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Creative Blending of Harmonic Spaces


Blending of cadences

 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)

Cadence blending
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).

MM major
(a) Melody harmonised with the Bach chorale major idiom.


MM minor
(b) Melody harmonised with the Bach chorale minor idiom.



MM low
(c) Melody harmonised with the blended major-minor Bach chorale space, using low values of blending parameters.


MM medium
(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).

CFs major
(a) Melody harmonised with the C major Bach chorale space.


CFs low
(b) Melody harmonised with the blended C and F# Bach chorale major spaces, using low values for blending parameters.


CFs adventure
(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.

Yebanks major
(a) Traditional Scottish melody harmonised in the G major key in the style of Bach chorale.


Yebanks 3
(b) Traditional Scottish melody harmonised with the blended keys of G and Bb major.


Yebanks 4
(c) Traditional Scottish melody harmonised with the blended keys of G and B major.


Yebanks 6
(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.

Ode to joy BC
(a) The theme of Ode to Joy harmonised in the style of Bach chorales.


Ode to joy jazz
(b) The theme of Ode to Joy harmonised in the style of jazz.


Ode to joy Bach-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.

Apopse CN-WT
(a) Traditional Greek melody harmonised in the harmonic style of Constantinides blended with whole-tone harmony.


Apopse JA-HM
(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)




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