LCCTO confirmed by Pitch Class Theory

[Bagatell]

I think the pitch class theory provides confirmation of George Russells concept of tonal gravity. I wrote a little song to prove it.

(C)=(0)

(C C# D D# E F F# G G# A A# B)
(0 1 2 3 4 5 6 7 8 9 T E)

Blues For Heather

I7 I7 IVM7 IVM7 II7 II7 V7 V7
Vm7 I7 IVM7 IVM7 VIm7 II7 IIm7 V7


C7 C7 Fmaj7 Fmaj7 D7 D7 G7 G7
Gm7 C7 Fmaj7 Fmaj7 Am7 D7 Dm7 G7


CEGBb CEGBb FACE FACE DF#AC DF#AC GCEF GCEF
GBEF CEGB FACE FACE ACEG DF#AC DFAC GBDF


(047E) (047E) (5904) (5904) (2690) (2690) (7056) (7056)
(7E56) (047E) (5904) (5904 (9057) (2690) (2590) (7E25)



(047E) |
(047E) |
(5904) |
(5904) |
(2690) |
(2690) |
(7056) |
(7056) |
(7E56) |____{unordered chord sets arranged vertically to allow the full force of tonal gravity}
(047E) |
(5904) |
(5904) |
(9057) |
(2690) |
(2590) |
(7E25) |


(047E) |
(047E) |
(0459) |
(0459) |_______(0 2 4 5 6 7 9 E) {subset}
(0269) |
(0269) |
(0567) |
(0567) |
(567E) | (0 2 4 5 6 7 9 T E) {superset} {pitch axis}
(047E) |
(0459) |
(0459) |
(0579) |________________________(0 2 4 5 7 9 T) {subset}
(0269) |
(0259) |
(257E) *

http://en.wikipedia.org/wiki/Pitch_class

http://en.wikipedia.org/wiki/Pitch_axis_theory

[DroneDaily]

thanks. someone else finally saw the similarities, this would be a good topic to discuss

[Bagatell]

I have posted the details on three other forums.

http://forum.ableton.com/viewtopic.php?f=1&t=163541

http://www.kvraudio.com/forum/viewtopic ... highlight=

http://www.idmforums.com/showthread.php ... post679589

I'll post them here if anyone wants me to.

Interesting the way people are responding to this.

[Bagatell]

OK.
Let me put it this way.

If it is possible to do so without getting into subsets, supersets or pitch axis theory, please try to explain how your progression "confirms" Tonal Gravity?

Thanks.

Ok saying one progression proves it is an exaggeration. But if you reduce any chord progression in the same manner you will end up with a similar stack of numbers with (0)s, the tonic, inevitably included. What else is (0) if not the LCT?

[Bagatell]

And you've even got two chords in there that don't contain the tonic.

I must be missing something here.

Those two chord are my point. They are merely inversions and when they are (sorry) reduced to their prime forms it looks like this


(047E) |
(047E) |
(0459) |
(0459) |_______(0 2 4 5 6 7 9 E) {subset}
(0269) |
(0269) |
(0567) |
(0567) |
(0126) | (0 2 4 5 6 7 9 T E) {superset} {pitch axis}
(047E) |
(0459) |
(0459) |
(0579) |________________________(0 2 4 5 7 9 T) {subset}
(0269) |
(0259) |
(0258) *

Any set of changes expressed like this must by definition start with (0) the chromatic tonic.


I hope you'll forgive my amateur enthusiasm but I had never seen a chart expressed like that before and as soon as I saw it, that column of (0)s leapt out at me.

[Bagatell]

Any arbitrary set of notes, when expressed in their prime form (i.e. their most compact inversion) will have the tonic as the first note in that set.

For example
All the notes from C to C, F to F etc
or
E,G,C
or
C# and C,
or
G and C
or
F# and C

[Bagatell]

If it were true, then, for example, the chord, A C E G (9047), which compacts to E G A C (4790) would have a "tonic" of E, and that simply is not the case in any theory of harmony that I am aware of.

A,C,E,G reduces to (0,3,5,8)

please excuse the smiley it's an artifact of using PC notation!

file:///home/steve/Downloads/CompToolsSA/PCSets/setfinder.html

[Bagatell]

Even with your own methods, F#-C could go either way, no?

Absolutely not F# -C is (6,0) C is the tonic

[Bagatell]

Regarding the intervals formed by the tones of C lydian with the tonic:
• C-D
Russell sees the "tonic" as C.
Hindemith sees the root as D.
Delamont sees the root as D.
• C-E
They all see the root and/or the "tonic" as being C.
• C-F#
Russell simply declares that C is the "tonic".
Hindemith says it doesn't have a root until it after it resolves to some other interval.
Delamont says that the acoustical root is Ab.
• C G
They all agree that C is the root/"tonic".
• C-A
Russell says the "tonic" is C.
Hindemith says the root is C.
Delamont says that the acoustical root is F.
C-B
Russell says that C is the "tonic".
Hindemith says that C is the root.
Delamont says that the acoustical root is F.

PC theory agrees with Russell on every point, which was my original claim.

[Bagatell]

Even with your own methods, F#-C could go either way, no?

Absolutely not F# -C is (6,0) C is the tonic

But if F# is taken as the "tonic" it's 06.

(6,0) = (0,6) 0,C is therefore the tonic.


I haven't read Allan Fortes book so I can't help you with that. My information is for the most part from the Composer Tools website and Michael Keiths "From Polychords to Polya"

[Bagatell]

OK. Look.

You said that "A C E G *reduces* to 0358", right?
[Your html smiley was supposed to be an 8, right?]

0358 in this system is C Eb F Ab, which is a 2nd inversion Fm7 chord.

So in order to "reduce" A C E G to 0358 first you have to reorder the notes in the chord to so to E G A C, which is indeed their most 'compact' arrangement, and then you have to transpose the pitches down a maj 3rd (i.e. 'reducing' the PC set) so that the lowest note is C, aka 0.

If we do that same process with the interval F#-C, the interval is already as compact as it can get.
You see this interval as having its upper tone as both the 0 and the "tonic" of the interval.
But when you transpose this interval so that the lower tone is C, in order to "reduce" the interval, then it's the lower tone of the interval that is the "tonic".
So, by your own methods, the lower tone of F#-C is the "tonic".

You don't need to transpose the (F#,C) (6,0) you only have to order them to arrive at the most compact form. Mr Nelson explains the process here.

http://www.composertools.com/Theory/PCSets/PCSets3.htm

[Bagatell]

I greatly appreciate the thought you have given to this thread and hope my replies here will get my point over.

You have used quotes around "root" and "tonic" implying that you are using the terms in varying ways. I am using the term tonic in the way Paul Nelson defines it.

tonic - In most music, there is one note which is the tonic and serves as the most important and fundamental note of the composition. This note is the same as the key. For example, if the key is C Major (as in Symphony in C major) then the tonic note will be "C".
The tonic note exerts a gravitational pull on all of the notes in a composition. Most melodies will eventually lead towards the tonic note, and most compositions will both begin and end with the tonic note.

You seem to be equating the 1st note from the right hand side in the "Normal" Form of a PC Set with the "root" or "tonic" of the interval or chord that the PC Set produces.
Do I at least have this aspect of your argument right?

No. I am concerned with the first term in the prime form.

Why should the most compact arrangement of a PC Set necessarily result in the root of an interval or of the chord comprised by that PC Set be the lowest note in the Normal Form of the PC Set?

The most compact from is the prime form. Why this should be the case for prime forms is a very good question and one that I wish I could answer.

And if the the intervals F#-C and C-F# both have C as the "tonic", as you appear to be claiming, then what does that say about the way that C operates within the F# lydian scale?

It says that C will operate in F# Lydian the same way that F# will operate in C Lydian.

Are you claiming that the tonic of F#-C is still C even within an F#maj7#11 chord?

It's C# isn't it? F#,A#,C#,E#,G#B

"But if you reduce any chord progression in the same manner you will end up with a similar stack of numbers with (0)s, the tonic, inevitably included. What else is (0) if not the LCT?"

0 is just zero.

True (0) is arbitrary. It just happens we have been using (0)=C

*Any* PC Set that you reduce to its Prime Form will have C as the lowest note. Geez.

No. It will have (0) as its first term and as already discussed (0) is arbitrary i.e. it can be any of the 12 notes.

"Any arbitrary set of notes, when expressed in their prime form (i.e. their most compact inversion) will have the tonic as the first note in that set."

The Prime Form of any PC Set *always has C as its lowest tone.

For cases where (0)=C yes, but you are free to use any of the 12 values for (0)

The lowest tone of the Normal Form of a PC Set is not necessarily the "tonic" or the "root" of the interval or chord produced by the PC Set.

Obviously not.

Let's take the notes of Dm7, D F A C = 2,5,9,12.
Compacted we get C D F A = 0,2,5,9.
This is the Normal Form of this PC Set.
Inverted it becomes 0,10,7,3 or 0,3,7,10.
The Normal Form of the inversion (after doing all the rotations, subtractions, comparisons and transposition) is therefore 0,3,5,8.
When we compare the Normal Forms of the original PC Set and the inverted PC Set we see that the Normal Form of the inversion is the Prime Form because the interval between the lowest and highest notes is smaller within the Normal Form of the inverted interval.
(8 - 0 vs 9 - 0.)
So, the Prime Form of Dm7 is 0,3,5,8. (Which is Fm7 in 2nd inversion.)
If I'm following you at all, you seem to think that this somehow proves that C, the "0" in all of the above, is the "tonic" of Dm7.
Y/N?

What is the Lydian Chromatic Tonic of Dm7?

Your initial presentation of all of this in your OP is filled with mistakes, as I've pointed out, and that, along with the way you present your ideas in textual conversation is making this all quite unintelligible to me.

Sorry if I'm missing something, but this all seems to be a dead end.

True my OP contains a number of errors, however they are inconsequential. When corrected you still have (0) as the first term in all the prime forms of the chords.

My contention is that (0) is Paul Nelsons tonic and something very similar to GRs LCT.

[Bagatell]

Joe, my example is example #23 from Jerry Cokers "Improvising Jazz" Blues for Alice if I'm not mistaken, Why don't you try it with Giant Steps or something a little more complicated?

I'll remind you of the Mr Nelsonsprime form calculator - saves a lot of time.

[Bagatell]

Geez.
Your example is absolutely nothing like the changes for Blues For Alice in any key.

It's usually in F and the changes are:

Fmaj7 / / / |Em7 / A7 / |Dm7 / G7 / |Cm7 / F7 / |

Bb7 / / / |Bbm7 / Eb7 / |Am7 / D7 / |Abm7 / Db7 / |

Gm7 / / / |C7 / / / |Fmaj7 / D7 / |Gm7 / C7 / ||

Your changes are also unlike the changes to any other jazz standard that I know (assuming that your chord symbols are actually correct and that all the mistakes are confined to the spelling of the chords and/or the PC Set representations of the chords).

I know about the Prime Form calculator tool on that web page.
thanks. i've been using it extensively throughout this conversation.

Now...
Please answer the questions I asked in my previous post so that we can all put this to rest.
This appears to be a dead end that is going nowhere and is a big waste of time.

If you say so. At least you now appear to have an inkling of what I'm getting at. Take it or leave it.

[chespernevins]

Bagatell,

I hope you hang in there and try to make your point clear. I have to admit that I don't quite follow so far. I have only skimmed the web sites you have referenced, so maybe I am not giving your ideas a fair shot.

I think I get the gist of the prime form, but can you spell out your idea a little more for someone like me who is uninitiated into this type of thinking?

CN