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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An open letter from Alice Russell. June 21, 2011, Brookline, Massachusetts. 1. DO NOT make insulting, mean spirited remarks about anyone or their work; there are a plethora of sites where you can rant unfettered. If you attack someone personally, your comments will be removed. You can post it, but I'm not paying for it. Go elsewhere, and let those artists who are actually interested in discussion and learning have the floor. 2. There will be NO posting of or links to copyrighted material without permission of the copyright owner. That's the law. And if you respect the work of people who make meaningful contributions, you should have no problem following this policy. 3. I appreciate many of the postings from so many of you. Please don't feel you have to spend your time "defending" the LCC to those who come here with the express purpose of disproving it. George worked for decades to disprove it himself; if you know his music, there's no question that it has gravity. And a final word: George was famous for his refusal to lower his standards in all areas of his life, no matter the cost. He twice refused concerts of his music at Lincoln Center Jazz because of their early position on what was authentically jazz. So save any speculation about the level of him as an artist and a man. The quotes on our websites were not written by George; they were written by critics/writers/scholars/fans over many years. Sincerely, Alice

Postby chespernevins » Fri Sep 25, 2009 6:57 am

Thanks ML!

MusicXML seems to be the recommended format for cross application sharing.

The filename should end in .xml
chespernevins
 
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Postby chespernevins » Sat Sep 26, 2009 2:15 am

From my first post:

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.


I found in the 1959 version of the book on page xxviii where it says "The concept of interval tonics has been applied in the grading of the intervals of each category".

Given this idea, and the ideas that ML and Ben have shared, I’m coming up with a little different method of generating the chart. Let's use the minor 2nd interval as an example.

1) use the prime order (1 5 2 6 3 7 +4 +5 b3 b7 4 b2 ) as the order of most ingoing to most outgoing, which ML and Ben both mention.

2) find the intersection of a given interval (in this case, a minor second), built on each of the primes, with the 7 tone order.

3) find the tonic of each of those intervals (in this case, minor seconds).

4) put the tonic of each interval in the order of the primes to find the most ingoing to outgoing (minor 2nd) intervals in the 7 tone order.

5) repeat with the 9 tone order, the 10 tone order, the 11 tone order, and 12 tone order.

Here are the steps in detail:

1) Take your primes:

b2 <-- most outgoing in the LCS
4
b7
b3
+5
+4
7
3
6
2
5
1 <-- most ingoing in the LCS


2) find the intersection of minor seconds built on each of the primes with the 7 tone order ( 1 5 2 6 3 7 +4). In the key of C, the 7 tone order is C G D A E B F#.


b2
4
b7
b3
+5
+4 <-- F# and G make a min 2.
7 <-- B and C make a min 2.
3
6
2 etc…
5 <-- (G and Ab NOT in the 7 TO)
1 <-- (C and Db NOT in the 7 TO)

3) The tonic of the interval of a minor 2nd is the top note. (See page 6 of new book or page xxvii of 1959 book).

The 2 intervals we have in the 7 tone order, and their tonics are:

The interval of F# and G, whose tonic = G
The interval of B and C, whose tonic = C


4) Put these tonics in order of ingoing to outgoing based on the order of the primes (with 1 being the most ingoing and b2 the most outgoing):

b2
4
b7
b3
+5
+4
7
3
6
2
5 <-- the note G (tonic of the F# G interval) is the second most ingoing note in the C LCS
1 <-- the note C (tonic of the B C interval) is the most ingoing note in the C LCS

So the ingoing to outgoing order of the minor seconds in the 7 tone order is:

7 (the B C interval)
+4 (the F# G interval)

5) Go back to step 2 and repeat the process with the 9 Tone Order

2) the 9 tone order is (1 5 2 6 3 7 +4 +5 b3). In C, the 9 tone order is C G D A E B F# G# Eb.

b2
4
b7
b3 <-- Eb and E make a min 2
+5 <-- G# and A make a min 2
+4 <-- this interval is already accounted for in the 7TO
7 <-- this interval is already accounted for in the 7TO
3
6
2 <-- D and Eb make a min 2
5 <-- G and Ab make a min 2
1

3) The tonic of the interval of a minor 2nd is the top note. We have these intervals and tonics:

G and Ab, whose tonic = Ab
D and Eb, tonic = Eb
G# and A, tonic = A
Eb and E, tonic = E

4) Put these tonics in order of ingoing to outgoing based on the order of the primes:

tonics, in order of ingoing to outgoing: A, E, Ab, Eb

this gives us the minor 2nds in this order:

G# A (+5)
Eb E (b3)
G Ab (5)
D Eb (2)

5) If we keep going, we get:


10 tone order:
b7
6

(This is different than the 1990s chart)

11 tone order:
4
3

12 tone order:
b2
1

Now we have the order of min 2nds:

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


The major seconds will be a little different because the tonic of a major 2nd is the lower tone of the interval.


1) the prime order (1 5 2 6 3 7 +4 +5 b3 b7 4 b2 )

2) find the major seconds in the 7 tone order

3) find the tonic of each of those intervals

4) order the tonics from ingoing to outgoing

5) repeat with the 9 tone order, the 10 tone order, the 11 tone order, and 12 tone order.

7 tone order:

b2
4
b7
b3
+5
+4
7
3 <-- maj 2
6 <-- maj 2
2 <-- maj 2
5 <-- maj 2
1 <-- maj 2


Spell out the intervals:


C D
G A
D E
A B
E F#

Get the tonics:

C D = C
G A = G
D E = D
A B = A
E F# = E

Order the tonics:

C, G, D, A, E

Get the order of major 2nds, ingoing to outgoing:

1
5
2
6
3


9 tone order (C G D A E B F# G# Eb):

b2
4
b7
b3
+5
+4 <-- F# G#
7
3 <-- already in 7TO
6 <-- already in 7TO
2 <-- already in 7TO
5 <-- already in 7TO
1 <-- already in 7TO

There’s only one major 2 in the 9 TO:

+4


10 tone order (C G D A E B F# G# Eb Bb):

b2
4
b7 <-- Bb C
b3
+5 <-- G# Bb
+4 <-- already taken in 9TO
7
3 <-- already in 7TO
6 <-- already in 7TO
2 <-- already in 7TO
5 <-- already in 7TO
1 <-- already in 7TO

Find the tonics of the intervals:

Bb C = Bb
G# Bb = G#

G# comes before Bb in the order of primes so our ingoing to outgoing order of major 2nds in the 10 TO is:

+5
b7


11 tone order (C G D A E B F# G# Eb Bb F):

b2
4 <-- F G
b7 <-- 10TO
b3 <-- Eb F
+5 <-- 10TO
+4 <-- 9TO
7
3 <-- 7TO
6 <-- 7TO
2 <-- 7TO
5 <-- 7TO
1 <-- 7TO

Intervals:

Eb F tonic = Eb
F G tonic = F

The order of tonics, ingoing to outgoing, is Eb, F, thus:

b3
4

12 tone order (C G D A E B F# G# Eb Bb F Db):

b2 <-- Db Eb
4 <-- 11 TO
b7 <-- 10TO
b3 <-- 11 TO
+5 <-- 10TO
+4 <-- 9TO
7 <-- B Db
3 <-- 7TO
6 <-- 7TO
2 <-- 7TO
5 <-- 7TO
1 <-- 7TO


Intervals:
Db Eb = tonic of Db
B Db = tonic of B

B comes before Db in tonal order so our order is:

7
b2

So the order of major 2nds is:

1
5
2
6
3
+4
+5
b7
b3
4
7
b2
Last edited by chespernevins on Sat Sep 26, 2009 12:46 pm, edited 2 times in total.
chespernevins
 
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Postby chespernevins » Sat Sep 26, 2009 1:16 pm

Thanks for your help, ML.
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Postby strachs » Mon Sep 28, 2009 7:30 am

The additional point about interval tonics was the missing puzzle piece for me.

Without the benefit of either of the older books, your step-by-step, visual description helped me to make sense of this chart. Until now, I was stumped.


Thanks
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Postby chespernevins » Tue Sep 29, 2009 8:29 am

chespernevins
 
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Postby chespernevins » Tue Oct 06, 2009 8:20 am

I have a few exercises that we used to play with in regards to TG. I like to think of them as a 'wash of sound'.


ML, if you have them handy and get a chance, I would be VERY interested to see what exercises you have!

Thanks.
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