User:Aura/Aura's Music Theory: Introduction

Introduction

I have been influenced by some aspects of the music theory of Harry Partch. However, I, for my part, have been influenced rather heavily by what little I know of the works of Hugo Riemann, and I've even picked up a few tricks concerning Locrian mode from Alexander LaFollett, as well as learning from my own experimentations with Locrian. While I can't remember which came first, I must say that the influence of Riemann's concept of Harmonic Duality on my work is strongly connected to my discovery that Ancient Greek modes were built from the Treble downwards, and, because when the Ancient Romans borrowed the Greek terminology, they evidently made the mistake of assuming that the Greek note names were built from the Bass upwards, resulting in a disconnect between the Ancient Greek musical system and Modern Western Music Theory.

In light of this information, and in light of the development of Western Music Theory since the time of the Romans, I think it would be a good idea to also build on the more historically accurate version of the Ancient Greek modes and Treble-Down tonality in general to the same extent as has been done for Bass-Up tonality. However, doing this involves discarding the commonly-held dogmatic assumptions in Modern Western Music Theory that all music is built from the Bass upwards and that the Bass carries both the rhythm and harmony while the Treble contains melody. Furthermore, it involves renaming some of the diatonic functions encountered in Modern Western Music Theory to be better accommodating to the idea of music that is built from the Treble downwards. So, in order to do this, what sort of foundation shall we use? Well, for one thing, I propose we take Riemann's concept of harmonic duality- as well as Partch's argument that the Overtone Series and the Undertone Series are equally fundamental- much more seriously. In addition to all this I think that Aaron Andrew Hunt has done a fantastic job in integrating the ancient idea of a comma and the modern idea of the Just-Noticeable Difference in pitch perception, and I have even taken from the research on his site in this area to establish core aspects of my standards in terms of pitch representation quality. However, I differ significantly with him in that in addition to the categories of "comma" and "chroma", I also work with "subchromas" and "parachromas", as due to my prior experience with 24edo, I can only assume that intervals that are less than 50 cents yet greater than 25 cents can also act as their own musical intervals.

As far as I'm concerned, the Octave is a fundamental intervals in both Bass-Up Tonality and Treble-Down Tonality. However, it seems to be that Hunt only sees an incomplete picture when it comes to why the Octave is fundamental when it comes to the acoustic physics. As stated by the Wikipedia article on the Undertone Series, Henry Cowell has rightly pointed out that subharmonics are rather difficult to avoid in resonance, and this physical phenomenon can been demonstrated in systems such as this relatively simple one. Thus, the fact the Octave occupies the same positions relative to the fundamental in these systems as it does in harmonic systems lends itself to the reasonable assumption that physical properties of the subharmonic series act as an additional basis for the Octave being fundamental in acoustic physics. However, there's more to the physics of Treble-Down tonality than this, for as this video demonstrates, there are physical phenomenon in the analog world in which we live that produce notes that are not directly on the subharmonic spectrum, notes which our current understanding of physics fails to account for. Furthermore, as I was talking with Sam about our respective ideas of consonance, one concept that emerged from our discussion was the idea of "contra-linear consonance", which can be paired with Sam's own ideas on what I'll refer to here as "linear consonance", and my own observations on this comport with other observations on Treble-Down tonality.

Seeing Familiar Concepts in a Different Light

Since Treble-Down Tonality is a thing, however ancient or obscure it may be, it pays to revisit some of the fundamental areas of Modern Music Theory and not only reexamine them, but to also give them a facelift- for example, Musical Function, and the contrast between Consonance and Dissonance. In the context of Microtonality, it is perhaps all the more important that we do this even as we bring new concepts to the table in order to build scales and make good music with them. While it shouldn't be surprising that among the things that need to be reevaluated is the direction of chord construction as this aspect is literally the basis for the terms "Bass-Up" and "Treble-Down", among the things that also need to be reevaluated are the roles of the Bass and Treble, how direction of construction affects chord progressions, and how direction of construction affects the Diatonic Functions of notes other than the Tonic. While there are plenty of other things that need to be reevaluated that I can't cover here, suffice to say, however, that when one looks at the big picture, one will see that Treble-Down Tonality is the exact mirror image of the more conventional Bass-Up Tonality, a fact which lends to interesting and unexpected musical possibilities that are not present in more conventional systems.

In Modern Western Music Theory and in Bass-Up Tonality in general, the Bass largely plays the role of accompaniment, playing host to chords and the occasional countermelody as the Treble plays host to the melody, these roles are actually reversed in Treble-Down Tonality. This has the effect of switching the roles of numerous instruments, including various percussion instruments, therefore, the roles of Bass and Treble need to be seen as dependent on the tonality's direction of construction. Furthermore, one needs to be mindful of the fact that the way individual pitches are stacked together to make chords is also affected dramatically by the difference between Treble-Down Tonality and Bass-Up Tonality- specifically of the fact that while in Modern Western Music theory starts with the lower pitches and adds progressively higher pitches on top to make chords- hence the term "Bass-Up Tonality", Treble-Down Tonality, as per the name, sees one start with the higher pitches and add progressively lower pitches underneath. I should point out that the same types of intervals that are stacked in Bass-Up Tonality are the same types of intervals that are stacked in Treble-Down Tonality, and they are even stacked in the same order- however, due to the direction of chord construction being different between Bass-Up Tonality and Treble-Down Tonality, this results in the chords having different shapes, and even where Treble-Down chords sound identical to Bass-Up chords, the Treble-Down and Bass-Up chords have different names due to being constructed differently, and having different follow-ups in chord progression.

Take for example a chord consisting of the notes F-Natural, A-Flat and C-Natural. This would be immediately recognizable as an F-Minor triad in Bass-Up Tonality, and octave reduplication of the root would thus mean a second F-Natural is placed above the C-Natural. However, in Treble-Down Tonality, this same triad would actually be a C-Antimajor triad, as the interval pattern starting from the top note, C-Natural, is the same as that of the corresponding C-Major, with a major third interval between the first and fifth of the chord, and a minor third between the third and the fifth, and furthermore, when one wants to reduplicate the root for a C-Antimajor chord, one would add a second C-Natrual below the F-Natural. Just in reduplicating the root of the chord, the otherwise identical F-Minor and C-Antimajor triads can be differentiated. When one wants to add say a major seventh to these two triads, the results differ again due to the direction of construction. In this case, the F-Minor triad would see an E-Natural added above the C-Natural to create a F-Minor Major Seventh chord, while adding a major seventh to the C-Antimajor triad would result in adding a D-Flat below the F-Natural, with the resulting chord- a C-Antimajor-Seventh chord- sounding identical to a D-Flat Major Seventh chord when octave reduplication of the root is not present. When octave reduplication of the root is present for a C-Antimajor-Seventh chord, one will immediately think of this chord as dissonant because of the clash between the Seventh and the octave reduplicated root, however, the Antimajor-Seventh chord actually functions as the Treble-Down counterpart to the Major-Seventh chord, and thus, the Antimajor-Seventh chord is more properly considered a consonance of the same caliber as its Bass-Up counterpart despite the dissonance in the bass. I can already anticipate someone asking why these two chords have similar follow-ups when they sound so different to the ear, and the answer to that is that in both Bass-Up Tonality and Treble-Down Tonality, dissonant intervals close to the main iteration of the chord root are dispreferred, and are analyzed as dissonances that need to be resolved.