Over the course of this last several months, I have been slowly nurturing a new harmonic system which is at least tangentially related to Bartók’s axis theory. By exploring the more extreme side of chromatic voice-leading, one can come to unique cadences which seem to “imitate” traditional ones, though they maintain a certain alien feeling. My goal in the creation of this harmonic system is to create what could be described as a “foreign” harmonic system which uses dense harmonies and chromatic voice leading to create the “sensation” of a cadence that one would hear in standard music.
Above, I have three different examples of these imitative cadences. In some regards, the directness of the bass motion (especially, for instance, ) all but necessitate that the listener gets a sensation of a dominant-tonic resolution, and ultimately a great deal of the “felt” cadence may itself be an accident of the motion in the bass. If this is the case, then perhaps the way that the higher harmonies are colorated (my unique terminology for the denseness of harmony, propensity of Major and minor intervals, etc.) will have a greater or lesser effect on a cadence’s tonal gravity.
I will now discuss a little bit of the like-function of the above examples. In my language, like-function can best be described as the “perceived cadential sensation” that any given example might have, i.e. which traditional cadence one of these new harmonies is imitating.
 This first example is the most centered chromatically and in terms of density between the three examples. I feel that it is less chromatically “shocking” than —but moreso than —and as well it is less densely written than  but more than .
I would consider the like-function of  to be that of a traditional ii–V–i cadence. It also has the interest detail that the relative intensity of the dissonance of the example becomes lighter throughout. So, the example feels more tonal as it continues.
I would say that there are three important threads of motion in the example to pay attention to: the highest voice is very tonal (especially when analyzed with the bass), and aside from the bass’ function, likely does a great deal to “tie” the listener to the sense of completion with the cadence; there is an interesting harmonic motion in the middle voices (B♭ min–G min–D min), which, relatively to the D minor key center, will be perceived as “darker” and moving to “lighter”; finally, the bass itself has a rigid ii–V–i motion to it, and if it were changed it is indisputable that the like-function of the example would change as well.
To be continued later…