Author Topic: Six-Tone Pitch Sets  (Read 8804 times)

fusion58

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Re: Six-Tone Pitch Sets
« Reply #15 on: July 03, 2010, 02:41:37 AM »
the "triadic" approach that swain is referring to (using two distinct triads with no shared tones) seems to be related to bergonzi's but since i do not possess the book(s) in question, i cannot know for sure.  i know that trombonist ed byrne has written etudes on this (in the form of his bichordal triad pitch collections) but:

although the consonant triads used as examples by swain are a subset of all possible hexads, or hexatonics my original query was not limited to those.  although i am not as excited about atonal music (schoenberg, etc...) as "millions," the set theory treatises of allen forte, john rahn and charles wuorinen (and a host of others i'm sure) have provided for us a complete list of all possible hexatonics (as well as collections of tones numbering greater or lesser than six) and it is this vast six-tone universe that i am exploring at the moment.  it is a bit overwhelming; however, i have recently produced guitar fingering studies of all the hexatonics and it is the warmup from hell (and no i don't play every one of them every day).

in producing these studies, i was struck by the "uniqueness" of the six-tone groups in how they were related to each other.  i'll produce a complete list here if anyone's interested.

thanks for the links phil!

That's interesting, and I would like to see that list as I'm forever on the lookout for new approaches to composition and the development of linear vocabulary.

It would be interesting if someone were to create a more-or-less comprehensive survey of the applications of 12-tone music and set theory to jazz improvisation, e.g., an overview that would present melodic ideas that were developed out of the theories in question and integrated into the jazz musician's vocabulary.

Maybe such materials already exist and I just don't know about them?  :)

fusion58

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Re: Six-Tone Pitch Sets
« Reply #16 on: July 03, 2010, 02:46:08 AM »


edit - forte relates the complements of the hexads by "z-relation" which is an interval analysis similar to what "millions" has done here - these terms may seem foreign to many; therefore, readers may wish to brush up on set theory by looking here:

http://www.composertools.com/

That matrix generator is really cool!

I would imagine it would work not only for twelve tone rows but for any melodic sequence for which you want to quickly find the inversion, retrograde inversion, etc.?

dogbite

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Re: Six-Tone Pitch Sets
« Reply #17 on: July 03, 2010, 09:16:58 AM »
That's interesting, and I would like to see that list as I'm forever on the lookout for new approaches to composition and the development of linear vocabulary.

It would be interesting if someone were to create a more-or-less comprehensive survey of the applications of 12-tone music and set theory to jazz improvisation, e.g., an overview that would present melodic ideas that were developed out of the theories in question and integrated into the jazz musician's vocabulary.

Maybe such materials already exist and I just don't know about them?  :)

you have already found them:

http://www.composertools.com/
« Last Edit: July 25, 2010, 03:29:14 PM by dogbite »
s/aka/db

millions

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Re: Six-Tone Pitch Sets
« Reply #18 on: July 05, 2010, 11:10:53 AM »
dogbite, this looks similar to the way Allan Holdsworth said that he generated the scales that he uses (see "Just For The Curious").

Quote:
"I started out using a fixed number, like the number 1, because of the transposing nature of stringed instruments, you can transpose real easy, which you can't do on other instruments. So I figured that if I started with, say, 5-note scales, that I could just permutate them all, like 1 through 5, then 12346, 12347, etc. through to 12."
"Then, I'd do the same with 6-note, 7-note, 8-note, and 9 notes. Then, I catalogued them, filed them away, and threw away all the ones that had more than four semitones in a row, in a straight row. And I just analyzed them, looked at them, until I could see chords within them."
"And then I realized that the way I think about chords is they're just parts of the scale that are played simultaneously; and as the chord changes go by, I don't so much think about a static chord voicing, staying, at all, changing; I just feel like the whole, the notes on the neck change. And I guess for me, the only thing that makes one scale different from another, is not the starting note, it's the separation of the intervals. So that's basically how I think of scales."

Dog, I think it would be extremely relevant and illuminating if you could show us how this might done; it would add to the "practical credibility" of all this set theory if you could; and this could tie-in with your book of possibilities, appealing to Holdsworth fans, a good selling point, IMHO; because your approach and his seem to be coming from the same "index of possibilities." If Holdsworth has proven that such an approach works, it could add new appeal to your book.

I need some confirmation on a few aspects of this; I have some questions, like why did Holdsworth stop at 9-note scales? I am thinking it got too chromatic after that.

Here are "ten really usable scales", from some of the scales which Holdsworth decided were "keepers" and discusses in the book/CD:

1. C major: 1-1-1/2-1-1-1-1/2
2. D minor/maj 7 (D melodic minor): D-E-F-G-A-B-C#-D: 1-1/2-1-1-1-1-1/2
3. A minor (maj 7, b6) (A harmonic minor): A-B-C-D-E-F-G#-A: 1-1/2-1-1-1/2--1 and 1/2--1/2
4. A minor/maj 7 #4 (E harmonic major): A-B-C-D#-E-F#-G#-A: 1-1/2--1 and 1/2--1/2-1-1-1/2
5. G# diminished (he thinks of it as G7b9 for use on altered dominants): G#-A#-B-C#-D-E-F-G-G#: 1-1/2-1-1/2-1-1/2-1-1/2 etc.
6. Bb major add #5 (jazz scale): Bb-C-D-Eb-F-F#-G-A-Bb
7. C dominant 7 (a C major with added b7): C-D-E-F-G-A-Bb-B-C
8. B jazz minor (add flat 7) (has natural 7 and raised 7): B-C#-D-E-F#-G#-A-A#-B
9. A jazz minor (add flat 6) (has raised 7 only, and flat 6): A-B-C-D-E-F-F-F#-G#-A
10. Symmetrical (used to modulate): F#-G-G#-A#-B-C-D-D#-E-F#
"In Spring! In the creation of art, it must be as it is in Spring!" -Arnold Schoenberg
"The trouble with New Age music is that there's no evil in it."-Brian Eno

millions

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Re: Six-Tone Pitch Sets
« Reply #19 on: July 05, 2010, 12:27:02 PM »
dogbite, thanks for the link to composerstools. It ia a very succinct summation of the set theory ideas, and free! ...Cheaper than buying the textbooks, although somehow having the books makes me take the info less for granted.

I mean, this is like walking in to an enormous room of possibilities. This is the great dilemma of the digital age; that we are faced with so many possibilities that a sort of "numbness" or paralysis sets in.

I especially liked the examples he gave of ways to use related PC sets & subsets. I can see that spending some time at a piano & playing some of these sets would be valuable, because there are supposedly audible similarities between sets.

"In Spring! In the creation of art, it must be as it is in Spring!" -Arnold Schoenberg
"The trouble with New Age music is that there's no evil in it."-Brian Eno

dogbite

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Re: Six-Tone Pitch Sets
« Reply #20 on: July 05, 2010, 07:13:48 PM »
dogbite, thanks for the link to composerstools. It ia a very succinct summation of the set theory ideas, and free! ...Cheaper than buying the textbooks, although somehow having the books makes me take the info less for granted.

I mean, this is like walking in to an enormous room of possibilities. This is the great dilemma of the digital age; that we are faced with so many possibilities that a sort of "numbness" or paralysis sets in.

I especially liked the examples he gave of ways to use related PC sets & subsets. I can see that spending some time at a piano & playing some of these sets would be valuable, because there are supposedly audible similarities between sets.



i agree. the information age has evolved into information overload. re: the six-tone sets (and others), i'll just pick one and warm up with it for a spell to step outside the box patterns. and like i said before, just because its fun. i agree also about obtaining hard copies of the textbooks (forte, rahn, etc...) but apparently they are only available used???
s/aka/db

millions

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Re: Six-Tone Pitch Sets
« Reply #21 on: July 06, 2010, 05:04:39 AM »
Holdsworth quote:
"I started out using a fixed number, like the number 1, because of the transposing nature of stringed instruments, you can transpose real easy, which you can't do on other instruments. So I figured that if I started with, say, 5-note scales, that I could just permutate them all, like 1 through 5, then 12346, 12347, etc. through to 12."

Okay, dog, help me out. What would these permutations look like?

12345
12346
12347
12348
12349
1234T
1234E,
then
12356
12357
12358
12359
1235T
1235E,
then
12367
12368
12369
1236T
1236E,
then
12378
12379
1237T
1237E,
then
12389
1238T
1238E,
then
1239T
12349E,
then
123TE. First permutation complete?

Also, his criteria was "discard if they have more than four semitones in a row (consecutively); none of the 5-note sets would include this, would they?
Should we change the nomenclature to include zero? as in 0-1-2-3-4 for a five-note scale?
« Last Edit: July 06, 2010, 02:35:22 PM by millions »
"In Spring! In the creation of art, it must be as it is in Spring!" -Arnold Schoenberg
"The trouble with New Age music is that there's no evil in it."-Brian Eno

dogbite

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Re: Six-Tone Pitch Sets
« Reply #22 on: July 06, 2010, 09:08:25 AM »
Holdsworth quote:
"I started out using a fixed number, like the number 1, because of the transposing nature of stringed instruments, you can transpose real easy, which you can't do on other instruments. So I figured that if I started with, say, 5-note scales, that I could just permutate them all, like 1 through 5, then 12346, 12347, etc. through to 12."

Okay, dog, help me out. What would these permutations look like?

12345
12346
12347
12348
12349
1234T
1234E,
then
12356
12357
12358
12359
1235T
1235E,
then
12367
12368
12369
1236T
1236E,
then
12378
12379
1237T
1237E,
then
12389
1238T
1238E,
then
1239T
12349E,
then
123TE. First permutation complete?

Of course, wouldn't Holdsworth have thrown some of these out, since his criteria was "discard if they have three semitones in a row (consecutively), and 1-2-3-4, as an example, fits this criteria?
Should we change the nomenclature to include zero? as in 0-1-2-3-4 for a five-note scale?


yes, many of them have three consecutive half-steps, thus sound like chromatic scale fragments.  also, many of them are forms of each other through inversion.  forte uses "zero" as the starting tone for prime forms.  it is not difficult to use a spreadsheet (such as ms works or excel) to plug in one of your forms as listed above and determine the other forms it is related to:

12345 would be 01234 through transposition

01234 could be inverted to 0123E through inversion, as would be
            
012TE, 019TE, and 089TE...

by the way, if you're using "1" as the "root," shouldn't your permutations include "12"?

in any case, the problem is to determine exactly which of these forms you have listed are related to each other.  the "prime form" is the inversion with the smallest interval between the first and last tones; therefore, 01234 would be the prime form since 0-4 is the smallest interval in the related sets:

01234, 0123E, 012TE, and 089TE.

readers please note that T is used for 10 and E for 11 in order to provide a single digit description for the tones 10 or 11 half-steps above the reference tone

so the tedious task is to determine the prime form for each of the above permutations to eliminate the ones that are not unique.
s/aka/db

dogbite

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Re: Six-Tone Pitch Sets
« Reply #23 on: July 06, 2010, 09:39:47 AM »
...
Dog, I think it would be extremely relevant and illuminating if you could show us how this might done; it would add to the "practical credibility" of all this set theory if you could; and this could tie-in with your book of possibilities, appealing to Holdsworth fans, a good selling point, IMHO; because your approach and his seem to be coming from the same "index of possibilities." If Holdsworth has proven that such an approach works, it could add new appeal to your book.

I need some confirmation on a few aspects of this; I have some questions, like why did Holdsworth stop at 9-note scales? I am thinking it got too chromatic after that.

Here are "ten really usable scales", from some of the scales which Holdsworth decided were "keepers" and discusses in the book/CD:

1. C major: 1-1-1/2-1-1-1-1/2
2. D minor/maj 7 (D melodic minor): D-E-F-G-A-B-C#-D: 1-1/2-1-1-1-1-1/2
3. A minor (maj 7, b6) (A harmonic minor): A-B-C-D-E-F-G#-A: 1-1/2-1-1-1/2--1 and 1/2--1/2
4. A minor/maj 7 #4 (E harmonic major): A-B-C-D#-E-F#-G#-A: 1-1/2--1 and 1/2--1/2-1-1-1/2
5. G# diminished (he thinks of it as G7b9 for use on altered dominants): G#-A#-B-C#-D-E-F-G-G#: 1-1/2-1-1/2-1-1/2-1-1/2 etc.
6. Bb major add #5 (jazz scale): Bb-C-D-Eb-F-F#-G-A-Bb
7. C dominant 7 (a C major with added b7): C-D-E-F-G-A-Bb-B-C
8. B jazz minor (add flat 7) (has natural 7 and raised 7): B-C#-D-E-F#-G#-A-A#-B
9. A jazz minor (add flat 6) (has raised 7 only, and flat 6): A-B-C-D-E-F-F-F#-G#-A
10. Symmetrical (used to modulate): F#-G-G#-A#-B-C-D-D#-E-F#

the process of identifying "useful" scales is defined by the purpose.  we all know that the traditional scales to learn are the ones you have mentioned, and that many of the six-tone sets are subsets of them.  in my book, i took advantage of set theory's inclusion of all possibilities - i mean who's to say that the strange subset of a hungarian minor scale won't be the coolest sound used by somebody experimenting with this stuff, consecutive half-steps notwithstanding...

i'll respond more tonite - stay tuned :)
« Last Edit: July 06, 2010, 06:11:05 PM by dogbite »
s/aka/db

Halfdim7

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Re: Six-Tone Pitch Sets
« Reply #24 on: July 06, 2010, 03:11:45 PM »
Well, I can vouch for dogbite's book, as I have an earlier edition.
It lays out the possible possible sets of notes in a very different way from other "scale" books I've encountered. It may be a little intimidating at fist(The fact that the book starts with 0 note scales is pretty unusual!), until you realize that everything has already been translated to the guitar. However, a tie-in w/ some real-world approaches could definitely make it easier to see the applications of his method.
....lame-ass, jive, pseudo bluesy, out-of-tune, noodling, wimped out, fucked up playing....

millions

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Re: Six-Tone Pitch Sets
« Reply #25 on: July 06, 2010, 03:15:34 PM »
dog, please note my correction, of my paraphrase of Holdsworth's quote: it should read "not more than four semitones in a row.

Of course, dog, you're right, when you say "...the process of identifying "useful" scales is defined by the purpose.  we all know that the traditional scales to learn are the ones you have mentioned, and that many of the six-tone sets are subsets of them..."

What I'm trying to do is to get you to talk about criteria, because the possibilities are quite large.

Let's assume that our goal is to play tonal music. Wouldn't a good criteria be to have scales which represent the aspects of this, such as major, minor, diminished, and augmented? The specifics of a criteria would run something like this, for a diminished chord or scale subset:
1. The scale must have a diminished fifth, and no "perfect" fifth should be present
2. The scale must have a minor third above 0, with no major thid, i.e, it must be a 0...3, not a 0...4 set. Etc.

Am I on the right track here?

Further, what is the criteria of a "practically useful" scale in tonal music? Should it always have a third & a fifth? Should it have 5,6, 7, 8 or 9 notes? At what point does a scale become unwieldy or too chromatic? 8 or 9 or 10 notes, 11, 12?

Also, Holdsworth briefly mentions scales which go into two octaves, perhaps three. Would these be the seemingly "unusable" rejected sets? For example, 0-2-3-4-5-7-8-9-10-11, which seems too chromatic to work as a one-octave scale, could become 0-3-5-8-11 in the first octave, then continue with 2-4-7-9-10 in the second, yielding a scale reading C-Eb-F-Ab-B-D-E-G-A-Bb spanning almost two octaves.

I strongly suspect that this is what is happening in the latest Holdsworth solos; he's exploring his old files of rejected sets, and octave-transposing them.

Some of what I've heard sounds like what many of the "free" jazz players were trying to do, but had reached the end of their jazz-based tonal resources. Maybe only Coltrane, in his study of Nicholas Slonimsky's "Thesaurus of Scales", was on to the "free" jazz in a more directed way. IMHO
"In Spring! In the creation of art, it must be as it is in Spring!" -Arnold Schoenberg
"The trouble with New Age music is that there's no evil in it."-Brian Eno

fusion58

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Re: Six-Tone Pitch Sets
« Reply #26 on: July 06, 2010, 08:28:36 PM »
...However, a tie-in w/ some real-world approaches could definitely make it easier to see the applications of his method.

Yep - musical examples are always great.

It would be nice to see some lines, phrases, or even complete solos with an analysis showing how the material was derived from set theory, etc.

dogbite

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Re: Six-Tone Pitch Sets
« Reply #27 on: July 06, 2010, 10:58:22 PM »
warning: big fat post ahead

there are quite a few terms used in the responses here that deserve a place at the table, such as:

method

criteria

examples


and i wish to continue a dialog of all of them including but not limited to the three terms i have chosen above. true story: in 1978 my first guitar teacher told me that the frequencies of musical tones were mathematically related to each other and i replied with a question, "how exactly?" and he could not tell me. i thus began a journey into harmonic theory and temperament that continues to this day.

i later asked a question of my second guitar teacher, "how many scales [arpeggios and all] are there anyway?" and he also could not tell me. mathematically it is a relatively simple problem [using combination and permutation formulas] but the problem then becomes, "how exactly do i describe them all?"

i had worked out the particulars of tone groups of 0 (duh), 1 (also: duh), 2 (not hard), 3 (harder but not a big problem), and 4 (this took a bit of time, but i got them all) but i got stuck on the 66 5-tone groups.

some time later, two forum acquaintances (millions was one of them) seemed familiar with (some of) the atonal practices of "set theory" (which i had seen before but had not yet recognized the value to my task) and at one point i found a list where all of the remaining groups were described in set theory notation such as "024579E" (the major scale) and i got this crazy idea: i know how to get a spreadsheet doc to convert set theory notation directly to guitar fingering diagrams - all i had to do then was verify the prime forms and input them - a bit of time later (not as much time as you might think) i had standard five-fret guitar fingering diagrams of every scale possible within the twelve-tone system!!!

i already had them all in the form of my Chromatic Pitch Sets book but they were not grouped in terms of common types (for example, the twelve major scales were there but not next to each other, limiting greatly the usefulness of the book) but now, they are grouped according to type - 352 of them.

ever seen one of those books with lots of scales? every time i see one it doesn't take me long to think of one that got missed. not here. i got them all. what you do with them is up to you, which leads me to:

method

it is not a method. i don't write method books because lots of other people do. i write resource books, and i have literally never seen such a resource before, not anywhere, and that is the uniqueness of this particular study. it is unique because there is none like it. sure you can figure them out, all of those fingerings, but you don't have to because i did it for you.

criteria

the criteria for choosing melodic and harmonic materials is often "scaled down" (hehe) to things like:

diatonic triads and seventh chords

scales consisting of only whole and half-steps with no consecutive half-steps: major, melodic minor, diminished and whole-tone,

scales producing only the four classical triads: add harmonic major and harmonic minor

and i really like the reference to "extra-octave" scales, where each octave need not be the same (remember the super arpeggio alternating in major and minor thirds? F A C E G B D F# A C# E G# B D# F#, etc...) and i got a fingering study on those too, but all this begs the question:

what on earth am i supposed to do with all this stuff?

in other words:

examples

here is a repost of something that millions just might remember from what the LCC guys called "the forum of doom." it is a bit contentious because i was talking about "side-slipping" all along where i was being harassed for examples and once a certain participant realized what the heck i was talking about just about came out and said, "oh yeah, i invented that you know" and i just about lost it and posted this, not long before erasing every post i ever made over there. yeah, i've posted there since but the reason i wish to share this is that it may illuminate my attitude on the examples issue:

"doesn't anyone out there have any imagination? some of what i'm posting is meant to provide fresh and unique ideas that border on the realm of the untried! personally, i am very interested in melodic devices that no one has used before, if that really is possible. and by the way, please check out ALL of my posts on this forum before giving me a hard time about providing specifics, as i have already done so - numerous times. i am not making this stuff up. but just to satisfy your curiosity, here's an excerpt from one of my posts found in the maj7b5 thread:

***begin excerpt***

"...But I DO know what the instruction I've received has taught me regarding the ways to develop melodic tension in a line. Both formal and informal instruction have I received - I have already told [name removed by dogbite] that I will not fall into the trap of quoting "I've been playing for a years and studied with b and been teaching for c years, so you have to listen to what I say..." kind of crap. It's meaningless.

Suffice to say that I've had the good fortune to learn from, teach with, and work for some of the finest players on the West coast. I do this music thing for a living - it is not a hobby for me. I teach forty to fifty private lessons a week or the bills go unpaid. I teach classes in music theory as well as beginning through advanced guitar instruction.

Some of the informal instruction I speak of is from studying methods of the likes of Joe Pass, Larry Carlton, Frank Gambale, Tommy Tedesco, Arnie Berle - oh shit, I'm name-dropping - please don't send in the name-dropping cops - I promise to do this no more!

Yes, these are guitar players. I am a guitar player. I have some experience performing and teaching other instruments, such as the flute, but I am primarily, at heart, to the core: a guitar player...

Why does this matter? Maybe guitarists look at some of these issues differently. I can play a four octave range without breaking a sweat. No reeds, no valve oil, no wooden sticks, just picks - and change the damn strings once in a while. The jazz guitarist whom I most respect is a guy called Joe Pass, so when he teaches, I listen. I know that Larry Carlton took lessons from Joe because he has said so publicly.

Okay - I'm beginning to ramble, but here's my point:

Larry Carlton spent a fair amount of time in an instructional video teaching how to create interest in a melodic line by:

1) Approaching a tonality from "its V chord"

2) Approaching a tonality from a half-step below

3) Applying a "triadic" approach using

a) the "super arpeggio", which is a series of alternating major and minor thirds [F A C E G B D F# A C# E G# B D# F# A# C#, etc...] and

b) major triads separated by intervals of minor thirds for a "13b9" sound [E major triad, G major triad, Bb major triad, Db major triad - weaving in and out of each other, essentially a diminished scale]

Carlton is not the only source of these ideas - Frank Gambale's method has similar devices; Joe Pass also - okay I agree the name dropping must stop; however, I cannot play for you to hear, nor can I post transcriptions for you to see, so I have a listening suggestion for you. Please stop bugging me for specific examples until you listen to this:

Larry Carlton - Last Nite - MCA Records (1987)

It was recorded live at the Baked Potato in North Hollywood

the performers are:

Larry Carlton - guitar
Terry Trotter - keyboards
Abraham Laboriel - bass
John Robinson - drums
Alex Acuna - percussion

and the set list is:

So What
Don't Give It Up
The B.P. Blues
All Blues
Last Nite
Emotions Wound Us So

There is video footage of some of the solos in the instructional video I keep bringing up:

"Star Licks Master Series - Larry Carlton"

The examples in the instructional part are transcribed, but not the solos from the album, which is unfortunate, but what the heck...

Listen also to "Kid Charlemange" by Steely Dan - the solo's Larry Carlton

I got more to say about all this and will continue in a later post, in particular I wish to follow through with my dialogue with [name removed by dogbite]., who has been patient with me as I recover from a vacation that was interrupted by my in-laws, but in closing I really feel the need to point out something that a wonderful instructor was trying to get me to understand:

This stuff takes YEARS to master. If you don't like what you hear right away, don't whine about it and ask for more. You may have to put it on the back burner for a while and approach it with a fresh perspective at a later time. It took me five years AFTER one of my teachers taught me one of these concepts in order for me to use it in real music. And I shit you not my friends - the Carlton video made it all come together for me 'CUZ I COULD SEE HIM DOING IT RIGHT AFTER HE TALKED ABOUT IT!

Please my friends, check out the suggested materials here - see a master do it - I am an idiot - you may not be convinced my my playing, 'cuz I'm light years behind the folks I've mentioned here - but you might be convinced by theirs...

If I'm coming across as heavy here, it is out of a genuine love of my art and craft. If I can help anyone with any of this, I will try my best to assist in any way practicable.

peace

Db"

***end excerpt***

i hope this is sufficient, 'cuz that's all this dog's gonna bite. i'm gonna go practice now...

db


and i hope y'all will still talk to me after sorting through the thinly veiled insults and innuendo (not directed at you guys but some forums can just make you crazy) but these things are in fact used by guys you have mentioned: gambale and holdsworth in particular. and no i'm not trying to sell books but the information is there for whomever wants it.

so these studies are created for you to do with what you will, and to open up the entire chromatic universe.

best,

dogbite
« Last Edit: July 06, 2010, 11:14:24 PM by dogbite »
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dogbite

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Re: Six-Tone Pitch Sets
« Reply #28 on: July 06, 2010, 11:50:25 PM »
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I need some confirmation on a few aspects of this; I have some questions, like why did Holdsworth stop at 9-note scales? I am thinking it got too chromatic after that.

i suspect you're right. forte's list (mine is modeled after rahn's which is slightly different, redefining a half-dozen of the prime sets) only includes three- through nine-tone scales and it may have been considered by early set theorists to be a silly thing to include dyads (and their complementary ten-tone sets) because of their inherent simplicity.

i mean, if you play a chromatic scale with one note missing what's it going to sound like? you guessed it: a chromatic scale with one note missing. just in case somebody hears it as uniquely different though, there are eleven modes of the resulting eleven-tone scale - go nuts with it if it gives you joy :)
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criteria
« Reply #29 on: July 07, 2010, 07:19:00 AM »
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Let's assume that our goal is to play tonal music. Wouldn't a good criteria be to have scales which represent the aspects of this, such as major, minor, diminished, and augmented? The specifics of a criteria would run something like this, for a diminished chord or scale subset:
1. The scale must have a diminished fifth, and no "perfect" fifth should be present
2. The scale must have a minor third above 0, with no major thid, i.e, it must be a 0...3, not a 0...4 set. Etc.

i think that this is a good starting point. some of the things i have discovered for myself in this regard are:

for major chords, the root (0) is the defining tone and the b2 (1) seems to be the most dissonant

for minor chords, the b3 (3) is the defining tone and the 3 (4) seems to be the most dissonant

for m7b5 chords, the b5 (6) is the defining tone and the 5 (7) seems to be the most dissonant

for dim7 chords, the bb7 (9) is the defining tone and the b7 (10) seems to be the most dissonant

for 7b9 chords, the b9 (1) is the defining tone and the 9 (2) seems to be the most dissonant

[set theory notation (number of half-steps above the root) is in parentheses above]

see a pattern? now let me contradict by example: play Cmaj7 on the instrument of your choice: C E G B

now program that into your BIAB and play these arpeggios in the following order:

C E G B

E G B D

G B D F#

B D F# A

D F# A C#, yes C#

and note that if you approach the #1(b2) in this manner, it really sounds quite cool, so now do this:

Cmaj7 play C E G B D F# A C#

Cm7 play Eb G Bb D F A C E

Cm7b5 play Gb Bb Db F Ab C G

Cdim7 play Bbb Db Fb Ab Cb Eb Gb Bb

C7b9 play Db F Ab C Eb G Bb D

and what have we found? an application of carlton's "super arpeggio"
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