Page 1 of 1

Close-To-Distant Revisited

PostPosted: Thu Nov 13, 2008 4:17 pm
by strachs
Back in the "Chart A Discrepancies" thread, I voiced an objection to the order of intervals introduced by the Lydian Chromatic Scale. It's still kind of under my skin, so I thought I'd post some references and thoughts to see if anyone else sees it this way.

Page 3 "An ascending order of six consecutive intervals of a fifth offers, more than any other order of intervals, the most scientifically sound basis upon which to structure an objective theory of music."
(Why stop at six - why is an exception OK in constructing the LCS, but not in the major scale?)

Page 3 "the Lydian tonic ... a self-organized tonal gravity field in which all tonal phenomena are graded on the basis of their close to distant relationship to it."
(The LCS does not actually conform to this - it gives greater authority to common practice by bypassing the true eighth tone in favor of one that yields a more useful chord-parenting scale. No more objective that the major scale IMO. The question here is close-to-distant grade)

In constructing a major scale out of stacked fifths, and using the lowered fifth as the uppermost tone, all you have done is followed the same procedure that Russell uses to construct the LCS - you have bypassed a fifth - or in this case bypassed five of them - to achieve a scale which suits your purposes. In the case of the major scale, it suited the purposes of horizontal music, but painted itself into a corner by ignoring the limitations of this arrangement. In the case of LSC, it is also "disrupting the perfect symmetry of fifths with its implied logic of chord/scale unity" (pg 4) in order to accommodate an objective that, to me, diminishes it's objectivity.

Russell's justification for this is on page 231: When discussing the process of creating a LC Scale starting on C, he introduces the CM, GM, DM, and then AM triads. "However, the introduction of the tone C# at this eight tone level of the LC Scale would mean a departure from Western harmony's intuitively (not formally) logical vertical development. It would mean that the I major, VI minor, II seventh, +IV minor seventh b5 and other chords produced intrinsically by the Lydian Scale would need to accommodate a tone contrary to their essential harmonic genre. Because of the Pythagorean ladder of fifths, the flat ninth C# sounding with a C major chord can sound like a natural extension of that chord's harmonic evolution. But other principal chords of the Lydian Scale (VI minor, II seventh, +IV minor seventh b5) have a more ingoing and functionally expansive relationship with tones other than the flat ninth C# of the Pythagorean scale of fifths."

He then says: "Don't worry, the chain of fifths has not been broken; the fifth (A-E) is simply bypassed."

Chord-parenting ability is used to justify a departure from the Pythagorean ladder of fifths. This is no more acceptable than using horizontal functionality to justify departure from it. After first using this ladder as the foundation of his concept, he then abandons it. If you reason that he hasn’t abandoned it, then neither did the major scale. Russell simply abandons the P5 order a little further up the ladder than the major scale does. Unlike the major scale, the LCS retains it’s awareness of horizontal and vertical states. The only thing that is wrong with this, is the inaccurate terming of Russell’s tonal orders as “close to distantâ€

PostPosted: Fri Nov 14, 2008 3:30 pm
by sandywilliams
The broken link in chain of 5ths in the ingoing-outgoing tonal orders in the realm of Vertical Tonal Gravity makes sense to me. The Circle of Close to Distant relationships in Horizontal Gravity is an unbroken circle of fifths.
If you were to present a series of scales that represent the different vertical tonal orders (as the LCC does), what scale would you list that includes the b2 as being part of the 8-tone order? Would it be sound more ingoing to you than the LA or LD? That might depend on the part of the world you were raised in. Does it generate useful modal genre? GR seems to have called an ‘audible’, no pun intended, by bumping the b2 to the end of the line.

PostPosted: Mon Nov 17, 2008 10:38 am
by strachs
Are we really achieving an "objective theory of music" if we decide our ingoing/outgoing relationships based on how they sound? Like you mentioned, that may vary depending on cultural conditioning.

Isn't the distance from a lydian tonic measured in perfect fifths? (the term "close-to-distant relationship" implies an actual distance rather than perceived level of dissonance or other quality that makes it seem "out" rather than "in".)

The absence of a historically significant scale based on the eighth Pythagorean tone does not alter that tone's distance from the lydian tonic.

PostPosted: Mon Nov 17, 2008 10:31 pm
by sandywilliams
It is important to distinguish between the Western Order of Tonal Gravity and the Circle of Close to Distant Relationships. The WOTG is tool for judging the ingoing-outgoing spectrum within the realm of Vertical Tonal Gravity. The Circle of Close to Distant Relationships is a tool for, among other things, looking at horizontal motion, within a piece of music. Though seeming similar, they are different, and serve different purposes.

PostPosted: Wed Nov 19, 2008 11:00 am
by strachs
Very interesting. I guess part of me wants to unify all aspects of my musical understanding - an impulse not unlike that which inspired Russell to go off and discover the Concept in the first place.

Part of Russell's aim was to discover some guiding principles that were so universal that, once grasped, would free one from a multitude of rules for every little aspect of music.

In the same spirit, I am just exploring the possibility that one "scale" (the Pythagorean ladder of 5ths, which I refer to in my personal notes as "P5") may provide all we need from a vertical and horizontal perspective.

If you feel that Russell's Lydian Chromatic Scale provides you with tools that P5 does not, then by all means use it. For me, I feel that it is redundant to use two such scales, when P5 seems to provide all I need on both levels.

The way I look at it, both the 8th tone and the 12th tone of P5 possess properties/qualities that can primarily be exploited in a horizontal fashion (controlling/describing movement from one tonal center to another). The 9th, 10th, and 11th tones in this order seem to provide resources more relevant to vertical "coloring" of a chord/scale. I prefer not to alter their order to accommodate the vertical, but to recognize how nature has laid out the properties/powers inherent in each new level.

I think the reason why these tones provides horizontal resources, is because by adding the eighth tone of P5, you have a scale which closely resembles the seven-tone order of a P5 scale in the sharp direction. Similarly, by adding the 12th tone of P5, you have a scale which closely resembles the seven-tone order of a P5 scale in the flat direction.

Similar to the way CMG's acknowledge the horizontal significance of the two LCSs closest to a primary LCS (and by the way, the horizontal scales Ionian and Mixolydian are mode I of those LCSs) in a sharp direction, tones 8 and 12 of P5 seem to possess characteristics that are primarily useful for horizontal movement.

It's interesting how viewing things this way seems to kind of mirror the orientation of the Major scale. In the major scale, the two tonal centers related to the primary one are often termed Subdominant and Dominant. One is a perfect fifth in the flat direction (which invokes the 12th tone of P5) and the other a perfect fifth in the sharp direction (which invokes the 8th tone of P5).

On the vertical side of things, all tones are considered to lie in the "sharp" direction, since their tonal significance exists in the moment, above an ultimate Lydian Tonic. So from a vertical point of view, the 8th and 12 tones of P5 contribute little, and are placed by Russell last in the chain (the 12th as 11 and the 8th as 12).

I guess after all this rambling, what I'm getting at is that, for me personally, I can get along just fine with just the P5 ladder, recognizing that it's 8th and 12th tones kind of "frame" the 7-tone order, and are not that significant vertically (although do contribute some interesting chords like "sus" chords spelled in thirds). For me, there's no need to work with two parent scales.

PostPosted: Wed Nov 19, 2008 12:03 pm
by strachs
Related brain-fart:

The Concept allows for two views of the scales with horizontal properties: 1. Modal Genre (Conceptual) that have both a horizontal and a vertical significance, and 2. vertical scales of the 11th tonal order (since they include the 4th degree).

So, in other words, the Major Scale can be viewed as either mode V of the parent Lydian Scale, or as an 11TO scale (replacing the seventh tone with the 11th). The Mixolydian mode too, can be viewed as mode II of the parent Lydian Scale, or as an 11TO scale (replacing both the sixth and seventh tones with the 10th and 11th tones).

Extending this latter view even further, we could produce the following table (excuse the periods, it's the only way I can achieve a table):

MT....Mode Name.......Pythagorean Tones Present...Scalar Intervals Present
I.......Lydian:.............1 2 3 4 5 6 7............................1 5 2 6 3 7 #4
V......Major:...............1 2 3 4 5 6 12..........................1 5 2 6 3 7 4
II......Mixolydian:.......1 2 3 4 5 11 12.........................1 5 2 6 3 b7 4
VI.....Dorian:.............1 2 3 4 10 11 12 .......................1 5 2 6 b3 b7 4
III....Aeolian:............1 2 3 9 10 11 12.......................1 5 2 b6 b3 b7 4
VII...Phrygian:...........1 2 8 9 10 11 12......................1 5 b2 b6 b3 b7 4
+IV..Locrian:.............1 7 8 9 10 11 12 ......................1 b5 b2 b6 b3 b7 4

If it works for Major and Mixolydian, it should, in principle, be an acceptable way of viewing the other modes, too; considering them as scales representing outer tonal orders. Of course, the most ingoing interpretation of these scales is as modes of the Lydian Scale (thus reducing the number of scales we need to work with). However, viewing them this way is not really different than having multiple names for other scales (Lydian Augmented=Melodic Minor, Lydian #2=Harmonic Minor). It is one way of revealing the vertical place that each of the tones has in relation to the Modal Tonic, in addition to knowing their relation to the ultimate Lydian Tonic. Again, having two different perspectives from which to view the same thing can be useful.

PostPosted: Wed Nov 19, 2008 1:18 pm
by strachs
Another cool quote, relevant no matter what your take is on all of this:

The Science of Musical Sound, by John R. Pierce (1983): "The rules that academics deduce by studying living music have many uses. The rules are fascinating in themselves. They can be a help in listening to music. They can be a help in learning to compose music. But they do not provide a means for grinding good music out mechanically."

What we look for in studying all of this are ways to shape our THINKING, and indirectly, our music.

PostPosted: Thu Nov 20, 2008 1:19 am
by dogbite

"Another cool quote, relevant no matter what your take is on all of this:

The Science of Musical Sound, by John R. Pierce (1983): "The rules that academics deduce by studying living music have many uses. The rules are fascinating in themselves. They can be a help in listening to music. They can be a help in learning to compose music. But they do not provide a means for grinding good music out mechanically."

What we look for in studying all of this are ways to shape our THINKING, and indirectly, our music."

and i was beginning to think that i was the only one who has read the scientific american library - i have the first ten (out of how many i do not know) volumes, of which this is obviously the most fascinating for me as a music theorist...

if i may add that russell believes that he has discovered something unique and wonderful about music in terms of the science, foundation, history, and evolution thereof in human culture. i have never even seen a method which claims to be a way of "grinding good music out mechanically" - for that there must still be a human element, a spark of creativity, a gift from...i don't know where from, but i think we all know what i mean...

LCC is a tool to put music into some kind of perspective so that we may, hopefully, see more clearly the forces at work which move us into hearing things the way that we do. is there a cultural expectation or bias at work here? i think there clearly is, but this does not negate the elements upon which all of this is built and i do believe that there is something real and demonstrable about what russell is telling us.

i think that sandy was on to something when he said that the circle of close to distant relationships is different than the WOTG (western order of tonal gravity) - the circle is comprised of twelve lydian tonics, each with its own WOTG and member scales. i don't know where i first saw this "ferris wheel" metaphor, but i think it is appropriate. i do not wish to go on pining for ("oh where, oh where is") book 2, but hopefully this will be the last time. and i truly hope that i haven't confused the issue any more than it needs to be.

happy thanksgiving everyone! i'll be back in about ten days...



PostPosted: Thu Nov 20, 2008 6:38 am
by strachs
I hope that no one takes from my little essays that I'm trying to belittle or otherwise discredit Mr. Russell or his work. The quote about "grinding out music mechanically" was not about Russell or his methods, but merely to point out the trap of coming to too rigid a view of interpreting music.

I have not been trying to prove Russell wrong, or anything. In the foreword to the book we are encouraged to adapt our own musical perspectives to the one presented in the book, and take from it a fresh view. I have endeavored to distinguish between what the book provides that is Universal, and what may be Russell's own toolset for applying the Universal. We all, of course, should create our own toolset for applying those same Universal principles articulated by Russell.

I think what set me in that direction within these posts was the disagreement sometimes experienced with respect to what parent scale and modal genre is involved in various musical excerpts. My point is simply that there is more than one possibility. I also see value in taking certain things to their logical conclusion rather than just accepting and applying what is stated outright in the book (such as viewing all modes from both a vertical and horizontal perspective, not just the CMG's).

Some of what is to come in book two may correct some of my notions. Maybe not. Anyway, anyone open-minded enough to read and try to understand Russell's book and Concept (which includes everyone in this Forum) can surely appreciate that all ideas - even his (and mine,) - can and should be questioned and probed in order to personalize them.

PostPosted: Thu Nov 20, 2008 12:54 pm
by strachs
Well, for one thing, I'm not really a Jazz guy (if you haven't already guessed), although I love and respect both improv and many jazz composers. Also, I'm not a pro musician, just a hobbyist. So, I'm not generally in a situation where I'm listening to/jamming with musicians and relating "live" to lydian tonics and the upper tones of complex chords. For some, that may disqualify me altogether from voicing anything in this Forum.

Anyway, so far, my application for the Concept has been in trying to get a better understanding of music I love: Bach, Chopin, Keane, Rush, Dream Theater, Joe Satriani, Debussy (early works, anyway), and yes, Miles Davis, Bill Evans, Thelonius Monk, too.

I am interested in finding a satisfying explanation for music that goes beyond the Lydian Scale and it's modes. As we have seen, even for early music (Baroque period, eg), there are many occasions where tones that are very effective cannot be explained/understood with just seven-tone scales and modes.

To analyze these (and I do not advocate my toolset for others, it just is what it is), I have been starting with printing out a page with rows of perfect fifths like this:

F C G D A E B F#/Gb C#/Db G#/Ab D#/Eb A#/Bb F C G D A E B F#/Gb C#/Db G#/Ab D#/Eb A#/Bb

I then circle or underline the tones I read in the music to determine the span of fifths that will frame the tones in question. For plain old diatonic stuff, that will, of course be seven tones; the Lydian Tonic being obvious.

For the Bach example over in the "Harmonic Minor" thread, I would circle (measure 14) the tones as they appear in the mesure:
F C G D A E B F#/Gb C#/Db G#/Ab D#/Eb A#/Bb F C G D A E B F#/Gb C#/Db G#/Ab D#/Eb A#/Bb

This made it clear that I was looking at the Bb 9-tone order (in LCS terms). However, to use a grid like this (which is useful to me, anyway), I have to say mentally "skip the B natural, because it's the 12th tone, and then F# is the 8th tone, so C# is the 9th tone". In working this way, it seems more intuitive and straightforward to me to simply number the tonal orders in their Pythagorean distance from the Lydian Tonic, rather than mentally renumbering them for the sake of showing their vertical significance.

In the end, it may be just semantics and personal preference, but for me, it's not more practical to re-number the tonal orders from their original Pythagorean order, but less practical.

So I'm not slamming Russell's scale as if he's totally off-the-wall and self-contradicting, or anything else. It's just that for me, I can't see a reason to tweak the order if P5 works for horizontal and vertical analysis. I can use the same row of 5ths to identify vertical tonal orders, and to compare adjacent horizontal states. To identify the tonal order, I just count to the right from my lydian tonic. To measure the distance horizontally, I likewise just count to the left or right. No extra scale needed.

In practical terms there may be no difference in the numbering of tonal orders for most musicians playing live against a chordstream. For someone like me, who is fairly slow in intuitively recognizing Modal Genre and distance to Lydian Tonics and such, the paper-and-pen approach is a necessity. In this context, clinging to the 5ths-only order has practical benefits.

PostPosted: Thu Nov 20, 2008 11:14 pm
by sandywilliams
Sounds like you would have enjoyed the 1959 edition of the LCC which came with a slide rule for helping figure out the various scales.

PostPosted: Fri Nov 21, 2008 10:47 am
by strachs
Ok, here's a link to the measure I was referring to in the post above. ... d=f916286f

Hope this helps you to understand the tones I was underlining above.

(you mean you can't read my mind? Woops. I'ts not that I can't use Finale, I'm just lazy. And you've been gracious enouph to do it for me, I was getting used to it. Mother is always looking after everybody.)

PostPosted: Fri Nov 21, 2008 2:08 pm
by strachs
Had some time to kill. Here is the entire Invention. ... d=f916286f

(Thanks for the encouragement to master Finale - I only have the free Notepad version, but it's still a pretty awesome tool.)

PostPosted: Fri Nov 21, 2008 8:02 pm
by dds1234
I personally prefer Sibelius.