Spazi armonici: altezze in relazione (percettiva) per uno studio tridimensionale della dicotomia armonica maggiore/minore

The need for studies that investigate the relationship between the harmonic system and tuning was already recognised by Dahlhaus [1990], who was aware that almost all theorists of harmony have created their theses on specific tunings that optimally represent consonances. However, they were not able to find a tuning that allows an equal consonance between all triads.

In the last decades, there has been an increasing focus on this problem from theorists such as Lewin [1982; 2011], Tymoczko [2011a] and Cohn [2012]. The topic is usually addressed as a secondary issue. An exception to this is Cohn [2011], which places triadic relations and tonal regions on two different dimensions.

This paper pursues the direction taken in my previous paper [2020], in which I hypothesised “a double harmonic dualism” generated by temperaments, which allows to obtain both major and minor triads from the interval’s inversion of opposite modes of triads, and directly connects intervals and triads.

Here, it was necessary to bring the fragmentary analysis of the phenomenon available in the literature, to relate the syntheses with the associated harmonic meanings, and finally to build a three-dimensional Tonnetz, approximated with different intonations, which forms alternative relations between triads and between equivalent enharmonic pitches.

Therefore, the main theoretical approaches on harmonic relations and functions are integrated and revised and put them in direct relation with different intervals’ spaces, highlight their limits and suggest alternative solutions to their problems. This opens new horizons that expand the theoretical boundaries, particularly through the use of the minor third as generator interval of the harmonic space.