Could there be a "new functional harmony" with 12 scale degrees?

[N__K]

The topic title says it, mostly.

Is it conceivable to take some of most common tonal aspects (that there is a "home chord" etc.) of traditional functional harmony, and expand it to 12 scale degrees, so that each of the 12 would have at least a "suggested function" of its own?

I suppose the simplest attempt would be to take existing 7 degrees, maintain [most of] their functional meaning while mapping them into 12 degree number range, and "fill out" functions for the remaining 5 degrees?

Arguably that has already been done to some extent in musical practice since 1800s (?), communicated in various ways such as chromatic roman numerals, additional guidelines and so on. But still, usually when talking functional harmony, a 7-scale-degree paradigm or simplified "Tonic-Dominant-Subdominant" relationships are being assumed.

[jancivil]

assumes a wholly unnecessary dichotomy of chromatic and function TBH. It functions, ie., dominant-tonic paradigm or it doesn't

"already ... to some extent" - to the breakdown of function, in fact. Schoenberg stretched it, early in his career, til it broke.
Lewin 1987_Verklärte Nacht & the "illegal" fourth inversion

a generation before that (or two, see note) Wagner came up with a structure where intervallically there's an aug 4, an aug 6 and an aug 9 from the bass...
https://en.wikipedia.org/wiki/Tristan_chord
It actually takes iv6 in A minor, and augments that 6th while placing an appoggiatura before the A of the harmony - so far we've F D# A*, which, with a C is identical to an Fmajor/minor 7 {"F7"}** - and de facto flats the 5, spelled #4 there, so F B D# G#*** sonorously for that moment same as an Fø7 {Fm7b5} but that functions as a secondary dominant to V in A minor. It shocked people.
* = Italian; ** = German; *** = French augmented sixths. Now, the augmented sixth goes back at least to JS Bach but that little trick made this sound nobody saw coming. The G# resolves to A, the harmony moves to V7, reflecting the appoggiatura with an A# (to is B) and then i finally.
Harmonic function quite prevails there despite the 'reach'.

The Wiki shows Chopin having done in 1828. Tristan is ca. 1865.

The ninth in the bass job - which NB: Schoenberg came up purely by ear - is ca 1899. The group that was to perform it said aw hell no to such a monstrosity as a fourth inversion. The thing premiered finally in 1925.

As to the "Tristan chord", note the foreshadow of the b5 substitute dominant. F A Cb Eb aka B D# F A.
So. not only does chromatic harmony quite well exist (and continue expanding) since JS Bach til the "emancipation of the dissonance" via Arnold S., jazz from the bop period forward reflects the same sea change, post WWII, where the full chromatic was desired and achieved by devices; while on the other hand 'ii - V - I' was abandoned for static sonorities and a modal emphasis ("cool").

[jancivil]

So, sorry, no, there already is that for a couple centuries now.

I noticed recently in my own music, which harmonically practically defies analysis in certain cases (in others not so very relevant), likes a 'home' area, or a relative home; now a new plateau or niveau that's quite like a subdominant; back to home; now a tension zone which may as well serve formally as dominant. While being far from tonal music, with an elastic-to-where-we-prob'ly-don't-care harmonic language.

[jsaras]

The Equal Interval System tackles that problem at the outset by disproving the primacy of the cycle of fifths, i.e., all the other root cycles are equally valid and it can be proven both mathematically as well as in practice. Eventually you realize that any root can simply go to any other root, especially if you have the technique to make it logical.

[BertKoor]

all the other root cycles are equally valid and it can be proven both mathematically as well as in practice.

Where did you get that from? And you haven't checked it? Because that's plain provable bullshit.

With 12 tones to cycle through, intervals of 2, 3, 4 and 6 semitones will get back to where they started without touching them all. What remains is 1 (duuuh) 5 and 7 semitones. Past 6 you have the inverse interval, so it's technically just the one Circle of Fifths.

[gaggle of hermits]

EIS I think is the Spud Murphy system. it's hard for anyone who hasn't done it (including me) to know whether it disproves anything as you don't get to know what's in the course until you've paid for the course.

if it's like MITA, which I think it is (or rather MITA is similar to EIS as it came along later), the idea is that you can pick any "root cycle" you like and it can be made to work. so you can use tritones, major thirds, whatever, in a manner that resembles Coltrane's giant steps progression. it's effectively Neo-Riemannian in that you use more or less conventional voice leading but combine that with root-cycle moves to come up with things that are decidedly non-tonal but which do work.

however, because of the overtone series, it's a bit of a stretch to say EIS disproves the primacy of the circle of fifths - it remains a powerful magnet for music.

[jsaras]

all the other root cycles are equally valid and it can be proven both mathematically as well as in practice.

Where did you get that from? And you haven't checked it? Because that's plain provable bullshit.

With 12 tones to cycle through, intervals of 2, 3, 4 and 6 semitones will get back to where they started without touching them all. What remains is 1 (duuuh) 5 and 7 semitones. Past 6 you have the inverse interval, so it's technically just the one Circle of Fifths.

You're only thinking of the root tones. The tones in each line of the treble structure will "travel" the same distance regardless of the root cycle used when using proper voice-leading. Spud proves it very early on in the course by simply counting the steps horizontally. I have no idea how he arrived at it and it would have never occurred to me to analyze it that way.

Secondly, even just employing equal interval root tone cycles, they can be transposed to start on all 12 roots. Or, you can be completely free with it, which is really the goal. You can stay in the "jail" of the circle of fifths if you want to, but it's been played out IMO.

[jsaras]

EIS I think is the Spud Murphy system. it's hard for anyone who hasn't done it (including me) to know whether it disproves anything as you don't get to know what's in the course until you've paid for the course.

if it's like MITA, which I think it is (or rather MITA is similar to EIS as it came along later), the idea is that you can pick any "root cycle" you like and it can be made to work. so you can use tritones, major thirds, whatever, in a manner that resembles Coltrane's giant steps progression. it's effectively Neo-Riemannian in that you use more or less conventional voice leading but combine that with root-cycle moves to come up with things that are decidedly non-tonal but which do work.

however, because of the overtone series, it's a bit of a stretch to say EIS disproves the primacy of the circle of fifths - it remains a powerful magnet for music.

Spud actually proves it on page 24A of the course. It looks like an insignificant "throwaway" page, but he shows that when you subtract the number of steps the treble voice moves from the distance that the bass moves through a cycle of inversions (4 bars), it ALWAYS comes up as "12". He somehow figured all of this out from the overtone series. Given that this happens regardless of the root cycle, there is no particular reason to consider the fifth as having any primacy.

[gaggle of hermits]

Spud actually proves it on page 24A of the course.

you're aware no-one else can see that who hasn't stumped up for a course, right? you might as well claim he invented anti-gravity.

however, I do have to break it to you that a cycle of four inversions will move a chord by 12 semitone steps. I'm not sure it's the magic you claim it to be.

[jsaras]

You’re still thinking of a single-dimensional Rubik’s cube. Explain how that happens as the root changes simulataneously. Write it out. It is unfortunate that the course material is not publicly available. That’s the choice of the current copyright holder.

[gaggle of hermits]

You’re still thinking of a single-dimensional Rubik’s cube.

ok. whatevs.

[gaggle of hermits]

@OP: the search phrase you're looking for is "neo-riemannian".

it basically underpins the method used in a lot of movie music, which is how it's wound up in a book by frank Lehman called, um, Hollywood harmony, though it has nowhere near the amount of theorising that regular tonal has acquired. you can look at it as a continuum with regular tonal at one end and the kind of serialism used in the 1960s planet of the apes at the other.

[jsaras]

You’re still thinking of a single-dimensional Rubik’s cube.

ok. whatevs.

You are looking at harmony vertically, not horizontally. The vertical aspect of the overtone series can also be applied horizontally, one line at a time.

[N__K]

@OP: the search phrase you're looking for is "neo-riemannian".

it basically underpins the method used in a lot of movie music, which is how it's wound up in a book by frank Lehman called, um, Hollywood harmony, though it has nowhere near the amount of theorising that regular tonal has acquired. you can look at it as a continuum with regular tonal at one end and the kind of serialism used in the 1960s planet of the apes at the other.

Thanks!

Looks like I've got more reading to do

[jancivil]

Neo-Riemannian relates triads to each other without considering function. This transformation preserves the P5, this other preserves the m3. You make a minor triad major by raising the third. C major is E minor through lowering C to B 'like a leading tone'. Minor is upside down major.
It can't be what is asked for in the OP, there's nothing in it for when function becomes foggy or elusive, it's objective manipulation of individual objects in and of themselves according to a scheme.
Coincidentally, I cited one David Levin who is considered a proponent of it, but to give an analysis of the beginning of the end as it were, for Schoenberg.
Who, I'm reading now was quite vehement in his polemics, the new system was "necessary" to burn away all the degenerate lush harmonies, such as his, perhaps some of the worst egresses if you think that's a thing.

But Neo-Riemannian doesn't tell us about Schoenberg's thinking, and the thing I remembered was the 'impossible' 4th inversion. Which was all ear, no theory.
someone may well find a magic in that kind of thing, and get a way of thinking that's new for them. I work by ear. I bet you could apply it analyzing my music, but all that thinking isn't for me.