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Reger, Supplement to the Theory of Modulation

Max Reger · section 4 of 7

From a-minor

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47) e-minor

Ex-47
Fig. 97 · Play this example in the reader ▶

Tonic a-minor, which can be immediately used, as it is at the same time the sub-dominant of e-minor. (Cadence!)

Original harmonic analysis
Fig. 98 · See it in the reader

48) b-minor

Ex-48
Fig. 99 · Play this example in the reader ▶

Tonic a-minor, minor-dominant e-minor, which e-minor is used, as it is also the sub-dominant of b-minor. (Cadence!)

Original harmonic analysis
Fig. 100 · See it in the reader

49) f♯-minor

Ex-49
Fig. 101 · Play this example in the reader ▶

Tonic a-minor; 1st inversion (chord of the sixth) of the diminished triad (g♯ b d) (aVII); translate this chord of the sixth (b d g♯), to f♯II (diminished triad g♯ b d [1st inversion] [in f♯-minor] on the 2nd degree). (Cadence!)

Original harmonic analysis
Fig. 102 · See it in the reader

50) c♯-minor

Ex-50
Fig. 103 · Play this example in the reader ▶

Tonic a-minor; 1st inversion (chord of the sixth) of the diminished triad (g♯ b d) (aVII); use this chord of the sixth, which is also f♯II (1st inversion!); tonic f♯-minor; use this f♯-minor, which is at the same time the sub-dominant of c♯-minor. (Cadence!)

Original harmonic analysis
Fig. 104 · See it in the reader

51) g♯-minor

Ex-51
Fig. 105 · Play this example in the reader ▶

Tonic a-minor; translate the chord of the sixth (b d g♯) (aVII) f♯II; dominant (C♯-major) of f♯-minor; use this C♯-major, which is at the same time the chord of the Dorian sixth (c♯ e♯ g♯) in g♯-minor; dominant (D♯-major) of g♯-minor; tonic g♯-minor. (Notice that the Dorian sixth must always go to the leading tone!)

Original harmonic analysis
Fig. 106 · See it in the reader

52) d♯-minor

Ex-52
Fig. 107 · Play this example in the reader ▶

Tonic a-minor; dominant E-major; (1st inversion); use this chord of the sixth (g♯ b e), which is at the same time the chord of the Neapolitan sixth in d♯-minor. (Cadence!)

Original harmonic analysis
Fig. 108 · See it in the reader

53) a♯-minor

Ex-53
Fig. 109 · Play this example in the reader ▶

Tonic a-minor; dominant E-major; 2nd super-dominant B-major (1st inversion); use this chord of the sixth (d♯ f♯ b), which is also the chord of the Neapolitan sixth in a♯-minor. (Cadence!)

Original harmonic analysis
Fig. 110 · See it in the reader

54) e♯-minor

Ex-54
Fig. 111 · Play this example in the reader ▶

Tonic a-minor; dominant E-major (1st inversion); use this chord of the sixth (g♯ b e), which is at the same time the chord of the Neapolitan sixth in d♯-minor; dominant (A♯-major) of d♯-minor; use this triad (a♯ c𝄪 e♯), which is also the chord of the Dorian sixth in e♯-minor; dominant (B♯-major) of e♯-minor; the chord of the seventh (diminished) on the 7th degree in e♯-minor is used; tonic e♯-minor.

NB. The diminished chord of the seventh (in minor on the seventh degree) always takes the place of the dominant!

Original harmonic analysis
Fig. 112 · See it in the reader

55) d-minor

Ex-55
Fig. 113 · Play this example in the reader ▶

Tonic a-minor; sub-dominant d-minor; use this d-minor, as the tonic in d-minor. (Cadence!)

Original harmonic analysis
Fig. 114 · See it in the reader

56) g-minor

Ex-56-57
Fig. 115 · Play this example in the reader ▶

Tonic a-minor; use this a-minor (a c e), which is at the same time the chord of the Dorian sixth in g-minor; the dominant of g-minor (replaced by the 1st inversion of the diminished triad on the 7th degree in g-minor, i. e. a c f♯); tonic g-minor.

Original harmonic analysis
Fig. 116 · See it in the reader

57) c-minor

Tonic a-minor; sub-dominant d-minor; use this d-minor (d f a), which is at the same time the chord of the Dorian sixth in c-minor; dominant (G-major), tonic c-minor.

Original harmonic analysis
Fig. 117 · See it in the reader

58) f-minor

Ex-58
Fig. 118 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the chord of the Dorian sixth in f-minor; dominant of f-minor (replaced by the diminished chord of the seventh on the 7th degree (e g b♭ d♭) of f-minor).

Original harmonic analysis
Fig. 119 · See it in the reader

59) b♭-minor

Ex-59
Fig. 120 · Play this example in the reader ▶

Tonic a-minor; sub-dominant d-minor; relative to the tonic (C-major) of a-minor; use this C-major, which is also the 2nd super-dominant of b♭-minor; dominant (F-major) (with seventh e♭) of b♭-minor.

Original harmonic analysis
Fig. 121 · See it in the reader

60) e♭-minor

Ex-60
Fig. 122 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the 1st inversion of the dominant (B♭-major) of e♭-minor (with seventh; chord of the six-five).

Original harmonic analysis
Fig. 123 · See it in the reader

61) a♭-minor

Ex-61
Fig. 124 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth, (d f b♭), which is at the same time the 1st inversion of the 2nd super-dominant (B♭-major) of a♭-minor; dominant (with 7♭) (E♭-major) of a♭-minor.

Original harmonic analysis
Fig. 125 · See it in the reader

62) d♭-minor

Ex-62
Fig. 126 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the 1st inversion of the 2nd super-dominant (B♭-major) of A♭-major; dominant (E♭-major with 7♭) of A♭-major; tonic A♭-major; use this A♭-major, which is at the same time the dominant (with 7♭) of d♭-minor.

Original harmonic analysis
Fig. 127 · See it in the reader

63) g♭-minor

Ex-63
Fig. 128 · Play this example in the reader ▶

As in Nr. 62; use this A♭-major, which is at the same time the dominant of D♭-major; use this D♭-major (with 7♭), which is at the same time the dominant of g♭-minor.

Original harmonic analysis
Fig. 129 · See it in the reader

64) c♭-minor

Ex-64
Fig. 130 · Play this example in the reader ▶

Tonic a-minor; relative (F-major) to the sub-dominant (d-minor) of a-minor; chord of the Neapolitan sixth (b♭ d♭ g♭) in F-major; use this chord of the sixth (b♭ d♭ g♭), which is at the same time the 1st inversion of the dominant (G♭-major) of c♭-minor; dominant (G♭-major with 7♭) of c♭-minor; tonic c♭-minor. (See Nr. 65.)

Original harmonic analysis
Fig. 131 · See it in the reader

65) f♭-minor

Ex-65
Fig. 132 · Play this example in the reader ▶

Tonic a-minor; relative (F-major) to the sub-dominant (d-minor) of a-minor; use this F-major as tonic. (Also in Nr. 64 at the same place); chord of the Neapolitan sixth (b♭ d♭ g♭) in F-major; use this chord of the sixth (b♭ d♭ g♭), which is at the same time the 1st inversion of the dominant (G♭-major) of C♭-major; tonic C♭-major (with 7♭♭), which C♭-major is at the same time the dominant (with 7♭♭) of f♭-minor.

Original harmonic analysis
Fig. 133 · See it in the reader

66) C-major

Ex-66
Fig. 134 · Play this example in the reader ▶

Tonic a-minor; sub-dominant (d-minor); use this d-minor, which is relative to the sub-dominant (F-major) of C-major. (Cadence!)

Original harmonic analysis
Fig. 135 · See it in the reader

67) G-major

Ex-67
Fig. 136 · Play this example in the reader ▶

Tonic a-minor; use this a-minor, which is relative to the sub-dominant (C-major) of G-major. (Cadence!)

Original harmonic analysis
Fig. 137 · See it in the reader

68) D-major

Ex-68
Fig. 138 · Play this example in the reader ▶

Tonic a-minor; minor dominant (e-minor) of a-minor; use this e-minor, which is relative to the sub-dominant of D-major. (Cadence!)

Original harmonic analysis
Fig. 139 · See it in the reader

69) A-major

Ex-69
Fig. 140 · Play this example in the reader ▶

Tonic a-minor; sub-dominant (d-minor) of a-minor; use this d-minor, which is at the same time minor sub-dominant in A-major. (Cadence!)

Original harmonic analysis
Fig. 141 · See it in the reader

70) E-major

Ex-70
Fig. 142 · Play this example in the reader ▶

Tonic a-minor; use this a-minor, which is at the same time minor sub-dominant in E-major. (Cadence!)

Original harmonic analysis
Fig. 143 · See it in the reader

71) B-major

Ex-71
Fig. 144 · Play this example in the reader ▶

Tonic a-minor; minor dominant (e-minor) of a-minor; use this e-minor, which is at the same time minor sub-dominant in B-major. (Cadence!)

Original harmonic analysis
Fig. 145 · See it in the reader

72) F♯-major

Ex-72
Fig. 146 · Play this example in the reader ▶

Tonic a-minor; minor dominant (e-minor) of a-minor; use this e-minor, which is at the same time minor sub-dominant in B-major; tonic B-major; use this B-major, which is at the same time sub-dominant in F♯-major. (Cadence!)

Original harmonic analysis
Fig. 147 · See it in the reader

Do not forget that upon the entrance of the new major-tonic, its scale is understood.

73) C♯-major

Ex-73
Fig. 148 · Play this example in the reader ▶

Tonic a-minor; chord of the Dorian sixth (f♯ a d) in a-minor; use this chord of the sixth (f♯ a d), which is at the same time chord of the Neapolitan sixth in C♯-major. (Cadence!)

NB. Notice the leading of the bass from f♯ to g♯! (The Dorian sixth requires to be led upwards!)

Original harmonic analysis
Fig. 149 · See it in the reader

74) G♯-major

Ex-74
Fig. 150 · Play this example in the reader ▶

Tonic a-minor; dominant E-major; use the 1st inversion of this E-major (the chord of the sixth g♯ b e), which is at the same time the chord of the Neapolitan sixth in D♯-major; dominant (A♯-major) of D♯-major; tonic D♯-major, is at the same time dominant in G♯-major.

Original harmonic analysis
Fig. 151 · See it in the reader

75) D♯-major

Ex-75
Fig. 152 · Play this example in the reader ▶

Tonic a-minor; dominant E-major; use the 1st inversion of this E-major (chord of the sixth g♯ b e), which is at the same time the chord of the Neapolitan sixth in D♯-major; dominant (A♯-major) of D♯-major; tonic D♯-major.

Original harmonic analysis
Fig. 153 · See it in the reader

76) A♯-major

Ex-76
Fig. 154 · Play this example in the reader ▶

Tonic a-minor; minor dominant (e-minor) of a-minor; use this e-minor, which is at the same time the minor sub-dominant of B-major; tonic B-major; use the 1st inversion of this B-major (the chord of the sixth d♯ f♯ b), which is at the same time the chord of the Neapolitan sixth in A♯-major. (Cadence!)

Original harmonic analysis
Fig. 155 · See it in the reader

77) E♯-major

Ex-77
Fig. 156 · Play this example in the reader ▶

Tonic a-minor; minor dominant (e-minor) of a-minor; use this e-minor, which is at the same time minor sub-dominant in B-major; use the 1st inversion of this B-major (chord of the sixth d♯ f♯ b), which is at the same time the chord of the Neapolitan sixth in A♯-major; dominant (E♯-major) of A♯-major; use this E♯-major as tonic, dominant (B♯-major) of E♯-major; tonic E♯-major.

Original harmonic analysis
Fig. 157 · See it in the reader

78) F-major

Ex-78
Fig. 158 · Play this example in the reader ▶

Tonic a-minor; sub-dominant (d-minor) of a-minor; use this d-minor, which is relative to F-major. (Cadence!)

Original harmonic analysis
Fig. 159 · See it in the reader

79) B♭-major

Ex-79
Fig. 160 · Play this example in the reader ▶

Tonic a-minor; relative (F-major) to the sub-dominant (d-minor) of a-minor; use this F-major (with 7♭), which is at the same time the dominant of B♭-major.

Original harmonic analysis
Fig. 161 · See it in the reader

80) E♭-major

Ex-80
Fig. 162 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the 1st inversion of the dominant (B♭-major) of E♭-major.

Original harmonic analysis
Fig. 163 · See it in the reader

81) A♭-major

Ex-81
Fig. 164 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the 1st inversion of the 2nd super-dominant (B♭-major) of A♭-major; dominant (E♭-major [with 7♭]) of A♭-major; tonic A♭-major.

Original harmonic analysis
Fig. 165 · See it in the reader

82) D♭-major

Ex-82
Fig. 166 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth (d f b♭), which is at the same time the 1st inversion of the dominant (B♭-major) of e♭-minor; use this e♭-minor, which is relative to the sub-dominant (G♭-major) of D♭-major. (Cadence!)

Original harmonic analysis
Fig. 167 · See it in the reader

83) G♭-major

Ex-83
Fig. 168 · Play this example in the reader ▶

Tonic a-minor; chord of the Neapolitan sixth (d f b♭) in a-minor; use this chord of the sixth, which is at the same time the 1st inversion of the dominant (B♭-major) of e♭-minor; use this e♭-minor, which is relative to the tonic of G♭-major. (Cadence!)

Original harmonic analysis
Fig. 169 · See it in the reader

84) C♭-major

Ex-84
Fig. 170 · Play this example in the reader ▶

Tonic a-minor; relative (F-major) to the sub-dominant (d-minor) of a-minor; use this F-major as tonic; chord of the Neapolitan sixth (b♭ d♭ g♭) in F-major; use this chord of the sixth (b♭ d♭ g♭), which is at the same time the 1st inversion of the dominant (G♭-major) of C♭-major; tonic C♭-major.

Original harmonic analysis
Fig. 171 · See it in the reader

85) F♭-major

Ex-85
Fig. 172 · Play this example in the reader ▶

Tonic a-minor; relative (F-major) to the sub-dominant (d-minor) of a-minor; chord of the Neapolitan sixth (b♭ d♭ g♭) in F-major, taken as the tonic; use this chord of the sixth (b♭ d♭ g♭), which is at the same time 1st inversion of the 2nd super-dominant (G♭-major) of F♭-major; dominant (C♭-major); tonic F♭-major.

Original harmonic analysis
Fig. 173 · See it in the reader