LCC Interval Categories Chart aka Tonal Gravity Chart

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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LCC Interval Categories Chart aka Tonal Gravity Chart

Postby chespernevins » Sun Sep 20, 2009 11:15 am

Here is the chart I have for the Interval Categories. This is the chart we have been referring to as the "Tonal Gravity" chart.

We have copies here on the forum of the 1950's version, but this is a version that was started in the 70s and had some edits made to it later.

This version is updated through 1993 or 1994.

http://www.4shared.com/file/134064594/6 ... 1990s.html

Can anyone shed light on how this chart was derived?

This chart does not seem to be generated in the same fashion as the 1959 version, which uses the ladder of fifths in intersection with Lyd, then Lyd Aug, then Lyd Dim, then the 9 TO scale, etc..

We expect some differences in that the new edition of the LCC changes the b7 to the 10 TO and the 4th to the 11 TO.

But there are other differences in addition to that.

For example, in the min 2nd category, in the 9TO, we have listed minor seconds on:

+5
b3
5
2

+5 makes sense because Lyd Aug is the first scale in the 9TO. But why is b3 listed next, which comes from the 9TO composite scale? Why not the 2, which comes from the Lyd Dim? If I am not mistaken, the 1959 instructions use the 9TO after the LA and LD scales are used.

If all the intervals simply come from the 9TO as a whole, what specifies their order?

I thought at first that the intervals might have been chosen by the consonance of the tonic of each of the intervals within the LCS. For example:

The tonic of a stand-alone min 2nd interval is the top note. Thus the tonic of a min 2nd on +5 in C would be A, the tonic of the b3 interval would be E, the tonic on 5 would be Ab and the tonic on D would be Eb.

If we grade the tonics of these intervals: A, E, Ab, Eb in order of consonance, we get the order given on the chart.

However, the 10TO minor 2nds category lists:

6
b7

By the same logic, the tonic of the min 2nd on 6 would be Bb, and the tonic on b7 would be B.

And Bb doesn't come before B in terms of consonance.

Any help would be appreciated!
Last edited by chespernevins on Sat Sep 26, 2009 12:54 pm, edited 1 time in total.
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Melodic Tonal Gravity

Postby chespernevins » Sun Sep 20, 2009 11:26 am

Here is the LCC Interval Chart expressed melodically, as suggested by Motherlode.

http://www.4shared.com/file/134064080/7 ... avity.html

I came across the question above as a started to try to label the scales each interval comes from.
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Postby chespernevins » Sun Sep 20, 2009 11:24 pm

Good stuff, ML.

My question, regarding the 1990s chart is, why does the 1959 chart give minor 2nd intervals as:

7
+4
+5
2
b3
5
etc...

and the 1990s version give:

7
+4
+5
b3
5
2
etc...
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Postby Ben Schwendener » Mon Sep 21, 2009 10:46 pm

Hi

This is a copy of an outdated version of the TG chart. The 1st edition of the book explains - basically - how the logic behind the basic Tonal Gravity Chart of intervals of a LC scale goes, so thats a good place to start.

Involved now in the Memorial concert for GR at Jordan Hall on Oct 2.

- Ben
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Postby chespernevins » Tue Sep 22, 2009 3:19 pm

Thank you, ML, for your clear explanation and Ben, for chiming in with the latest info.

I am attempting to construct a chart using the 1959 rules but with these scales:

LYD

LA
LD
9 Tone Order

LYD b7
Aux Aug
10 Tone Order

Aux Dim
11 Tone Order

ADB (if needed) or just
12 Tone Order

Here's hoping I'm on the right track....
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Postby Ben Schwendener » Tue Sep 22, 2009 4:34 pm

To figure out the TG chart, just follow the prime order. remember that the TG chart is of the LC scale, and that the seven chord-producing Principle Scales are just the clearest vertical representatives of the orders - they didn't create the chart, the LC order of TG did!
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Postby chespernevins » Wed Sep 23, 2009 9:43 am

Ok, here's what I have for min 2nds.

http://www.4shared.com/file/134836243/c ... _min2.html

Am I on the right track? Is it better to go straight from the 7TO to the 9TO, or do we account for all +5s first and then all b3s?

Thank you!
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Postby chespernevins » Wed Sep 23, 2009 9:04 pm

D'oh!

I didn't do the "WHERE YOU LEFT OFF" part. Something about how I interpreted all this made me think I would start at the Lyd Tonic each time.

But now I am thinking that:

1) the methodology is the same as the 1959 book
2) use the primes instead of the circle of fifths
3) use the tonal orders instead of the member scales
Last edited by chespernevins on Thu Sep 24, 2009 7:56 am, edited 2 times in total.
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Postby chespernevins » Wed Sep 23, 2009 9:15 pm

These results make more sense to me, and I think you might recognize it a little more readily, ML:

7
+4
+5
5
b3
2
b7
6
4
3
b2
1

http://www.4shared.com/file/134975470/5 ... t_II1.html
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Postby strachs » Thu Sep 24, 2009 7:13 am

In the 2001 edition, the Tonal Gravity Chart is referred to in a footnote, indicating that it will (would have?) appear in Volume II. That volume is dedicated to HTG and SVTG.

Do the earlier editions point out how it is applicable on those levels?
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Postby chespernevins » Thu Sep 24, 2009 10:00 am

Hey Strachs,

As far as I know, there is no direct discussion of how the TG chart relates to HTG or SVTG in the 1959 version. That would be awfully interesting in relation to your recent analysis.
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Postby chespernevins » Thu Sep 24, 2009 10:13 am

motherlode wrote:
The purpose of the chart, as you know, is only to add clarity to the words.
When I look at your chart it would be very helpful to know exactly which TO is contributing which characteristic tone(s) to make up the Primes...at a glance.
<snip>

Think about how you can make the chart clear to a person relatively new to what's being discussed here.


Thanks for your guidance on this, ML.

Here are the min 2nds formatted much like the existing chart.

http://www.4shared.com/account/file/135 ... t_III.html

I *think* I'm on the right track here. My main question now is should I define seperate 8 and 9 Tone Orders, or just go with the 9TO as a whole?
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Postby chespernevins » Thu Sep 24, 2009 7:14 pm

ML,

7TO = 1 2 3 +4 5 6 7 (Lyd scale)
8TO = 1 2 3 +4 5 6 7 +5 (Lyd scale and the +5)
9TO = 1 2 3 +4 5 6 7 +5 b3 (Lyd scale, +5 and b3)


I don't often hear the 8 TO mentioned. The orders seem to often be referenced as 7 TO, and then next comes the 9TO as the "consonant nucleus".

edit later:

Chapter II of the 2001 book is called: The Lydian Chromatic Scale. Its Eleven member Scales and Five Tonal Orders.

The Five Tonal Orders listed on page 14 are the 7, 9, 10, 11, and 12 Tone Orders.

7 = 1 5 2 6 3 7 +4 (ingoing tonal gravity)
9 = 1 5 2 6 3 7 +4 +5 b3 (consonant nucleus)
10 = 1 5 2 6 3 7 +4 +5 b3 b7 (semi-outgoing)
11 = 1 5 2 6 3 7 +4 +5 b3 b7 4 (semi-outgoing)
12 = 1 5 2 6 3 7 +4 +5 b3 b7 4 b2 (outgoing)

Given this, I am now leaning towards using the 9TO as a whole, with no "8 TO".
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Postby Ben Schwendener » Thu Sep 24, 2009 8:18 pm

The TG chart illustrates the 144 graded intervals of the LC Scale - it may be applied to the Vertical, Horizontal and Supra-Vertical Levels of TG - keeping in mind that these Levels have specific Laws or requirements for manifesting as the 'Prevailing' Level of TG in the music (if thats your intent).
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Postby Ben Schwendener » Thu Sep 24, 2009 8:20 pm

oops - this was in reply to the post at the bottom of page 1...
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