Generic Shapes of 4 notes: item 9. Examining the span of the GS and associations between them.

Generic Shapes of 4 notes: item 9. Examining the span of the GS and associations between them.

When I looked at these 4 note GS (4GS) and the twenty Rotations (R) that reside in the 5 Primary 4-note shapes, and tried to implement them into playing, I noticed that the span (between the highest and the lowest note of the GS) of each shape had something in common. The span ranges from a 7th interval to that of a 4th, and most of the GS have these common span extremities but with the middle 2 notes remaining creating a different effect or colour. Just learning a few of the sequences, in your ear, should add some melodic richness and strength. It's exciting.. !!


To review: 4GS x 5 Primary GS have been outlined by:

a) 4 pure rotations of each of the 5 Primary GS (inversions in a broken arpeggiated manner) resulting in 20 GS which are defined or measured from the intervals (diatonic/tonal) within it.

b) These 20 4GS then are reckoned from a common root to reenforce the definition of each GS.

Since the span of a 'piano' hand easily reaches a 7th, all the spans smaller than that are accessible too.

Twenty 4GS: generated from the above process (Primary GS are in Bold)

GS1   GS2  GS3 GS4
1235 1247 1367 1456

GS5  GS6  GS7  GS8
1345 1236 1257 1467

GS9  GS10 GS11 GS12
1245 1347  1256  1457

GS13 GS14 GS15 GS16
1234  1237  1267  1567

GS17  GS18  GS19  GS20
1357   1356   1346   1246

The next step is to arrange these into groups according to the span of the lowest and highest notes, starting with 1—7 and generally going down the above list from 1235 — 1357 [correctly: 1246].

Those GS with a span of a 7th:

1247 [GS2]
1367 [GS3]

1257 [GS7]
1467 [GS8]

1347 [GS10]
1457 [GS12]

1237 [GS14]
1267 [GS15]
1567 [GS16]

1357 [GS17]

Those GS with a span of a 6th:

1456 [GS4]

1236 [GS6]

1256 [GS11]

(none from GS-1234 [GS13—16]

1356 [GS18]
1346 [GS19]
1246 [GS20]

Those GS with a span of a 5th:

1235 [GS1]

1345 [GS5]

1245 [GS9]

(none from GS-1234 [GS13—16]

(none from GS-1357) [GS17—20]

Those GS with a span of a 4th:

1234 (the only one).

It might be fun and rewarding to try GS with a common span but with changing inner notes, over a tune.

I think that these ideas are learned and then forgotten. As one solos with a couple of these aspects in mind they may creep in. Over time the relearning and reformatting these shapes will emerge as one plays in spontaneous a manner as possible and then there is some other aspect that has to be learned—and then perhaps forgotten for a while and then learned again to the point perhaps where they are both remembered and forgotten at the same time. I find I have to keep at it if I want the benefits and structure that occur when soloing etc. when 'subconsciously' applying what gets learned (and then gone but not forgotten:). Of course this is part of a longer period process but I usually find that when I play with something from all this that the reward is immediate which deserves a celebrate-tional return to practising these in keys over scales and sequences. Try to learn a small part of this at a time and collect some success along the way. It's working for me if and when I truly apply myself to it.

Se the music graphics below that illustrate the above and with a few other possibilities and aspects as well.

Generic Shapes GS Item 8. Generic Shapes from 20 Rotations of the original (1—20) with 6 Basic Permutations applied over each.

Generic Shapes (4GS) Item 8. R (1—20) applied to 6 BP.

I realize that what I haven't mentioned so far is the application of 4-note-GS to chords/Scales/Improv. Suffice to say that for now that virtually any of 20 GS derived from the 4 Rotations of the 5 Primary 4GS can be adapted to fit over any chord scale from any note of that scale. There may of course for musical reasons, be necessary adjustments and even changing the GS itself or fragmenting it and so on. They can be made available in useful in creative ways. Things have to be worked out. To quote Hal Galper, 'you have to do the process in order to learn the process' (Yeah Hal). I will delve into some ideas on this in a later blog.

I would like to outline each of the 4GS (1—20) in R1, described in the last blog entry, through its 6 BP. I know this seems endless but there are quite a few avenues to explore in 4GS before going on to 5GS and 3GS. So there will be a few more entries coming up. I just remembered that we're talking about 96 GS x 5 Prime GS (A—E) = 480 GS in total. That is a high number on its own but when broken now into how each GS is created from these 5 Primary GS, clarity will emerge: and what fun to work with. I'm liking the idea !!

Taking each 4GS in R1 through 6 BP. Each Row is a 4GS from (1—20) and each column is a Basic Note-order permutation (BP (1—6). Each of the 5 Primary 4GS that the 20 GS are derived from through R1—R4 as described in the previous blog entry Item 7, are printed in Bold/Italics to make it little clearer where the 20 GS (shapes) are coming from. See Figure 1. below. I will put in a comparative set of musical examples below to illustrate further.

Figure 1.

This will help to give some variety to each while allowing a connection with the previous GS across the Row. It might be a fun thing to go down the columns as well. Take a look at the same examples in the music graphics below in Figure 2.

Figure 2.

The 20 GS in 4 Staggered Starts (or so informed by Lane A. as 'Internal Rotation') over each BP. This was outlined in full as 96 GS per Primary 4GS in Figure 8 of this blog dated April 16, 2015. The best way to link up BP and rotations is to take the GS in question say in BP1 and look down to the next BP which would be BP2 and this can be implied with any permutation of any GS there. Just look directly down the grid/matrix to the next BP in position to stagger the next GS. You'll find it.

Obviously the BP can be played in one position or in a sequence (see this blog for May 6 2015 Figure 2). However facilitating the idea of repeating BP in place (one position), requires a 'convenience' arrangement or an organizing of repeated GS through BP in an order that will ensure that there are no two adjacent notes repeated. This new order of BP follows the 3 prograde BP and then 3 Retrograde BP to achieve this. See Figure 3 below.

Figure 3.         BP1 Prograde BP3 Progr  BP5 Progr  BP2 Retrogr  BP4 Retro  BP6 Retro

Continuing on with this connecting GS and BP without repeating any notes between GS. Here the reorganized BP sequence (as directly above), is given treatments with R (1—4) and S (1—4). The result seemed connected and is, but also has surprising wheels as Rotations (R) and Staggered Starts (S) (or now called Internal Rotations). See Figure 4 below where I have lined up the Staggered Starts.

Figure 4.

I know it may seem like a lot but again, once the 6BP are learned and 4 Rotations and 4 Staggered Starts (internal rotation), the job of creating these 'creative' lines is made easier. Now learning 'S' can be practised away from the piano. It does take some drilling but working an succeeding with one 'BP' at a time can reap unexpected rewards. Here's some finger number games I played on my steering wheel (not recommended) while driving to Kelowna from Edmonton. This features staggering the starts sequentially.

4GSA BP1/S(1—4).

1235
2351
3512
5123

Do the same for GSA—E

4GSA BP2/S(1—4).

5321
3215
2153
1532


4GSA BP3/S(1—4).

1325
3251
2513
5132

4GSA BP4/S(1—4).

5231
2315
3152
1523

4GSA BP5/S(1—4)

1253
2531
5312
3125

4GSA BP6/S(1—4)

5312
3125
1253
2531

Comments ? welcome !!

Generic Shapes item 7. 4GS (A—E) featuring the 20 GS from R1—4 as S1 in BP1.

Generic Shapes item 7. 4GS (A—E) featuring the 20 GS from R1—4 as S1 in BP1.

Most of you will understand what I'm saying in the above title. In fact when dealing with the primary Generic Shapes and the 4 rotations (R) of each 4GS from 4GS (1—4) x the 5 Primary 4GS, one can see that there are only 20 actual shapes before Staggered Starts (S) (1—4) and Basic Permutations (BP) are applied. Notably some one (Lane .A.) called the Staggered Starts, internal rotations, which is quite explanatory and I thank him for that. I will be sticking to my designation 'S' for now.

What I'm proposing as a way to readily learn these is to put all the shapes (4GS A—E) generated by Rotations (R) [1—4] on a single root and number them accordingly 1—20.

4GSA R1 is number 1,
4GSA R2 is number 2,
4GSA R3 is number 3,
4GSA R4 is number 4.

To capsulize and to conserve this idea these numbers (1—20) will be designated as 4GS1, 4GS2, 4GS3, 4GS4. Reducing it to only 'GS' 1—20 would be more efficient at this point. Repeating this process from (above) 4GSA (R1—4), and continuing on using the remaining 4 primary GS, see below: (N.B. this presents a comparative view).

Note that the notes based on a 'C' root or bottom note are presented using only BP1 and S1. The scalar numbers are represented in the column of numbers on the right side, below.

4GSA R1 = GS1     CDEG   1235
4GSA R2 = GS2     CDFB    1247
4GSA R3 = GS3     CEAB    1367
4GSA R4 = GS4     CFGA    1456

4GSB R1 = GS5     CEFG     1345
4GSB R2 = GS6     CDEA     1236
4GSB R3 = GS7     CDGB    1257
4GSB R4 = GS8     CFAB     1467

4GSC R1 = GS9     CDFG     1245
4GSC R2 = GS10   CEFB      1347
4GSC R3 = GS11   CDGA     1256
4GSC R4 = GS12   CFGB      1457

4GSD R1 = GS13   CDEF     1234
4GSD R2 = GS14   CDEB     1237
4GSD R3 = GS15   CDAB     1267
4GSD R4 = GS16   CGAB     1567

4GSE R1 = GS17   CEGB     1357
4GSE R2 = GS18   CEGA     1356
4GSE R3 = GS19   CEFA      1346
4GSE R4 = GS20   CDFA      1246

See Figure 1 which illustrates the above and how all the shapes look like they do when all R (1—4) of all 5 primary 4GS are generated from a single root note. It is interesting to go down the notes column and see the relationships and the similarities of these shapes going up and down that column.

Figure 1.

The processing of R (1—4) from a single GSA as an example.

Here is a summary of 4GS1—20 as described above.

Playing these as exercises in keys from a common tone as illustrated might be useful. I like to apply in tunes over changes and then I usually find out I don't know them well enough through source scales like all Majors, and Minor including Melodic minor ascending (Jazz Minor). Enjoy !!

Generic Shapes item 6: A New View Of Permutations of 4-Note GS.

Generic Shapes Item 6 is here just to point out the viewpoint of each GS from a single start. The five primary 4-note GS (A—E) x 6BP x 4R or to put it in long hand: The five Primary 4-note Generic Shapes (as discussed in the previous blogs) or GS (A—E) times 6 Basic Permutations (BP) times 4 Rotations (R) times 4 Staggered Starts (S) are presented with all 5 Primary GS (A: 1235, B: 1345, C: 1245, D: 1234, and E: 1357, from a single start (S).

4GSA:

4GSB:

4GSC:

4GSD:

4GSE:                     S1-R1    S1-R2    S1-R3   S1-R4   S2-R1    S2-R2    S2-R3   S2-R4

Dear reader, I hope you find this interesting. There is much more to explore of course and I'm continuing on to outline how this might be applied. Melodies like these GS can be acquired and re-fashioned into endless melodies with a fresh approach and yet retain the essence or foundation of the original. Lots to look here but working a few of these changing patterns into tunes is surprising fun.

Generic Shapes Item 5, a 7th chord as a 4GSE (4-note Generic Shapes using 1357)

This GS is the last of five, 4-note Generic Shapes which were outlined 4 blogs ago. It spells out a 7th chord, being 1357. It is likely the most familiar 4-note shape so it presents itself with inversions (R) quite handily. The remaining permutations operate the same as the others. To review: 4GSE can be treated with 6 Basic Permutations (BP), 4 Rotations (R), and 4 Staggered Starts (S) as before. The permutation process is outlined in Figure 1 below, using CMa7 as an example.

Figure 1.

Basic Permutation: BP1—6

CMa7:    BP1                 BP2                 BP3                  BP4                 BP5                   BP6  
             1357..................7531................1537.................7351................1375.................7513
             Prograde........... Retrograde...... Prograde..........Retrograde......Prograde..........Retrograde

Rotations: R1—4
               R1                                 R2                                R3                               R4
                1357............................3571(8)........................5783............................7835        

Rotations: R1—4 in a comparative view: all from a single bottom note (C).

               R1                                 R2                                R3                                R4
              1357..............................1356............................1346.............................1246
intervals:  3.......3........3                 3.......3.......2                 3......2.......3                 2.......3.......3          

Staggered Starts: S1—S4 (CMa7 in BP1 and R1)

              S1                                S2                                  S3                                  S4
               1357.............................3571............................5713..............................7135

Staggered Starts: S1—S4 in an ascending scale-tone sequence.

             S1                                  S2                                 S3                                S4
            1357.............................3571............................5713..............................7135
            CMa7.............................Dmi7...........................Emi7............................FMa7 etc.

 The 96 possible 4GSE (1357) using a CMa7 as an example.

Figure 2.

Remember that this is just an exposition (of sorts) outlining all five 4-note shapes in BP, R, and S.

 I don't expect that I'll learn them all in every way possible but I will learn a few and work with those and try to work in a process. It takes time and effort as any successful musician will know. Happy Hunting.

Generic 4-Note Shapes: 4GSD (1234)

Generic 4-Note Shape: 4GSD (1234—Tetrachord).

This is the 4th primary shape of 4-note Generic Shapes (GS) [1234] and is probably more familiar to everyone compared to some of the others. This one has certain quirks and characteristics. I've been reading my own blogs and applying it to my melody making and there is definitely something new emerging even without practising it directly.


4GSD (1234)

This 4GS is basically a scale fragment and can be placed anywhere in any diatonic 7-tone or 8-tone scale. So it could have a number of chromatics applied to an original. Since is is a tetrachord, I'll attempt to outline some chromatic alterations before moving on to working out the Basic Permutations (BP) and the Rotations (R) and Staggered Starts (S). Generally all these are described as tetrachords.

Some examples of 4GSD (1234) from C:

1234—Major tetrachord (CDEF)
12b34—Minor tetrachord (CDEbF)
1b2b34—Phrygian tetrachord (CDbEbF)
1b234—Harmonic tetrachord (CDbEF)
123#4—Lydian tetrachord (CDEF#)
1#23#4—Lydian #2 tetrachord (CD#EF#) (found in Harmonic scales)
12b3#4—Lydian b3 tetrachord (CDEbF#) (found in Harmonic scales)
1b2b3b4—Diminished tetrachord (CDbEbFb[E]) (found in Symmetrical Diminished scales)

12b3b4[3] Cliche tetrachord (CDEbFb[E])
1b2bb3b4[3] Cliche tetrachord retrograde (CDbEbb[D]Fb[E])

While all these tetrachords don't appear in every diatonic scale, they may appear in the source scales of Major, Harmonic Minor, Melodic Minor scales and Symmetrical Diminished scales [half-whole]—[whole-half]. NB for more on this refer to An Approach To Jazz Piano chapter 23 where I've outlined where tetrachords are found in these scales—or look it up.

Tetrachords (4GSD) found in the Major Bebop Scale

The Bebop scale is one source of the tetrachords (12b3b4 and 1b2bb3b4).

Here are the 4GSD found in a Major Bebop scale: See Figure 1.

Figure 1.

Exploring the diversity of shapes within 4GSD through Basic Permutations (BP), Rotation (R) and staggered starts (S)

Using a simple example: CDEF a Major tetrachord in C Major etc. the first permutation device to be outlined in this series are the BP. See Figure 2.

Basic Permutations of note order in 4GSD using CDEF as an example.

Figure 2.

Permutations using Rotations (R) in a 4GSD yields some surprising results visa-vis the variety of GS shapes. Using our example of 1234 in rotation (inversion) R, the result is:

R1 = 1234
R2 = 2348
R3 = 3489
R4 = 489[10]

See Figure 3.

Figure 3.

The next and last method of permutation features (C)4GSD (1234) in BP1 and R1 with permutations/variations using 'Staggered Starts' (S) i.e. (1234) in BP1 and R1 featuring S1—S4.

It starts with middle-CDEF (R1) S1 ||  DEFC[middle-C] R1 S2   ||   EFC[middle-C]D  ||  FC[middle-C]DE. See Figure 4.

Figure 4.

In Figure 5 is an outline of all (in C) 4GSD in BP (1—6), R (1—4) and S (1—4).


Figure 5.

                      BP1-R1-S1    R1-S2   R1-S3    R1-S4     R2-S1     R2-S2   S3            S4

Try playing some of these in a scale tone sequence as exemplified in figure 4. There is a lot here and it is definitely overwhelming so I am going to take a couple of ideas and work with them in tunes.

Generic Shapes: 4 notes continued.

Generic Shapes continued: Generic Shape C (4GSC) 1245 is explored.

Review 4GSA (1235) and 4GSB (1345) from previous two blogs (Melodic Generic Shapes in Jazz Improv—#2 GS (1235) and GS (1345) compared and applied, Melodic Generic Shapes in Jazz Improv... a practise in discovery) to get an understanding of the permutation treatment of the three remaining 4-note GS (4GS):

4GSA (1235)
4GSB (1345)

Remaining 4GS:

4GSC (1245)
4GSD (1234)
4GSE (1357)

These shapes are familiar to most musicians one way or another. The first two 4GSA and 4GSB have been discussed. The remaining three 4GS are outlined similarly with some new thoughts on implementation and practising ideas.

4GSC (1245)

The designation of 4GSC denotes that this is a 4 note Generic Shape, with the 'C' standing for the primary shape: 1245. 

The qualities and characteristics of this GS is one of a suspended resolution tendency. In a major scale tonal setting for example on C (CDFG) the F note (4th) generally has a tendency to fall to the third (making this GS as 1235). Of course as a Generic Shape (GS) it can be utilized, adapted, and transformed in many ways. In a minor chord the stress of the suspended aspect is softened somewhat.

Using our C major example, the first order of permutations is to apply the 6 available changes of note order (Basic Permutations—BP). 

BP1 (prograde), CDFG
BP2 (retrograde), GFDC
BP3 (skip one, down one), CFDG
BP4 (the retrograde to BP3), GDFC
BP5 (skip the 3rd note [F] and play the 4th note, and return to the 3rd note), CDGF 
BP6 (retrograde to BP5). GFCD

See Figure 1 below.

Figure 1.

Exercises in BP awareness.

Since it is difficult technically, with repetitive notes when playing these BP in one GS position, try playing them in order (BP1—BP6) through a scale tone sequence. NB this very exercise can be used with any 4GS(A—E). Exercises to follow.

This example in 4GSC is used as the primary GS in this scale-tone sequence in C major (the shapes conform to the diatonic notes found in the C major scale). See Figure 2

Figure 2.

CDFG ('C'BP1), AGED ('D'BP2), EAFB ('E'BP3), CGBF ('F'BP4), GADC (GBP5), EDAB (APB6)

Basic Permutations in pairs.

Here are some exercises that use only 2 adjacent BPs as in the C major scale: (using in this case BP1 alternating with BP2). All the possibilities may not work as easily as this but many will. See figure 3 for a couple of workable examples. NB that the shapes in Figure 3 follow the same shapes as Figure 2.

Figure 3.

(C)BP1...(D)BP2,    (E)BP1...(F)BP2 ....etc...
CDFG—AGED,     EFAB—CBGF

GS3 continued with alternating pairs of BP travelling up in a C major scalar sequence (using BP3 and BP4 as an example). See Figure 4. All this has been done before but I'm hoping it's a good idea to document the possibilities here and especially the pairs that work. Obviously sequences other than this diatonic 2nd sequence can be used: 4ths for example.

Figure 4.

(C)BP3....(D)BP4, (E)BP3...(F)BP4, (G)BP3...(A)BP4
CFDG — AEGD, EABF — CGBF, GCAD—EBDA... etc.

Here's a complete list of 21 available BP pairings. This graph shows the fading effect as the pairs accumulate. This is because as the BP numbers get higher, they have already been paired with the lower numbers. They are presented in columns. I have included those BP that are paired with themselves.

6 ———— + 5—————+ 4————— +3—————+2—————+1—....= 21 pairs

BP1 + BP1 — BP2 + BP2 — BP3 + BP3 — BP4 + BP4 — BP5 + BP5 — BP6 + BP6
BP1 + BP2 — BP2 + BP3 — BP3 + BP4 — BP4 + BP5 — BP5 + BP6
BP1 + BP3 — BP2 + BP4 — BP3 + BP5 — BP4 + BP6
BP1 + BP4 — BP2 + BP5 — BP3 + BP6
BP1 + BP5 — BP2 + BP6
PB1 + BP6

This graphic could foster a lot of practising and is obviously applicable to all 5 of the 4-note GS being outlined in this series. It is staggering to think of learning all these in all 4GS not to mention the permutations available by Rotation R and Staggered Starts/Rotations S.


4GSC (1245) Forms from Rotation and Staggered Starts (R and S).

4GSC (1245) Forms from Rotation and Staggered Starts (R and S) and some applications. Not all the Generic Shapes have a pentatonic source, but 4GSC does have an association with a pentatonic scale (12356). Using our example based on a C root: CDFG it can easily be seen that this group of notes can be found in the F pentatonic scale: CDFG are found on 5 of F pentatonic. This GS is also found within a Bb Pentatonic: CDFG are 2356 of the Bb pentatonic scale. In turn these pentatonic note groups serve any purpose that a pentatonic scale might have (I will write something on this pentatonic thing—but for now if you have access to my book: An Approach to Jazz Piano, there is material in there that attempts to outline this). Using the same example: CDFG serves within the chords of F, Bb, Eb, Ab, and even in C major (where the 4th degree is a tendency tone). Figure 5 outlines permutations by Rotation (R) and Staggered starts (S).

Figure 5.

CDFG in a Staggered Start as each repetition of the same GS Rotation (1) [CDFG]

CDFG — DFGC — FGCD ——  GCDF
1245    —  2451   —  4512   ——  5124
C24     — Dmi11 — F26(no 3) —  G7sus4

In the graphic below, all 96 permutations of a 4-note GSC (1245) are notated. The next blog will outline exercises using GSD (1234) and GSE (1357).

Figure 6.

The next blog will feature an outline of GSD (1234) [tetrachord] and GSE (1357) [7th chord].