Chord-Scale System

[jazz oud]

Going back over this thread, what a wild and interesting ride.

[Jeff Brent]

I've been incredibly busy lately, which is why I haven't been keeping up with my correspondence here. My apologies.

Once I have finished reading Mathieu (about 100 pages to go), I will attempt to address all the different issues that have been addressed to me.

Until then, I'm holding back on writing about this subject

I'll start a new thread, though, called "Just Intonation" or "Harmonic Experience" or some such. This thread needs a break.


@motherlode:

You are certainly the same motherlode that frequents the Lydian Chromatic Concept forum.

You know who I am, and I know who you are, Haroun. If you are truly interested in hearing me play and listening to some of my original compositions all you have to do is to click on my trio's website link below.

Or you may want to contact Schell Barkley (dogbite both here and on the LCC forum) and ask him about his favorite cuts of mine online to save you some time and direct you to the créme de la créme. (Schell is the co-author of my book Modalogy).

Originally Posted by motherlode

Could you point me to some of your (sheet) music around here somewhere?
I'd like to play some of your writing.

I realize that I'm being called out here, but I don't mind.

Once you have chosen a tune or two that you would truly like to play, let me know and I'll supply you with the transcriptions you require.

~~~

PS:

Originally Posted by jazzoud

And you conveniently left out my statement, which exactly addresses the issue, and which you do not acknowledge in your response:

Since I agree with this self-evident truth, I saw no reason to include it in my response.

If I disagreed, I would've said so.

It stands to reason that higher harmonic roots generated by a fundamental are more important notes than non-root notes generated by selfsame fundamental, ie; the fundamental "promotes" itself in favor of other tones.

Also note that there appear to many issues here, not just one. I'm not sure who makes the rules about what "the issue" is and what "the issue" isn't, but I don't have a problem with threads meandering (or maybe "evolving" is a better word).

I'm also not sure which of the issues brought up in this thread is "The issue" in your mind - I'm ok with that too ...

[jazz oud]

By "the issue" I merely meant "the issue on which we seem to be disagreeing", nothing more. Of course one is free to discuss any and all issues, but you seemed to be treating issues that we apparently agree on as if we disagree. I was just trying to clarify that none of the comments apparently directed at me or JonR were about anything we disagreed on in any meaningful way.

Since you directed your comments at me, I was confused that you seemed to think I believed a bunch of things that I never remotely indicated I believed. As far as I'm concerned, radial symmetry is an interesting phenomenon, but I've yet to see anything indicating that it means anything. I would like to hear some support for the idea that it means something, but so far it just seems like assertions and observations that "this can be described this way". I am not hostile to the idea that you have found something truly meaningful, but unless I am missing something, you haven't provided any compelling rationale for giving radial symmetry status as an explanatory principle.



I don't know what "higher harmonic roots" (emphasis mine) means, but I don't think it is self-evident that higher harmonics (above the 7th) are more important than tones generated from multiplicative ratios of the lower harmonics (2-5). The 7th is a gray area IMO.

[Jeff Brent]

Originally Posted by jazz oud

I am not hostile to the idea that you have found something truly meaningful, but unless I am missing something, you haven't provided any compelling rationale for giving radial symmetry status as an explanatory principle.

It appears that you don't have a copy of Modalogy at hand, and that handicaps our discussion somewhat.

Assuming you remember Jairazbhoy's 32 thaat study (only ten of which are commonly used), classical Hindustani music is based on a backbone of the fixed open 5th drone interval sa-pa/Root-P5 (which I do, btw, consider to be a chord) and the other notes can be rearranged to taste (komal re/m2 or suddha re/M2; komal ga/m3 or suddha ga/M3; suddha ma/P4 or tivra ma/#4; komal dha/b6 or suddha dha/M6; komal ni/b7 or suddha ni/M7). These configurations all contain seven notes. This is similar to the Chromatic Cube's approach.

At the third level of RS, the tritone B F is introduced. Either note a minor third from central D.

This resulting tritone surrounding D is the structure that supplies the backbone of the Chromatic Cube (B and F remain constant throughout), and (similar to the Hindustani system) all other notes are subject to alteration (C or C#; E or Eb; G or Gb, G or G#, A or Ab, A or A#).

Have you had a good look at the Chromatic Cube concept? It's the unified field of scales, man. All the scales in occidental musics are right there - BAM!

And the Chromatic Cube rides on the shoulders of Radial Symmetry.


Do I need to send you one of the books or something? I don't have your address though.

[Ken Valentino]

Originally Posted by Jeff Brent

The presence of the interval of a fourth in the lower structure of the major scale subdivides the tonality of that scale into two tonalities; the one on its fourth degree, and the one on its root.

In other words it's easy to build a root on the IV. I agree.

Originally Posted by Jeff Brent

Playing either of the root sequences below clearly identifies D as the tonic among these three notes:
[center]
D G D A D
T S T D T

D A D G D
T D T S T

Well you started and ended with D and the D was the most repetitious, so it wasn't a fair fight. Even so the first example was more obvious (tonal) than the second.

Originally Posted by Jeff Brent

In theory/composition class, I was taught that the lowest note defines all those above.

Lowest is just one tendency. It's not always the clear winner.

Originally Posted by Jeff Brent

D is consonant with G and reciprocally G is consonant with D (the third harmonic is consonant with the 1st, 2nd, 4th, 8th octave harmonics, etc).
All perfect intervals are consonant. Both perfect fourths and perfect fifths are consonant.
Earlier this year, I had a lengthy discussion with a Dutch theorist (whom Levine introduced me to), regarding the centuries-old debate of whether of not the perfect 4th is consonant or dissonant.

The initial question is: Which notes are perfectly consonant with D?

D is perfectly consonant with A, and reciprocally A is perfectly consonant with D.

G is perfectly consonant with D, just as D is reciprocally perfectly consonant with G.

Excluding the octave and unison, there are two and only two notes that are perfectly consonant with D.

Well the fact that a perfect interval is simpler than some other interval (consonant) is true. There is another tendency however, which note in the relationship is simpler? This is why even though a 3 1 is more complex than 41 it actually can resolve on the 3 1. In a 3 1 connection the 1 is simplest whereas in 4 1 the 4 is simplest. The ear would usually rather have its reference point as the simplest note.

As far as the lydian thing, it works great if doing extensions, but if directly connected to the key a tritone usually isn't a good thing. When doing all these perfect 5th relationships its very easy for the ear to remeasure and not worry about the connection to the key at all. If this is happening then calling it a #4 is not why it's working. It's probably the 3 of the 2 or the 5 of 7 or many others. The point is most other connections would still be better than a tritone connected directly to the key.

[motherlode]

*****

[jazz oud]

Originally Posted by motherlode

(As a side note, I also attended Oum's funeral in Cairo back in the 70's, Jazz Oud)

Wow. That must have been incredible.

[Bob Pearce]

Originally Posted by motherlode

I'm talking directly to you Jeff, not dogbite or any one else...

And I'm simply asking,"...do you have any original music (written) that you might be willing to share to best illustrate and clarify your points?"

It's a 'Yes' or 'No' question.

You and I both know, once the sound is affixed to the paper it has forever been remove from the realm of happenstance and conjecture.

Jeff, I've made a lot of money doing what I do.
It serves absolutely no purpose trying to call you out or whatever...

I don't know you!
------------------------------------------------------------
In regards to the Lydian Chromatic site...

I just don't frequent...I live there! As well I should, because I was around from the concept's inception (late-50's early 60's).
It's important for me to be there doing what ever I can to help those that wish to understand.

I've written music for everybody from Aretha to Tommy Durden using those very concepts. I have eight (8) children to feed, Jeff. Yes, that's right!

That's more responsibility than any of you here! So I have to get it right.

Coltrane, Miles, Duke, Mingus, and many others...are people that I knew and had many conversations with.
Look, I attended Coltrane's funeral, Jeff.
(As a side note, I also attended Oum's funeral in Cairo back in the 70's, Jazz Oud)

You say you know me...but you don't know who you're talking to.

As Stravinsky once quipped to his critics,"...the words without the music".

Relax.

Can I have your autograph?

[Jeff Brent]

Originally Posted by George Russell !!

The presence of the interval of a fourth in the lower structure of the major scale subdivides the tonality of that scale into two tonalities; the one on its fourth degree, and the one on its root.

Originally Posted by Ken Valentino

In other words it's easy to build a root on the IV. I agree.

Minor clarification: The first quote above is not mine (as implied by your post), those words belong to George Russell.

[guitarjazz]

This guy:
http://www.youtube.com/watch?v=LWb2a4r8z18

Brilliant!

[dogbite]

what's this thread about?

one of the reasons i've disappeared from forums, not just this one but also LCC and one other where rudeness had evolved into unbelievable heights, is how people keep talking past each other. most of the posters on the last part of this thread are friends of mine to varying degrees, from here as well as LCC, in particular, jeff and mr. oud as well as guitarjazz and motherlode from LCC...

there are some points being made that are facts and others that are opinions or subjective conclusions based upon those facts and opinions and may even constitute a belief system. for example, the pythagorean comma of approximately 21.5 cents is a fact; however, the conclusions based upon the (again approximately) 1.955 cents error between the 3:2 P5 and the 12TET P5 are opinions which may or may not be part of an individual's belief system...

the syntonic comma of approximately 21.5 cents is the direct result of the major third JI ratio of 5:4 in the context of four JI P5 intervals; again, this is fact but the conclusions regarding the implications of this are opinion. jazz oud's suggestion of a two-dimensional grid or lattice as a description for JI embrace both the pythagorean and syntonic commas as facets (whether elemtents or artifacts if you prefer) of the system of JI as a tonal system. for those late to the discussion who are looking for quick and immediate answers to these questions i truly apologize for there are none to be found here, or anywhere else for that matter...

edit
---
for example, does anyone know just how many texts, including LCC, incorrectly assign the 13th harmonic as being closer to the major rather than the minor sixth?
---
end edit

here's what i believe: while i am a fervent champion of 12TET, i truly believe that it works because it approximates very well the JI ratios and not the other way around. the first comma of any kind encountered in harmonic theory is the 1.955 cents (more specifically 3/(2^(19/12)), read as the quantity 3, divided by the quantity 2 raised to the power of 19/12; this is one twelfth of the pythagorean comma) error between the JI and 12TET fifth and in my opinion, this error is small enough to be negligible and when you stack two fifths together in a series or progression (ii V7 I anyone?), i don't hear a 4 cents error, i hear a fifth of a fifth. my conclusion is that i no longer care about the 1.955 cents error inherent in P5s of the system (of 12TET) and i just let it be. isn't the ability to freely transpose to any of twelve keys (tonal centers or whatever) worth the 2 cents? and that's my two cents

as to the major and minor thirds and sixths, there is a greater error to be considered (over 13½ cents) and i truly believe that wind, brass and fretless string players should (and do) make microtonal adjustments in order to blend with the prevailing harmonies; however, as primarily a guitarist i must confess that i no longer care - of course i care but what i really mean is that the logarithmic spreading of these errors equally through out the circle of keys is simply too powerful of a "fix" (yes, an imperfect fix to mathematically impossible conundrum) to not embrace wholly. in other words, blend all you want: push, pull, roll in or out but i got twelve equally tempered notes on the table and i just hear any discrepancies as slightly out of tune versions of each other and for me, it's enough.

again, my two cents

as to the relative consonance or dissonance of the perfect fourth, we are totally talking past each other here. the perfect fourth is but a single interval without context; does the I 6/4 (second inversion) chord have a desire to resolve? perhaps, but i think that has more to do with expectation and cultural conditioning than anything else. is the acoustical root (of the perfect fourth in isolation) the upper tone? sure it is but does that make the interval dissonant? nope; that's nineteenth century thinking and i didn't buy it in the 1970s and i don't buy it now. wiki calls it "conditionally consonant;" now how's that for a non-answer!

as to RS (radial symmetry) i think that some people may be misinterpreting what "i" feel it represents. it's about "structure," not "tonality" and although i love the dorian mode, i also feel that classical thinking (6:5:4 major triad go up and down a fifth) that indicates an ionian tonal center has merit as well as russell's stacked 3:2 fifths, implying lydian. many progressions in popular music indicate a drive toward aeolian and even mixolydian - i may come off as sort of a musical pantheist here but i don't really think there's any real disagreement. my contribution to modalogy comes in the form of, "hey look at this, i think it's really cool," rather than "here is the undeniable science that you must embrace above all else."

again, what's this thread about? i don't know anymore but i don't mind responding to a specific question or two if anyone cares to ask, whether about my contributions to modalogy or anythng else; further, my response was not aimed at any comment in particular and as such my have been more rambly than i had intended. i do miss my dialogs with jazz oud (when do i get to hear your new album?) and everyone else but i confess that i find some of the bickering tiresome, as it seems circular and pointless and endless but hey; i don't want to leave on a sour note:

respect to all who have participated - y'all have a great weekend!!!

[Ken Valentino]

Originally Posted by Jeff Brent

Minor clarification: The first quote above is not mine (as implied by your post), those words belong to George Russell.

Well that first comment was just to break the ice anyways. What about the rest of it?

[jazz oud]

Originally Posted by dogbite

here's what i believe: while i am a fervent champion of 12TET, i truly believe that it works because it approximates very well the JI ratios and not the other way around.... isn't the ability to freely transpose to any of twelve keys (tonal centers or whatever) worth [ET]?

I fully agree with this. However, I do think that for ear-training purposes it is helpful for many people to approach it from pure intervals first, since resonance is such a deeply ingrained phenomenon. A reference works best when one knows the referent.

as to the major and minor thirds and sixths, there is a greater error to be considered (over 13½ cents) and i truly believe that wind, brass and fretless string players should (and do) make microtonal adjustments in order to blend with the prevailing harmonies; however, as primarily a guitarist i must confess that i no longer care - of course i care but what i really mean is that the logarithmic spreading of these errors equally through out the circle of keys is simply too powerful of a "fix" (yes, an imperfect fix to mathematically impossible conundrum) to not embrace wholly. in other words, blend all you want: push, pull, roll in or out but i got twelve equally tempered notes on the table and i just hear any discrepancies as slightly out of tune versions of each other and for me, it's enough.

I get your point, but I do think that pianists and guitarists need to be aware of this so the can adjust voicings to make this process smoother [when working with singers, especially]. Long before I began investigating this, I had catalogued which voicings didn't work well with particular melody notes, so one needn't necessarily understand it theoretically, just be aware that there are different tunings for notes and one must know how to compensate for that.

None of which suggests getting rid of ET or that another system would be better for our purposes (jazz and other modern chromatic music).

as to RS (radial symmetry) i think that some people may be misinterpreting what "i" feel it represents. it's about "structure," not "tonality" and although i love the dorian mode, i also feel that classical thinking (6:5:4 major triad go up and down a fifth) that indicates an ionian tonal center has merit as well as russell's stacked 3:2 fifths, implying lydian. many progressions in popular music indicate a drive toward aeolian and even mixolydian - i may come off as sort of a musical pantheist here but i don't really think there's any real disagreement. my contribution to modalogy comes in the form of, "hey look at this, i think it's really cool," rather than "here is the undeniable science that you must embrace above all else."

I agree with all of this. As far as the presence of RS and the utility that it presents in connecting the relationships between various keys/scales/pitch relationships, it is definitely very interesting.
To the extent that there is any disagreement, for me it is primarily that Jeff seems to be making rather grandiose claims about it being an underlying explanatory/generative principle rather than a useful and interesting phenomenon. Even if he's right, it would be better (IMO) to just discuss the observations and let people come to their own conclusions (as you are doing). Regardless, it is interesting and I respect both of you on your hard work on this.

i do miss my dialogs with jazz oud (when do i get to hear your new album?)

Likewise. We've done the main tracks, I'm going over the takes now and making notes. We may add some extra percussion, then mixing etc. We ran into some delays getting into the studio, but should be done sometime in January. You might get to hear something before then, though

[ChesperNevins]

Hi all,

This has been a great thread (wild ride for sure)! You guys are great. I've really enjoyed Jazz Oud's posts in particular, so thanks JO.

I haven't been on these forums in a long while and signed on when I heard Motherlode was online. Anyway, then I went back and read the thread from the beginning, so forgive me that I am late in contributing.

One thing I wanted to throw in the ring was regarding the question of an inherent limiting factor of 7 notes in the "chain / ladder of fifths".

Hopefully this post is as on topic as can be expected in this thread?

Jeff Brent says:


1. In relation to the three notes G D A, an ‘acoustic root’ of G
explicitly implies the II-V-I progression via extension of the V-I
perfect cadence: D > G.

A > D > G
II > V > I


Taking the ‘acoustic root hypothesis’ out to its logical conclusions:

A > D > G > C
VI > II > V > I

Now C is the acoustic root.


A > D > G > C > F
III > VI > II > V > I

Now F is the acoustic root.


A > D > G > C > F > Bb
VII > III > VI > II > V > I

Now Bb is the acoustic root.


A > D > G > C > F > Bb > Eb
IV# > VII > III > VI > II > V > I

Eb Lydian: Eb F G A Bb C D Eb

Now Eb is the acoustic root.

The ‘acoustic root’ chain bolded above is the veritable backbone of
George Russell’s derivation of the Lydian scale, his main
justification for that scale’s ‘primacy’, and a founding principle of
the entire Lydian Chromatic Concept.

from George Russell’s LCC 1980’s edition (pg 50-iii)

According to Hindemith, the tonic of an interval of a fourth is the
upper note, while the tonic of an interval of a fifth is the lower
note. Consequently, in viewing the major scale as a chord, both
intervals indicate that the tone on the fourth degree is the tonic of
the chord. The C major scale, therefore, is actually an F major chord.
[…]

The presence of the interval of a fourth in the lower structure of the
major scale subdivides the tonality of that scale into two tonalities;
the one on its fourth degree, and the one on its root.

The absence of a fourth in the structure of a Lydian Scale enables the
whole scale to emphasize the root tonality.


from GR’s LCCOTO volume 1, 4th edition 2001 (Page 3)

Tonal Gravity, or “tonal magnetism,”within a stack of intervals of
fifths flow in a downward direction […]; the tone F# yields to B as
its tonic – F# and B surrender “tonical” authority to E, and so on
down the ladder of fifths – the entire stack conferring ultimate
tonical authority on its lowermost tone, C. In this way, an order of
six fifths represents a self-organized GRAVITY FIELD.

But, you knew all that already, right?


The fatal flaw here is that there is no inherent limiting factor in
the acoustic root cadential chain (GR: order).

There is no reason to stop at three notes, four notes, five notes, six
notes, seven notes, eight notes, nine notes, … or a hundred notes,
etc. It could keep going on and on forever.

A > D > G > C > F > Bb > Eb > Ab
#I > IV# > VII > III > VI > II > V > I

A > D > G > C > F > Bb > Eb > Ab > Db
#V > #I > IV# > VII > III > VI > II > V > I

A > D > G > C > F > Bb > Eb > Ab > Db > Gb
#II > #V > #I > IV# > VII > III > VI > II > V > I

A > D > G > C > F > Bb > Eb > Ab > Db > Gb > Cb
#VI > #II > #V > #I > IV# > VII > III > VI > II > V > I

A > D > G > C > F > Bb > Eb > Ab > Db > Gb > Cb > Fb
#III > #VI > #II > #V > #I > IV# > VII > III > VI > II > V > I

The acoustic root hypothesis (if I truly understood your meaning of
“works downwards in fifths”) quickly descends down a slippery slope
into a bottomless abyss.

There is no ‘logical conclusion’, because the sequence never actually concludes.

My thoughts on this are based on the following:

1) imagine that this chain is on the cycle of fifths
2) the idea of interval tonics based on the chain/ladder of fifths

Let's use a chain/ladder of fifths built on Ab as a starting point (purposefully including the A, which is outside of the 7 note Ab Lydian scale).

A > D > G > C > F > Bb > Eb > Ab
#I > IV# > VII > III > VI > II > V > I

First example:

We agree that the tonic of the interval Ab-Eb is Ab, but what if we wanted to test this idea using the chain/ladder of fifths idea?

To test if Eb is the tonic, we can ask if Ab is in a chain of fifths built on Eb.

Here's what that would look like:

Ab > Db > Gb > B > E > A > D > G > C > F > Bb > Eb
IV > bVII > bIII > #V > #I > IV# > VII > III > VI > II > V > I

Ab is 11 fifths around the cycle from Eb. Ab is very distantly related to Eb in the chain of fifths.

To test if Ab is the tonic of the Ab-Eb interval, we can ask if Eb is in the chain of fifths built on Ab.

Here's what that looks like:

Eb > Ab
V > I

Eb is one fifth around the cycle from Ab. Eb is very closely related to Ab based on the chain of fifths idea.

The conclusion drawn here is that Ab is the tonic of the Ab-Eb P5 interval. Based on the number of fifths, we find Eb is more closely tied to a
root of Ab than Ab is to a root of Eb, and therefore Ab is the tonic of the Ab-Eb interval.


===

Let's try Ab-C, to pick a another random interval which is still within the first seven notes of the chain.

C is four fifths around the cycle from Ab.

C > F> Bb > Eb > Ab
III > VI > II > V > I

Ab is eight fifths around the cycle from C.

Ab > Db > Gb > B > E > A > D > G > C
#V > #I > IV# > VII > III > VI > II > V > I

Ab is the tonic of the Ab-C interval.

===

What about Ab-D.

They are exactly opposite on the cycle, so either one could be the tonic.

D > G > C > F > Bb > Eb > Ab
IV# > VII > III > VI > II > V > I

G# > C# > F# > B > E > A > D
IV# > VII > III > VI > II > V > I

===

Here's the turning point: the interval Ab-A.

A > D > G > C > F > Bb > Eb > Ab
#I > IV# > VII > III > VI > II > V > I

A is 7 fifths above Ab.

However, Ab(G#) is only 5 fifths up from A.

G# > C# > F# > B > E > A
VII > III > VI > II > V > I

A has more pull on Ab(G#) than Ab does on A.

A is the tonic of the A-Ab interval.

Ab no longer "owns" this level of the ladder because it is no longer the tonic of the interval.

Ab no longer "owns" ANY of the notes above D. Therefore, that's the end of the "chain/ladder".

This limiting factor creates a ladder of fifths of exactly 7 notes.

I imagine that this is what G. Russell means by the statement:
“an order of six fifths represents a self-organized GRAVITY FIELD.”

Does this mean that a ladder of fifths is a fundamental law of music?
I don’t really know, but there is a certain consistent logic here.

[jazz oud]

ChesperNevins,

Very interesting presentation.
The only comment I would make is that the assumption of 5ths being the sole generative principle is not necessarily a universal given.

As soon as you allow 3rds (due to the 5:1 harmonic), things look different:

Take your Ab - A example (excuse me for changing formatting, but a lattice approach is clearer when allowing both 3rds and 5ths):

C# - G#
A  - E

               A
Ab - Eb - Bb - F

From this perspective, it is far easier to generate a G# from an A root than an A from an Ab root.