Two cadences, such as the tonal Perfect cadence and the
renaissance Phrygian cadence (more generally, two chord transitions)
may be blended giving rise to new cadences, such as the Tritone
Substitution progression (a cadential type that emerged in jazz,
centuries after the main tonal/modal input cadences). The generated new
cadences feature important characteristics from both of the input
cadence spaces, such as the ascending and descending leading notes to
the tonic, preserving thus the closure effect of the resulting ‘new’
cadential formula. (Eppe et al. 2015, Zacharakis et al. 2015)
Perfect
cadence
Phrygian
cadence
Tritone
substitution cadence
Backdoor
cadence
Blending of chord transition
matrices
Chord transition blending can be employed to allow the blending of
whole chord transition matrices from different spaces. Chord
transitions from different chord transition matrices are blended and
ranked. When only the top ranking blends are preserved, then the system
has introduced a way to connect the two input chord spaces. If more
blends are selected then the composite transition matrix becomes more
populated allowing more connections between the spaces. If the
probabilities of the new ‘invented’ transitions are low, then the chord
generation system creates chord sequences mostly within each of the
constituent input spaces occasionally allowing passage from one to the
other. If the probabilities of the new blended transitions are
increased, then the whole space becomes unified and movement between
most or all of the chords of both spaces is enabled. This latter strong
blending between input spaces can generate new harmonic spaces that are
radically different from the initial input spaces.
In the following
examples manual analysis of harmonic progressions through the use of
Latin roman numeral notation of tonal harmonisation was made in certain
cases. The pitch content of the chords was always kept intact, and the
bass line was manually altered in very few cases (indicated by * in the
scores) in order to avoid stylistic inconsistencies or achieve more
effective voice-leading. Manual reworking of the inner voices was
applied where needed, although a strict application of common-practice
voice-leading rules was not pursued.
Example
1 – Blending major and minor
tonalities
A special purpose melody (without the third and sixth degrees of the
major-minor scales) is harmonised, firstly, in the major mode,
secondly, in the harmonic minor mode, and then in the blended
major-minor chord transition space (two harmonic versions).
(a) Melody
harmonised with the Bach chorale major idiom.
(b) Melody
harmonised with the Bach chorale minor idiom.
(c) Melody
harmonised with the blended major-minor Bach chorale space, using low
values of blending parameters.
(d) Melody
harmonised with the blended major-minor Bach chorale space, using high
values for blending parameters.
Example
2 – Blending different major
keys for modulation purposes
A special purpose-made melody, featuring a distant key transposition (C
– F# major) is harmonised, firstly, in C major mode (unsuccessful/awkward harmonisation in the F# region), then, in the
blended C – F# major space (two versions: low and high blending values).
(a) Melody
harmonised with the C major Bach chorale space.
(b) Melody
harmonised with the blended C and F# Bach chorale major spaces, using
low values for blending parameters.
(c) Melody
harmonised with the blended C and F# Bach chorale major spaces, using
high values for blending parameters.
Some comments regarding the three modulation examples shown above:
a) Melody harmonised with the C major Bach
chorale space. This harmonisation does not incorporate any blending of
keys, so the harmoniser attempts to assign chords without modulating
away from C major. The result reveals that the melodic shift towards F#
major has been ignored.
b) Melody harmonised with the blended C and F# Bach chorale major spaces, using low values
for blending parameters. The system is now able to identify the
modulating segment of the melody, and manages to suggest functionally
correct chords for both the shift towards F# and the return to C major.
(c) Melody harmonised with the blended C and F# Bach chorale major spaces, using high values
for blending parameters. The system harmonises the modulations and
introduces chromaticism within each tonal region, with unexpected
assigned chords in several cases.
Example
3 – Creative blending of
different major keys
A traditional scottish pentatonic melody “Ye Banks and Braes” is
harmonised in the style of Bach chorales, firstly, in G major alone,
then, three more times blending
G major with Bb major, B major and C# major respectively. The blended
harmonisations illustrate a radical departure from the initial common
practice tonal harmony (Bach chorale style) towards chromatic harmony
(harmony of the romantic period); the more distant blending of G-C#
major results in a more 'adventurous' harnomisation.
(a)
Traditional Scottish melody harmonised in the G major key in the style
of Bach chorale.
(b)
Traditional Scottish melody harmonised with the blended keys of G and
Bb major.
(c)
Traditional Scottish melody harmonised with the blended keys of G and B
major.
(d)
Traditional Scottish melody harmonised with the blended keys of G and
C# major.
Example
4 – Creative blending of Bach
Chorale with classical jazz styles
Beethoven’s Ode to Joy theme is harmonised in the classical tonal
style, in the classical Jazz style and in a blended idiom between the
two.
(a) The
theme of Ode to Joy harmonised in the style of Bach chorales.
(b) The
theme of Ode to Joy harmonised in the style of jazz.
(c) The
theme of Ode to Joy harmonised in the blended style of Bach chorales
and jazz.
Example
5 – Creative blending of
diverse harmonic spaces
A traditional Greek melody “Apopse ta mesanychta” in Aeolian mode
is creatively harmonised once in the blended space that combines
Constantinidis’ harmonic style with whole-tone harmony, and once in the
blended space of Jazz harmony with Hindemith’s harmonic idiom.
(a)
Traditional Greek melody harmonised in the harmonic style of
Constantinides blended with whole-tone harmony.
(b)
Traditional Greek melody harmonised in the harmonic style of jazz
standards blended with Hindemith's harmonic idiom.
References
Eppe, M.,
Confalonieri, R., Maclean, E., Kaliakatsos-Papakostas, M.,
Cambouropoulos, E., Schorlemmer, M. and Kühnberger, K.-U. (2015).
Computational invention of cadences and chord progressions by
conceptual chord-blending. Proceedings
of the 24th International Joint Conference on Artificial Intelligence
(IJCAI) 2015.
Zacharakis, A.,
Kaliakatsos-Papakostas, M., Cambouropoulos, E.: Conceptual blending in
music cadences: A formal model and subjective evaluation. In:
ISMIR.
Malaga (2015)