lydian dominant theory

8/3/2019 Lydian Dominant Theory

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Lydian-Dominant Theory

for

Improvisation

by

Norm Vincent

Lydian-Dominant Music Theory assumes the 12-Tone Tempered Scale

and the naturally occurring Physics of the OverTone Series. A smallamount of high school level Algebra is used in this treatise as MusicTheory is highly Mathematical. In fact, in Plato's Scheme of things,Mathematics is derived from Music! Music (i.e. organized vibrationalfrequencies) is Primal. This sounds like modern physics to me.

Although one does not have to be a Mathematical Wizard to do Music,exciting new research has shown a definite link between the two. MusicalPerformance involves very high-level integrated mental processes we haveonly begun to explore in a Scientific manner. I find it regrettable that

knowledge known to ancient peoples has become lost, suppressed, anddistorted. It is my intention that this treatise be a "first step" toward thedevelopment of a truly scientific exploration of the Domain of Music and allits ramifications. We will start with the basic physical facts.

The OverTone Series

The OverTone Series is a naturally occurring physically demonstrable set ofFrequencies present above any given pitch. The relative mix of these upper

frequencies is different for every tone generator. This is why differentmusical instruments sound remarkably different even though they aresounding the same pitch. The OverTone Series is infinite in extent, but inpractice, only the first few are important to us here as the relative volume ofthe upper partials gradually becomes inaudible.

OverTone # 1 - 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...

Note # 1 - 1 5 1 3 5 b7 1 2 3 #4 5 6 b7 7 1 ...

Note Name C - C G C E G Bb C D E F# G A Bb B C ...


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Try this experiment on a Piano. Hold Down the Sustain Pedal. Strongly Hitand Release a low 'C'. What do you hear? I hear all sorts of other stringsvibrating. The sounding strings are not accidental, they are strictlydetermined by the OverTone Series. These associated frequencies are calledHarmonics.

The exact single-octave Harmonic Series values are given in the nexttable. It is an ordering of the Rational Numbers. These values are used thesame way the fundamental values of Sines and Cosines are used inTrigonometry. You simply multiply the initial pitch by these values toderive the frequency of the desired harmonic.

OverTone # 1 - 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...

Note # 1 - 1 5 1 3 5 b7 1 2 3 #4 5 6 b7 7 1 ...

Harmonic # 1 - 1 3/2 1 5/4 3/2 7/4 1 9/8 5/4 11/8 3/2 13/8 7/4 15/8 1 ...

A few comments on the OverTone Series relevant to Lydian-DominantTheory. Notice the natural occurrence of the b7 and the #11. Also notice thenatural occurrence of the Chord {1 3 5 b7} and the Scale {1 2 3 #4 5 6b7 1}. I will refer back to these facts later on in this treatise. The OverToneSeries is explained in greater depth in my book Natural Music Theory.

The 12-Tone Tempered SystemOur modern 12-Tone Tempered Scale is derived from the PythagoreanSpiral of 5ths.The 12-Tone Tempered Scale approximates the values ofthe Pure Harmonics of the naturally occurring OverTone Series usingonly the ratio for the 5th (3/2).

What is a 5th? Briefly, what is known as a 5th is the first distinct (other thanoctave doublings) OverTone to emerge from the OverTone Series and isassociated with the number 3. Experiments on strings by ancient peopleshowed that when you take a string tuned to any starting pitch and divide itinto 2's you get octave doublings. When you divide it into 3's, you get what isknown as a perfect 5th. When you divide it into 5's, you get what is known asa Major 3rd. When you divide it into 7's, you get what is known as a Minor 7th.This process can continue to any desired level and is explained in greaterdepth in my book Natural Music Theory.

The formula for the Pythagorean Spiral of 5ths is:

p(3/2)k k is any Integer and p is any starting Pitch.


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Twelve intervals of a 5th almost closes in on itself - the "snake almostswallows its tail". The discrepancy has been known about since ancient timesand goes by various names. I call it - the Pythagorean Error Factor.Consider the following table consisting of Twelve 5thsUp (#) and Twelve 5thsDown(b).

0 1 2 3 4 5 6 7 8 9 10 11 12

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

C F Bb Eb Ab Db Gb Cb Fb Bbb Ebb Abb Dbb

In naturaloccurring pure intervallic evolutions, a B# in notequivalent to aC. Likewise, a Dbb is notequivalent to a C. Both B# and Dbb are audiblydifferent from C. However, it was discovered in early classical times

(European) that if you take an almost imperceptible amount (2 cents) awayfrom each 5th, you can get a Cycle of 5ths that does close in on itselfperfectly. The "snake eats its tail". Bach's Well Tempered Clavierwas a greatsuccess in promoting the new system. The gain is tremendous - we nowhave 12 different Keys to modulate to that all sound remarkably good. Thecost is that each 5th is 2 cents flat, a price that most are willing to pay forthe usefulness of the system. In the 12-Tone Tempered system B#=Dbb=C.Thus we end up with a true Pythagorean Cycle of 5ths.

To the right is a table showing thisCycle that is very concise andinformative. From it we can clearlysee each of the 15 Standard Keysand their relationships to each other.The Dominant relationship goescounter-clockwise. Notice theenharmonic keys. This is where theFlat Keys merge into the Sharp Keysdue to Tempering.

From this information we can

construct what is known as theChromatic Scale This Scale contains12 exactly equal intervals of a semi-tone (1/2 step).

{ C=B#, C#=Db, D, D#=Eb, E=Fb,F=E#, F#=Gb, G, G#=Ab, A, A#=Bb, B=Cb }

The exponential formula for our 12-Tone Tempered System is:

p2(k/12) k is any Integer and p is any starting Pitch.


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Why is the number 2 in this formula? Because the result multiplying ordividing any frequency by 2 is an 'octave' higher or lower. The Psycho-Acoustical perception of the same/different quality of octaves isdiscussed in great depth in my book Natural Music Theory.

The value of a chromatic interval is p2(1/12). The accepted Modern Standardis A=440 cps, but any base pitch will do. In fact, the base pitch has beensteadily rising. It was A=432 in Beethoven's time.

The 12-Tone Tempered System is not without its problems. As opposed tothe fact that 5ths and 4ths are only slightly out of tune, other intervals aregrossly distorted. In particular, the out-of-tune-ness of the Major 3rd led towhat is known as Just Intonation - the harmonic value (5/4) being usedrather than the Pythagorean (81/64). Similar problems exist with the b7,

#4, and other theoretically important notes.

The Cosmic Quirk involving the number 12, legendary for its numbermysticproperties, in evolving our common 12-Tone Tempered System andthe evolution of other N-Tone Tempered Systems from Cycles different from(3/2), some of which are more exact than the 12-Tone Tempered, aredeveloped in great detail in my book Natural Music Theory.

Discussion of Dominance in Music

Before we go any further, I will define Lydian-Dominant. Lydian is a wordfound in old Greek treatises on Music referring to the classical 7-note (so-called Dia-Tonic) Scale with the 4th Scale degree raised (#) a half-step. Theeasy way to remember this is by playing a Scale on a Piano starting on 'F'and pressing only the white notes. As the 4th degree of an F-Major Scale is aBb, we clearly have a different Scale - the Lydian Scale. This Scale is aMajor Scale with a #4th degree. In the exposition that follows, I will be doingall examples in the Key ofC. The CLydian Scale is spelled: { C D E F

# G A BC }.

The notion ofDominance is quite complex. Western polyphonic Multi-KeyedMusic based on the 12-Tone Tempered Scale has led to the concept of theDominant 7th Chord. It is a psycho-acoustic tension and releasephenomenon. This is how it is postulated to work in the European ClassicalMusic Theory.

The four note Chord formed on the 5th degree of the Major Scale is called

the Dominant 7th Chord. It is formally referred to as the V7 Chord. Thepresence of the Dominant 7th (b7) in the Chord sets up a tension that needsto be released. Classical theory states that this tension is released by

resolving to the Key Root Chord, also known as the I Chord - G7 C.


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The table to the right shows anidealized form of this resolution.What, exactly, causes this resolutionto occur? Remember, we are dealingwith psycho-acoustic phenomena

which is highly subjective and thetopic of much debate down throughthe ages continuing to the presentday. For now, let's put politics aside.

You are encouraged to do the following edecide for yourself.

xperiment on a Piano or Guitar and

In the G7 Chord, the root (G) and fifth (D) are quite consonant, as are theroot (G) and Major third (B). The Major third (B) and the fifth (D) form an

interval of a Minor third, also considered consonant, as do the fifth (D) andthe Dominant 7th (F). The interval between the root (G) and theDominant 7th (F) was considered dissonant in old classical theory. Mostmodern theorists are not so strict and would consider the interval as colorfulif not downright consonant.

This leaves us with the interval B-F. This interval was actually outlawed bythe Medieval Christian Church and marked with the name IntervalloDiabolo. This Interval spans 3 whole tones. There are many names for thisinterval - diminished 5th, augmented 4th, #11th, and my favorite - TriTone. A

TriTone is naturally formed between the Major 3rd

and the Dominant 7th

.Because of the relative consonance of all the other intervals in the G7 Chord,most, if not all, of the tension in this Chord is caused by the presence of thisTriTone interval. Lydian-Dominant Theory is, literally, the study ofTriTones.

In Western Classical Music Theory, this

interval was always resolved inwardly.

We are now at the first really important place in Lydian-DominantTheory.


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The TriTone interval also resolvesoutwardly as easily and as naturally as

it resolves inwardly.

You should try this out repeatedly on a Piano and let your ear be your finalarbiter. These resolutions are symmetric and, I believe neither has anyprecedence over the other. I agree with most modern theorists, that theyare equivalent and neither should be preferred for any subjective reasons.So what does this mean???

All students of Jazz soon discover the ubiquitous Chord progression:

II m7 bII7 I Maj7

Consider the Chord progression of the verse part ofThe Girl From Ipanemaby Antonio Carlos Jobim. It goes like this:

FMaj7 G7 Gm7 Gb7 FMaj7 Gb7

What in the world is that Gb7 doing all over the place??? By classical rules,this should be a C7 as it is the Dominant 7th Chord in the Key ofF. Howdoes the Gb7 cause the desired resolution to the I Maj7 Chord? This is theheart of Lydian-Dominant Theory. In the table that follows I will spell out therequisite chords, identify the relevantTriTone - the rest is magic.

The operational TriTone is {E - Bb}(remember Fb=E). Each of these

Dominant 7th

chords has the sameTriTone !!! As stated earlier in theanalysis of the generalizedDominant 7th, it is the TriTone thatcauses the tension that gets resolved.

Notice also that C and Gb arethemselves TriTones. Consider this. It would seem that the root (I) of theChord and it's closely allied 5th are quite exchangeable. It is the TriToneCore of the Chord that is Invariant. We will see later just how ambiguousTriTones can be. One can actually "get lost" aurally in an improvisation with


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many sequential Lydian-Dominant changes in the Chord progression. Thusthe first Postulate of the Lydian-Dominant Music Theory.

Postulate 1

Any Dominant 7th Chord can be replaced by its TriTone equivalent

with no loss of resolving power.

This postulate is the Fundamental Assertion of Lydian-DominantTheory. Once we recognize the power of Lydian-Dominant structures and

introduce them into our music, we find that the word modulation takes onan entirely new and exciting meaning. I would also add, that along with thisnewfound modulating flexibility, a wealth of harmonic richness is alsorealized. Classical music theory shortchanged itself terribly by banningand/or ignoring this fundamental theoretical fact implied by the OverToneSeries and realized by the 12-Tone Tempered Scale.

Understanding and appreciating the fundamental assertion of the firstPostulate - TriTone Dominant Substitution - is but the beginning of ourjourney. Next we will study and develop the essential core elements that are

the "building blocks" of Lydian-Dominant Theory - the TriTones.

Postulate 2

There are 6 TriTone pairs

TT1 = { c - f#/gb } TT4 = { a - d

#/eb }

TT2 = { g - c#/db } TT5 = { e - a

#/bb }

TT3 = { d - g#/ab } TT6 = { f/e

# - b/cb }

Each pair is associated with two interchangeable Dominant 7th Chords. Thatis, they may be substituted for each other to provide harmonic richnessand/or chromatic movement as can readily be seen in the Chord progression

snippet from The Girl From Ipanema used above.


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The following table enumerates the 6 Dominant7 pairs and their associatedTriTones. Read this table up and down the columns - the involved TriTone isin between.

C

7

G

7

D

7

A

7

E

7

B

7

/C

b7

a#/bb - e/fb f/e# - b/cb c - f#/gb g - c#/db d - g#/ab a/bbb - d#/eb

F#7/Gb7 Db7/C#7 Ab7 Eb7 Bb7 F7

Now we know whythat Gb7 is there in Jobim's Song. In fact, all of his workis heavily Lydian-Dominant. Check out his compositions Wave andDesafinado to see what I mean.

The BIG Fact is, that Jazz is heavily permeated with Lydian-Dominant

Chord Progressions and Melodic development. Swing, Blues and theirderivatives in the Pop/Rock styles less so, but still Lydian-Dominant. SouthAmerican forms like Samba and Bossa Nova and Tango are, again, heavilypermeated with Lydian-Dominant Chord Progressions and Melodicdevelopment. Likewise, the Afro-Cuban inspired Salsa forms. Certain 20thCentury Classical Composers have also ventured into Lydian-Dominant,Debussy, Ravel, Stravinsky to name just a few.

You should become aware of an odd thing with these pairs. Are theyaugmented 4ths (#11) or are they diminished 5ths (b5)? In Natural Music

Theory (pure Harmonic Series intervallic evolutions), there is a definitedifference. In the 12-Tone Tempered System there is not. The veryprocess of Tempering obliterates any difference.

Indeed, the TriTone interval is anArtifactof the 12-Tone Tempered System- it doesn't even exist in non-tempered systems. Approximations of it doexist in pure Scale, in fact, an infinite number of them. But as the TriTonehas a value ofp2(1/2) , ( any starting pitch p times the square root of2 ),all the Harmonic Series (which is based exclusively on rational numbers)can do is spit out closer and closer approximations to the TriTone. This is not

at all as weird as it seems at first glance. A famous Mathematical Proof,attributed to Euclid, may be found in any high school Geometry textbookshowing that:

No rational number, that is, an number of the form a/b , where a, b arenatural numbers, can equal 2. TriTones are intimately related to thisnumber that caused the Pythagoreans so much trouble with ir-rationalnumbers. This topic and other related items are explored in greater depth inmy book Natural Music Theory.


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Postulate 3

There are 6 Dominant7 b5

Chords.

C7 b5 = F#7 b5 = { C E Gb/F# Bb/A# }

G7 b5 = Db7 b5 = { G/Abb B/Cb Db F }

D7 b5 = Ab7 b5 = { D/Ebb F#/Gb Ab C }

A7 b5 = Eb7 b5 = { A/Bbb C#/Db Eb G }

E7 b5 = Bb7 b5 = { E/Fb G#/Ab Bb D }

B7 b5 = F7 b5 = { F A Cb/B Eb/D# }

This is the quintessential Lydian-Dominant Chord. It is both Lydian andDominant. This Chord puts the 'A' in Take The 'A' Train, the 'Des' inDesafinado, the 'Tune' in Bernie's Tune, and that special sonic twist in somany Lydian-Dominant compositions.

The Chord is comprised oftwo TriTone pairs a Major 3rd apart. In the case ofthe C7 b5 - F#7 b5 pair, they are {c - f#/gb } and { e - a#/bb }. Play thisChord - listen to it. Grab the 4 notes in the C-F# pair - { f# a# c e }. Now

play a C bass note - listen. Now play an F# bass note - listen. What do youhear? I hear the same tonality in each case. Nothing really changes exceptthe voicing, i.e. a particular rearrangement of notes.

For the Improviser, this is really important. The first problem encounteredwhen analyzing a particular Chord progression is figuring out what Scale(s)are implied by which Chord(s). It doesn't matter how fast your fingers areor how good your tone is if you're playing the wrong notes - it'll still soundbad. This is the major problem I have with some Improvisational Methods oflisting a seemingly different Scale to each and every Chord in a

progression. I find it more confusing than helpful, especially to the novice.

The fact is, that the underlying scalar note group frequently does notchange at all ! More often than not, whole sequences ofChord changesdefine the same note group. It doesn't matter which notes in a particularScale you choose to include in a motif, its still the same underlyingtonality. This is why Handel sounds as homogeneously boring as a lot ofmore modern music of all kinds - the whole song is defined by onescalar group! You might see a lot of Chord changes, but all that is reallychanging is which note(s) the bass player is currently emphasizing. For the

Improviser, nothing changes at all - its same Scale throughout.


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Once the student progresses up to Lydian-Dominant, they find that whatlooks like wicked hard Chord changes are really not so bad at all. There areonly 6 Dominant7 b5 Chords, not 12 as with most other chords. This makeslearning them take half the time. All that remains is to fit them in properly.Lydian-Dominant is actually easier than it looks. Things get even simpler in

the next postulate.

Postulate 4

There are 3 TriTone Quad Diminished Sub-Systems

DQ1 = Cdim = Ebdim = F#dim = Adim = { C Eb/D# Gb/F# A/Bbb }

DQ2 = C#dim = Edim = Gdim = Bbdim = { C#/Db E/Fb G Bb/A# }

DQ3 = Ddim = Fdim = Abdim = Bdim = { D/Ebb F Ab/G# B/Cb }

This is the infamousDiminished7 Chord. As we can easily see, the quadsform 3 mutually exclusive sets of 4 notes. Each group is comprised of 2interlaced TriTones a minor 3rd apart. Notice that 4 super-imposed minor

3rds equals an octave in the 12-Tone Tempered System. This note group istotally symmetric any way you look at it.

DQ1 = TT1 + TT4 = { c - f#/gb } + { a - d#/eb }

DQ2 = TT2 + TT5 = { g - c#/db } + { e - a#/bb }

DQ3 = TT3 + TT6 = { d - g#/ab } + { f - b/cb }

No group of notes has caused more problems for Music Theorists than this

one. Just naming the intervals is problematic within the old system. Below isa technically correct naming of a C dim7 Chord.

C - The Root - we'll see ...

Eb - A Minor 3rd above the root C - O.K.

Gb - A Diminished 5th above C - A Minor 3rd above Eb - O.K.

Bbb - What shall we call this interval???


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Bbb is a Minor 3rd above Gb and it is a diminished 5th above Eb. But whatinterval is it above C??? I have heard it called a diminished 7th. InStandard Musical Nomenclature, 7ths are designated as major and minoralong with 2nds, 3rds, and 6ths - 4ths and 5ths are called perfect, and alongwith roots, can be diminished, and, augmented. So what is a

diminished 7th???

I claim there is no such thing as a diminished 7th. This Chord is a 100%totalArtifactof the 12-Tone Tempered System. It doesn't exist at all inany OverTone Series derived Systems. It is an emergent property of the12-Tone Tempered System and is central to Lydian-Dominant Theory.Interestingly, other Tempered Systems have analogous structures and arediscussed in depth in my book on Natural Music Theory.

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 that werename this wonderfully ambiguous Lydian-Dominant note set thediminished 6th Chord - C dim6. As justification in addition to the aboveanalysis, I would point out that this Chord is remarkably close in sound andfunction to the minor 6th Chord, a Chord more commonly used in olderAmerican music, and still important in some indigenous styles like Tango.This Chord has an ambivalent tonality and differs from the dim6 in that the5th is perfect rather than diminished.

Cm6 = { C Eb G A }

Cdim6 = { C Eb Gb A }

Furthermore, if we invert the 6th in the C m6 thereby changing the root noteto A instead ofC, we derive the modern Jazz Chord, the A m7 b5 - the so-called half-diminishedChord. This Chord will be discussed in depth later onin this treatise.

The dim6 sub-systems also define 3 Lydian-Dominant Scalar entities calleddiminished scales. They will be discussed later on in this treatise. Thediminished quads are integrally involved in several other important Lydian-Dominant Chords which leads us to the next postulate.

Postulate 5


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There are 3 Sets of Dominant7 b9 Chords, one for each Diminished

Quad Sub-System.

Technically speaking, there are 12 of these chords. In Lydian-Dominantreality however, they each fall into one of the 3 Diminished Quad Sub-Systems. I will show this using:

DQ1 = {c eb/d# gb/f# a/bbb }

Consider the Chord:

F7 b9 = { F A C Eb Gb }

As discussed before, most of the "action" (tension-release) in a Chord iscreated by the 3rd and 7th. In this Chord the b9 also contributes significantly.

Play this Chord alternating the b9 (Gb')with the octave (F'). What does yourear think of this? We already know that in a Dominant Chord, the 3rd and 7thare a TriTone. In this Chord, the 5th and b9th form another TriTone! Onceagain, as in the Dominant7 b5, there are two TriTone pairs in the sameChord.

But this is a property of diminished quad sub-systems - is there one lurkingwithin this Chord. Sure is. The 3rd, 5th, b7th, and b9th form a dim6 Chord!This is the substance of this postulate. The "action" in this Chord is causedby every note butthe root. This is one of the most striking aspects of the

Lydian-Dominant System - that roots are frequently extraneous to thefunction of a Chord. They can be exchanged in certain proscribed ways.In this case, DQ1 contains the "action" notes for:

F7 b9 = { F + DQ1 = ( A C Eb Gb ) }

Ab7 b9 = { Ab + DQ1 = ( C Eb Gb Bbb ) }

B7 b9 = { B + DQ1 = ( D# F# A C ) }

D7 b9 = { D + DQ1 = ( F# A C Eb ) }

Notice also, that the exchangeable roots themselves form a dim6 quad !!!Grab the diminished quad on a Piano with the right hand. Now play eachroot in turn and listen. Do you hear what I hear? The "action" notes are thesame no matter how you choose to voice them. Changing the root notesalters the note set (thus the sonority changes), but the tension/resolutionmechanism is invariant. Lydian-Dominant is very cool. The same thinggoes for the other two quads and figuring them out I leave to you as an

exercise.


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Don't forget - this note-group is in the Dominant7 Chord-Space and, assuch, can be substituted for its TriTone equivalent! Lydian-Dominant iswickedcool. A frequent companion of the X7 b9 is the subject of the nextpostulate.

Postulate 6

The minor7 b5 / minor6 Chord.

As mentioned briefly above, this note group has a dual nature. It also calledthe "half-diminished" Chord. This makes some sense in that it is formedby adding a b7 to a diminished triad. However, this pseudonym hides the

fact of the dual nature of this Chord - it can be looked at as a 6th

Chord or a7th Chord, dependent on other factors such as melodic leading, resolution,and rooted-ness.

Cm7 b5 = { C Eb Gb Bb }

Ebm6 = { Eb Gb Bb C }

When used as a m7 b5, it is most commonly the first part of what I call a

minor II-V-I:

Major II-V-I Dm7 - G7 - C M7

minor II-V-I Dm7 b5 - G7 b9 - C m9

Though this is the most common usage of this Chord, especially in Jazzcompositions, the subtle ambiguity of this note group lends itself to other

uses. It doesn't have to resolve to a I mx Chord through the V7 b9- it can just as easilygo other places though not anyplace. Check out Stella By

Starlight.

When this note group is used as a m6 Chord, it is quite common to find it

used as a I Chord! There are innumerable songs that do this Remember, allthat has changed is the root note. It's the same basic tonality, butemphasizing a different bass note gives this note group a different quality.This note group is truly ambivalent in character and has power in manydifferent directions.

Actually, the m7 b5 is the OverTone SeriesInverse of the Dominant7 Chord

making it an important fundamental theoretical construct - want to know


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more? The derivation of this Chord and that ofminoritself are presented indepth in my book on Natural Music Theory.

Postulate 7

There are 4 Augmented Triad Sub-Systems.

Notice that 3 super-imposed Major 3rds exactly equals an octave in the 12-Tone Tempered System. Like the dim6 sub-systems, the 4 Augmented sub-system triads are totally symmetric and form 4mutually exclusive sets of3

notes. They are:

AT1 = Caug = Eaug = Abaug = { C E G#/Ab }

AT2 = Ebaug = Gaug = Baug = { Eb/D# G B }

AT3 = F#aug = Bbaug = Daug = { F#/Gb A#/Bb D }

AT4 = Aaug = C#aug = Faug = { A C# F/E# }

Though not properly Lydian-Dominant, the 4 augmented triads are heavilyinvolved in Lydian-Dominant Theory in at least two important ways. First,the scales that underlay this Chord are all Whole-Tone (altered) Scalevariants. These scales can also underlay other important Lydian-DominantChords. I will have more to say on this later in this treatise. Second,Augmented Triads are usually used as Dominant 7th or 9th Chords makingthem Lydian-Dominant and subject to all the other Lydian-DominantPostulates.

Here's where the fun begins again. These 4 augmented sub-systems imply 4

corresponding Augmented7

sub-systems as well. I'll show you the T1 sub-system and leave the other three for you to do as an exercise.

C aug7 = { AT1 = ( C E G# ) + Bb}

E aug7 = { AT1 = ( E G# C ) + D }

Ab aug7 = { AT1 = ( Ab C E ) + Gb }

As with the diminished sub-systems, these augmented sub-systems are a100% total Artifactof the 12-Tone Tempered System. As shown above in


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Postulate 5, the X7 b9 is essentially a diminished quad plus one of 4 relatedroots, themselves forming another diminished quad. With these aug7 notegroups, we have an augmented triad plus 3 related Dominant sevenths,themselves forming another augmented triad!

The Aug7 Chord is not as common used as many other Lydian-DominantChords, but because it in the Dominant Group, it turns up in strategicpositions in many songs and must be handled properly. As mentioned brieflyabove, the augmented sub-systems are intimately connected with Whole-Tone Scales which brings us to our next postulates after a short digression.

Before we get to the next postulate I want to briefly discuss the WesternClassical bias (from the Greeks) toward the 7-note (so called) Dia-TonicScale and an important bit of nomenclature

Despite the fact that we in the Western Cultures have come to enshrine"Rational Thinking" as the epitome of human evolution, and view anycontinued reliance on pre-rational systems as atavistic and downrightignorant, we have nevertheless perpetrate on each unsuspecting generationsince the "Enlightenment" a plethora ofnumber mystic systems whichare unquestionably accepted as "cosmic" Law.

Case in point - ask anyone why there are 7 days in a week and you willusually get stunned silence and strange looks for a reply. Some willdesperately be mentally searching for a "logical" reason (there must be one)for these commonly encountered systems. You may get a straightforward"... and God rested on the 7th day." from a Religionist, and though Irespect their right to their strongly held convictions, I don't feel that I ambound by them in any way. The point is, that there is No cosmic reason atall why the number 7, or any other number for that matter, should bespecially favored.

In Music Theory, we use the two terms Scale and Chord without muchdiscretion. In fact, there is no real difference between them. It only depends

on how far we space out the intervals and even this is poorly defined. If wespace out the intervals in whole and halfsteps the note-group is usuallycalled a Scale. If we super-impose Major and minor thirds, it is usuallycalled a Chord. Problem is, some scales have intervals of a min 3rd, andsome chords have intervals of whole step. I and many modern musictheorists use the term ChordScale. I also use the term note-group. Thismakes more sense to me than trying to define a difference that does notexist.

Consider the following analysis:

C-Major Scale = { C D E F G A B }


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C Maj13 Chord = { C E G B D F A }

A better way to show this is:

F-Major Scale = { F G A Bb

C D E } C13 Chord = { C E G Bb D F A }

C13 is in the Dominant7 Group in the Key ofF. In both cases, the note-group is identical and the same ChordScale is defined. There happens tobe 7 notes in it and, indeed, there are a lot of 7-note scales. But, there aremany other ChordScales with a different number of elements that are just asuseful and legitimate as the dia-tonic.

The number 12 (as in 12-Tone Tempered System, inches in a foot, months

in a year, hours of day/night, and various groups of Apostles ) is also totallybunged up with number mysticism. As usual, I discuss this issue in greatdepth in my book on Natural Music Theory.

Postulate 8

There are 2 Whole Tone Scalar Sub-Systems.

WT1 = AT1 + AT3 = TT1 + TT3 + TT5 = { C D E F#/Gb G#/Ab A#/Bb }

WT2 = AT2 + AT4 = TT2 + TT4 + TT6 = { F G A B/Cb C#/Db D#/Eb }

This is a totally symmetrical Scale of 6 notes! It is constructed of nothing butWhole steps. Play them on your instrument - was your ear fooled? They are

even more fun to sing - try it. This Scale is a Lydian-DominantArtifactofthe 12-Tone Tempered System. It is not found in natural OverTone Seriesharmonic derivations. Once again, tempering allows the "snake to eat itstail".

The Whole-Tone Scale and its altered variants underlay many Lydian-Dominant Chords. Basically, they fit any Chord with a diminished 5th or anaugmented 5th or both They can also be used when a #11 or a b13 ispresent. I will show how they can be used to fit the common Lydian-Dominant Chord - the Dominant7 b5.


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C7 b5 = { C E Gb Bb }

CWT = WT1 = { C D E Gb Ab Bb }

Notice that we have 4 notes ofWT1 already in the Chord itself! The twonotes that are missing are D and Ab. The D is easily justified as a 9th. As 9thsare, in reality, only the 2nd note of a Major Scale, and this is a Major Chord,it can always be used in a situation like this. The Ab is more of a problem tojustify. Technically, C7 is a Major Mode Chord and as such, a Major 6th shouldbe played giving us an A rather than an Ab. Indeed an A can be playedturning our Scale into one of the many Whole-Tone variants. However, usingthe Ab gives us a slightly "outside" sound. In particular, it provides sonicvariance using a non-critical note - the 6th. This is very important to theImproviser.

Next, I'll show how the Whole-Tone Scale can be used to fit anaugmented 7th Chord.

C aug7 = { C E G# Bb }

CWT = WT1 = { C D E F# G# A# }

Notice that we have 4 notes ofWT1 already in the Chord itself! The twonotes that are missing are D and F#. As above the D is easily justified as a9th. This time, the F# is the problem to justify. Strictly speaking, as this is aMajor Chord, we should have an F rather than a F#. Indeed an F can beplayed turning our Scale into a Whole-Tone variant. However, using the F#gives us a slightly "outside" sound. In particular, it provides sonic varianceusing a non-critical scalar note - the 11th. This is very important to theImproviser.

A comment on "playing outside"

Jazz players are famous for "playing outside" (i.e. playing non-chordscaleimplied notes) in the course of their improvisations. Indeed, it is animportant part of the Jazz Style. I believe, however, that not all "outside"notes are justified at the theoretical level. Some "outside" notes are justplain wrong - i.e. not at all justifiable within the structure of the Chordprogression. Too often, "playing outside" is used as an excuse for playingwrong notes due to an inadequate analysis of the Chord Progression impliedHarmonic Structure of a piece.


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Postulate 9

There are 3 Diminished Scalar Sub-Systems.

DS1 = ( DQ1 + DQ3 ) = { C D Eb F F#/Gb G#/Ab A/Bbb B/Cb }

DS2 = ( DQ2 + DQ1 ) = { G A Bb/A# C C#/Db D#/Eb E/Fb F#/Gb }

DS3 = ( DQ3 + DQ2 ) = { F G Ab/G# Bb/A# B C#/Db D/Ebb E/Fb }

This is a totally symmetrical Scale of 8 notes! It is constructed of alternateWhole and Half-steps. Play them on your instrument - was your earfooled? They are even more fun to sing - try it. This Scale is a Lydian-Dominant Artifact of the 12-Tone Tempered System. It is not found innatural OverTone Series harmonic derivations. Once again, Temperingallows the "snake to eat its tail".

The diminished Scale comes in two flavors DSwh and DShw depending on howthe diminished Scale is constructed - whole step first or half-step first. The

following table shows the difference.

1 1 1 1

CDIM(wh) = C D Eb F F#/Gb G#/Ab A/Bbb B/Cb C'

1 1 1 1

CDIM(hw) = C C#/Db D#/Eb E/Fb F#/Gb G A Bb/A# C'

Notice that CDIM(hw) = C#

DIM(wh) !!! All we do is start on a different note inscalar sub-system. This is generally true of every one of these scales leadingto the following relations.

DSwh1 = DShw2

DSwh2 = DShw3

DSwH4 = DShw1


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There are many ways to use these scales. In either flavor, they remainwonderfully ambiguous and their use now and again over the proper Chordchanges, though tricky, creates much sonic richness. I will show some waysto use these scales and leave others for you to investigate as an exercise.

I will use the classic Lydian-Dominant Chord progression elaborated onextensively above:

The Lydian-Dominant II - V - I IIm7 - bII7 - I MajxLet's work in the Key ofC. The Chord progression we need to fit is: Dm7 -Db7 - CMajx - the x signifying some form of Major Chord like a C6, a CMaj7,or a CMaj9.

LD II-V-I Dm

7

D

b7

CMaj

9

DDIM(wh-up) (D E F G) (A

b Bb Cb Db) D'

* Set1 Set2 *

DDIM(wh-down) (D' C B A) (Ab Gb F Eb) D

Notice that there is an Up and a Down version of the Scale, both beingconstructed of alternating whole & half-steps. The Scale D DIM(wh) is

composed of 2 sets (called tetrads from Greek Music Theory) of 4 notes. Inthe Up version, Set1 is the first4 notes of a Dm Scale and Set2 is the first4 notes of a Abm Scale. In the Down version, Set1 is the last4 notes of aDm (Dorian as implied by the Key of C) Scale and Set2 is the last4 notes ofthe corresponding Abm Scale.

I hope by now that you have noticed that D & Ab are TriTones !!! Thisshouldn't be a surprise to you anymore. Play the chords and theaccompanying scales on the Piano - listen. They are super-diminishedeveryway you look at them. Try playing them in "thirds" - in "fourths". See if you

can find other ways to use these wonderfully ambiguous Scale patterns.

For now, I will conclude this treatise with an excerpt from my book onNatural Music Theory. It deals with the actual OverTone Series impliednote-groups that underlie Lydian-Dominant Theory. To appreciate itssimplicity one only has to look carefully at the OverTone Series and list thenote-groups by Doublings.


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OverToneNote#

NoteName

Analysis

1 F C0 Fundamental

2 1 C1

3 5 G1Fifth

4 1 C2

5 3 E2

6 5 G2

7 b7 Bb2

Dominant7

8 1 C3

9 2 D3

10 3 E3

11 #4 F#3

12 5 G3

13 6 A3

14 b7 Bb3

Lydian-DominantScale

15 7 B3 Leading Tone

16 1 C4 Doubling

Postulate 0

The Primal Lydian-Dominant ChordScale

C7 { C D E F# G A Bb }

This ChordScale is Legendary. It is found the world over and is usuallyassociated with the local culture's Goddess. Notable among these are theGreek Sappho of Lesbos and the Hindu Saraswati - Goddess of Music,Mathematics & the Sciences. It is a wonderful Scale and wholly derivedfrom the OverTone Series generated Harmonic Series. This knowlege isAncient! Most people today don't know that Plato, Aristotle, Euclid, Ptolemy,

and who-knows-how-many others wrote extensivelyabout Music Theory. Itis written about in the Vedas, the World's oldest books. It is amazing to me


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to be constantly re-discovering facts known to humans so long ago and thenforgotten in the headlong rush of Civilization's March.

Discussion based on the previous OverTone Series Table:

Note the 'natural' note-group progression:

First, you produce a Pitch, any Frequency

Next, you get a Doubling (see below)

Then, a 5th - the first interval created that is not a Doubling. This interval(3/2)x generates the 12-Tone Tempered (Pythagorean) Scale

Then, you get a Chord - C7 - The Dominant7 Chord. It is 100% naturallyderived from the OverTone Series.

Lo and Behold, this Chord implies the Lydian-Dominant Scale - CLD, not

the Pure Major, nor the Myxo-Lydian as older Music Theories claim. A Leading-Tone into the next Doubling. I will have more to say about this

concept in the book.

The process continues to Infinity with new chordscales emerging that

transcend and include those already manifest. As usual, I discuss this issue

in great depth in my book on Natural Music Theory.

Notice my use of the word "Doubling" instead of "Octave". The word

octave contains a built-in and totally unwarranted bias toward 7-note scales- it literally means the "eighth" note. It is true that there are manywonderful and important 7-note Scales, but this fact hardly justifies prioritystatus. Doubling is a Psycho/Physio-Acoustical phenomenon - it has nothingat all to do with scales.

Concluding Remarks:

As we continue our studies, I will point out Lydian-Dominant elementswhere ever they occur in the Songs we learn and the Improvisations wecreate for them. Regularly and methodically practice the preparatoryexercises that I have created for you to learn the Lydian-Dominant System.Your hard work and diligence will reap great rewards as your Improvisationsdevelop the tremendous sonic richness implicit in the Brave New WorldofLydian-Dominant Music Theory.

Norm Vincent

NorthStar Studios - April [email protected]

lydian dominant theory

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