​My current journey is to get more fluent with diminished chords and the symmetrical diminished scale.  When I see a Diminished 7th chord on a chart, I rarely have anything more up my sleeve then finding the root and climbing an arpeggio.  The sound definitely works but it can get a bit trite, especially over multiple choruses.  The fact that the diminished sound was such a huge part of pioneer Charlie Christian and then the be-boppers, not to mention Barry Harris's Sixth-to-Diminished concept, I've felt the need to visualize the Diminished arpeggios and scales better, at least in one context.

I'm already aware that the diminished sound can be applied with any dominant. The 'half-whole' symmetrical diminished scale can be used from the root of a V to get altered tones, but what about Diminished chords in Bossas or even folk and classic show tunes?

The best I can gather, the Diminished is like connective tissue that links the meat of the Diatonic chords.  Altered sounds on a Five chord is really just a way to lead the ears back to the I chord, often chromatically instead of scale-wise.  When you see a Dim.7 for a whole bar, typcially the same idea is happening -- it is a chromatic walk to the next harmony.  My plan is to get a baseline visualization for any diminished around the Major scale and then adjust accordingly.  My approach -- outlined in the PDF below -- is inspired by the bars in 'Shadow of Your Smile' which moves from Cmaj7 to C#dim7.

My strategy starts on page 1 of the PDF with a set of 'anchors' over the course of the fretboard.  Specifically I am trying to learn a set of 3-note voicings on the middle strings where I tend to gravitate toward when comping.  The voicings are just repeats of two shapes.  Sometimes it is helpful to actually give a name to shapes to aid the memorization -- I'm calling these 'arrow' and 'cup' shapes (the arrow's 'point' is towards the bridge and the cup's 'base' is toward the nut).

The first goals is to learn how these shapes 'sit' against the 'mode boxes' of the fretboard.  I visualize the fretboard by segments where you can vertically play a mode with the mode's root on the sixth string.  I'm learning these 'anchors' by looping two bars of Cmaj7 followed by two bars of Diminished 7.  For each mode-box, I start slow and work up speed alternating between the Major scale and then the arpeggio.  From these anchors I am extending the diminished arpeggio shape out.  The ensuing pages 2-8 show arpeggio shapes for other strings.  As I practice, I'm starting just with the 'corny' arpeggios as a line back to the major scale harmony.  For each segment of the fretboard, I want to visualize the map of these arpeggios over the major scale. 

Page 9 of the PDF begins the rest of the half-whole 'Symmetrical Diminished'. The second 'half' of the scale is rendered for each shape on page 1-8.  The other half of the half-whole scale is the same arpeggio voicings, just one semi-tone up from the anchors.

The 'Symmetrical Diminished' is a synthetic scale comprised of two sets of diminished arpeggios.  Every other note has a semi-tone or whole-tone interval.  The pages 9-16 show what I am calling the 'consonant' half of the scale.  All the notes of the scale one semi-tone up are in the Major scale, save the #5.  Even though #5 is not classically consonant with the major scale, it is okay to resolve on a Maj7#5 chord.  The #5 is consonant in the Barry Harris world.

The arpeggios in pages 1-9 I will call the 'Dysonant' half of the scale.  Even though they have a Perfect Third and Perfect Fifth, you are never going to resolve a Major 7 chord with flat 9 or a flat 7.  These are the same arpeggios in the 'Sixth to Diminished' concept.  They are the diminished arps that alternate between Maj6/min7 voicings to complete the Barry Harris chord scale.

Interesting, the 'Consonant'arpeggios have the voicings you might use for a V7b9 chord.  The major #5 is the b9 of the Dominant chord in a Major key. 

Together, both the 'Consonant' and 'Dysonant' arpegios make up my Symmetrical diminished scale for navigating over a C#o7 from a Cmaj7.  The end goal is to be able to go into this scale at any point, from any point in any Major scale.

Of course this pdf leaves out a third set of diminished arpeggios, which contains the root, the b3, the sixth, and the #11 of the major. These arpeggios lead to other Symmetrical Diminished scales which I am not going into in order to keep things from getting too out of hand. If you think of the 'altered Five' application of the Symmetrical Diminished using the scale in the PDF (the 'anchors' combined plus a semi-tone up) gives you the b9, #9, #11, as well as the root, the third, sixth and the b7 of the Five chord.  The only alteration you are missing is the #5 of the Five.  In the end, in order to play the remaining Symmetrical Diminished scale, you would simply use the 'anchor' voicings in page 1-9 as 'avoid' notes -- avoiding the Major scale's 5, b9, b7 and P3.  In terms of the Five chord, that would mean avoiding the 5, 7, #11, and #3 of the Dominant.

By learning the 'anchors' in page 1 for each mode-box, then learning the other voicings connected to them, then adding the notes a semi-tone up, I hope to get a go-to framework for coming up with diminished sounds relating to the major scale.

Below is the the Harmonic Minor Scale and it's diatonic arpeggios.  This PDF is similar to those for the Major Scale and Melodic Minor Scale, so check out those posts if you haven't.  The PDF outlines the Harmonic Minor, it's seven modes and the diatonic arpeggios.

As with the other Scale PDFs, it might be worthwhile to start with the arpeggios for each mode.  Not only are they less notes to focus on, but they are lines in themselves that make succinct, harmonic 'sense' out of the modes.  Once you understand the chord tones for a mode, then you can 'flesh out' the rest of the scale around it.

For the novice jazzer, it is less useful to understand this material for compositional movements, than to just be aware of the arpeggios that are buried within this scale.  While the Harmonic Minor is a great choice for the Min-Maj7 chords and sounds in tunes like Nica's Dream and Nardis, the harmonic minor is probably most used in jazz for altered sounds -- using the Phrygian Dominant over a #11 chord or the Ultra-Locrian for tri-tone colors over a functional Dominant.  Just learning the harmonic scale will give you access to these sounds, but being able to pick out all the arpeggios within it can give you a richer starting point for your lines.

Another key use of the Harmonic Minor in jazz is the 'Barry Harris' approach.  Barry Harris has a whole cosmology of scales and tones that starts with chromatics, splits into diminished and ends with sixth chords.  The 'Barry Harris' scale -- the Major#5 -- is really the third mode of the Harmonic Minor in this PDF.  Check out his 'Sixth-to-Diminished' theory which is at the heart of his teachings.  If you act as if the Third Mode of the Harmonic Minor is the 'One' chord for Major tunes, you can develop a unique perspective into the tunes of the Swing and BeBop era.  Either way, if you are familiar with the arpeggios in the Harmonic Minor and Melodic Minor scales, you will be able to spot them when transcribing the lines of Charlie Parker and other boppers when they go 'outside' the harmony.

Below is a reference for learning the Melodic Minor Scale diatonically.  The Melodic Minor is sometimes referred to as the 'Jazz Minor' due to its applications to Jazz.  You may have gotten hip to the fact that the 7th mode of the Melodic Minor can be used serve up altered sounds over a functional Dominant (a V going to a I).  At some point I also realized that the fourth mode of the Melodic Minor can be used over #11 Dominants.  Learning the totality of the scale with diatonic context of all the arpeggios will give much greater command over these sounds.

While the Melodic Minor only differs from the Major scale by one note, I still find myself struggling to visualize it thoroughly over the fretboard, certainly more than Major scale.  My ability to visualize the Major scale was significantly bolstered by learning all the diatonic arpeggios in the scale, across all the scale 'boxes' where the modes sit with the root on the sixth string.  Learning arpeggios also significantly strengthened my ability to generate lines strongly outlining the harmony. 

You can focus on parts of the neck by breaking it up into 'r6 mode boxes'.  These scale 'boxes' I term with the 'r6' meaning 'root is on the 6th string.'  For instance, 'III-r6' represents the way the notes sit when you play the Phrygian scale with its root on the sixth string.  This lines up as a box, or chunk of the fretboard which is easier to concentrate on, especially at first.

Just like the the Major scale, there are seven notes in the Melodic Minor.  Each of these seven 'degrees' has a mode, chord, and arpeggio associated with it.  Modes are simply the same notes of a scale arranged with a different note serving as the root.  The arpeggio for each degree can be found by skipping every other note in the mode until the next octave is reached.  An arpeggio is basically the notes of a chord played sequentially.

Below are the scales and chords for each degree of the Melodic Minor Scale:

​The Melodic Minor scales are:
I  - Melodic Minor (R, 2, b3, 4, 5, 6, 7)
II - Phrygian #6 (R, b9, b3, 4, 5, 6, #6)
III - Lydian Augmented (R, 2, 3, #4, #5, 6, 7)
IV - Dominant #11 (R, 2, 3, #4, 5, 6, b7)
​V - Mixolydian b6 (R, 2, 3, 4, 5, b6, b7)
VI - Locrian #2 (R, 2, #2, 4, b5, #5, b7)
VII - Super Locrian (R, b9, b3, 3, b5, #5, b7)

The accompanying chords are:
I  - Min-Maj7 (R, b3, 5, 7)
II - Min #6 (R, b3, 5, b7)
III - Maj7 #5 (R, 3, #5, 7)
IV - Dom.7 #11 (R, 3, 5, b7)(#11)
​V - Dom.7 b13 (R,3, 5, b7)(#13)
VI - Min7b5 (R, b3, b5, b7)
VII -Min7b5 (R, b3, b5, b7)
​
I recommend starting with the Melodic Minor arpeggios in the middle section of the PDF.  Take four or five days and run over the arpeggios for one mode (probably start with Min/Maj7) in all the different r6 mode boxes.  Maybe put on a relevant backing track and definitely a metronome.  By the fifth day, you should really concentrate on connecting between the boxes and try to work horizontally or diagonally.

After you have the arpeggios, the scales are just the rest of the notes to flesh them out.  Start with the most useful scales for playing over Dominants, like the Lydian Augmented and Super Locrian.

Finally, learn to run all the arpeggios within a particular mode box.  This will reinforce both the scale pattern and the diatonic progression within the Melodic Minor.

While you are not going to necessarily find a lot of complex harmonic movements of the Melodic Minor in Jazz tunes, learning the diatonics of the Jazz Minor will give you greater facility at minor two-fives and the ability to super-impose these scales in other applications.

The world of harmony as explained by a Barry Harris creation story...

First there was nothing.  From nothing, God created the chromatic scale -- the world for all music to inhabit.

​The world of the living is 12 notes:
World = Chromatic Scale
C, C#, D, D#, E, F, G, G#, A, A#, B

The world is divided in half, creating Man and Woman. Each of them takes 6 tones of the world.
Man: C, D, E, G, A
Woman: C#, D#, E, G, A, B

There are three babies from these parents -- all diminished. Each diminished receives 2 tones from man and and 2 tones from woman whole-tone scales. The formula for diminished is 1, b3, #11, bb7(6).  The b3 and bb7 are 'chromosomes' from the opposite parent.  All diminished scales are inversions of one of these three sets of notes.

C, Eb, Gb, A
C#, E, G, Bb
D, F, Ab, Cb

The 'Man' and 'Woman' Parents (whole-tones) are the first major scales.  They have Major 3.
Children (diminished) are the first minor scales.  They have Minor 3.

So far we know there is 1 chromatic scale.
There are 2 whole tones scales.
There are 3 diminished scales.

Those 3 diminished babies (birthed by the two diminished scales) will now have babies.  The first baby is the dominant.  You get this baby by altering one "chromosome" aka, lowering one tone a half-step.  

Dominants (1,3,5,b7) - are diminished with one tone moved down a half-step.  Each diminished can have four baby dominants. 

Example, Cdim can have B7, D7, F7, Ab7 babies.

C, Eb, Gb, A becomes
B [C down half-step], D#(Eb), F#(Gb), A =  B7

C, Eb, Gb, A becomes
D, Gb, A, C = D7

C, Eb, Gb, A becomes
F, A, C, D#(Eb) = F7

C, Eb, Gb, A becomes
Ab, C, Eb, Gb = Ab7

The diminished 'scale' is created putting two of the three diminished arpeggios together -- all the chromosomes of a diminished, and all the tonics of the baby dominants.  Following the Root world of C, that would be:
C, D, Eb, F, Gb, Ab, A, B

This is known as the 'Whole-Half' Diminished scale which starts with a whole-tone jump followed by a half-tone jump.  This gives us a Major 9 and a Minor 3.

All the diminished children (birthed by the two Whole-Tone scales) have babies.  The first baby is the Dominant.  You get this baby by altering one "chromosome" aka, lowering one tone a half-step.  

Dominants (1,3,5,b7) - are diminished with one tone moved down a half-step.  Each diminished can have four baby dominants. 

Example, Cdim can have B7, D7, F7, Ab7 babies.

C, Eb, Gb, A becomes
B [C down half-step], D#(Eb), F#(Gb), A =  B7

C, Eb, Gb, A becomes
D, Gb, A, C = D7

C, Eb, Gb, A becomes
F, A, C, D#(Eb) = F7

C, Eb, Gb, A becomes
Ab, C, Eb, Gb = Ab7

If you raise a tone of a diminished a half-step and the baby you get is a Min6 (1, b3, 5, 6)

C, Eb, Gb, A becomes
Gb, A, Db[C up half-step], Eb =  Gbmin6 (Eb-7b5)

The Half-Diminished and Minor 6 arpeggios are inversions of each other.

Raise two tones of a diminished a half-step and the baby you get is a Maj6 (1, 3, 5, 6)

C, Eb, Gb, A becomes
A, C#[C up half-step], E[Eb up half-step], F#(Gb)  =  A6 (F#min7)

The Major 6 and Minor 7 arpeggios are inversions of each other.

Lower two different tones of a diminished a half-step and the baby you get is also a Maj 6 (1, 3, 5, 6)

C, Eb, Gb, A becomes
D[Eb down half-step], F#(Gb), A, B[C down half-step]  =  D6 (Bmin7)

From the Chromatic split you get the Whole-Tone.
From the Whole Tone's intermingling, you get the three diminished.
By moving one or two tones up or down from the diminished arpeggios, you get all the Major 6, Minor 7, Half-Diminished, and Dominant arpeggios.

From each diminished:
lower one tone a half-step = dominant
raise one tone a half-step = min6 (min7b5 inversion)
raise two different tones a half-step = Maj6 (min7 inversion)
lower two different tones a half-step = Maj6 (min7 inversion)

I made this chart to highlight the Essential Chord Tones (ECTs) for each chord in a diatonic progression relative to the numbers in the Key scale (Ionian Major).  My shorthand for this concept is the "Diatonic Exchange Rate." 

When you play the root of the ii chord, you are just playing the second note of the Key scale.  The third of the ii chord is simply the 4 of the Key scale.  If you think of just these number for each chord in the progression, you can focus on the intervals of the Major scale instead of thinking about arpeggios relative to the Major scale.

I thought this might be helpful to come back to in light of chord solos.  In a chord solo, we have a melody, say on the 'B' string.  For each note we want to accompany with a chord, we have to find at least one ECT common to the chord for the rest of our fingers.  For a ii chord, we would really implicate a minor strongest if we have the flat 3rd of the ii.  Instead of finding the root of the ii and then finding its b3, I would rather just go directly to that note, which happens to simply be the 4 of whatever key I'm in. 

The chords are ordered in 4ths/5ths, common to progressions in Western music.  If you go bottom to top, you are moving in 4ths.

On the second page I grouped the ECTs in order of precedence.  Minors differentiate themselves from Major by virtue of the b3, where as Dominants differentiate by the b7.  You will see a pattern here: moving in 4ths, the third is the seven of the next chord in the sequence.

In the PDF below, I have diagrammed the arpeggios in each 'mode box' for diatonic chords with the 'diatonic exchange rate' pasted on each note.  I excluded the IVmaj7 on the first page for room, but it is diagrammed on page 5.  I also added some extra diagrams for altered dominants.

According to Carol Kaye, most jazz soloing was developed in the forties and fifties off chords, not scales.

The chromatic, major, minor and other scales were used more as 'traveling notes' to get to essential tones and arpeggios.

I am making an effort to stop visualizing in scales and start visualizing arpeggios.  Take Cmaj, as played with C on the third fret of the 5th string.  I immediately recognize there is a box there shaped like the root-6 Mixolydian scale pattern.

But now I'm trying to learn how arpeggios sit in this 'box' for the 'ii' chord, the 'V' chord and the 'I' chord.

You can practice the diatonic sequence within this box, just using arpeggios.

Cmaj7 (I), D-7 (ii), E-7(iii), Fmaj7(IV), G-7 (vi), and B-7b5(vii).

The chart below shows the sequence within the root6 Mixolydian box.  Practice the arpeggios starting with the root and work your way through the sequence (I, ii, iii, IV, V, vi, vii).  Say out loud what chord you are going to play next (i.e. 'ii chord').  Then say the interval as you play each note of the arpeggio.  Also practice these arpeggios starting with the 7th interval moving in the diatonic sequence.

Once you know the arpeggios related to each other in a 'box', you can start playing with lines in a 2-5-1, visualizing each arpeggio within this box.  After that, move to another 'box', like the root6 Ionian box, and repeat the exercise -- playing arpeggios in the diatonic sequence.  Then play the arpeggios for a 2-5-1.

Once you have a good visual feel of the arpeggios and their intervals in a 2-5-1 sequence, try a 3-6-2-5-1 sequence.

Why did I stagger the sequence in the chart above so oddly?  Let's break down the diatonic sequence a little more.

The minor iii chord can substitute for a major I chord.  Play each of the arpeggios and listen for yourself.

Think of the iii minor as part of the I.  This is why the 3-6-2-5-1 works as a turnaround.  It starts on iii which is like starting on I, passing in 4ths on the cycle back to the I.

Similarly, the major IV, is part of the ii chord.

The vi chord is also part of the I one chord -- the arpeggio of vi7 works out to I6 -- a Major 6 chord.

The half-diminished vii can be thought of as a dom.9 chord.  A common guitar 2-5 is to play, say A-7 with the root on the bottom, then move the b7 a semi-tone down to create a D9 chord, which is essential the min7b5 vii chord of G.  Try playing the B-7b5 arpeggio over the D9 and you will hear.

In the chart above you can see these relationships horizontally.

You can also play a min7 arpeggio of the ii over the min7b5 arpeggio of the vii (e.g., A-7 over F-7b5).  The min7b5 chord is the 'ii' of a minor ii-V-i progression.

Learning this will help you see substitutions more clearly.  Whenever you have a minor, just think of it as a 'ii' chord.  That means you have a 'iii' minor a whole tone above that and a relative 'IV' major a semi-tone after that.  This is what Carol Kaye calls the 'slide rule' effect. 

You can 'reference your triads' to see what chords work over a change.  For instance, if you do your triads for G7 (start on the 6 string root), you work your way up and see that G7 works with D-, F, A-, C, E-, G, B-b5.   You can play D- over G7 -- think about the common vamp between the D-7 and a G9.

I am back to learning arpeggios again, this time I'm focusing on just learning 4-note arpeggios, trying to "anchor" them to the diatonic 'boxes' I am thoroughly familiar with.  I'm practicing solos by quickly finding these arpeggios with each chord change and also visualizing the corresponding mode shape learned through the 'CAGED' method.

For songs with faster changes, there isn't time to play a two-octave arpeggio, so learning these 'bite-sized' versions let me nibble at a change before it's gone.

I'm using 'iiR5' to connote where the root of the 'ii' falls on the fifth string within the diatonic boxes I've memorized.  The box 'r6 Mixolydian' is a scale shape I visualize, a 'box' which is equivalent to the Mixolydian mode where the root is on the sixth string.  I know the 'boxes' for Ionian, Dorian, Phrygian, Mixolydian and Aeolian modes with a sixth-string root.  I learned these boxes through the CAGED method.

Part of my practice is playing an arpeggio and finding a corresponding mode 'box'.  As minor chords can either be the ii, iii or vi -- they correspond to different modes, and different 'anchors' on the diatonic boxes.

Another part of the practice is staying within a box and finding the ii and it's corresponding arpeggio.  Then find the V and I.