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Discussions on the theoretical basis of the LCC

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Postby sandywilliams » Sun May 01, 2011 9:27 am

Welcome, Joey. The password was only to keep the forum from being inundated with daily porn spam, apparently being posted by 'bots. It was a real problem. Once the password was used there were no more problems.
Now to your questions.....
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Postby chespernevins » Sun May 01, 2011 2:40 pm


Welcome to the forum. I agree with you that opening the forum to more people would be beneficial.

I enjoyed checking out your web site and myspace page. You sound great!
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Postby chespernevins » Mon May 02, 2011 1:45 am

Hey Joe. Finally got a chance to read through your entire post. Interesting stuff. Is there a particular text that walks through hearing chords based on a comparison to the OTS?

My experience of interval tonics is far less sophisticated than yours. I think it comes from my old solfege days, when we would tune each note to the tonic of a major scale. It was clear in that system that in the key of C, C was the tonic of the C-D interval. C-E, C-G, C-B all clearly had C as the tonic as well. The sixth, A, might tune to G and then to C, but C was still the tonic. F would tune to E and then to C, but it seems easy to understand, as the LCC says, how F could be considered the tonic of the C-F interval. F#, when it appeared in a C Major progression, would tune to G and then to C as well.

Given that, and the cycle of fifths, it's easy to figure out the tonics of the rest of the intervals (in LCC terms).

I think the LCC is key oriented is a similar way. So Hindemith's B-C interval having B as the tonic doesn't work in this model. With this interval, we could hear C resolving to B. This would suggest B as the tonic, but this is a horizontal type of resolution, whereas the vertical tonic of B-C would be C.

One of the things discussed in the newer book but not the older is Conceptual Modal Genres, which is an interesting look into horizontal tonal gravity.
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Postby chespernevins » Tue May 03, 2011 2:46 am


I haven' read the stuff in the 4th Ed yet that deals with CMG's.
I'll get there. give me time.

That's ok, it'll take some time to understand what you've written here too!

*I* see the dom7(9,#11,13) chord as being the chordal entity that fills that bill.
I.e. This is the extended chord that has the strongest sense of root.
Any other chord that can possibly exist will be a clouded or distorted version of this chord and will have a less pronounced feeling of root and will be less consonant sounding.

One could imagine a version of the LCCOTO that uses the lydian b7 scale and the dom7(9,#11,13) as the main point of departure, rather than the lydian scale, but that would mean a total revamping of the concept of Tonal Gravity as somehow being based objectively on the overtone series in some as yet to be conceived manner.

I can totally see why you would look at the dom7#11 chord as being a primary, stable color, based on experience and also on your point about the OTS.

However, the order of ingoing to outgoing prinicipal scales is very much based on its multiple chord families, not just the I chord. So Russell will often reference chordscale unity with a scale's I Major and VI minor chord.

One of the strengths of the LCC is that it presents the best of "relative" scale relationships along with "parallel" scale relationships.

Look at the VI minor chord of the Lydian b7 chordscale:


This seems more outgoing than the VI minor chord of the Lydian.
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Postby chespernevins » Thu May 05, 2011 5:29 am

So we're left with the common denominator between all of his scales as being the LT and the +IV.
It's obvious that he views the tritone interval, especially the 12TET tritone, as being at rest, in no need of resolution, contrary to what most other theorists happen to believe.
And that notion seems to be at the heart of it all, but I just don't know the details of why it's at the heart of it all.

You're very perceptive to notice this right off the bat. I think you're right; this is probably essential to the whole thing. It's all about the ladder of fifths and the fact that the tritone is at the farthest limits of that ladder, with the lydian tonic at the base. So the tritone is as far from the root as it is going to get (in F lyd, F-B). Contrast this with the C major scale, where the ladder is still F up to B, but the ionian tonic is on C.

Another way to say the same thing is that it has to do with the placement of the tritone within the scale. The vertical scales will tend to have the tritone on I and #IV of the scale (or the min III and VI of the relative minor). The horizontal scales will tend to have the tritone on the IV and VII (or the bVI and II of the relative minor)

Why should every chord-scale relationship that is to be applied to a min chord necessarily posses that tritone between the chord's b3 and its maj 6th?

They don't. Just the vertical ones.

In my experience, using the mode of Harm Maj that he calls "lyd dim" is one of the last scale choices that most experienced jazz players would think of on a dim7 chord.
It's often a very good choice, if the right Harm Maj scale is selected, but it's usually not at the top of most people's list as it is in GR's.
A great many dim7 chords are poorly named and are often really inversions of a different dim7 chord or are misnamed inverted dom7b9 chords.
So for a player to get in the habit of thinking first of using the lyd dim scale from the root of every dim7 chord he encounters will be fraught with confusing sounds.

This is really a non-issue, except maybe for students who are new. Just because a scale is considered vertical does not mean that it is supposed to be the right scale for a given harmonic context. A common misconception is that just because Lydian is vertical scale number I means to play Lydian over every major chord! Not the case. The Ionian scale might be more appropriate for some contexts. I think even Russell mentioned on an album cover somewhere that he "was primarily a horizontal composer", or something to that effect.

If you wanted to play on a C- chord, you could choose Eb Lydian, of course, or any of the chart A variations such as Eb Lyd Aug, Eb Lyd Dim - this stuff is obvious from chart A. But you might just as well choose C Aeolian. In the LCC, this is a horizontal scale based on Ab Lyd III. So you could play C aeolian with a lot of emphasis on the C- chord, or you could put more emphasis on the Ab chord for a suspended, unresolved tension kind of sound, or a combination of both. You could play any of the Ab Lydian altered scales that give you a good sound, such as Ab Lyd Dim (which you could resolve to the C- chord), or Ab Lyd b7 and resolve it to C-. The idea is that a flat lying Lydian scale, such as Ab is to Eb (parent of C-), resolves to the sharp lying Eb Lydian. So you could play with the attitude of resolving the whole Ab "lydian chromatic scale" to C- as well.

Now I know that you could generate all this stuff using your own tools, because you have a lot of knowledge of your own, but I'm trying to show you that there is a lot of organization and flexibility with this lydian vertical and horizontal stuff.
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Postby guitarjazz » Thu May 05, 2011 11:58 am

Goodrick's book takes a chord progression and shows it's interpretation through parallel , derivative , and LCC thinking. When you start asking why GR called it Lydian Diminished instead of Harmonic Major you have to take into account the advantages or disadvantages of these various choices.
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Postby guitarjazz » Thu May 05, 2011 2:35 pm

Converting to lydian is quite similar to Pat Martino's 'converting to minor' method. Have you ever seen that?
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Postby strachs » Thu May 05, 2011 8:04 pm

First of all, welcome to the forum. Many are probably surprised I have not chimed in on such a theoretical discussion. It's purely to do with being busy - I'm totally interested in this side of things.

Before exchanging anything in real-time, let me catch up a little by quoting you a bit and commenting, and you'll see to some degree where I stand in comparison to where you stand.

"I do not believe that it is really on a strong theoretical foundation. "

You're not alone on that. But be careful not to dump what the LCC has to offer solely on this basis.

"I, as do many other participants on this forum, have a hard time wrapping my head around why it is that GR decided to skip the 7th 5th in the ladder of 5ths above the LT in his Order Of Tonal Gravity. "

"either Tonal Gravity is based on the ladder of P5ths or it isn't. "

Right. Just as LISTENING to a side-by-side comparison of Lydian versus Ionian led Russell to postulate that the underlying reason was a ladder of fifths, LISTENING to things that happen at various "nodes" of the ladder, for some/most of us, demands a different explanation - one that can account for the Lydian/Ionian distinction AND the need-to-skip-the-8th-tone thing (among other manifestations of whatever the underlying force at work is).

"Please explain this to me.
What am I missing? "

The reason no one is explaining it to you is because there's nothing to explain. It IS a contradiction, and the LCC's SYSTEM is at odds with it's THEORY. I think that people's denial of this stems from their respect for the man and his musical output and the respect he had, rather than from actually seeing the LCC as contradiction-less (I'm aware that's not a word).

"it's my understanding that 20th Century science has since proven that combination tones exist only within the human ear and are a byproduct of the way the inner ear happens to work. "

True, but then again, does it need to work anywhere else? Do we listen with something other than our ears?

"the human ear (or the human consciousness) is perfectly happy to accept the impure intervals of 12 tone equal temperament ("12TET") as acceptable stand-ins for their similarly proportioned cousins that exist within the OTS."

Agreed, so while it's certainly not necessary to adopt a purist, "Equal Temperament is the Devil" bent, we should recognize that ET is not the 'internal norm' that we reconcile all we hear against. That being said, we must be willing to recognize that many of the notions we have about interval proportions are derived from and dependant on ET. For example, that two "semitones" equal a "whole tone", that two of these equal a major third, and that a "tritone" is a third plus a second, and at the same time is exactly half of the octave. Notions like this are misleading, and cause us to think that the #4 must have some kind of special relationship with the tonic, because it's the "exact center" of the octave. This thought is expressed on pg. 244, and although written by Reed Gratz, not Russell, it's included as a proof of the Concept, which it really is not. (tangent - sorry)

Anyway, point being: although our sense of harmony does not fall apart completely in ET or any other 'out-of-tuneness', we need to know the template our ear is using to relate the tones, and that is the Overtone Series (OS).

"we still experience the 13th of a dom13 chord *as if* it is a representative of the 13th partial"

On this point, I'm not squarely in agreement with your understanding. Same with the 11th partial, and to a degree, the 7th partial as well. I want to start my own thread about all this, and I keep promising to do so, and never do. Just busy at this point. I'll do it, though, I promise.

"Russell seems to think of the ladder P5ths within 12TET as somehow replacing the OTS as the standard for harmoniousness in the human ear/psyche.
I don't, as of yet, think he's really made the theoretical case for that viewpoint."

Me too.

"most musicians are totally unaware of any of these theories"

Glad I'm not the only one who finds this unfortunate.

"calculation of the difference tones is not really essential to the endeavor of finding an interval's root and that all they need to consider is the frequency ratio of the interval which will always imply a "1", with that "1" being the root of the interval."

I've found that, other than using "cents", which is hard to calculate (uses logarithmic stuff that I'm no good at), a useful way to notate frequency ratios for size comparison is to octave-reduce everything so that the lower tone is 1 and the upper tone is between 1 and 2. For example, a perfect fifth is 1.5 (3/2), a just major third is 1.25 (5/4), a Pythagorean major third is 1.265625 (81/64), and so on.

"the tuning of the A7 chord would be 36:45:54:64"

Amazing to see I'm not the only one living post-Hindemith who does this kind of thing. You're a brother from another mother.

I.e. Our ears hear min triads as being the distorted cousins of major triads. "

Don't you think this kind of reasoning is kind of 'fudge-factor-ish'. Is this really much of an improvement over Hindemith's minor third interval tonic? I've got another idea. It will be in my theory post.

"Most of the posts I've read here so far on this forum seem to just take GR's assertions about interval "tonics" at face value without questioning them.
I think they need to be questioned."

I agree. And this is one of the fundamental ideas I find both Hindemith and Russell fell short on - their too-strict definition of intervals and interval tonics, failing to note that the OS provides several "versions" of most intervals, and that the "version", as well as it's particular qualities and effects, can be evoked by creating context for the interval (using more certain, less ambiguous intervals) that favors one version or another. Like playing a ladder of fifths Lydian scale versus a major triad. In the former, the context makes it plausable to the ear that the M3 in this structure just might be the 1.265625 ratio that the 81st partial makes with the root. However, in the major triad, I don't think there's any way the ear can relate the M3 to the tonic by any other relation than the 5th partial (1.25 ratio). Two versions, context made the selection. The same can be done with ALL intervals that have more than one "version" that is made up of simple frequency ratios, and so "interval tonic" is not such an absolute, invariable thing that must drive our understanding of all else.

"Every other system of chord-scale relationships operates similarly."

It may be just my inference, but I'm under the impression that all the modern chord-scale systems originated with the influence of LCC. So, although it may not be 100% on the money theory-wise, you've got to give the man credit for being so infuential, yet so unrecognized, for even suggesting chord-scale equivalence/unity. It's popularity is not a case against Russell, but probably in his favor, actually.

"The Sym Dim scale doesn't really introduce any new traditionally defined chord types at all."

You have to recognize that LCC is not just about matching EXISTING scales with EXISTING chords. It's about figuring out what MAKES them a match, harnessing that understanding, and going beyond just scales and chords into FORCES that you can exploit and bend to your will. It's a bigger picture. More like providing you with Cyan, Magenta, an d Yellow, and you can make your own colours out of them. Better than just a box of pre-chosen Crayolas! (more work, but more personal, too)

"What I don't get is why he sees the necessity of applying some sort of a lydian or altered lydian scale to every other type of chord. "

Me too. Since I don't follow the ladder thing, I don't accept the cost-benefit ratio of re-learning and re-naming everything in favor of the Lydian Tonic. There's another way. It's in my post (not posted yet, of course).

"The major key system came about when composers realized that their just intonated scales would allow for 3 pure maj triads whose roots were all in P5th relations to each other."

I'm glad you recognize this. In the LCC, the Major scale is seen as just a less-than-objective scale because it can't parent extended major chords the way Lydian can. You've wisely recognized that the Major scale was never devised or intended to provide larger vertical structures, such as full tertian arrrangements up to the 13th like we hear in our century.

Anyway, I wanted to just comment a little on your deep contribution to our forum, and by all means, feel free to disagree with Russell, or any of us, and we're all cool with it. If what you say is as reasoned as you've come up with so far, we all love to hear it.
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Postby guitarjazz » Thu May 05, 2011 10:21 pm

In the LCC, on PMG VI chords the root of the chord is not a component of the lyd aux dim or the lyd aux dim blues scales.
The root the chord is a component of both those scale. So for a Cmin chord using Eb aux dim the notes would be CDEbFGbG#AB
Using the Eb aux dim blues it'd be CDbEbEF#GABb
Feel free to respell those enharmonically any way you wish.
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Postby guitarjazz » Fri May 06, 2011 1:03 pm

[quote]For Cm, with an LT on Eb, the Eb lyd aux aug scale would be:
Eb F G A B Db Eb
No C in that scale.[/quote]
And that's why I like it. Of course, there are only two whole-tone scales. The one with the Lydian Tonic can be reconciled with the chord. The other one is more out-going. There is a great Bob Berg line using the whole-tone scale starting on the bIII of a minor chord. It is on one of his solo records and I'd have to do some research to find the title.
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Postby guitarjazz » Fri May 06, 2011 2:04 pm

Martino's 'converting to minor' mental process is very similar to the thought process one uses when dealing with Vertical Tonal Gravity in the LCC. The LCC has more possibilities but the basic idea is similar. I wasn't really trying to reconcile anything with anything else but if I was, I'd say that Martino's system can be completely reconciled by the LCC but not the other way around, thus no explanation for using whole-tone scales in the PM minor system.
I have no doubt Pat can pull whole-tone scales out of his pinky any time and anywhere he chooses!
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Postby guitarjazz » Fri May 06, 2011 3:17 pm

joegold wrote:Well sure.
*Anything* can reconciled by the LCC (assuming that one buys into its validity) because ultimately it's just the chromatic scale.

Very true. I think it's validity is to be judged by whether or not you find it useful.
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Postby NateComp » Fri May 06, 2011 6:11 pm

C Whole Tone (C D E F# G# Bb C) over A minor is certianly a cool "color" and one that I've used quite a bit after working with the LCC for a while.

Like Joe said, it's similar to A Mel Min but with a b2 and no root.

Back in the old forum, Dogbite had termed this type of application as an "un-scale" because of the missing root, which is an idea that I started to explore quite a bit. I first saw that idea with some of Scott Henderson's pentatonic applications, like using B Minor Pentatonic (B D E F # A B) over C Major 7. You end up with 7 9 3 #11 13 and no root, which I think is a very cool sound, so the no-root scale idea isn't new, but something that LCC turned me onto more of.

I really like what happens on PMG II when you go through all 7 Primary Scales:

II of C Lydian supports:
D 7th = D F# A C
D 7th Sus 2 = D E A C
D 7th Sus 4 = D G A C
D 9th = D F# A C E
D 9th Sus 4 = D G A C E
D 11th = D F# A C E G
D 13th = D F# A C E G B

II of C Lydian Augmented:
D 7th = D F# A C
D 7th Sus 2 = D E A C
D 7th b5 = D F# Ab C
D 7th #11 = D F# A C G#
D 9th = D F# A C E
D 9th #11 = D G A C E G#
D 13th #11 = D F# A C E G# B

II of C Lydian Diminished:
D 7th = D F# A C
D 7th Sus 4 = D G A C
D 7th b9 = D F# A C Eb
D 7th Sus 4 b9 = D G A C Eb
D 11th b9 = D G A C Eb G
D 13th b9 = D F# A C Eb G B

II of C Lydian Dominant
D 7th = D F# A C
D 7th Sus 2 = D E A C
D 7th Sus 4 = D G A C
D 7th #5 = D F# A# C
D 7th b13 = D F# A C Bb
D 9th = D F# A C E
D 9th Sus 4 = D G A C E
D 9th b13 = D F# A C E Bb
D 11th = D F# A C E G
D 11th b13 = D F# A C E G Bb

II of C Whole Tone:
D 7th b5 = D F# Ab C
D 7th #5 = D F# A# C
D 7th b5 #5 = D F# Ab A# C
D 7th b5 b13 = D F# Ab C Bb
D 7th #5 #11 = D F# A# C G#
D 9th b5 = D F# Ab C E
D 9th #5 = D F# A# C E
D 9th #5 #11 = D F# A# C E G#
D 9th b5 b13 = D F# Ab C E Bb

II of C Whole/Half Dim:
D 7th = D F# A C
D 7th b9 = D F# A C Eb
D 7th #9 = D F# A C F
D 7th #11 = D F# A C G#
D 7th b9 #11 = D F# A C Eb G#
D 7th #9 #11 = D F# A C F G#
D 13th b9 #11 = D F# A C Eb G# B
D 13th #9 #11 = D F# A C F G# B
D 13th b9 #9 #11 = D F# A C Eb F G# B

And then something REALLY INTERESTING happens when we get to the 12th tonal order: C Half/Whole Dim in the context of PMG II (D7) is an "un-scale": C Db Eb E F# G A Bb C - NO ROOT!

The presence of the Maj 7 interval (C#/Db) and the absence of the root (D) really proved to me that George's organization vertically is spot on. Out of the 12 chromatic scale tones, what would you avoid on a Dom 7 chord? The Maj 7, which is why it's last on the list. The really interesting thing is that the scale still has plenty of tones to support different flavors of D7, regardless of the missing root. If the bass player sounds a "D", you can still build:

II of C Half/Whole Dim:
D 7th = (D) F# A C
D 7th Sus 2 = (D) E A C
D 7th Sus 4 = (D) G A C
D 7th #5 = (D) F# A# C
D 7th b9 = (D) F# A C Eb
D 7th Sus 4 b9 = (D) G A C Eb
D 7th b13 = (D) F# A C Bb
D 7th b9 b13 = (D) F# A C Eb Bb
D 9th = (D) F# A C E
D 9th b13 = (D) F# A C E Bb
D 11th = (D) F# A C E G
D 11th b9 = (D) F# A C Eb G
D 11th b13 = (D) F# A C E G Bb
D 11th b9 b13 = (D) F# A C Eb G Bb

Beyond that, you can INCLUDE the root into a melody line that will start to sound like a Dominant Bebop scale:

C Half/Whole: C Db Eb E F# G A Bb C
D Dominant Bebop: D E F# G A B C C# D (D Mixo with Maj 7 as a passing tone)

Like Motherlode's post of bebop ideas, if you descend in 8ths:

D C# C B A, you get Root 7 b7 6 5, with the Root b7 and 5 falling on "strong beats".

So, with C Half/Whole, you can sneak the Root in with D C# C Bb A to get Root 7 b7 b6 5, still with Root b7 and 5 on strong beats, which I think is a pretty cool sound.

You could even leave the Root out, start on the 3 and descend F# E Eb Db C, giving you 3 9 b9 Maj7 b7 with 3 b9 and b7 falling on the strong beats and Maj7 as a WAY OUT passing tone.

I also noticed this idea appearing on PMG VI Minor chords.

VI of C Lydian:
A min = A C E
A min 6th = A C E F#
A min 7th = A C E G
A min 7th Sus 2 = A B E G
A min 7th Sus 4 = A D E G
A min 6/9 = A C E F# B
A min 9th = A C E G B
A min 9th Sus 4 = A D E G B
A min 11th = A C E G B D
A min 13th = A C E G B D F#

VI of C Lydian Aug:
A min = A C E
A min 6th = A C E F#
A min/maj 7th = A C E G#
A min/maj 7th Sus 2 = A B E G#
A min/maj 7th Sus 4 = A D E G#
A min/maj 9th = A D E G# B
A min/maj 9th Sus 4 = A D E B G# B
A min/maj 11th = A C E G# B D
A min/maj 13th = A D E G# B D F#

VI of C Lydian Dim:
A dim = A C Eb
A dim 7th = A C Eb F#
A min 7th b5 = A C Eb G
A dim/maj 9th = A C Eb F# B
A min 9th b5 = A C Eb G B
A dim/maj 11th = A C Eb F# B D
A min 11 b5 = A D Eb G B D
A min 13th b5 = A C Eb G B D F#

VI of C Lydian Dom:
A min = A C E
A min 6th = A C E F#
A min 7th = A C E G
A min 7th Sus 4 = A D E G
A min 6 b9 = A C E F# Bb
A min 7th b9 = A C E G Bb
A min 7th Sus 4 b9 = A D E G Bb
A min 11th b9 = A C E G Bb D
A min 13th b9 = A C E G Bb D F#

VI of C Whole Tone (an "un-scale" with no A Root)
Assuiming the bass player sounds an "A":
A min = (A) C E
A min 6th = (A) C E F#
A min/maj 7th = (A) C E G#
A min 6th b9 = (A) C E F# Bb
A min/maj 7th b9 = (A) C E G# Bb
A min/maj 11th b9 = (A) C E G# Bb D
A min/maj 13th b9 = (A) C E G# Bb D F#

VI of C Whole/Half Dim:
A dim = A C Eb
A dim 7th = A C Eb F#
A dim/maj 7th = A C Eb G#
A dim/maj 9th = A C Eb F# G# B
A dim/maj 11th = A C Eb F# G# B D
A dim/maj 11th b13 = A C Eb F# G# B D F

And then once again, when we get to the 12th tonal order: C Half/Whole Dim in the context of PMG VI (A min), we get: C Db Eb E F# G A Bb C.

The 12th tonal order for PMG VI adds the final note of the chromatic scale, the Major 3rd (C#). So just like with PMG II, where the final tonal order was the Maj 7 on a Dom 7 chord, the final tonal order for PMG VI is a Maj 3 on a min chord.

The scale still supports:
(VI of C Half/Whole Dim with C#, the Major 3rd as a passing tone)
A dim = A C Eb
A min = A C E
A min 6th = A C E F#
A dim 7th = A C Eb F#
A min 7th b5 = A C Eb G
A min 7th = A C E G
A min 6th b9 = A C E F# Bb
A dim 7th b9 = A C Eb F# Bb
A min 7th b5 b9 = A C Eb G Bb
A min 7th b9 = A C E G Bb
A min 6th #11 = A C E F# D#
A min 6th b9 #11 = A C E F# Bb D#
A min 7th #11 = A C E G D#
A min 7th b9 #11 = A C E G Bb D#
A min 13th b9 #11 = A C E G B D# F#
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