Method for exploring new structures and clusters within any tonality

[JakeAcci]

Hey all

I was geeking out with a permutation calculator and some other tools and found some sensible systematic ways to find all possible chord structures and clusters within a pitch collection.

Motivation being that I've been doing a lot of improvised solo guitar lately and have been excited to look for some new textures, especially within less familiar tonalities, like harmonic major. (but even just in the plain old major scale I've found stuff that's new to me)

Writing out the method and the concepts in post format would take some time (brevity is not a strength of mine) so I was just curious to gauge if there was any interest before diving in. My feelings certainly won't be hurt if there's not, the stuff would be a little off topic from our usual conversation and I know a lot of folks scoff at mathematical or mechanical means of finding new sounds.

Anyway, let me know.

[bako]

I feel sometimes this is how my brain works on it's own (a permutation calculator) but I wouldn't mind delegating some of this to a machine.

There is much potential within a given note collection. It is less likely that we will ever play something if we have never been exposed to it.
Mathematics are a simple way of displaying possibility. Even the act of inversion is a simple mathematic operation.
The intervals, sounds and fingerings need to be learned and understood to be integrated into our playing, to morph the mechanical into something expressive.
We learn from books and charts, transcribing and emulating others, moving our fingers around till we find something we like and various other modes of exploration, experimentation, implementing formulas and theory and maybe even from something someone says on the internet.

Permutation is just another tool. I, for one would like to see what you are up to.

[djangoles]

I'm interested.....a couple of weeks ago I found a permutation tool online and was plugging into it from a master list 12 or 13 of the most used chords in all keys.

I would then take the lists that it would generate and try to connect each smoothly with voice leading. It was a good exercise but unfortunately

I had to start working on a bunch of real music for a live Vaudeville type of show that I'll be playing in next month.

[M-ster]

... I, for one would like to see what you are up to.

Ditto. Let 'er rip, Jake.

[JakeAcci]

Cool, thanks for the responses. I will get around to posting some stuff and probably the best part for me is that one or some of you might have suggestions for more direct paths to get similar results.

[cosmic gumbo]

Jazz engineering...I like it! I need to find a calculator to determine how much stress a jazz structure can withstand before it suffers from structural failure. Like Thelonious Monk said, "All musicians are subconsciously
mathematicians."

[JakeAcci]

Ok, took quite a while, here it is:

https://docs.google.com/document/d/1...NVXgTL8mM/edit

I know full well there will be critics...it's not a "how to play" guide, just a "hey, here's something new to try..."

I enabled comments on the file (just right click) and am open to all responses. At minimum, I hope this interests or opens up some doors for the reader.

[M-ster]

Cool document. Thanks for writing/presenting it, Jake! Now, for some time to study it ...

[JakeAcci]

Thanks and you're welcome, Man!

[NSJ]

Thanks for taking the time to post. Will grok this tomorrow at some point.

[bako]

How do you deal with 8 note structures numerically?
1-7 is very clear in a 7 note scale. It's very easy to generate the structures on each degree because each number ties into a diatonic interval.

[0zoro]

Thanks Jake! This looks like an interesting method of thinking/exploring.

[NSJ]

So, yeah, having read it once through, I came to this realization:

This is essentially what Alan Holdsworth does. He eschews conventional drop 2 and drop 3s (he refers to these as rather mundane and ordinary sounding) when comping and reserves the right to pick out any diatonic notes from the key in any order/sequence/voicing he desires. He uses the obtuse term "Note families" . The only limitation is physical: can he grab them?

This is why he also plays his chords finger style: impossible to do with a pick.

[JakeAcci]

How do you deal with 8 note structures numerically?
1-7 is very clear in a 7 note scale. It's very easy to generate the structures on each degree because each number ties into a diatonic interval.

Bako,

I hear you.

Here's my best attempt at a solution for 8 note pitch collections.

Below is a list of all four note structures possible in an 8 note pitch collection, in the same style as the list in my doc, with the the scale degrees listed as 12345678.

Since it can be confusing to find chord forms from this list, the best solution I have at this point is to customize it based on the specific pitch collection you want to use.

You can simply copy the list into a new doc and use the "find and replace" feature in any word processing application to automatically swap all the numbers for actual scale degrees from the pitch collection you want to use. The find and replace features allows the user to do this for a large list automatically rather than having to manually go through each line.

If we're dealing with the Half/Whole scale you would

find and replace 2 with b2 or b9

find and replace 3 with #2, b3, or #9

find and replace 4 with 3

find and replace 5 with #4, b5, or #11

find and replace 6 with 5

find and replace 7 with 6 or 13

find and replace 8 with b7

The list in basic 12345678 form:

1,2,3,4
1,2,3,5
1,2,3,6
1,2,3,7
1,2,3,8
1,2,4,3
1,2,4,5
1,2,4,6
1,2,4,7
1,2,4,8
1,2,5,3
1,2,5,4
1,2,5,6
1,2,5,7
1,2,5,8
1,2,6,3
1,2,6,4
1,2,6,5
1,2,6,7
1,2,6,8
1,2,7,3
1,2,7,4
1,2,7,5
1,2,7,6
1,2,7,8
1,2,8,3
1,2,8,4
1,2,8,5
1,2,8,6
1,2,8,7
1,3,2,4
1,3,2,5
1,3,2,6
1,3,2,7
1,3,2,8
1,3,4,2
1,3,4,5
1,3,4,6
1,3,4,7
1,3,4,8
1,3,5,2
1,3,5,4
1,3,5,6
1,3,5,7
1,3,5,8
1,3,6,2
1,3,6,4
1,3,6,5
1,3,6,7
1,3,6,8
1,3,7,2
1,3,7,4
1,3,7,5
1,3,7,6
1,3,7,8
1,3,8,2
1,3,8,4
1,3,8,5
1,3,8,6
1,3,8,7
1,4,2,3
1,4,2,5
1,4,2,6
1,4,2,7
1,4,2,8
1,4,3,2
1,4,3,5
1,4,3,6
1,4,3,7
1,4,3,8
1,4,5,2
1,4,5,3
1,4,5,6
1,4,5,7
1,4,5,8
1,4,6,2
1,4,6,3
1,4,6,5
1,4,6,7
1,4,6,8
1,4,7,2
1,4,7,3
1,4,7,5
1,4,7,6
1,4,7,8
1,4,8,2
1,4,8,3
1,4,8,5
1,4,8,6
1,4,8,7
1,5,2,3
1,5,2,4
1,5,2,6
1,5,2,7
1,5,2,8
1,5,3,2
1,5,3,4
1,5,3,6
1,5,3,7
1,5,3,8
1,5,4,2
1,5,4,3
1,5,4,6
1,5,4,7
1,5,4,8
1,5,6,2
1,5,6,3
1,5,6,4
1,5,6,7
1,5,6,8
1,5,7,2
1,5,7,3
1,5,7,4
1,5,7,6
1,5,7,8
1,5,8,2
1,5,8,3
1,5,8,4
1,5,8,6
1,5,8,7
1,6,2,3
1,6,2,4
1,6,2,5
1,6,2,7
1,6,2,8
1,6,3,2
1,6,3,4
1,6,3,5
1,6,3,7
1,6,3,8
1,6,4,2
1,6,4,3
1,6,4,5
1,6,4,7
1,6,4,8
1,6,5,2
1,6,5,3
1,6,5,4
1,6,5,7
1,6,5,8
1,6,7,2
1,6,7,3
1,6,7,4
1,6,7,5
1,6,7,8
1,6,8,2
1,6,8,3
1,6,8,4
1,6,8,5
1,6,8,7
1,7,2,3
1,7,2,4
1,7,2,5
1,7,2,6
1,7,2,8
1,7,3,2
1,7,3,4
1,7,3,5
1,7,3,6
1,7,3,8
1,7,4,2
1,7,4,3
1,7,4,5
1,7,4,6
1,7,4,8
1,7,5,2
1,7,5,3
1,7,5,4
1,7,5,6
1,7,5,8
1,7,6,2
1,7,6,3
1,7,6,4
1,7,6,5
1,7,6,8
1,7,8,2
1,7,8,3
1,7,8,4
1,7,8,5
1,7,8,6
1,8,2,3
1,8,2,4
1,8,2,5
1,8,2,6
1,8,2,7
1,8,3,2
1,8,3,4
1,8,3,5
1,8,3,6
1,8,3,7
1,8,4,2
1,8,4,3
1,8,4,5
1,8,4,6
1,8,4,7
1,8,5,2
1,8,5,3
1,8,5,4
1,8,5,6
1,8,5,7
1,8,6,2
1,8,6,3
1,8,6,4
1,8,6,5
1,8,6,7
1,8,7,2
1,8,7,3
1,8,7,4
1,8,7,5
1,8,7,6


Here is the same list after going through that 'find and replace' process which took maybe twenty seconds:

1,b2,#2,3
1,b2,#2,#4
1,b2,#2,5
1,b2,#2,6
1,b2,#2,b7
1,b2,3,#2
1,b2,3,#4
1,b2,3,5
1,b2,3,6
1,b2,3,b7
1,b2,#4,#2
1,b2,#4,3
1,b2,#4,5
1,b2,#4,6
1,b2,#4,b7
1,b2,5,#2
1,b2,5,3
1,b2,5,#4
1,b2,5,6
1,b2,5,b7
1,b2,6,#2
1,b2,6,3
1,b2,6,#4
1,b2,6,5
1,b2,6,b7
1,b2,b7,#2
1,b2,b7,3
1,b2,b7,#4
1,b2,b7,5
1,b2,b7,6
1,#2,b2,3
1,#2,b2,#4
1,#2,b2,5
1,#2,b2,6
1,#2,b2,b7
1,#2,3,b2
1,#2,3,#4
1,#2,3,5
1,#2,3,6
1,#2,3,b7
1,#2,#4,b2
1,#2,#4,3
1,#2,#4,5
1,#2,#4,6
1,#2,#4,b7
1,#2,5,b2
1,#2,5,3
1,#2,5,#4
1,#2,5,6
1,#2,5,b7
1,#2,6,b2
1,#2,6,3
1,#2,6,#4
1,#2,6,5
1,#2,6,b7
1,#2,b7,b2
1,#2,b7,3
1,#2,b7,#4
1,#2,b7,5
1,#2,b7,6
1,3,b2,#2
1,3,b2,#4
1,3,b2,5
1,3,b2,6
1,3,b2,b7
1,3,#2,b2
1,3,#2,#4
1,3,#2,5
1,3,#2,6
1,3,#2,b7
1,3,#4,b2
1,3,#4,#2
1,3,#4,5
1,3,#4,6
1,3,#4,b7
1,3,5,b2
1,3,5,#2
1,3,5,#4
1,3,5,6
1,3,5,b7
1,3,6,b2
1,3,6,#2
1,3,6,#4
1,3,6,5
1,3,6,b7
1,3,b7,b2
1,3,b7,#2
1,3,b7,#4
1,3,b7,5
1,3,b7,6
1,#4,b2,#2
1,#4,b2,3
1,#4,b2,5
1,#4,b2,6
1,#4,b2,b7
1,#4,#2,b2
1,#4,#2,3
1,#4,#2,5
1,#4,#2,6
1,#4,#2,b7
1,#4,3,b2
1,#4,3,#2
1,#4,3,5
1,#4,3,6
1,#4,3,b7
1,#4,5,b2
1,#4,5,#2
1,#4,5,3
1,#4,5,6
1,#4,5,b7
1,#4,6,b2
1,#4,6,#2
1,#4,6,3
1,#4,6,5
1,#4,6,b7
1,#4,b7,b2
1,#4,b7,#2
1,#4,b7,3
1,#4,b7,5
1,#4,b7,6
1,5,b2,#2
1,5,b2,3
1,5,b2,#4
1,5,b2,6
1,5,b2,b7
1,5,#2,b2
1,5,#2,3
1,5,#2,#4
1,5,#2,6
1,5,#2,b7
1,5,3,b2
1,5,3,#2
1,5,3,#4
1,5,3,6
1,5,3,b7
1,5,#4,b2
1,5,#4,#2
1,5,#4,3
1,5,#4,6
1,5,#4,b7
1,5,6,b2
1,5,6,#2
1,5,6,3
1,5,6,#4
1,5,6,b7
1,5,b7,b2
1,5,b7,#2
1,5,b7,3
1,5,b7,#4
1,5,b7,6
1,6,b2,#2
1,6,b2,3
1,6,b2,#4
1,6,b2,5
1,6,b2,b7
1,6,#2,b2
1,6,#2,3
1,6,#2,#4
1,6,#2,5
1,6,#2,b7
1,6,3,b2
1,6,3,#2
1,6,3,#4
1,6,3,5
1,6,3,b7
1,6,#4,b2
1,6,#4,#2
1,6,#4,3
1,6,#4,5
1,6,#4,b7
1,6,5,b2
1,6,5,#2
1,6,5,3
1,6,5,#4
1,6,5,b7
1,6,b7,b2
1,6,b7,#2
1,6,b7,3
1,6,b7,#4
1,6,b7,5
1,b7,b2,#2
1,b7,b2,3
1,b7,b2,#4
1,b7,b2,5
1,b7,b2,6
1,b7,#2,b2
1,b7,#2,3
1,b7,#2,#4
1,b7,#2,5
1,b7,#2,6
1,b7,3,b2
1,b7,3,#2
1,b7,3,#4
1,b7,3,5
1,b7,3,6
1,b7,#4,b2
1,b7,#4,#2
1,b7,#4,3
1,b7,#4,5
1,b7,#4,6
1,b7,5,b2
1,b7,5,#2
1,b7,5,3
1,b7,5,#4
1,b7,5,6
1,b7,6,b2
1,b7,6,#2
1,b7,6,3
1,b7,6,#4
1,b7,6,5

[JakeAcci]

Here is the process for making lists of any size chord structure derived from any size pitch collection, staying within the format of the lists I've already presented

Go to this site: Combinations and Permutations Calculator

Select the following

Types to choose from: The size of your pitch collection minus one

Number chosen: The number of notes in your chord structure minus one

Is order important: Yes

Is repetition allowed: If you select "Yes," you allow for notes to be doubled in octaves. If you select "No," you don't.

In "List Them" type in a number for each scale degree, but exclude the root/1.

You could do this a few ways. For a five note scale you could simply type in "2,3,4,5." For a nine note scale, "2,3,4,5,6,7,8,9."

Then later, if you want, you'll copy and paste the list into a different document, and use the find and replace function to customize it to the pitch collection you want.

Alternatively, you could just enter the list (under "list them") as the scale degrees you want, excluding the root. For example, for minor pentatonic you could enter "b3,4,5,b7"

I prefer the former option (just using 2,3,4,5,) then copying and pasting, find/replace, because that way you produce a list that can be customized to many different pitch collections.

Select "cdv" on the right so that the structures will be listed vertically.

Select "list"

Now you have the list, all you need to do is enter the root ("1") at the beginning of each structure.

To do that somewhat automatically, go to http://alphabetizer.flap.tv/index.php

Enter in the list just created

On the left where it says "Add ________ to the beginning of each item" enter in "1," (with the comma)

Then hit alphabetize.

Now you have a list within the same format as the lists I've presented, but for any size chord form and any size pitch collection.

Hopefully this is clear…the websites are simple to use and this process takes about 30 seconds.

[bako]

Jake. Yeah flats and sharp numbers gets the job done. I've been digging the Permutation Calculator.
Now I'll check out the Alphabetize tool to clarify order and the Randomizer to mix things up.

Wayne Krantz in his OS book used numbers and b numbers just to keep things consistent and simple addressing chromatic structures.

The post tonalists use 0 1 2 4 5 6 7 8 9 T E with 0 representing C. It does takes some practice to apply rapid thought to action.

Jon Damien in his books used a cool chart for 3 note chords in 7 note scale.
He uses numbers to describe the diatonic interval.

C D E is 2 2 meaning there is a 2nd from C-D and also from D-E
E F G is also 2 2
C E B is 3 5 a 3rd from C_E and a 5th from E-B

He also groups things into close and open triad, cluster, quartal, 7th no 5th, 7th no 3rd, octave family.
One of the more elegant presentations I've seen.

I have applied his method to chromatic scale to 3 and 4 note chords by adding b/# intervals but not the cataloging.

I did use the permutation tool for 3 and 4 notes for the common jazz scales.
I used note names which works fine but I also like the key neutrality of numbers.

Any other smart internet tools you got up your sleeve. Wish list: one that pulls the inversions together from the master list.
Thanks for your initiative here.

Best,
Bako

[JakeAcci]

Cool Bako. Which Damien book is this?

Any other smart internet tools you got up your sleeve. Wish list: one that pulls the inversions together from the master list.

I'm not sure what you mean.

[JakeAcci]

Also, I think I already posted, but a reminder that the alphabetizer site has a randomize function as well.

[JakeAcci]

One thing that I feel might need to be addressed - the whole document and thread so far deals with the discovery of vertical structures...obviously it's a pursuit that I think is worthy of time and energy, but several four note chords played in a row are in a sense four melodies being played with the same rhythm.

Another document (that's probably beyond me at this point in my musicianship) could deal with the possible movements of voices within several "chords" played in sequence - parallel, contrary, oblique, etc. Modal transposition of interesting chord structures can result in some nice sounds, but there is more artistry and composition involved with connecting multiple melodies together to then potentially get a piece of music that engages the listener.

It's my goal to have an ear for chords and melodies that allows me to improvise with chords, and melodies, with an awareness of each melody that's being played as well how all notes are going to sound together vertically.

[bako]

The Chord Factory as well as his Composition book both have the same chart.

[JakeAcci]

Just a bump - just wondering if anybody got any mileage out of this. If not, that's fine, it's sort of a strange and very open ended idea, but I was just curious.

Also, Bako, I'm not sure what you meant by "Wish list: one that pulls the inversions together from the master list." Maybe we can come up with something.

[bako]

It is great to have the instant snapshot that appears in seconds with the permutation tool.
I have gotten some mileage out of it already and have already tortured a few students with it's rather complete worldview.
It is not unlike things I have done previously but the permutation tool is faster than me.
More time spent playing and less time writing.

Wish list: Since you made 3 good tool/app suggestions I was wondering what others you might know about.
There are many ways to order pitch collections, somewhat addictive having a machine do all the heavy lifting.

[flextones]

Thanks for sharing this information. I have Schillinger's Kaliedophone but he only goes up to pentads which are 5 voice clusters. This gives me three extra voices to mess with.

[JakeAcci]

Excellent, thanks for the feedback bako and flextones and those who left comments on the gdoc. I'm glad my efforts served some purpose.

I personally was messing around with the method to find clusters and interesting structures within harmonic major, but I've gotten a little side- tracked with other things.

'plane'-ing structures up hexatonic scales is probably next on the list for me, I really like how the intervals change as you transpose up...

Also:
-if anybody has suggestions about the document I'm all ears...where it may need improvement in any way
-if there are additional functions that you'd like quick access to but currently do not have, let me know and maybe we can find something together
-if anybody has ideas on how to take these methods further, that would be cool - especially things involving counterpoint, rather than all voices moving parallel

[JakeAcci]

Doing some ear training today I heard this four note melody:

A# down to B up to C# up to G

Something about those notes, that melody, seemed new but also familiar. I did a little analysis, transposing it up a half step (B C D G#) to make it easier, mentally, to deal with:

Notes are C D G# B

it's a G#diminished triad with a C

could be from

C harmonic minor
C harmonic major
A harmonic minor
A melodic minor
C/Eb/Gb/A WH
B/D/F/Ab HW


chords that make some sort of sense to me:

From C harmonic minor:

Fm6#11

G triad w 4 and b9

Ab ma7b5#9, no 7

From C harmonic major:

Cma9#5 no 3 (enharmonically the #5 is really a b6, there is no 5)

Fm6#11

G triad w 4 and b9

E7b13

Ab ma7b5#9, no 7


From A harmonic minor:

Aminmaj9/11 no 5

Cma9#5 no 3

D(m)13b5 no 3

E7b13


From A melodic minor:

Aminmaj9/11 no 5

Cma9#5 no 3

D13b5 no 3

E7b13

D13b5/F# (then it's a full D13b5 chord, 3rd ion the bass)

Ab7b5#9no7


Any other chords it could be , something I'm missing? Bm6b9? Bb7 w 9 and b9? Though it's within the diminished scale my ears are having trouble hearing it as a diminished chord..D dominant and Ab dominant are covered above, but I can't really hear it as F or B dominant.


possible voicings:

G#,B,C,D

G#,B,D,C

G#,C,B,D

G#,C,D,B

G#,D,B,C

G#,D,C,B

B,G#,C,D

B,G#,D,C

B,C,G#,D

B,C,D,G#

B,D,G#,C

B,D,C,G#

C,G#,B,D

C,G#,D,B

C,B,G#,D

C,B,D,G#

C,D,G#,B

C,D,B,G#

D,G#,B,C

D,G#,C,B

D,B,G#,C

D,B,C,G#

D,C,G#,B

D,C,B,G#

Activity for when I have an afternoon free: take the voicings above that are playable on the guitar, transpose them through all the possible chord scales mentioned.