Topics
Intro
Explanation of diminished chords and theory based on Barry Harris and other explorations.
The Diminished Family Theory
Intro
Before we go into the application of these scales, lets explain how Barry came up with this concept in the first place
This concept has actually been around for a long time as it's been a common arranging technique used for early big band writing. However, Barry discovered it from a completely different angle and categorized it, gave it names, and has been developing the endless possibilities ever since
Playing With The Universe
Intro
Lets define our bounds and restrictions and what we can play with.
Step 1: Defining The Universe
So to start, Barry has a quite unique perspective on the theoretical side of music which you won't find taught at any music school. He takes quite a spiritual approach starting with the 12 notes of the chromatic scale.
Chromatic Scale
1 2 3 4 5 6 7 8 9 10 11 12
C Db D Eb E F Gb G Ab A Bb B
Step 2: Splitting The Universe Into Atoms
Now, these are all the notes in our western music and Barry refers to this as our musical universe, or the 12 disciples, or the 12 zodiac signs, or the 12 months of the year. But basically, he refers to these 12 notes as being god (stay with me now).
He then goes on to say that God then made man and woman or Adam and Eve, which he refers to as being the 2 whole tone scales, which gives you all the possible notes in our universe.
Whole Tone
C D E Gb Ab Bb || Db Eb F G A B -> 12/6 = 2 Whole Tone scales
Step 3: Splitting Atoms Into Molecules
So what happened next, then man and woman had children, 3 children, which Barry refers to as the 3 possible diminished chords available to us in our musical universe.
Diminished
C Eb Gb A || Db E G Bb || D F Ab B -> 12/4 = 3 Diminished Chords
Step 3.1: Tracing DNA
Each of these 3 diminished chords, as Barry puts it, share a 50/50 split of DNA, or chromosomes from the 2 whole tone scales, or their parents.
Whole Tone
C D E Gb Ab Bb || Db Eb F G A B -> 12/6 = 2 Whole Tone scales
1 2
Diminished
C Eb Gb A || Db E G Bb || D F Ab B -> 12/4 = 3 Diminished Chords
1 2 1 2 2 1 1 2 1 2 1 2
Learning We Can Manipulate Matter
Since each of the diminished chords share a 50/50 split, you can get to any diminished chord from either one of the 2 whole tone scales.
This already starts to gives us some options to create harmonic movement with, and is a sneak peak of the entire ideology of diminished oriented music theory.
This way of thinking is all very logical and a really elegant way to start to see these relationships. So lets continue with an even more mathematical view.
Our Resulting Playground
Per Barry, if 12 is all of our notes, the chromatic scale, lets play with it.
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Whole Tone If we divide 12 by 2, we get 2 different 6 note scales, the 2 whole tone scales.
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Diminished If we divide 12 by 4, we get 3 different 4 note scales, the 3 diminished chords.
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Augmented If we divide 12 by 3, we get 3 different 3 note scales, the 3 augmented chords.
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Tritones If we divide 12 by 6, we get 6 different 2 note scales, the 6 tritone chords.
Chromatic
C Db D Eb E F Gb G Ab A Bb B -> 12/12 = 1 Chromatic Scale
Whole Tone
C D E Gb Ab Bb || Db Eb F G A B -> 12/6 = 2 Whole Tone scales
Diminished
C Eb Gb A || Db E G Bb || D F Ab B -> 12/4 = 3 Diminished Chords
Augmented
C E Ab || Db F A || D Gb Bb || Eb G B -> 12/3 = 4 Augmented Chords
Tritone
C Gb || Db G || D Ab || Eb A || E Bb || F B -> 12/2 = 6 TritonesDeriving The Diminished Family
Intro
Notice how we mentioned we can get to any of the 3 diminished chords from the 2 whole tone scales by just modifying 2 notes, since each of the 3 diminished chords share a 50/50 split of DNA from both whole tone scales.
If this is true, that means we can do the inverse, and get to either of the 2 parent whole tone scales by unmodifying 2 notes.
Great! What if we were to take this further. What else can we get to from a diminished chord by modifying some number of notes.
Lets take this idea and run with it, and define every possible harmonic movement we can achieve from a diminished chord. As we go, we will notice this will outline so very interesting movements.
Modification 1: Move 1 Note Down -> Dominant 7th Chord, Built On Root In Next Door Neighbor Diminished Family
Intro
So lets take a Co7, made of C Eb Gb A.
Its interesting to note when first dealing with diminished chords, is that 1 single diminished chords is shared by 3 other chords, as the all share the same notes, just starting on a different note.
Modifying Notes
Lets solidify this by using notes.
Diminished Chord 1
C Eb Gb A || Eb Gb A C || Gb A C Eb || A C Eb Gb -> 4 notes = 4 Diminished Chords
So if we lower any one of these diminished chord tones, we get a dominant 7th chord. And since we can do this to any of the chord tones, we have 4 different dominant 7th chord options.
Diminished Chord -Mod Dominant 7th = Clean Version
C Eb Gb A C -> Cb Eb Gb A = B Eb Gb A B dom7
C Eb Gb A Eb -> C Ebb Gb A = D F# A C D dom7
C Eb Gb A Gb -> C Eb Gbb A = F A C Eb F dom7
C Eb Gb A A -> C Eb Gb Ab = Ab C Eb Gb Ab dom7
So whatever note gets lowered, that becomes the root note for the new dominant 7th chord.
Modifying Solfege
Lets abstract this to solfege in C major, so we can do this change in any key.
Diminished Chord 1
Do 3/4 5/6 La || 3/4 5/6 La Do || 4/5 La Do 2/3 || La Do 2/3 4/5 -> 4 notes = 4 Diminished Chords
So if we lower any one of these diminished solfege tones, we get a dominant 7th chord. And since we can do this to any of the solfege tones, we have 4 different dominant 7th chord options.
Diminished Chord - Mod Dominant 7th = Clean Version
Do 2/3 4/5 La Do -> Ti 2/3 4/5 La = Ti 2/3 4/5 La Ti dom7
Do 2/3 4/5 La 2/3 -> Do Re 4/5 La = Re 4/5 La Do Re dom7
Do 2/3 4/5 La 4/5 -> Do 2/3 Fa La = Fa La Do 2/3 Fa dom7
Do 2/3 4/5 La La -> Do 2/3 4/5 5/6 = 5/6 Do 2/3 4/5 5/6 dom7
Notice that we have resulted in 4 m6 chords build on the original notes of the next door neighbor diminished chord.
TODO EXPLORE THIS: So we can use this dominant 7th chord to go across diminished families????
So whatever solfege gets lowered, that becomes the root solfege for the new dominant 7th chord.
Doing the Reverse, Dominant 7th Chord to Diminished
This also gives us a new option of where to move from a dominant 7th chord.
We have found out that by raising the root of any dominant 7th chord, we get the original diminished chord it came from.
4 Dominant Chords, Now What?
As these 4 dominant chords are related to each other since they all come from this one diminished chord, Co7 (again the same as Ebo7, Gbo7, Ao7), the 4 dominant chords all work and play well together.
TODO: something very confusing will write down later
brain metled :) will do tmr with fresh brain
Modification 2: Move 1 Note Up -> Minor 6th Chord, Built On 2 Notes Above In Current Diminished Family
Intro
Again, lets take a Co7, made of C Eb Gb A.
And note again that this 1 single diminished chords is shared by 3 other chords, as the all share the same notes, just starting on a different note.
Modifying Notes
Lets solidify this by using notes.
Diminished Chord 1
C Eb Gb A || Eb Gb A C || Gb A C Eb || A C Eb Gb -> 4 notes = 4 Diminished Chords
So if we raise any one of these diminished chord tones, we get a minor 6th chord. And since we can do this to any of the chord tones, we have 4 different minor 6th chord options.
Diminished Chord -> Minor 6th = Clean Version
C Eb Gb A C -> Db Eb Gb A = Gb A Db Eb Gb m6
C Eb Gb A Eb -> C E Gb A = A C E Gb A m6
C Eb Gb A Gb -> C Eb G A = C Eb G A C m6
C Eb Gb A A -> C Eb Gb Bb = C Eb Gb Bb Eb m6
So whatever note gets lowered, a diminished 5th above that or 2 notes up the chord above it becomes the root note for the new minor 6th chord
Modifying Solfege
Lets abstract this by using solfege.
Diminished Chord 1
Do 3/4 5/6 La || 3/4 5/6 La Do || 4/5 La Do 2/3 || La Do 2/3 4/5 -> 4 notes = 4 Diminished Chords
So if we raise any one of these diminished solfege tones, we get a minor 6th chord. And since we can do this to any of the solfege tones, we have 4 different minor 6th chord options.
Diminished Chord - Mod Dominant 7th = Clean Version
Do 2/3 4/5 La Do -> 1/2 2/3 4/5 La = 4/5 La 1/2 2/3 4/5 m6
Do 2/3 4/5 La 2/3 -> Do Mi 4/5 La = La Do Mi 4/5 La m6
Do 2/3 4/5 La 4/5 -> Do 2/3 Sol La = Do 2/3 Sol La Do m6
Do 2/3 4/5 La La -> Do 2/3 4/5 6/7 = 2/3 4/5 6/7 Do 2/3 m6
Notice that we have resulted in 4 m6 chords build on the original notes of the current original diminished chord.
So whatever note gets raise, a diminished 5th above that or 2 notes up the chord above it becomes the root note for the new minor 6th chord
Doing the Reverse, Minor 6th Chord to Diminished
This also gives us a new option of where to move from a minor 6th chord.
We have found out that by lower the 5th of any minor 6th chord, we get the original diminished chord it came from.
Modification 3: Move 2 Consecutive Notes Up, Move 2 Consecutive Notes Down
Intro
Again, lets take a Co7, made of C Eb Gb A.
And again, for anyone skipping sections, lets note again that its interesting to note when first dealing with diminished chords, is that 1 single diminished chords is shared by 3 other chords, as the all share the same notes, just starting on a different note.
Modifying Notes
Lets solidify this by using notes.
Diminished Chord 1
C Eb Gb A || Eb Gb A C || Gb A C Eb || A C Eb Gb -> 4 notes = 4 Diminished Chords
So if we raise any 2 non consecutive diminished chord tones, we get a major 6th chord. And since we can do this to any of the chord tones, we have 4 different minor 6th chord options.
Diminished Chord --++Mod Major 6th = Clean Version
C Eb Gb A C Gb -> Db Eb Gb A = Gb A Db Eb Gb m6
C Eb Gb A Eb A -> C E Gb A = A C E Gb A m6
C Eb Gb A C Gb -> C Eb G A = C Eb G A C m6
C Eb Gb A Eb A -> C Eb Gb Bb = C Eb Gb Bb Eb m6
So whatever note gets lowered, a diminished 5th above that or 2 notes up the chord above it becomes the root note for the new minor 6th chord
Modifying Solfege
Lets abstract this by using solfege.
Diminished Chord 1
Do 3/4 5/6 La || 3/4 5/6 La Do || 4/5 La Do 2/3 || La Do 2/3 4/5 -> 4 notes = 4 Diminished Chords
So if we raise any one of these diminished solfege tones, we get a minor 6th chord. And since we can do this to any of the solfege tones, we have 4 different minor 6th chord options.
Diminished Chord - Mod Dominant 7th = Clean Version
Do 2/3 4/5 La Do -> 1/2 2/3 4/5 La = 4/5 La 1/2 2/3 4/5 m6
Do 2/3 4/5 La 2/3 -> Do Mi 4/5 La = La Do Mi 4/5 La m6
Do 2/3 4/5 La 4/5 -> Do 2/3 Sol La = Do 2/3 Sol La Do m6
Do 2/3 4/5 La La -> Do 2/3 4/5 6/7 = 2/3 4/5 6/7 Do 2/3 m6
Notice that we have resulted in 4 m6 chords build on the original notes of the current original diminished chord.
So whatever note gets raise, a diminished 5th above that or 2 notes up the chord above it becomes the root note for the new minor 6th chord
Doing the Reverse, Minor 6th Chord to Diminished
This also gives us a new option of where to move from a minor 6th chord.
We have found out that by lower the 5th of any minor 6th chord, we get the original diminished chord it came from.
Modification 4: Move 2 Non Consecutive Notes Down, Move 2 Non Consecutive Notes Up
Movement Across The Family
Moving Across Siblings: IV to F (in key of F)
Moving Across Siblings: I to F (in Key of C)
Where Did Scales Come From
Whole/Half or Half/Whole Diminished Scale
Something to do with Modification 1: Drop 1 Note
This is also a way to see where the 8 note W/H or H/W diminished scale comes from, because if you pu t together the 4 related dominants roots, which are below each diminished chord tone, they make up another diminished chord, which is a semitone below the original diminished chord.
C -> B, Eb -> D, Gb -> F, A -> Ab = B D F Ab (Bo7) If you put the notes of these 2 diminished chords together, they make up the 8 note diminished scale. So Co7 + Bo7 = 8 note diminished Scale.
C Eb Gb A + B D F Ab = B C D Eb F Gb Ab A (8 note W/H or H/W diminished scale )
Please redu this later