~ sequence ~ permutation ~

diatonic cycles
descending 3rds moving up stepwise
bbbbcbab / bbbbcbag / chant
 
 
 
 
 
 
 

~ phrasing ~

~ antecedent ~ consequent ~

'the art of artistic balancing melodic ideas, cycles of pitches and finding the flip side ...'

melody
chords
motive
h
h
subdivide

"To avoid criticism ... do nothing, say nothing, be nothing." Elbert Hubbard

1 3 2 4 3 5 2 ... 1 2 3 2 1Tranes

d

St's go ... sequence. Is the

INTERVAL PATTERN OF OPENING LICK

IBID

IBID diatontoc etc.

 

understand diatonic
1 4 5 major and minor
relatives and modes
scales to arpeggios
arpeggios to chords
color tones and style

major over a One chord 765654543432321ala I Remember April

done links to . Is the

INTERVAL PATTERN OF OPENING LICK

IBID

IBID diatontoc etc.

 

understand diatonic
1 4 5 major and minor
relatives and modes
scales to arpeggios
arpeggios to chords
color tones and style

Art ~ theory keys. Is there a series of musical theory keys, that studied roughly in listed order, combine to unlock an inner perspective that builds a foundation for endless explorations for the curious and evolving musical artist? There could very well be.

understand diatonic
1 4 5 major and minor
relatives and modes
scales to arpeggios
arpeggios to chords
color tones and style

In principle. A sequence is an order of events that form a loop.

A permutation is simply a rearranged variable of the elements in a sequenced loop.

understand diatonic
1 4 5 major and minor
relatives and modes
scales to arpeggios
arpeggios to chords
color tones and style
http://www.jacmuse.com/artistictechniques/sequence.htm

Musical sequence / permutation:
Composing music is sometimes said to be “10 % inspiration combined with 90% persperation.”
The ideas and discussions which follow address this 90% persperation aspect of the art of musical composition. Whether the composed music is written out and perfected by rewrite or spontaneously improvised and perfected by practise, similar principles for thematic development are involved.
To “create refreshing melodic ideas and develop them thematically”, that is cool. Improvising artists can prepare themselves for the spontaneous emergence of nice ideas by internalizing fundamental principles of permutation and the sequencing of melodic ideas. When the nice melodic idea arrives via “10% of inspiration”, there is still 90% of coolness to extract out of the lick by various means.

“Sequence" is defined here simply as an "order of successive events", each event musically termed a "episode” (gl) within the sequence. To "permutate" is to simply to take one idea and create other ideas from it. This is done by simply rearranging the original elements. For example, the letters:

(A B C) permutates to (C B A) and is sequenced into (A B C) (C B A) (A B C) (C B A) etc.

In the above example we have simply reversed the order of the “elements”, creating a “permutation” of the original “core” (gl). We then “sequenced” this core by creating a series of “episodes”, each of which mirror elements of the original components. The newly permutated idea oftentimes retains a semblance of both its theoretical structure and emotional / intellectual direction. The recombination of musical elements from a principle theme or variation is usually termed to “permutate.” Linking two or more occurences of a theme, variation or permutation together potentially becomes a “sequence.”

The format which follows simply extracts “cores” of ideas from each of the various melodic resources so far discussed and permutates them through various “filters” (gl). Main focus is given to the major / Ionian mode, the major triad and the minor / Aeloan mode. Theses two distinctive groups creating the major and minor tonal environments and countless melodies. The “filters” are various diatonic, chromatic or intervalic “treatments” (gl) that we “permutate” our melodic idea through, searching for new versions of coolness. Here is a chart listing potential melodic resources and permutation / sequence “filtering” possibilities.

“cores” (created from) permutated / sequence filters (treatment of cores)
one idea / rhythmic simply repeated over and over (vamp)
sounds of nature emotional environment of the tune
melodies of songs / pitch structure of the tune / form
major scales diatonic intervals: 2nds, 3rds, etc.
minor scales chromatic motion/ /enhancement
triads / arpeggios cycles of thirds / fourths / fifths etc.
guide tone lines sequential combinations of intervals

Composers of music create melodic motifs and develop them into compositions. Players interpret the music by learning the core and filtering it through the structure of the tune. Choose a melodic resource, create a “core” melodic idea from that group of pitches and “permutate” that idea through a “filter.” If this seems a bit text book, it is. The key to collect here is that upon finding a sound we think is cool, we can determine it’s “core and filter”, and by knowing these aspects , employ to our best advantage. The above list of musical elements is part of what our college professor used to call “grist for the mill.” I think what Dr. Miller was getting at was simply that part of the initiation and training of the improvising musician was to explore through the artistic elements available. To experiment and exercise with the resources thru prolation, to look for new ideas and create new melodies. One may rarely if ever spontaneously “improvise” a chromatic sequence of ascending triads, but by shedding this possible permutation off the bandstand, a new idea might emerge. A new idea that does become part of a players vocabulary and perhaps the motif of a new song. Exploring 1: Perhaps the simplest kind of sequence is also the oldest? One rhythmic idea with one pitch which is repeated, like a chant, over and over. Example 1.
In continiously repeating a sequence, a “groove” can “come to life” which has the potential to be a bit hypnotic to the human psyche, settling down the thought process and clearing the way for pure thought. The first two measures in ex. 1 above create a mini “call and response” (gl) musical phrase, which is in of itself an age old basis of communication. As part of spiritual ceremonies, the “call” by one group of voices that prompts a “response” by another, unites folks spiritually together. Joining voices in this manner and repeating one idea as a chant becomes very powerful, a living force of collective consciousness, one that can “lighten” the soul and burden of the believer. Here is an elemental call and its response in the minor tonal environment. Example 2 in “F” minor.
Blues music and its basic 3 chord / 12 bar form could also be viewed as a “filter” for permutating and sequencing ideas and when coupled with the principles of the call and response format, create a well worn format for expression. Here is the above idea “filtered” thru the 12 bar Blues form. Ex. 3

Lets filter the above 12 bar Blues through the major tonality filter. Example 4.

A bit vanilla huh? Lets combine ex. 3 and 4 together. Example 5.

Starting out with just a simple rhythmic idea in ex. 1, we permutated and sequenced our idea through various “filters.” First, we created a “call and response”, then formatted this idea through the minor Blues filter. That was a bit disappointing so we tried the major Blues filter. That version was deemed to “vanilla” so we tried the combining of the two tonality filters and created ex. 5. Al-though repetitious, ex. 5 is a basis for evolving a more complex melody, if so desired and would “work” if I needed to come up with a new Blues “head” right now! Does it all come down to simply exploring and experimenting? Is playing one pitch rythmically equally as powerful as a million?
Exploring 2: One important use of permutation and sequencing is in creating “themes and variations.” So much of our physical and spiritual world is based on a central “theme” from which are created “variations.” In this scenario, we simply take the elements we like from our “melodic idea” and recombine or arrange them seeking a new melodic idea with a similar emotional and artistic statement. Going back to our first melody, Handel’s “Joy to the World”, lets create a variation on this theme using techniques of permutation / sequence. Here is the melody / guide tone line. Ex. 1

First to extract the first 3 pitches and sequence this core into an 8 bar phrase. Ex 2.

Here the rhythm pauses in bar 15 and 19, the sequencing is interupted. Ex. 3.

Another shift in the rhythm and the line is a smooth, permutate of the first pitches and idea. Ex.4

This next pass combines elements from each of the above ideas. The following idea is the “polished” variation on the original 4 bar theme. Example 5.

So now I have two melodies. One being a variation on the other, both with a similar expression within a similar emotional context. Improvising musicians love to do this. Its what they do best. Create one idea from the next. Truly a very exciting thing to do! Whatever one’s “natural gift” of coming up with cool melodies, when paired with the study of permutation and sequence, we set the initial guidelines for shaping and emergence one’s musical “voice.” The above transformation from one melody to the next is partly a process of selecting an idea, phrase or aspect of a melody that you dig, then trying different ways to abuse that “cell” or “motif” to suit your musical tastes. Historians suggest that L.V. Beethoven is the master of development, who probably right next to Duke Ellington inspired the lick that “music is 10% inspiration and 90% persperation!”

Exploring 3: Running a core theme through the format of the tune has historically been a favorite activity of the improvising Jazz musician. So much like theme and variations but now more strongly coupled with a sort of “road map” as to where the tune is going. In the following examples, I extract a motif from my composition “I Can’t Believe You Didn’t Know”, see page 14, and adapt it through the first 4 bar “A” section of the tune. This adaption is concerned with the written harmony of the tune, permutating the pitches of the melodic idea as it moves through the chord changes, looking at some options. Termed playing “inside” the chord changes, our improvised melody can to a certain degree be organized by the harmony of the tune. This is a very joyous, challenging and popular activity for the improvising creative musician generally referred to as “soloing.” (gl)
Here is the “as written” first 4 bars, the guide tone line is the half notes. Swing @ 160. Ex.1

F major G min A min Bb major
With such a strong guide tone line and harmonic direction, one way to start our “solo” might be to simply diatonically encapsulate the pitches of the guide tone line melody of the first 4 bars. Ex. 2

F major G min A min Bb major
Or non diatonically. Example 3.

F major G major A major Bb major
Big difference huh? Overall, these last two examples are quite similar, I’ve simply slipped in the “major triad filter” and all of a sudden things change, moving “outside” (gl) of the diatonic realm. Try to slip in different filters when your shedding, see what happens. If you come up with something nice, run it thru the cycle of fourths, if it still is “holding up”, use it in a tune. This may become a “signiture” lick for you, a part of your vocabulary which creates your “voice.”

Diatonically arpeggiating the written chord changes is always a sure way to go. Example 4.

F major G min A min Bb major
Permutation of the above arpeggiated idea. Example 5.

Substituting additional harmonies into the written line to further expand the melodic possibilities can be a big part of ones approach. Either diatonic or nondiatonic pitches are commonly used. Ex. 6.

F maj F# dim G min G# dim A min D 7 Bb maj 9
In the above example we simply place “passing chords” between our written chord progression and outline the colors in the melody, spicing up our harmonic progression and creating new options.
Exploring 4: Lets go back to our first melodic idea and extract a new guide tone line. Ex. 1

In this pass, lets extract the just the first pitch of each of the four measures of this phrase. Ex. 2

As we can see in the above example, the “C” major triad emerges from the line, (“C”, “E”, “G”). With it’s three part structure, this powerful building block is ideally suited for endless permutation and sequencing possibilities. Played confidently, triads always work. Lets create some lines by permutating and sequencing the major triad through various filters (gl) or treatments. The following eight examples build triad configurations on the diatonic scale degrees of “C” Ionian.

Ascending diatonic triads moving stepwise. Example 3.

Permutation of above idea, simply reversing direction of every other arpeggio. Example 4.

New permutation of the three note triad. Example 5.

New idea, starting on the third of the chord, triad or arpeggio. Example 6.

Permutation of the above idea. Very popular model. Example 7.

New idea, starting on the fifth of the chord, triad or arpeggio. Example 8.

Permutation of the above idea. Example 9.
Run the music of examples 3 thru 9 through the cycle of fourths.
New idea for permutation of diatonic triads, starting from the fifth. Example 1.

Permutation of the above idea using a four note “cell.” Example 2.

The following ideas sequence major triads through various use “filters.” These filters are interval based and simply move major triads around. Ascending triads by half step. Example 3.

Ascending triads moving downward by whole step. Resequence this idea moving upward. Ex. 4

Cycle of fourths. Major triads moving by perfect fourth. Resequence w/ cycles of fifths. Ex. 5

Cool min. 3rd / fourth / 1/2 step resolving cadential motion. Common triadic turnaround. Ex. 6

J. Coltranes minor third / fourth triadic post bop symmetry. Quite fun in brighter tempos. Ex. 7.

Triads play a huge part in all styles of American music. Jazz melodies such as “In the Mood”,
“All of Me”, “Cherokee”, “Air Mail Special”, “Spring Can Really Hang You Up the Most”, “Birdland” and “Giant Steps” are just a few compositions have melodies that are clearly structured around tonic major triad pitches. From Pop Jazz dance tunes to complex harmonic and melodic organization, triads are a key melodic component. So cool. Abuse the above ideas to initially explore theoretical ideas working with triads, then begin experimenting in your own directions.

Filters used above; diatonic, chromatic, whole step, perfect fourths, minor thirds / fourths. Are there others? Of course, the mix and match possibilities are limited only by our own imaginations.
Explore 5: Going back to our first theme, Handel’s “Joy to the World” is in essence a major / Ionian mode. Lets look at easy diatonic permutations and sequences created from this group of pitches.

Intervalic sequence of two pitches in ascending thirds. Example 1.
Permutation of the above idea. Simply changing directions. Example 2.
Permutation of the above idea. Look to the interval studies section for more intervalic ideas. Ex. 3
Here is a simple three note “core” moved diatonically by step. Example 4.
Permutation of the above idea. Example 5.
Permutation of the above idea. Example 6.
Here is a common four note group (1,3,4,5) moved upward diatonically by step. Example 7.
Permutation of the above idea. Example 8.
Permutation of the above idea. Example 9.

As time permits, run ex. 1 thru 8 thru the cycle of fourths, fifths, chromatic and whole tone filter(s).
To musically permutate and sequence melodic ideas while avoiding redundancy is the real challenge. Especially if the cool “cell” comes along while playing live, that’s always fun. Again the idea of creating one melodic idea per chorus and permutating and sequencing that idea through the format of the tune. Big challenge. To continually develop the idea we just played while telling a story which builds and climaxes. Yes!
Explore 6: Lets extract just the major pentatonic group from the color above, create a guide tone line, extract a core idea and filter it through our list of permutation and sequence techniques. Ex. 1
Our core idea comes from the first 2 bars above, which is then diatonically sequenced. Ex. 2
Here the above core is sequenced through the cycle of fourths. Example 3.

Permutating and sequencing the core idea upward chromatically. Example 4.
Permutating and sequencing the core idea downward by whole step. Example 5.
Permutating and sequencing the core idea downward by whole step. Example 6.
New three note idea diatonically sequenced. Example 7.
Permutation of above idea. Example 8.

As a solist in the Jazz format, coming up with one nice core idea from the original melody and “working” that one idea through the format of the tune is historically an important part of the live performance format of Jazz music. “Working” one core idea per chorus and permutating that
idea into each successive chorus helps to tell important stories and build strong climaxes.

Sequencing musical ideas. Simply in that this is the same pitch above our root as the perfect fourth, just now moved up an octave. Again we bump into the idea that with the colortones, the music theory of the natural diatonic 11th is usually more about chords than melody. Thus, having an 11th usually implies that we also have some sort of 9th in our chord. And having a 9th implies we've a 7th in the chord as well. 'The finger bone's connected to the hand bone, the hand bone's connected to the wrist bone' ... all in a perfectly closed loop. Ex. 1.

chords
melody
loops of pitches

A melodic cell. This half step above the tonic is often simply referred to by its numerical designation. Generally we'll use the sharp (#) when ascending away from the tonic and the flat (b) designation when descending towards our tonic pitch. I also call this pitch a blue note, but I'm probably the only one that does.

half step
music notation

melody

chords
rhythms

Theory names: This half step above the tonic is often simply referred to by its numerical designation. Generally we'll use the sharp (#) when ascending away from the tonic and the flat (b) designation when descending towards our tonic pitch. I also call this pitch a blue note, but I'm probably the only one that does.

half step
music notation

Symmetrical motions. This half step above the tonic is often simply referred to by its numerical designation. Generally we'll use the sharp (#) when ascending away from the tonic and the flat (b) designation when descending towards our tonic pitch. I also call this pitch a blue note, but I'm probably the only one that does.

half step
music notation

Encapsulate pitches. This half step above the tonic is often simply referred to by its numerical designation. Generally we'll use the sharp (#) when ascending away from the tonic and the flat (b) designation when descending towards our tonic pitch. I also call this pitch a blue note, but I'm probably the only one that does.

half step
music notation

Where in the music / sharp # 1. There are a couple of things we generally do with the sharp One. Melodically we'll often use one pitch to anticipate by half step the start of our line. We can do the same thing with a chord. Generally we call this simply a half step lead in. Harmonically, upon the sharp One scale degree we build a fully diminished 7th chord. This becomes a passing chord to Two. Example 1.

half step lead-in
diminished 7th chord
passing chord

Chromatic down from Five in a blues. There are a couple of things we generally do with the sharp One. Melodically we'll often use one pitch to anticipate by half step the start of our line. We can do the same thing with a chord. Generally we call this simply a half step lead in. Harmonically, upon the sharp One scale degree we build a fully diminished 7th chord. This becomes a passing chord to Two. Example 1.

half step lead-in
diminished 7th chord
passing chord

Although we might find this event in a blues or pop tune, it's rare indeed. So that leaves jazz, where everything can find a place to hang its hat and contribute. I often term the sharp One diminished the 'great accelerator' for its ability to get things cookin' in a hurry, creating that sense of forward motion in the music.

great accelerator
forward motion

As a blue note, blues Cats often just want to push the tonic pitch as far as it'll go, looking for the nuance between the pitches. Even a super wide vibrato could be sharp One. Did someone say whammy bar?

blue notes
whammy bar

Where in the music / b2. Heading in the other direction, descending towards the tonic, there are two solid events that are very common in the literature, both originally based on dominant chords and mostly in the Jazz stylings. One is in the Bossa Nova and the Latin Jazz styles, there is a core vamp that romps from One to flat Two. This is commonly called a montuno.

literature
dominant harmony
vamp

The montuno. Latin influenced montuno, as its name implies, comes from the mountains. So we might conclude it has origins in the folk music. Of possibly Cuban descent, it has been mixed into the salza (sauce) of the Latin grooves we cherish today. With endless variations and its heart in the clave beat, musicians of many stripes dig the basic vamp to help get the dancers up. While used in this discussion to describe a flat Two located musical device, this one location is just the tip of an iceberg of coolness for those still in the hunt :) (1)

clave beat
vamp

#23 ~ The tritone sub game changer. Sorry for the cliche lick but this 'b2' rascal can surely be a game changer for the evolving guitarist. For there is a rather crucial harmonic motion and concept found with flat Two, related to the tritone substitution concepts beloved by jazz artists.

tritone subs
cliche licks
tritone substitute

In this event, we simply build a dominant chord whose root pitch is a tritone interval away from the written Five chord. It'll work with any dominant chord built on any scale degree of any key center, major or minor. Theory wise, this 'tritone sub' chord substitution results in a dominant chord built on flat Two and resolving downward by half step to our chosen tonic pitch.

dominant chord
tritone interval
written chord
scale degree
key center

Where in history. These types of half step motions probably entered the American pop sounds during the Ragtime era of the later 1880's and forward. From there forward, it would not be uncommon anywhere in the blues and jazz literature, both of which were a solid part of America's pop through the 1940's.

half step motions
Ragtime
Swing
V7b9

The sharp One diminished is most likely from the 30's as the American swing era took hold. The tritone substitute probably from the late 30's / early 40's. For it was around this time that the diminished chord / V7b9 enters more predominantly in the music.

Ragtime
Swing
V7b9

Guitarist Charlie Christian might very well have had a strong hand in developing and establishing the tritone substitute. His 1941 "Airmail Special" contains a bridge of chromatically descending fully diminished 7th chords, possibly replacing the cycle of dominants common in that era as modeled after the 1930 hit "I Got Rhythm," by George and Ira Gershwin, whose chord progression and form eventually became know as 'rhythm changes', providing a model compositional vehicle for jazz artists.

Charlie Christian
Airmail Special
Gerswin Brothers
rhythm changes
form in music

The Latin influenced montuno, as its name implies, comes from the mountains. So we might conclude it has origins in the folk music. Of possibly Cuban descent, it has been mixed into the salza (sauce) of the Latin grooves we cherish today. With endless variations and its heart in the clave beat, musicians of many stripes dig the basic vamp to help get the dancers up. While used in this discussion to describe a flat Two located musical device, this one location is just the tip of an iceberg of coolness for those still in the hunt :) (1)

clave beat
vamp

Interval. The theoretical distance between the tonic pitch and sharp One / flat Two is a half step, one fret on our guitars. Theoretical terms describing this interval include augmented unison and minor second. Ex. 1.

augmented unison
minor second

Melody with b2. In this next idea our b2 resolves upwards as a leading tone into Two, which is clearly outlined by the eighth note arpeggio. Five follows then the resolution to the 5th ofg our tonic C major. Also, using an off beat pickup rhythmically helps too create the sense of forward motion, energizing our lines. Here starting on the 'and of 4' is cool and classic. Example 2.

pickup

In the above idea we do use the # One pitch for the half step lead in but for sure any of our pitches can often provide the a similar lift to the line. Five to One is common. The blue third to major third also. Any and all are available of course. The half step motion into the root of a new chord, making the pickup note its leading tone, all landing on the first beat of a new measure is all rather common throughout the styles.

Sing the line. We can get a real feel for the energy of the sharp One idea by singing the line we're going to play. Often termed 'scat' singing, to sing the line then play the line helps insure our ideas speak from our heart.

Harmony. In this next idea we simply use the half step lead-in for our Two / Five / One cadential motion. Sharp One into Two, then from above down by half step to Five, the again from above into One. As guitarists, we'll generally use the exact same chord voicing for each of our half step motions. This type of voice leading is also often termed parallel motion or plaining in the keyboard instruments. Example 3.

half step lead in
Two / Five / One
cadential motions
chord voicings
parallel motion
root motion by half step:
C# to D
Ab to G
Db to C
resolution

The half step lead in as depicted above is one powerful component. While mostly in the realm of the jazz artist, it does find its way into the blues, especially when cats are working the 12/8 magic. As a rhythmic component, when used over a steady quarter note walking bass line and 2 and 4 high hat drum groove, the half step lead in allows the chordal instrument to judiciously sound their chords in anticipation of the bass and drums, oftentimes just a wee bit out front, getting things to swing just right.

12 / 8 magic
walking bass
2 and 4
swing video

Advanced players can and will often use this technique on all of the changes when performing. Add in substitutions and the various colortone possibilities and things can expand dramatically with just a few components in place. Of course, so much of this coolness is written into the jazz language and literature.

substitutions
color tones
jazz literature

Why in some cases, the American jazz music is so well crafted that all we have to do sometimes is push the written buttons on the page and the magic just pours right out, the swing is so deftly built right in :) The old time American classic "Careless Love" can truly be just such a song.

reading music

Sharp One diminished chord / major key. This next idea features what I often call the great accelerator of our more advanced chord progressions. Kind of crazy how a relatively simple physical motion for guitarists can create such dramatic results in the positive energy and sense of forward motion we can gain. Example 4.

diminished chord
advanced chord progressions
forward motion

The above chord voicings are pretty standard, stock voicings. All of the chords are root position and would create a big, solid harmonic motion. These types of voicings in such close proximity to one another work fine in many musical settings; with a big band, in brighter tempos, or in rhythm sections with no other chordal instrument.

voicings

In a big band setting, we're probably chomping four beats per chord in 4/4 time, a la Freddie Greene, to help drive andmotor the pocket along. There are initially three sets of voicings for this progression for the evolving guitarist, each set capturing the root position, chromatic bass motion of the changes and starting on the 6th, 5th ( as in the example just above ) and 4th strings respectively.

chomping
Freddie Greene
# One diminished chord progression

Sharp One diminished color in the line. Here's a melodic idea slipping in the sharp One diminished motion as outlined in the chords just above. Example 4a.

diminished scale shape
five shapes with # i dim 7 color

C maj 7

C# dim 7
D -7
G7b9

Scale shapes. Nice color yes? Inserting the diminished color surely spices up the line. We've a couple of additional ways to use this sound, the main one being in how there is a fully diminished 7th chord in the upper part of V7b9. Gaining this insight of b9, coupled with the leading tone potential of the diminished color, is oftentimes the next giant step in the theory for the advancing jazz leaning guitarist.

V7b9

In jazz guitar, one pedagogical approach is to master seven basic shapes. Five cover the major / minor / modes and one each for augmented and diminished colorings. From these physical shapes we can generate both our most common arpeggio and chord shapes. We then begin the process of 'mix and match' between the shapes and search for the coolness within.

pedagogy

Sharp One diminished chord / minor key. Crazy as it sounds, theory wise we use the same diminished 7th chord pitches for both our major and relative minor groups with one key center. The major 6th interval from major to relative minor inverts to a minor 3rd, the core interval for constructing our diminished colors, thus our chord pitches are identical. This next idea mirrors the above sharp One diminished motion but in the minor tonality. Example 4b.

Sharp One diminished 7th = Six 7b9. This sharp One diminished passing chord motion in a minor key exampled just above is not all that common in the literature. Actually, can't seem to recall ever seen it or playing it. Theoretically of course everything is possible. What is in the literature is motion from a tonic minor One chord to Six 7b9 which is usually then followed by Two-7b5 to V7 altered then resolving back to One.

V7b9
literature
V7 altered

This is simply the very common and oh so essential motion of the One / Six / Two / Five chord sequence but here in a minor key, making it a wee bit more obscure. Let's examine the pitch relationships between the sharp One dim 7 chord ( #i°7) and the Six 7b9 (VI 7b9) chords. Example 4c.

1 / 6 / 2 / 5
arpeggio degrees
root / 1
minor 3rd
diminished 5th
diminished 7th
.
( #i ) C# dim 7
C#
E
G
Bb
.
arpeggio degrees
root / 1
major 3rd
5
minor 7th
b9
( VI ) A7b9
A
C#
E
G
Bb

Simply different root pitches? So it seems mon ami. The bass line often tells the tale of a song's story. The chords built on them are often just different parts of arpeggios borrowed from one another. So in the upper part of our Six 7b9 chord we've a fully diminished 7th chord? Yes absolutely. It's very cool color 'built right in' that opens a vast universe of possibilities. We'll not only find this exact situation in the major keys but in all and any of our other various V7b9 chords as well. Here's a solution for subbing Six for # One diminished 7th in a minor key. Example 4b.

mon ami
bass line / the story
diminished chords
V7b9

An essential composition to learn. This last idea includes the opening changes to Thelonius Monk's "Round Midnight."A tune so well crafted and loved by players and listeners alike, that it is probably being played out in the world in a couple of places while you're reaing this. For us guitarists, it is a great melody to play in octaves and also a possible chord melody too. Wes Montgomery had a nice hit with this composition.

jazz tunes
melodies in octaves

Sharp One Blue note. Not all too sure there is such a thing in our theories as a 'sharp One' blue note, maybe it's just a way sharp tonic pitch. Regardless, pushing the tonic north and then some more can raise some hairs and hackles and get the dancers a prancin'. I've seen it time and time again. We are not really talking a wide vibrato here, a la B.B. King. although that approach will surely push the pitch sharp.

blue notes
vibrato
B. B. King

As a jazz flatwound string guy I maybe bend a couple of pitches month. So this degree of bending is generally beyond my way of thinking and doing. Of course my notation software won't go there so we'll have to go to the video tape to find this sweet spot.

# One blue note video magic

The flipside of sharp One is flat Two. We can recreate the ascending sharp One position by simply going the other way; by descending towards our tonic pitch from above. While we know the letter names of the pitches as enharmonic equivalents, and they are the same of course, in theory how we use them and what we build upon them surely plays a role in their 'proper' identity. As a rule of thumb, do sharps always go up and might the flats always move in a downward direction?

enharmonic

Montuno / flat Two. In this next idea, we create a basic montuno vamp that utilizes the tonic to flat Two motion we find within the Latin styles. We not only readily find this motion within the literature but often improvise such vamps as intro's and outro's in performance. Example 5.

intro / outro
jam vamps

These last two voicings are very solid Bossa Nova shapes. When played on a traditional Bossa guitar, the nylon stringed classical guitar, they sound and feel warm, rich and solid. Once comfortable with the shape, try alternating the bass pitch between the tonic as shown in the example and the 5th of the chord, located on the lower 6th string. Oftentimes an easy do with giant results for this is a true core of bossa nova guitar :)

Bossa / Latin chord shapes
alternating bass video

Montuno / flat Two / minor tonality. This next idea gets a lot of milage in jazz, especially in the last couple of decades or so. It also works well going in as an intro or out, as an outro. Here we use the tonic minor 9th to major 9th coloring to set the mood. This type of coloring can work well in all sorts of grooves. Adjust the rhythm as your musical style demands. Easy alternating bass motion with these changes. Example 5a.

9th
grooves

This motion might be a way into developing the ability to making the bar lines go away in your grooves. A tricky thing to do but one that many contemporary Jazz Cats love to do. Guitarist Pat Metheny just might be the original wizard who mastered this bar line magic and then consistently shared it globally. Do note the triangle sysmbol for the Db major chord. Just a shorthand symbol for major. The minus symbol (-) is of course is minor.

bar lines go away

Tritone substitution / flat Two. Of all of the things I've learned over the years with guitar, it's a pretty safe bet that I've gotten more mileage out of the concepts surrounding the tritone sub than any other one theory component. Picking up the concept after a college big band rehearsal from trombonist and true friend and mentor Kirk Lamberti, I remember being simply stunned by a combination of its conceptual simplicity while sensing its eventual consequences on the music.

tritone sub

T'was amazing in how what little I had under my fingers that day dramatically evolved in that one spark of theory newness, creating a whole new level of musical coolness. This important evolution was not only in the tritone sub's cadential sound but somehow ... and this I don't fully understand yet ... it evolved my rhythm / chording / comping to swing ever so much harder. Perhaps this is part of the 'evolution of sleekness' of our musical components that artists discover.

cadential motions

Simplistic beauty. We can initially illustrate the tritone sub in the essential jazz cadential motion of Two / Five / One. All we'll do is replace our dominant / Five chord with another dominant chord type, whose root pitch is a tritone interval away from the written dominant chord. Thus the name of 'tritone sub.' It looks like this in letter names in the key of C major. Example 6.

dominant harmony
numerical chord progression
Two
Five
One
written changes
D - 7
G 7
C major 7
tritone sub changes
D - 7
Db 7
C major 7

Cool? Hopefully fairly easy to do for the most part. In the guitar method section we'll find this basic tritone sub motion in each of our five scale shapes and evolve the whole tamale from there.

Why it theoretically works. Examining the pitches of the two dominant chords, the G7 and the Db7, we can see that the tension creating core of these two chords are the same two pitches. Example 6a.

chord
root
3rd
5th
b7th
G 7
G
B
D
F
Db 7
Db
F
Ab
Cb (B)

Three becomes seven and vice versa. Interesting huh? Not only are the roots of our chords a tritone interval apart but the pitches that work the magic within the chords are also a tritone apart. Those hip to this motion are of course already in the know. Cats just getting to this level of theoretical possibility should experiment with the changes and see if it will work in their music. Regardless of one's current theory hipness, there's a giant evolution of the harmony possible based on this initial chord substitution principle, one that just may be essential to the evolving guitarist within you :)

evolution of the harmony

Chord type / Three and Seven. When we as theorists start to focus in on the third and seventh in our groupings, we open up the potential to discuss chord type, which is simply becomes a numerical way to define a harmonic component's qualities. The core theory of chord type and quality is decided by simply determining the major / minor qualities of the third and seventh within any chord or arpeggio.

arpeggios

Thinking along the lines of chord quality can put us in the theory bonus, as we now get to view things simply by mathematic interval, grouping like constructed components into unique families or categories of sounds and colors. Free from letter names, our theory mascinations know no bounds.

families of chords

Theory cats think along the lines of chord type to; find substitution chords as in the above tritone sub ideas, in streamlining the theory to a numerical perspective, helping to organize the shedding in preparation for perfprmance, in soloing through chord changes as well as over the changes etc.

substitution
shedding / chord type
( start here :)

Chord type in jazz. In jazz music and its performance, and of course depending on the players, time spent together, instrumentation, rehearsal time and the type of gig itself, when players see or think of a G7 chord, potentially lots of options can open up. There's G7 of course and its various voicings, the various color tones associated with the dominant harmony aspects of G7 become possibilities, .

We can extend this idea for all of the chords we might see in the music we are performing. Part of the evolution of a players sound can be to discover such potentialities such as the tritone sub and weave it into their existing palettes.

evolution of the artist

Chord type in jazz. In jazz music and its performance, and of course depending on the players, time spent together, instrumentation, rehearsal time and the type of gig itself, when players see or think of a G7 chord, potentially lots of options can open up. There's G7 of course and its various voicings and inversions, the various color tones associated with the dominant harmony aspects of G7 and their inversions become possibilities, there's substitute chords with their color tones, voicings and inversions and further on into polytonal considerations.

the jazz artist
voicings
chord inversions
color tones
polytonal chords

Our own evolution becomes based on what our ears will accept as cool and correct ... One way to explain this evolution might simply be, that if we took the first chord or chords we ever learned when we first picked up our gits, which for me was probably an open C major into an A minor chord, the "Teenager In Love" chords, and today 40 years later played the various ways I might play C major to A minor today, what I need to ask myself is that even if I knew then what would eventually become the hipper changes I know now, would my ears then have accepted the more advanced chords to function the same way in the music as the chords I first learned? Probably not. Could I have used my jazz voicings of today in that musical setting then? Probably not. So our way of hearing things, what our ears will accept as 'correct' for the music we're creating at any given point, will evolve over the years. This may be the initial case with accepting the flat Two, tritone substitution chord for V7.

"Teenager In Love"
I / vi / IV / V
chord function

Of course the style of music we're playing is often the determining factor in the chords we choose. Maybe that's why I love the jazz language for its ever expansive nature of both discovered and to be discovered array of musical colors. But the digressed discussion here is more about one's own ability to handle the various degrees of stability and tension that our various chordal choices provide. To realize, understand and dig this artistic evolution. Examine the following evolution of tonic function C chords in the major tonality. Example 7.

musical styles
palette
tension / release

From Metallic 5th's ... These chords are, in theory, tonic C chords for the key of C major, for all but the 5th's have a root pitch C and a major 3rd E in the voicing. Thus, they can function as tonal centers in C major. What we as artists are tasked to do, among many things of course, is find the chords that sound the proper degree of stability for the music we are performing.

That way back in the beginning my first C chord of choice was the open C triad. Then I needed a blue 7th chord to hang in the blues music. Then a major 7th coloring to play standards. Then bored with major 7 colors things gradually evolved to became a bossa major 9. Then the polytonal #11 came along. Then that giant Hollywood 6/9 chord and tertian harmony evolved towards quartile stacking. Then through tireless theoretical discovery, that #15 monstrosity.

standards
quartile chords

So what do it mean Jacmuse? Probably that all of this and some spare change might buy us a cup of coffee :) And that our ever evolving ability to accept new colors, as in this example of tonic chord stability, helps us to evolve our art. Having this flexibility may also advance one's abilities to evolve melodies that are initially based on open C chords and reshape them to accept other less stable tonic support.

for the price of a cup of coffee

And of course vice versa, better to understand how to stabilize the higher atmospheric ideas when they come along. To create melodies and music of a less predictable cadential nature which charts out our core theory evolution of our American styles. And that the ability to morph stylistically through the theory can continue to open new doors of creative exploration over the course of our careers. We simply strive to achieve a sense of the boundless potential available with the same basic core group of 12 pitches.

core evolution
12 pitches

In my world, John Coltrane's music is the musical map that outlines the evolution in the tonic chord changes discussed above. Mr. Coltrane's biographers hip us to Trane's work ethic, encouraging my direction of thought of how he simply exhausted things at each level, necessitating the creation of greater and greater challenges in the music he was creating.

Luckily, we have his original compositions to study and recreate his evolution. Luckily we have recorded music that oftentimes includes his 'searching' and the exhausting of possibilities at each level of artistic development. Luckily we have Mr Coltrane's tenor voice and ideas paired right next to Miles Davis' trumpet voice. And side by side, we might better hear and understand, by comparing their generally contrasting improvisational voices, Mr. Coltrane's Trane's searching, exhausting and eventual evolution of the music they were performing.

John Coltrane
Trane's evolution
Miles Davis

Review. The sharp One and flat Two positions in relation to our tonic pitch offer some interesting possibilities in regard to tension and release of the art we create. The diminished color has emerged yet again. The essential jazz tritone substitution has made a first appearance, creating a first step into the advanced evolution of American harmony as rediscovered and further advanced by John Coltrane. The montuno of the Latin / bossa flavors opens up a parallel universe to the straight ahead jazz for our explorations.

I'm always thinking about creating. My future starts when I wake up every morning ... Every day I find something creative to do with my life.

Miles Davis
#1
2
#2 / b3
3
4
#4
b5
5
#5
b6
6
b7
7
8
9
#9
-10th
10th
11
#11
12
b13
13
b14
14

15

#15

Footnotes:

(1)Mauleon-Santana, Rebeca. 101Montunos, p. iv. USA Sher Music Co.,Ca. 1999

(1) Isacoff, Stuart. Temperament ... The Idea That Solved Music's Greatest Riddle, p. 40-42. USA Alfred A. Knopf, New York. 2001

(2)Aebersold, Jamey and Slone, Ken. The Charlie Parker Omnibook. New York: Atlantic Music Corp., 1978.

( start here :)