"For clarification, are you saying GR designates Eb as the root of a C minor triad? I think I need a clarification of terms. What are the distinctions among the terms: root, tonic, center of tonal gravity, Lydian tonic, or bass note re the triad? I realize that these distinctions can be controversial and are the stuff of dissertations and theory journals. But how are you using them in this context or reflecting your reading of Russell? "
Eb is the center of Tonal Gravity for a C minor chord. The Eb Lydian Tonic rests on C, the Modal Tonic. The root of the chord is the modal tonic.
Interval chart and Outgoing Vertical Melody
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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
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
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This is a correct LCC analysis, of course. But in the context of this discussion of intervals:Eb is the center of Tonal Gravity for a C minor chord. The Eb Lydian Tonic rests on C, the Modal Tonic. The root of the chord is the modal tonic.
Example I:9 on p.6 is titled "Interval Tonic Justification for the Lydian Scale", which gives the impression that the analysis of these intervals is something that exists prior to the "Justification of the Lydian Scale".
So it's self-referential to then say that the tonic of a minor third interval is the upper tone because it's the Lydian Tonic. And when PH's chart lists the tonic of a minor third interval as the lower tone, it does bring up questions.
Is there an absolute answer to the root note of a minor third?
George says on p.6 that "It is *possible* to form all twelve types of intervals with the Lydian Tonic also being the tonic of the interval." So I wonder if this chart is less of an absolute than simply showing that you *could* consider the root of a minor third interval to be the top note if you were in the context of C Major or C Lydian and your bottom note was A.
My ear tells me that the root of the minor third interval could be either tone, depending on context. If that is true, then it all comes down to how we want to theoretically justify our answer. (In LCC terms, I see a minor third as vertically having the upper tone as tonic and in horizontal terms, the lower tone could be heard as the tonic. I think this goes along with dogbite's pithy but insightful post on the modal tonic and lydian tonic.)
So perhaps the LCC encompasses PH's analysis of the interval with distinctions of vertical gravity and horizontal gravity, or something else.
But really, I still don't understand the PH analysis enough to compare.
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sandywilliams
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"My ear tells me that the root of the minor third interval could be either tone, depending on context."
i agree with this and may even further posit that tonal gravity may provide many tonics to a single chord, due to its context. for example:
Fm7 Bbm7 Eb7 Ab Db G7 C
let's analyze the chord G7
modal tonic is G (the root of the chord)
lydian tonic is F (the root of the lydian chromatic scale)
horizontal tonic is C (the key of the phrase)
supra-vertical tonic is Ab (the key of the tune)
vertical tonal gravity defines the tonic of the moment, the "now"; horizontal tonal gravity defines the tonic of the time segment or group of chords for a given amount of time, the "resolving tendency" towards or away from a "tonic station" - this given amount of time i speak of could literally be anything at all:
play Db7 C with a harmonic rhythm of two beats per chord at a tempo of 144 bpm; then one measure per chord; two measures per chord; four; eight; etc...
if we increase the amount of time per chord to an absurd extreme, such as "Db7 today, C by next tuesday", it becomes clear that the strength of a chord's horizontal gravity is dependent upon the ability of the listener to perceive increasing amounts of time between chords. for example, if i can't remember what the last chord was, how can it affect the chord i hear now?
if you play the Db7 for three days, isn't it obvious that the justification for the tonic of C becomes "academic"?
am i making sense?
this posit introduces a "humanistic" factor to the question at hand, that the listener's own perceptions are an integral part of the answer to these queries.
pithy?
i agree with this and may even further posit that tonal gravity may provide many tonics to a single chord, due to its context. for example:
Fm7 Bbm7 Eb7 Ab Db G7 C
let's analyze the chord G7
modal tonic is G (the root of the chord)
lydian tonic is F (the root of the lydian chromatic scale)
horizontal tonic is C (the key of the phrase)
supra-vertical tonic is Ab (the key of the tune)
vertical tonal gravity defines the tonic of the moment, the "now"; horizontal tonal gravity defines the tonic of the time segment or group of chords for a given amount of time, the "resolving tendency" towards or away from a "tonic station" - this given amount of time i speak of could literally be anything at all:
play Db7 C with a harmonic rhythm of two beats per chord at a tempo of 144 bpm; then one measure per chord; two measures per chord; four; eight; etc...
if we increase the amount of time per chord to an absurd extreme, such as "Db7 today, C by next tuesday", it becomes clear that the strength of a chord's horizontal gravity is dependent upon the ability of the listener to perceive increasing amounts of time between chords. for example, if i can't remember what the last chord was, how can it affect the chord i hear now?
if you play the Db7 for three days, isn't it obvious that the justification for the tonic of C becomes "academic"?
am i making sense?
this posit introduces a "humanistic" factor to the question at hand, that the listener's own perceptions are an integral part of the answer to these queries.
pithy?
Terms (GR).
Appendix IV
Root: nothing
Modal Tonic: i.e., 'courtesy' modal tonic (Chart A). The 'tonic' of the chordmode representing the chord. For minor triad: Lydian scale degree VI.
Lydian Tonic: The 'root' of the parent Lydian scale. For example, C min triad: Eb. (However, alternative and conceptual tonic degrees could be VIh, +IV, IIIh, or VIIh. (Chart A)
Bass Note: the lowest note.
Center Of Tonal Gravity: the Lydian parent scale 'tonic' see above.
So Sandy, as anticipated, accurately represented the C minor triad as it first occurs on Chart A, assuming an Eb Lydian Chromatic Scale.
Horizontally speaking, 1st choice for a minor chord is as a ii (LCC VI) unless it’s a vi (LCC III) or a iii (LCC VI)
In practice, one can choose what the tonic of the chromatic scale is, then build a minor triad, or any chord, on any degree of the chosen chromatic scale. (Put it in an interesting context, to paraphrase GR) It’s ‘gravity’ will be a function of it’s relative ‘remoteness’ from the tonic of the chromatic scale.
(I still don’t see how a stand alone minor triad has intrinsic tonal gravity out of context. Out of context, the tonic of the chord (as GR & PH agree) is the lower note of the perfect fifth.(For the sake of integrity, an 'acoustic' 5th, based on C 128 is 96, a tempered 5th 95,89. Nobody's perfect.))
How one discerns the chords ‘remoteness’ is a function of the interval between the chord tonic and the tonic of chosen chromatic scale context. (Other symmetrical scales not withstanding). How one gets there and back is the root progression and its intervallic relationships. Jazz musicians usually negotiate this through alterations, modal interchange, and tritone substitutions. In any event, there are harmonic intervals in the chord voicing, and melodic intervals in the root progression.
So, how ever you do it, the intervals are important, thus how one discerns the tonic of an interval is important.
PH takes 108 pages to explain his interval roots:
Octave-root down, P5 root-down, minor & major third-root down, minor and major 7th-root down. In their inversions, the roots are up. The root of the tritone is ambiguous
GR presents his chart, regarding which the following questions remain:
-Why is a Maj 3rd root down, while the Min 3rd root up?
-Similarly with Maj 2nd v. Min 2nd.
-Why is the Maj 3rd root down, while the Min 3rd root up?
-Similarly, Maj v. Min 7th, Maj v Min 6th.
If someone can help me out here or just point out a reference, that would be appreciated.
Appendix IV
Root: nothing
Modal Tonic: i.e., 'courtesy' modal tonic (Chart A). The 'tonic' of the chordmode representing the chord. For minor triad: Lydian scale degree VI.
Lydian Tonic: The 'root' of the parent Lydian scale. For example, C min triad: Eb. (However, alternative and conceptual tonic degrees could be VIh, +IV, IIIh, or VIIh. (Chart A)
Bass Note: the lowest note.
Center Of Tonal Gravity: the Lydian parent scale 'tonic' see above.
So Sandy, as anticipated, accurately represented the C minor triad as it first occurs on Chart A, assuming an Eb Lydian Chromatic Scale.
Horizontally speaking, 1st choice for a minor chord is as a ii (LCC VI) unless it’s a vi (LCC III) or a iii (LCC VI)
In practice, one can choose what the tonic of the chromatic scale is, then build a minor triad, or any chord, on any degree of the chosen chromatic scale. (Put it in an interesting context, to paraphrase GR) It’s ‘gravity’ will be a function of it’s relative ‘remoteness’ from the tonic of the chromatic scale.
(I still don’t see how a stand alone minor triad has intrinsic tonal gravity out of context. Out of context, the tonic of the chord (as GR & PH agree) is the lower note of the perfect fifth.(For the sake of integrity, an 'acoustic' 5th, based on C 128 is 96, a tempered 5th 95,89. Nobody's perfect.))
How one discerns the chords ‘remoteness’ is a function of the interval between the chord tonic and the tonic of chosen chromatic scale context. (Other symmetrical scales not withstanding). How one gets there and back is the root progression and its intervallic relationships. Jazz musicians usually negotiate this through alterations, modal interchange, and tritone substitutions. In any event, there are harmonic intervals in the chord voicing, and melodic intervals in the root progression.
So, how ever you do it, the intervals are important, thus how one discerns the tonic of an interval is important.
PH takes 108 pages to explain his interval roots:
Octave-root down, P5 root-down, minor & major third-root down, minor and major 7th-root down. In their inversions, the roots are up. The root of the tritone is ambiguous
GR presents his chart, regarding which the following questions remain:
-Why is a Maj 3rd root down, while the Min 3rd root up?
-Similarly with Maj 2nd v. Min 2nd.
-Why is the Maj 3rd root down, while the Min 3rd root up?
-Similarly, Maj v. Min 7th, Maj v Min 6th.
If someone can help me out here or just point out a reference, that would be appreciated.
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sandywilliams
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Look at at the intervals in relationship to the tonal orders,,7 tone, 9tone..etc.
Hopefully this will shed some light on the interval tonic idea. With c up to eb:
Eb is in the 9 tone order in relating to a C LT , but C is in a 7 tone, ingoing order in related to an Eb LT. The most ingoing wins!
Hopefully this will shed some light on the interval tonic idea. With c up to eb:
Eb is in the 9 tone order in relating to a C LT , but C is in a 7 tone, ingoing order in related to an Eb LT. The most ingoing wins!
Last edited by sandywilliams on Thu Nov 01, 2007 1:30 pm, edited 1 time in total.
Shouldn't the interval standing alone have a tonic related to the overtone series. PH uses the first 7 overtones, but given what most people can actually hear, the first three, fundamental, octave fifth, it makes just as much sense to stack fifths. The LCC tonal order nicely accomodates common practise, but skips a fifth kind of undermining its use in the present case. In any event, doesn't relating an interval or chord to its parent scale differ differ from ascertaining it's tonic. It seems tonal gravity may have less to do with a chord or interval's tonic, than with it's remoteness (vis-a-vis the overtone series or circle of fifths) from a given note, (which note may be considered a lydian tonic) .The latter lets you know where you are, so you know how to get back.
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sandywilliams
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