tetrachords, hexatonic motion, and modal … · ex. 3: tonic and phonic triads and their respective...
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|————Phrygian tetrachord—————|
|—————Ionian tetrachord—————-——|
Ex. 1: Overtones and “undertones”: extrapolated from Arthur von Öttingen, Harmoniesystem in dualer Entwicklung (1866).“The tones of the major triad are common components of the tonic fundamental; those of the minor triad have a common
phonic overtone.”
TECHNOLOGIES OF SYMMETRY INBRAHMS’S “DOUBLE” CONCERTO
Roger Moseley, Cornell University
Ex. 2a: The symmetrical relationship between Ionian and Phrygian tetrachordsin the formation of Ionian (major) and Phrygian scales
Ex. 2b: Riemann’s “minor-major” or “harmonic major” scaleTonic = D (D+)
Ex. 2c: “Major-minor” or melodic minor scalePhonic = A (°A); °G when inverted
Ex. 3: Tonic and phonic triads and their respective Gegenklänge
Ex. 4: Brahms/Lingg, “Immer leiser wird mein Schlummer,” op. 105 no. 2
Ex. 5: Brahms, Double Concerto, op. 102, I: 1-4
TETRACHORDS, HEXATONIC MOTION, ANDMODAL SHIFTS IN THE FIRST MOVEMENT
[———Phrygian tetrachord————] + [——Ionian tetrachord———] = A melodic minor (or conceivably E harmonic major)
(mm. 1-4)
A flat+ A flat/G#- E+ E-
C+ C- A flat+ A flat/G#-
E7 = V7
continued...
(mm. 268-79;neo-Riemannian
annotations)
diatonic (circle of fifths) hexatonic
melody:
key: °E (in Riemannian terms)
Sunday, February 21, 2010
|————Ionian tetrachord—————| |————Phrygian tetrachord————|
|————Phrygian tetrachord————|
|————Ionian tetrachord————-——|
|————Phrygian tetrachord—————|
|—————Phrygian tetrachord——————|
|—————Ionian tetrachord—————-——|
|————Phrygian tetrachord—————|
|————Ionian tetrachord————-——| |————Ionian tetrachord————-——|
|————Ionian tetrachord—————|
|————Phrygian tetrachord—————|
Ex. 3: Tonic and phonic triads and their respective Gegenklänge
Ex. 4: Brahms/Heine, “Der Tod, das ist die kühle Nacht,” op. 96 no. 1 (1886), mm. 5-6 and 22-25
Ex. 5: Brahms, “Double” Concerto, op. 102, I: 1-4.
TETRACHORDS, HEXATONIC MOTION, ANDMODAL SHIFTS IN THE FIRST MOVEMENT
[———Phrygian tetrachord————] + [——Ionian tetrachord———] = A melodic minor (or conceivably E harmonic major)
(mm. 1-4)
A flat+ A flat/G#- E+ E-
C+ C- A flat+ A flat/G#-
E7 = V7
continued...
(mm. 268-79;neo-Riemannian
annotations)
diatonic (circle of fifths) hexatonic
melody:
key: °E (in Riemannian terms)
Sunday, February 21, 2010
|—————Gegenklang (iv)—————||—————Tonic (major)—————|
|—————Gegenklang (V)—————| |—————Phonic (minor)—————|
Opening oriented around E, the phonic “root”
Ex. 6: Brahms, “Double” Concerto, I: 268-93Performed by Julia Fischer (violin), Daniel Müller-Schott (cello), and the Netherlands
Philharmonic Orchestra Amsterdam, conducted by Yakov Kreizberg
TETRACHORDS, HEXATONIC MOTION, ANDMODAL SHIFTS IN THE FIRST MOVEMENT
[———Phrygian tetrachord————] + [——Ionian tetrachord———] = A melodic minor (or conceivably E harmonic major)
(mm. 1-4)
A flat+ A flat/G#- E+ E-
C+ C- A flat+ A flat/G#-
E7 = V7
continued...
(mm. 268-79;neo-Riemannian
annotations)
diatonic (circle of fifths) hexatonic
melody:
key: °E (in Riemannian terms)
Sunday, February 21, 2010
(as described by Richard Cohn)
Ex. 7: Joachim, “Abendglocken,” op. 5 no. 2, central episodePerformed by Florin Paul (violin) and Birgitta Wollenweber (piano)
Ex. 9: Brahms, “Double” Concerto, I: 396-417
Geg. = Gegenklang
Geg. Geg. Geg. Geg.
STINGS IN THE TAIL? GEGENKLÄNGE IN THECODA OF THE FIRST MOVEMENT
Geg. Geg.
Geg. Geg.
(mm. 396-400;Riemannian annotations)
(mm. 409-17)
C+ °E
°A
F+ °A
Sunday, February 21, 2010
alla zoppa rhythms (characteristic of the style hongrois)
Ex. 8: The symmetrical relationship between Joachim’s “Gisela” and “Frei aber einsam” mottos,which outline an Ionian and Phrygian tetrachord respectively
Ex. 10: Brahms, “Double” Concerto, III: 175-202
MODAL AMBIGUITY AND GEGENKLÄNGEIN THE FINALE
D+
D+°A °A D+ Geg. Geg.
(mm. 175-85;Riemannian annotations)
(mm. 196-202)
Geg. Geg.°A F+ °A
Sunday, February 21, 2010
alla zoppa rhythms