade for tenor, horn, and strings, Op. 31 I (Prologue) and II (Pastoral)

A

Written in the just scale. Some of its notes sound very different from our equal-tempered scale

95
Q

Piano Sonata No. 12

A

By Mozart. He moves down the circle of fifths, using a pattern of rising fourths and falling fifths.

96
Q

Fugue No. 2 in C minor

A

By Bach. He moves down the circle of fifths

97
Q

Jordu

A

Written by Duke Jordan, performed by Clifford Brown. He moves down the circle of fifths, using rising fourths and falling fifths.

98
Q

Bagatelle No. 2

A

By Beethoven. He moves up the circle of fifths

99
Q

Quartet No. 14 in G major.

A

By Mozart. He moves up the circle of fifths

100
Q

Frühlingstraum

A

By Franz Schubert. Melody is identical up to octave equivalence, but sounds very different depending on circumstance.

101
Q

Die Krähe

A

By Franz Schubert. The melody is very uninteresting in pitch-class space

102
Q

L’escalier du diable

A

By Ligeti. Etude 9. Meant to create an effect like that of the Shepard tones. Unlike actual Shepard tones, it rises

103
Q

Vertige

A

By Ligeti. Etude 9. Meant to create an effect like that of the Shepard tones. Unlike actual Shepard tones, it rises.

104
Q

Coloana infinita

A

By Ligeti. Etude 14. Meant to create an effect like that of the Shephard tones. Comes very close to doing so.

105
Q

Contrapunctus No. 5

A

By Bach. The subject is reflected through A.

106
Q

Free Variations

A

By Bartók. The right hand inverts the left hand.

107
Q

From the Diary of a Fly

A

By Bartók. Melodic inversion through the G axis between G and A♭

108
Q

Voiles

A

By Debussy. It is written in the symmetric whole-tone scale, but veers off into the pentatonic scale.

109
Q

Regard du Père

A

By Messiaen. It is written in Oct0,1.

110
Q

Chez Petroushka

A

By Stravinsky. It is the first use of the Petrushka chord.

111
Q

Prime form of a chord

A

P1 = 0
Pr is as small as possible
The sequence is as small as possible with respect to lexicographic order

HONR 204E (5 decks)

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