The River Trip - Carried Along By HTG

The main body of the LCC and its practical application, including all 4 published versions of Book 1 with their inserts: the 1959 tan cover; the 1959 light green cover Japanese edition; the 1970‘s white cover, which adds an illustrated River Trip to the 1959 edition, and the currently available Fourth Edition, 2001.

The authorization code is the first word on Page 198 of the Fourth Edition of the LCCTO.

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The River Trip - Carried Along By HTG

Postby strachs » Fri Sep 11, 2009 1:12 pm

One of the much-appreciated analogies offered in the LCC is the "river trip" thing, helping one understand different approaches to navigating a succession of chords.

I think there is more that can be understood by the analogy of a river.

Unlike a road, a river has a current that travels in one direction. It is much easier to swim, wade, or paddle downstream than upstream. To go against the current, much more effort is required, more energy must be expended.

Something similar happens with Horizontal Tonal Gravity. As the diagram on pg 5 shows, C major (or F Lydian Vh) resolves to C Lydian. The river of HTG flows in the sharp direction.

The fundamental model of the simplest known horizontal resolution is II - Vh (in traditional terms, the V7-I progression, or 'perfect' cadence). The Vh triad exists in this lydian scale on MT V as a tonic station, but also exists in the next sharp-lying LS as PMG I, a vertical entity in it's own right. The CMG's reveal a resolving tendency, not only from chord to chord, but from LS to LS. The gravity flows in a sharp direction, and can be compared to the current of a river. All that is needed to flow down it is to aim for a CMT, then treat that CMT as the PMT for that chord type.

When I analyze music that is very horizontally-minded, like Bach, for example, I find that much of his music involves starting in one LS, jumping back to a scale several steps in the flat direction, and then letting the current of the river take him back to the original LS. (Obviously he wasn't thinking in these terms, but he felt the current nontheless, and found ways to exploit it).

What some in this forum have expressed (not recently, but within the last couple of years) is: The LCC is very open-ended - now how do I use it to create a chord progression? I'm not saying I can provide an easy answer to that, but I think that (especially in the absence of book II) this alternate river analogy might help.

Unfortunately, you're going to find me using terms that are coloured by my newly discovered polymodal, non-ladder approach to vertical structures. However, I think this works very well with the above river analogy, and may even help us to harness the power of the concept a little more.

To demonstrate what I'm talking about, I'm going to be using Bach's Prelude and Fugue #12 BVW881 in F minor. If you don't have it, it's available in PDF (and several other formats) here:

http://www.allpianoscores.com/audio_scores.php?id=68

The terminology I have chosen for now to refer to "quotations" from flat-lying lydian scales, is Q1, Q2, Q3, Q4, and Q5. The number indicates how many steps from the flat direction the LT is being borrowed from. Q2 maps to Lb7, Q3 to LD/L#2, and Q4 to LA (see my recent ramblings if you can't understand all of this). You'll see soon why I'm expressing the larger-than-lydian scales this way rather than by TO level.

My LCC analysis is posted here (sorry, link no longer works, and I don't have the original file - my approach has evolved yet again, so I'll be posting a more recent analysis of this same fugue shortly):

http://www.4shared.com/file/131975936/8 ... VW881.html

I have not had time to complete the analysis of the Prelude, yet, but the first 28 measures, and the entire Fugue are analysed with LS, MG, and Q# where applicable (I even noted in parentheses what actual note is being quoted, and in many cases what the tonic station "would be" in the 'from' scale).

Although melodic minor is generally regarded as equating to LA, I have found that in this context, Lb7 (being the same notes as LA, but with a different LT allegiance) provides a better description of it, at least in Bach's particular usage of it. I can go into detail about this if you're interested, but for simplicity, suffice it to say, I'm dealing with melodic minor as Lb7 (in my system, Q2), and harmonic minor as L#2 (in my system, Q3).

Let's start with the Fugue. In general, you can see Bach starting out within Db, moving easily to Ab (one step sharp), and to Eb (one step sharp again). In almost all cases, when moving from one scale to another, he aims for a CMT of the current scale, and then treats it as a PMT in the sharp-lying scale. In other cases, in order to go back to the flat-lying scale, he aims (as in ms 8-9) for a CMT (IIIh, a minor type), but sounds a m7b5 chord, or MG +IV of the Db scale, from which he again aims for that scale's IIIh CMT, and makes that minor triad a PMG of the sharp-lying Ab LS.

He follows the current of the river towards CMG's, and either continues down the river by treating the formerly CMG triad as a PMG triad, or by replacing the triad with a more outgoing chordmode of a flat-lying LS. In both cases he aims for the CMG's and then places something else on that expected MT.

For the less adventuresome sections, he simply climbs down predictably from rung to rung on the MT ladder (ms 16-21, 32-37, 66-71, etc) in a familiar cycle.

So what's the advantage of considering your "out" tones as flat-lying LT's instead of higher rungs on a ladder?

First, when the melodic minor scale is used (I'm treating it as Lb7), it is based on a LS two steps sharper (downstream) than the PPS of the minor triad it is going to resolve to. This is a weak resolution, then, since it does not propel you down stream, but rather a bit upstream (not really, you're actually tricked because the chord resolves to Vh of the Lb7 scale - the triad on that degree is only minor because of the scale quotes from two steps flat, imposing the quality of MGVI onto MG Vh. The true parent of that "minor" triad is actually three steps upstream from here). This results in a rather weak resolution (heard in ms 40-41, 50-51, and 74). In contrast, the harmonic minor resolution (VII - IIIh) has a stronger "current" driving it, because the LS movement is in the proper sharp direction, and the "borrowed" LT is from three steps upstream, giving it added horizontal "goal pressure" to move downstream. In this Fugue, Bach usually does not "resolve" his melodic-minor-coloured 7th chords directly to a tonic station, but often follows the melodic minor material with a harmonic minor treatment of the same 7th chord (ms 6-7, 13-14, 64-65, 71-72, 76b-77).

Now let's look at the Prelude for a minute. In a similar manner to the Fugue, the Prelude does some bouncing around in one scale, then in another, and so on. The melodic minor scale is also drawn upon for this here. However, since the E was quoted by the Db LS (three steps flat, Q3), that tone has prepared the ear for what is to come. Later, in measures 24 to 26, the bass line starts drawing from the flat direction again, first Gb (actually converting to GbL), then Fb in ms 26. Since the Fb (E) has already been heard in the context of DbL, it could be seen as a quote from three steps flat, changing Db's VI MG to a m7b5 flavor. However, the next measure shows that this is more than a LT quotation this time. The Bbm7b5 chord is actually MG +IV of EL (or Fb if you like), as the chords that follow agree with. The Abm triad in ms 26b is MGIIIh of EL, and the next chord, although still in E/Fb Lydian, quotes from a yet further flat-lying LS, D (Q2), making the +IV chord a Bb7b5 chord, which then resolves to it's VII CMT (Eb), now back once again in the DbL domain as MG II.

The harmony hinted at something upstream (ms 1 & 9), then actually made the leap upstream (ms 26), reached a little further still (ms 27a), then yeilded at once to the current, back to the LS where the peice began (ms 27b/28).

I think this demonstrates that, once a little flat-lying material (a quoted LT) is introduced, the possibility is opened up that other resources from that flat-lying scale are within reach, and if utilized, the trip back downstream is made easily enouph, due to the current of HTG. Along the way, any verticality at all can be utilized, but especially when the succession of chords yeilds to the HTG posessd by the CMT's.

Now, there's only so far upstream one can reach without going entirely into unrelated territory (taking giant steps, pardon the pun), but if the distance is travelled incrementally, rather than all at once, the chordstream (again, pardon the pun) can be traversed smoothly.

I haven't had much opportunity yet to explore this in improvisation, but I welcome you to give it a try and comment on your results. Whether you choose to think in terms of LT quotation, or continue with the LCS and it's tonal orders does not affect your ability to think of HTG as a river. The approach that can easily be copied from the Bach example is just this: take advantage of the HTG force that pulls you toward the CMT's. If you want to continue downstream, convert that tonic triad (or entire chordmode if you wish) to it's PMG identity in the next sharp-lying LS. If you want to go back upstream before yeilding again to the current, sound a more outgoing MG on the CMT - the HTG will still support the sounding of the MT, but you will be drawing on a more flat-lying (upstream) LS, since the chord you use is on a more outgoing MT of that flat-lying scale.

Additionally, you may find that treating any "out" tones you make use of as even more flat-lying material (borrowed LT's), fits well with the analogy of a river's irresistable current.
Last edited by strachs on Fri Aug 02, 2013 9:41 am, edited 1 time in total.
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Re: The River Trip - Carried Along By HTG

Postby tonalsearcher » Fri Mar 01, 2013 3:43 am

The river trip analogy is my favourite part of the LCC. That and the rocket analogy speak volumes about how Russell felt about how improv changed from the earlier local key based exploration to further less 'home' bound playing. I remember clearly when getting into the method how after hours studying the diagrams those little drawings led the way. That and when he talks about his conversations with Miles where Russell explains how he felt that what Miles was exploring was the implied harmonies between each chord which the method could explain easily but conventional harmony didn't have an obvious analysis. Those sections made it clear to me that this was something different, spiritual almost.
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Re: The River Trip - Carried Along By HTG

Postby chespernevins » Fri Mar 01, 2013 9:19 am

I wish Strachs's analysis was still at the link he provided above. I'd like to check it out again.
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