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Posted: Tue Apr 28, 2009 10:08 am
by strachs
Yes, the tonal centers are equidistant, just like the tones of an Aug chord. This will undoubtedly be the meaning of the triangle in that diagram on the title page (the one with "deep south" and "far north" markings). I guess a square would mean tonal centers a minor third apart. Did Coltrane ever use that structure?

Posted: Tue Apr 28, 2009 11:53 am
by dds1234
I had the idea of calculation using only the circle of fifths... It never worked out because I only used a straight line as a center figure, and couldn't remember how a hexagon was shaped. :D :D

I once went to the extent of writing down the angles or geometrical shapes of all of the intervals based on F natural. That's the reason I am not a musician! :lol:

I tend to navigate away from the current topic... :/

Posted: Tue Apr 28, 2009 12:41 pm
by strachs
http://www.georgerussell.com/

It's on the title page of the 2001 edition, but also appears on George's web site.

Book two will be all over it I'm sure.

I'm not suggesting a geometrical approach to music (although there are definitely "parallels" that can be "drawn" - pardon the pun).

Posted: Tue Apr 28, 2009 2:03 pm
by strachs

Posted: Tue Apr 28, 2009 10:08 pm
by sandywilliams
I don't have my book handy but I think that diagram represents the three forces mentioned at the end of the book, passive, active, and neutral. Vertical Tonal Gravity is passive. Horizontal Tonal Gravity is active, and Super-vertical is neutral I believe. The diagram makes sense because flat-lying scales tend to be horizontal, thus active. I'll give it another look when I get hold of my book.
Have you ever seen the cycle drawings Coltrane did that Yusef Lateef published?

Posted: Wed Apr 29, 2009 9:23 am
by strachs
Is there an image available on the web?

Posted: Wed Apr 29, 2009 10:07 am
by strachs
Tonicization is obviously a horizontal concept.

Russell uses the Giant Steps solo on pg 95-98 to demonstrate VTG in use, but also points out the horizontal relevance of the tonic stations that are resolved to via the 7th chords.

At this point in the book, CMG's have not been discussed yet, so Russell describes the resolutions as mode II of one parent scale resolving to mode I of another scale one step sharp - the major chord being expressed with a "horizontal scale", the major scale.

Does anyone else find this kind of treatment overly complicated?

I like to relate to the horizontal resolving mechanism in terms of CMG's rather than horizontal scales, for one thing, because it is much simpler in terms of how many scales you need to relate to. The number of parent scales referenced on pg95/96 would have been basically cut in half if the resolutions were viewed as IIv-Vh (or even VI-II-Vh in some cases) rather than considering the tonic station chord to be I with a horizontal scale imposed over it.

The whole Giant Steps theme could be traversed using only three parent LC Scales: E, C, and Ab.

Am I the only one who sees it this way?

Posted: Wed Apr 29, 2009 3:01 pm
by sandywilliams
[quote="strachs"]Is there an image available on the web?[/quote]
You can see most of it here:
http://www.georgerussell.com/

Posted: Thu Apr 30, 2009 7:06 am
by strachs
sandywilliams:

Yeah, I've mentioned that diagram several times in the Forum. I didn't know that was Coltrane's.


motherlode:

No, he doesn't.

Posted: Thu Apr 30, 2009 8:43 am
by sandywilliams
Sorry.. I was cornfused. I don't know if the Coltrane diagrams are on the web.

Posted: Mon May 04, 2009 11:35 am
by strachs
dds1234:

you may find this article interesting:

http://danadler.com/misc/Cycles.pdf

Posted: Tue May 05, 2009 12:17 am
by dds1234
Excellent... Straight forward and to the point! strachs, I agree with motherlode about your contribution to this thread and forum alike. Thank you!! :D

I'm going to let some of my friends/students check this out... I'm sure they don't understand why I am such a harsh advocate for learning the cycle of fifths.

My idea when first making different angles and geometrical shapes on the cycle of fifths diagram was to make it so I could calculate ALL of the intervals easily and efficiently. I really gave up on it as I was afraid it would take too much of my mental processing power to be practical.

Furthermore all of this spawned from seeing an odd chart with a triangle in the middle of the circle of fifths... John Coltrane (and later George Russell) really made me realize the pure mathematical approach to music and... today I am entirely warped from my original state of mind.

Posted: Tue May 05, 2009 7:45 am
by strachs
I have my guitar student (an absolute beginner) use the cycle of fifths to create a chart of all the key signatures. I have him recreate it from scratch from time to time. I don't let him play scales up to speed until he first works out the key signature and names all the notes on the spot. He's becoming amazed at how this small investment of thought pays off big when trying to figure out a song.

Traditional music instruction is so backward leaving this essential understanding until years into the program. To me, it's a fundamental. Even long before concepts like modulation and modal genre are introduced, there's absolutely no justification for memorizing scales and keys BEFORE learning how they are constructed.

I think the Concept itself would be so much more accessible if the cycle of fifths were introduced early in one's musical education. What are treated as "shortcuts" in musical education, are really not shortcuts at all, because they impose severe limitations on one's understanding, with the goal of showing tangible "results" in the form of repertoire.

Don't stop advocating the cycle. As we know, it yields beautiful fruit early in the season and late.

Posted: Tue May 05, 2009 2:19 pm
by dds1234
Exactly strachs, well put. This is a subject I really enjoy talking about! If it was on the same subject of this topic I would rant and rant... and rant some more! :D :D :D

I attempted to have a beginning guitar student but... He was infuriated by my insistence of not teaching basic chords until he got down the basic intervals. I taught a beginning bass player friend of mine about a year ago and he has grown to be really great with only fifty hours or so of practice.

Was there a point of realization for you guys and the pure mathematics of music? It wasn't until about four years into playing an instrument when I realized how it is all entwined.
-I feel a bit blessed that I am self taught, I had much less to unlearn than many others studying the concept.
--For a few months the cycle of fifths consumed me... The thought of taking all intervals, chords, scales, etc. from just twelve letters placed in a circle... Who wouldn't be as interested as I was/am?!

On the subject of teaching again, how do you think a musician would turn out learning the concept at a virgin state of mind? It might seem like a harsh undertaking but... as many people have stated "there is simplicity in complexity."



Forgive me, I veer.

Posted: Tue May 05, 2009 2:20 pm
by dds1234
(By the way, you seem like a harsh teacher strachs!)