LearnJazzPiano.com archives: Lydian concept paper online
Scot -- 11/22/2004, 18:19:26 -- #9177
http://www.lydiandominant.com/theory/lydian-dominant_theory.html

This one is hurting my head :)  It's cool, though, I enjoy reading about stuff I use and finding out the underlying formulas and science behind it.

What do you guys think?

Dr. Whack -- 11/23/2004, 06:05:58 -- #9188
wow....my head hurts too...I've always found the physics of music interesting, and I guess in some way my very limited knowledge of it has helped from a compositional point of view...and since improvising is supposed to be spontaneous composing...hmmmm....(but I've always hated thinking about my postulates and postules while I was playing:)

orson -- 11/23/2004, 09:38:28 -- #9190
I think it is really interesting that the tritone is related to the square root of two.  I did not know that.  I wonder if that is why the tritone was banned by the church?  Well, indirectly I guess they are inextricable, but was the church particularly worried about the presence of irrational numbers in music (numbers such as pi that are not whole, and can't be expressed as a ratio of whole numbers)?  Apparently irrational numbers really bothered the greek mathematicians, who  tried to keep their existence a secret.

7 -- 11/23/2004, 23:27:43 -- #9201
Below is an excerpt from the abovementioned article:

>>>>>>>

I claim there is no such thing as a diminished 7th. This Chord is a 100% total Artifact of the 12-Tone Tempered System. It doesn't exist at all in any OverTone Series derived Systems. It is an emergent property of the 12-Tone Tempered System and is central to Lydian-Dominant

Bbb/A is clearly a Major 6th (in disguise) above the root C. It acts like a 6th, it sounds like a 6th, so why not call it a 6th !!!

I seriously suggest (7's italics) that we rename this wonderfully ambiguous Lydian-Dominant note set the "diminished 6th Chord" - C dim6.

As justification in addition to the above analysis, I would point out that this Chord is remarkably close in sound and function to the minor 6th Chord, a Chord more commonly used in older American music, and still important in some indigenous styles like Tango. This Chord has an ambivalent tonality and differs from the dim6 in that the 5th is perfect rather than diminished.

Cm6 = { C Eb G A }
Cdim6 = { C Eb Gb A }


Furthermore, if we invert the 6th in the Cm6 thereby changing the root note to A instead of C, we derive the modern Jazz Chord, the Am7b5 - the so-called half-diminished Chord.

<<<<<<<

I have some disagreements with the above.

Would the author like to see the symbol

m6b5

replace the symbol

dim7

Because it's kinda like

m7b5 ???

Why replace the 7 with a 6 when the harmony is clearly double tritone land?

Why dim6 vs dim7 ???  Does it save any typestrokes?

*******
Then he comes in with If it walks like a duck and talks like a duck it must be a duck.

"Bbb/A is clearly a Major 6th (in disguise) above the root C. It acts like a 6th, it sounds like a 6th, so why not call it a 6th !!! "

Really?

To him it sounds like a 6th against the root.

I don't really hear the dim7 (6th if you will) as a "6". What I hear is the jangliness of it against the b3.

Here he is clearly either revolutionary or unaware of the basics of tertian harmony.

Tertian Harmony = Stacked Thirds.

dim7 chord = R-m3-m3-m3 = Stacked minor Thirds

NOT


Cm6b5
R-m3-m3-aug2

6th chords (C6, Cm6, etc.) have always been a thorn in the side of purist tertian theorists, but now to add one more? Ouch!
*******

Somewhere he implies that the only time that a dim3 is used in a chord is in the instance of the diminished 7 which he wishes to abolish.

How about: 7#5 = R-M3-M3-dim3

That type of chord is expressed perfectly in tertian harmony with a diminshed 3rd.

Major intervals contracted become minor and minor intervals contracted become diminished. Major intervals expanded become Augmented.

*******

Are there other schools of theory that say that the dim7 doesn't actually exist but in reality they've been lying to you all along it's really a "diminished 6th"?

7

Scot -- 11/24/2004, 01:15:49 -- #9202
I'm not yet ready to make a coherent and intelligent response to your post :)  I'm still on postulate 5, I think :)

Dr. Whack -- 11/24/2004, 07:34:56 -- #9205
yeah...me too...as usual, my short attention span didn't let me get that far...I can kinda see his point, but why change the name of the wheel?

staggs89 -- 11/24/2004, 08:47:03 -- #9209
Normally we progress from one level of tonality to another by a series of Major, minor, then diminished, when lowering a note.
Cdim refers to just the triad C,Eb,Gb. Cdim7 means a Cdim triad is present along with the diminished seventh note above C. Just an easy way we have always asked for the C,Eb,Gb,Bbb aka C,Eb,Gb,A, chord. If you want C,Eb,Gb,Bb, then you must ask for Cm7b5.  staggs89

Jazz+ -- 11/24/2004, 13:24:36 -- #9214
Cm6 = { C Eb G A } FUNCTIONS as a i minor

Cdim6 = { C Eb Gb A } FUNCTIONS as a Rootless V7b9  (D7b9, F7b9, Ab7b9 and B7b9)

7 -- 11/24/2004, 22:04:48 -- #9222
Correction:

I said:

"Somewhere he implies that the only time that a dim3 is used in a chord is in the instance of the diminished 7 which he wishes to abolish."

I meant to say:

Somewhere he implies that the only time that a  diminished interval (unrelated to a 5th) is used in a chord is in the instance of the diminished 7 chord which he wishes to abolish.

*******

Re: Jazz+'s post above

When the diminished 7 chord functions as a rootless V7b9, it is  still tertian and does not contain any augmented 2nd intervals
(Cdim6 = C Eb Gb A = R-m3-m3-aug2).

ex:
D7b9 = D F# A C Eb = R-M3-m3-m3-m3

AND NOT ANY OF THE FOLLOWING:

R-M3-m3-m3-aug2 = D F# A C D#
R-M3-m3-aug2-m3 = D F# A B# D#
R-M3-aug2-m3-m3 = D F# G## B# D#

Y'all get my drift ...

If you choose to invert the chord to be voiced as

D C Eb F# A (1 b7 b9 3 5)

you could argue that an aug2 exists between the b9 and 3rd of the chord, but isn't that a little silly considering that tertian harmony initially always defines chords by spelling them out in root position?

Jazz+, when you say that

"Cdim6 = { C Eb Gb A } FUNCTIONS as a Rootless V7b9  (D7b9, F7b9, Ab7b9 and B7b9)"

Do you mean to say that "Cdim6 ALWAYS functions as a rootless V7b9" OR do you mean to say that "Cdim6 SOMETIMES functions as a rootless V7b9"?

Just wondering ...

*******

I try to keep an open mind about these things and if someone can prove the value of spelling diminished 7th chord as a so-called "diminished 6th chord" (with an augmented second instead of a minor 3rd), I'll eat my words.

Jazz+ -- 11/24/2004, 22:40:37 -- #9223
I will say that it is common knowledge that thge diminished 7 chord frequently or more often than not functions as a disguised V7b9 (rootless) chord. I would be reluctant to say anything always functions one way, that would be too restrictive.
I don't care much about the spellings, I know that classiscal the spell the dimished 7th as bb7, but on the keyboard the diminished 7 interval looks like a Major 6th interval and that's where I deal with them, not the classroom.

docz -- 11/26/2004, 00:57:38 -- #9238
I've always thought of the dimminished chord as a stack of minor thirds.  Like 7 said... it's such a weird chord, there are just three of them.

Cdim = Ebdim/D#dim = Gbdim/F#dim = Adim
C#dim/Dbdim = Edim = Gdim = A#dim/Bbdim
Ddim = Fdim = Abdim/G#dim = Bdim

And yes you can add any particular root to this chord to make up other chords, which only just shifts the harmonics of the chord slightly...

However when noting down theese chords, I prefer to just say Cdim, not Cdim7 or  Cdim6, allthough Cdim6 seems weird to me.. since bb6 would end up as a 5, so that doesn't make sense at all, a better way would be Cmb56 it would be more correct if one were to use something else instead of "dim". But if I saw that on  a sheet, I would be thinking "What the hell is that chord? Then play it out and think... oh... it's just a dim... why didn't he just say so"


Doc-Z

albetan -- 11/28/2004, 11:00:48 -- #9289
I enjoyed a lot this article of Lydian-Dominant Theory.
I recommend to all of you to save this article for future references.  

What’s the Lydian-Dominant Scale?
The Lydian-Dominant scale is the natural scale that comes from first 13  physical overtones.
C D E F# G A Bb C
The author calls it “Lydian” because of #4 and “Dominant” because of b7.
In my file about extended chords i mention extended C7 chord as:
C E G Bb D F# A
In a successive order: C D E F# G A Bb C,
A cool way of improvising with that scale against a C7 chord.

Very interesting Postulates 1 and 2 over tritones.

In Postulate 3: “There are 6 Dominant 7b5 chords”:
Play two intervals of mayor third separated by a tone:
C   E   Eb Bb  = C7b5
Gb Bb  C  E    = Gb7b5
Both chords have the same notes, they are substitutes.

In Postulate 4: “There are 3 tritone quad diminished sub-systems”
Play two tritons separated by an interval of minor third:
C  F#  A  Eb  
Contracting it: C   Eb   F#  A
Playing those tritones in different order, you have four diminished chords with same notes: Cdim Ebdim F#dim Adim.
That discussion about dim7 or dim6 is obsolete, as mentioned by 7. Today we write Cdim.

Postulate 5: “There are 3 sets of dominant 7b9 chords”
Same argument as in postulate 4 about diminished chords.

Postulate 6: The m6 and m7b5 dual nature.

Postulate 7: There are 4 augmented triads.
Play two successive intervals of mayor third:
C  E  G#,   E  G#   C,  Ab  C  E :  same notes.

Postulate 8: There are 2 whole tone scales.

Postulate 9: There are 3 diminished scales.

The figure of overtones applied to harmony:
See the figure of overtones.
Analyzing the first five overtones from C:1   2   3   4   5
C   C   G   C   E
We find the natural major triad.

Analyzing the first 7 overtones from C:
1   2   3   4   5   6   7
C   C   G   C   E   G   Bb
We find the seventh chord.

Analyzing the first 9 overtones from C:
1    2   3   4   5   6   7   8   9
C   C   G   C   E   G   Bb  C   D
We find the ninth chord.

Analyzing the first 11 overtones from C:
1   2   3   4   5   6   7   8   9   10   11
C   C   G   C   E   G   Bb  C   D   E    F#
We find the 9#11 chord.

Analyzing the first 13 overtones from C:
1   2   3   4   5   6   7   8   9   10   11  12   13
C   C   G   C   E   G   Bb C   D   E    F#   G    A
We find the 13 chord.
And by ordering all notes successively we have the Lydian-Dominant Scale:
C   D   E   F#   G   A   Bb   C.

albetan -- 11/28/2004, 11:28:29 -- #9290
And speaking of overtones, old pipe organs work in basis of overtones.
An 8 feet pipe produces C sound. A half of size (4 feet) doubles the frequency producing an octave up.
I an old thread titled Organists i exposed this:
"Eight feet stops (8´) produce the natural sound of keys.
4´stops sound an octave up,
2´stops sound two octaves up,
1´stops sound 3 octaves up,
16´stops sound 1 octave lower,
5 1/3´stops sound a fifth up,
2 2/3´stops sound a fifth over the octave,
1 3/5´stops sound a third over 2 octaves,
1 1/3´stops sound a fifth over 2 octaves,"

In 1934 Robert Hammond applyed those principles to his drawbar organ, adding a variety of 8 grades of intensity in each bar.

sid -- 11/28/2004, 12:41:26 -- #9294
Good work Alberto.  The overtone relationship also explains the straight lydian major scale:
C plus its strongest overtone (other than the octave), the 5th = G
E plus its 5th = B
Which means that Cmaj7 (C E G B) is a particularly stable chord, made of two interlocking 5ths.
Continue this pattern:
G plus its 5th = D
B plus its 5th = F#
D plus its 5th = A
Rearrange all these notes and you get C lydian (C D E F# G A B).  George Russell argues that this, and not the C major scale, is the scale most logically related to the Cmaj series of chords.

Continue this pattern and you add C# E G# B D# F# A# C# F...
In other words, you run through the complete chromatic cycle and get back to C again.  So  you could argue that, logically, ANY note can fit to the major chord, though some notes are more "distant" (to use Russell's term) than others.  This is one way of structuring the voodoo art of "playing outside".  Russell talks about breaking through into the "chromatic universe", where the full resources of the chromatic scale are always available to the improviser, no matter what chord progression he or she is working with.

Why is it so difficult to put this philosophy of melodic freedom into practice?  Mostly I believe it's psychological - personal inhibitions, fear of the unknown, the infant-like need to cling to the comforting mother-figure represented by the chord progression.  No wonder so many jazz musicians turned to chemicals to unblock the channels.

sid

albetan -- 11/28/2004, 16:34:23 -- #9301
Thanks Sid for your opinion.

You mention "Which means that Cmaj7 (C E G B)"
In my file "Extended Chords" i expose Cmaj7 extended chord:
C  E  G  B  D  F#  A.
So contracting notes we have:
C  D  E  F#  G  A  B   C   a Lydian scale.

In that mentioned file i suggest F# as an optional sound for Major and Seventh chords. I feel that it sounds better than natural F and now i'm understanding it above the light of overtones.

Scot -- 11/28/2004, 20:51:29 -- #9306
You guys don't make it easy for me :)

Keep up the good work- now >I< have a lot of studying to do!

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