![]() It is possible to catalogue at least one characteristic triad for each diatonic mode, which usually coincides with the triad that, in that melodic field, contains within it most of the notes that make that mode recognisable and distinguishable from the others. Returning to the question of polymodality, we can say that the mixing of two diatonic modes does not merely generate a new scale, but also a new harmony that is articulated within it. The extremely chromatic nature of the theme inhibits any kind of tonal perception, but one rather senses a continuous, moderate tension in an undefined development. ![]() The result is a theme that twists on itself, and like a wheel it could go on spinning endlessly: in fact, it is no coincidence that its most natural development is that of a canon form, as I have achieved in this passage ( Figure 10). Again in the Concertino, one of the main themes has been constructed by starting from the selection of the tritone interval E♯ (enharmonic of F) - B and delimiting the melodic field of the theme within this space, which is the middle of an octave furthermore, I have limited the possible melodic intervals to only second and thirds (F♯ - B♭ is in fact an enharmonic diminished fourth interval of a major third). The techniques of compositional investigation, by intervallic selection or modal preference, can also be useful to limit the melodic field in the construction of a theme, as is the case with twelve-tone themes. In today's classification, we define modal scales as the seven scales that can ultimately be derived from the seven degrees of the major scale. In our time, in fact, the vast majority of consumer music is composed on the basis of principles reflected in modal harmony, and in this sense we should not forget the fundamental contribution of non-European music in this direction, especially jazz music of the 1950s and what is known as modal jazz (Russell, 2001). The modal conception was eventually abandoned in favour of functional harmony, a system derived from polyphony and equable temperament, in which the power relationships were determined by the adherence of each chord or scale degree to a function of rest ( tonic), tension ( dominant) or a middle ground between the two ( subdominant) nevertheless, the mode persisted in many musical contexts and was the focus of renewed interest among composers as early as Romanticism, with a legacy that continues to this day. In the Western musical tradition it is possible to trace the birth of modern melodic expressiveness back to the epochs before the use of polyphony, in which monodic singing, both sacred and profane, was used in everyday social activities: each song was constructed respecting a specific container of available tones, called mode, which was obtained following a precise alternation between tones and semitones the relationships of tensions that were formed within each mode determined its colour and its peculiar and exclusive characteristic. Bartók's musical research stems from the integration of the aspect of number and symmetry with that of the modality typical of folk music. In my case, I found first in Bach and then in Bartók the extraordinary capacity to harness numerical architectures that are as perfect and complex in their construction as they are sublime to listen to. The relationship between mathematics and expressiveness, between number and instinct, the two primordial aspects of our artistic humanity, is of great fascination for musical research: number, due to its abstract nature, can be a vehicle for escaping the temptation of automatism, the memory of what has already been done, and is a compositional cue that rewards the bold. In the 1980s, the first algorithms capable of composing music based on a series of preset rules were introduced, and today a Google Doodle can make any melody sound “bachian” directly from your smartphone, but what no computer has so far been able to compose is a fugue that combines respect for the rules of counterpoint with the expressive beauty that characterises the works of the masters.
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