#1
...can anyone explain to me how to calculate hexachordal combinatoriality from a given set class? I seriously cannot comprehend it.

...modes and scales are still useless.


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#2
No. Nobody can explain it. Not even Hector C. Combinatoriallo, the inventor of the formula. It can only be grasped through solitary study and deep meditation; this is a journey you must make for yourself, with only a sassy talking animal (born of sleep deprivation and prescription stimulants) to guide your steps.
#3
Quote by AeolianSeventh
No. Nobody can explain it. Not even Hector C. Combinatoriallo, the inventor of the formula.

That is actually true. The author that I'm reading the text on completely drops the ball here and just assumes you know what the hell is going on.

...modes and scales are still useless.


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#4
I'm assuming this is for atonal/post-tonal theory stuff, like Joseph Strauss? I can't help you but out of curiosity, what book are you learning from, would you recommend learning PTT, and would you recommend the book you have (probably not since it's dropping the ball on this particular problem you're having)?
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#6
Quote by MadMudgeN
I'm assuming this is for atonal/post-tonal theory stuff, like Joseph Strauss? I can't help you but out of curiosity, what book are you learning from, would you recommend learning PTT, and would you recommend the book you have (probably not since it's dropping the ball on this particular problem you're having)?

Yep it's from Straus' 3rd edition. Most of it is actually pretty concise and understandable if you take the time to comprehend it but this last section is a goddamn brick wall. Right before my final exam too, great.


Yes, I definitely recommend learning post tonal theory if you are a serious composer. It adds a lot of techniques and approaches to what you can do. I don't agree with how in-depth they take it, since beyond an early point no one can identify the concepts employed without the process of lengthy analysis of the visual score. But there's still some useful things to help you organize your composition.

and it doesn't seem like anyone knows....

...modes and scales are still useless.


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Last edited by Xiaoxi at Apr 23, 2011,
#7
I'm really into heavy theory and this is almost impossible to learn, I didn't even bother with it. For gods sake i'm only 17, I don't need to learn this. I'll stick with the rest for now and maybe learn this in a couple years. I just don't understand how to calculate it. I don't think anyone would need this though.
#8
WTF IS EVERY1 TALKING ABOUT!? teach me your ways oh ones who use big words!
#9
Quote by TMVATDI
WTF IS EVERY1 TALKING ABOUT!? teach me your ways oh ones who use big words!
Yeah I'm just about as lost as you are. I'm going to stick to my tonal harmony, thank you.
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#10
Quote by food1010
Yeah I'm just about as lost as you are. I'm going to stick to my tonal harmony, thank you.


Mmmm.... yeah.

CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
#12
Quote by z4twenny
http://www2.nau.edu/~krr2/12tone/12tone2.html

It's amazing how a little visual cue can clear up everything.

Now I get it!

Basically, many hexachordal sets (any collection of 6 unique pitch classes) have a kind of symmetrical property that, using the right transformation, can address the other 6 unique pitch classes to make up the aggregate (collection of all 12 pitch classes).

Simple example:

Diatonic Hexachord; 6 notes from the diatonic major scale: C D E F G A
In serial terms where C = 0, C#/Db = 1, D nat = 2, etc, this would be set class 0,2,4,5,7,9

If you transpose this set class by 6 semitones (T6), or a tritone away up or down, you'll get: 6,8,10,11,1,3, which is exactly what's missing from the original set to address all 12 chromatic pitch classes.

In this way, the original hexachord is able to generate a related hexachord through transformation to create the aggregate!

Transformations are also possible by inversion, retrograde, and retrograde inversion for certain heaxchordal sets (these are way too messed up to explain...)

...modes and scales are still useless.


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#13
Quote by Xiaoxi
It's amazing how a little visual cue can clear up everything.

Now I get it!

Basically, many hexachordal sets (any collection of 6 unique pitch classes) have a kind of symmetrical property that, using the right transformation, can address the other 6 unique pitch classes to make up the aggregate (collection of all 12 pitch classes).

Simple example:

Diatonic Hexachord; 6 notes from the diatonic major scale: C D E F G A
In serial terms where C = 0, C#/Db = 1, D nat = 2, etc, this would be set class 0,2,4,5,7,9

If you transpose this set class by 6 semitones (T6), or a tritone away up or down, you'll get: 6,8,10,11,1,3

In this way, the original hexachord is able to generate a related hexachord through transformation to create the aggregate!

Transformations are also possible by inversion, retrograde, and retrograde inversion for certain heaxchordal sets (these are way too messed up to explain...)

i actually kind of got this, but idk the words "retrograde," "transformation," and "aggregate". tell me, how does one get into this super-theory junk? do i need college education or just a few books?

u guys in this thread are crazy music-smart...
#14
Quote by TMVATDI
i actually kind of got this, but idk the words "retrograde," "transformation," and "aggregate". tell me, how does one get into this super-theory junk? do i need college education or just a few books?

u guys in this thread are crazy music-smart...

Let's just say if you really need it, you'll end up in a situation where you'll learn it. Otherwise, save yourself the headaches.

...modes and scales are still useless.


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#15
Quote by Xiaoxi
Let's just say if you really need it, you'll end up in a situation where you'll learn it. Otherwise, save yourself the headaches.

what if im just a super-interested ocd-filled headache-seeker?
#16
Then pick up Intro to Post Tonal Theory, 3rd edition or later, by Joseph Straus (it's kinda pricey though). Also, have cotton balls in hand for when your nose starts bleeding.

...modes and scales are still useless.


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#17
There is a comprehensive mathematical theory to this which describes algebraic ideals of ring homomorphism of permutation groups as belonging to musical equivalence classes.

I'd look it up but it would make me head hurt and it still does not explain HOW to actually apply these ideas.

Some music professor found out I was a math major in college and started slinging these terms around, I knew the math (beautifully abstract) but he was talking about actual compositional techniques .... I still have nightmares.
#18
Quote by Zen Skin
There is a comprehensive mathematical theory to this which describes algebraic ideals of ring homomorphism of permutation groups as belonging to musical equivalence classes.
Sounds like an even fancier way of saying set theory and the concept of modular systems... (which belongs both to music and math)

Some music professor found out I was a math major in college and started slinging these terms around, I knew the math (beautifully abstract) but he was talking about actual compositional techniques .... I still have nightmares.

Do you mean it was daunting to apply these concepts to composition or do you mean the idea of applying these math concepts to music is horrific?

...modes and scales are still useless.


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Last edited by Xiaoxi at Apr 24, 2011,
#19
Quote by TMVATDI
i actually kind of got this, but idk the words "retrograde," "transformation," and "aggregate". tell me, how does one get into this super-theory junk? do i need college education or just a few books?

u guys in this thread are crazy music-smart...


Retrograde:

1, 2, 3, 4 becomes 4, 3, 2, 1 - a common technique in twelve-tone music.

Transformation:

1, 2, 3, 4, by adding, say, 2 to each value becomes 3, 4, 5, 6

Aggregate:

A collection. So an aggregate of the original series with a retrograde becomes 1, 2, 3, 4, 4, 3, 2, 1

Or an aggregate of the original series with a transformation becomes 1, 2, 3, 3, 4, 4, 5, 6 (this would be a series aggregation... a serial aggregation would be 1, 2, 3, 4, 3, 4, 5, 6)

CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
#20
Quote by axemanchris
Retrograde:

1, 2, 3, 4 becomes 4, 3, 2, 1 - a common technique in twelve-tone music.

Transformation:

1, 2, 3, 4, by adding, say, 2 to each value becomes 3, 4, 5, 6

Aggregate:

A collection. So an aggregate of the original series with a retrograde becomes 1, 2, 3, 4, 4, 3, 2, 1

Or an aggregate of the original series with a transformation becomes 1, 2, 3, 3, 4, 4, 5, 6 (this would be a series aggregation... a serial aggregation would be 1, 2, 3, 4, 3, 4, 5, 6)

CT

that retrograde is what Schoenberg did right?
#21
Quote by axemanchris
Retrograde:

1, 2, 3, 4 becomes 4, 3, 2, 1 - a common technique in twelve-tone music.

Transformation:

1, 2, 3, 4, by adding, say, 2 to each value becomes 3, 4, 5, 6

Aggregate:

A collection. So an aggregate of the original series with a retrograde becomes 1, 2, 3, 4, 4, 3, 2, 1

Or an aggregate of the original series with a transformation becomes 1, 2, 3, 3, 4, 4, 5, 6 (this would be a series aggregation... a serial aggregation would be 1, 2, 3, 4, 3, 4, 5, 6)

CT

Almost but not quite.

Transformations are any operations involving altering the series. The example you mentioned specifically is transposition up 2 (or up a whole step). But other transformations include inversion, retrograde, and retrograde inversion.

The aggregate specifically refers to the set of all 12 chromatic pitch classes and no less. Anything less would be considered diads/decachords, trichords/nonachords, tetrachords/octochords, etc. Collection refers to the original set of unique pitch classes that are used, so the collection would not be 1 2 2 3 3 4 4 5 5 6, etc. It would still be 1,2,3,4,5,6.

Quote by toine
that retrograde is what Schoenberg did right?

Yep, but transformations are essential techniques used by all serial composers. Berg, Webern, Stravinsky, Babbitt, Crumb, Crawford, Feldman, Boulez, list goes on and on...

...modes and scales are still useless.


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#22
Quote by Xiaoxi
It's amazing how a little visual cue can clear up everything.

Now I get it!

Basically, many hexachordal sets (any collection of 6 unique pitch classes) have a kind of symmetrical property that, using the right transformation, can address the other 6 unique pitch classes to make up the aggregate (collection of all 12 pitch classes).

Simple example:

Diatonic Hexachord; 6 notes from the diatonic major scale: C D E F G A
In serial terms where C = 0, C#/Db = 1, D nat = 2, etc, this would be set class 0,2,4,5,7,9

If you transpose this set class by 6 semitones (T6), or a tritone away up or down, you'll get: 6,8,10,11,1,3, which is exactly what's missing from the original set to address all 12 chromatic pitch classes.

In this way, the original hexachord is able to generate a related hexachord through transformation to create the aggregate!

Transformations are also possible by inversion, retrograde, and retrograde inversion for certain heaxchordal sets (these are way too messed up to explain...)
This isn't really my thing, but to me demonstrates how some people can make things way harder than they need to be. What you said took me a second, but makes perfect sense.
#23
Quote by grampastumpy
This isn't really my thing, but to me demonstrates how some people can make things way harder than they need to be. What you said took me a second, but makes perfect sense.

I don't disagree, and have mixed feelings about serialism. But keep in mind that I just explained it in is an oversimplified, "lite" version of a microscopic concept that skips a lot of fundamentals which are harder to comprehend. There is a useful purpose for why concepts like these exist and are presented in this way. You could express the act of kicking a soccer ball in a mathematical formula, or you can describe the physical act of it with plain words. The latter is obviously easier, but the former belongs to the larger concepts of physical science, which most would agree is important and necessary.

On the surface and considering the practicality of writing this kind of music for the general audience, there is no doubt in my mind that most of the developments in serial music will bypass just about everyone's ears. Straus suggests that by organizing a set class through these mathematical concepts, the music will retain a sense of unity and pattern that the listeners will pick up on, ultimately making for a satisfying listening experience. I disagree, I think the atonal nature of 12 tone serialism is too disorienting for anyone in the present to hear the patterns given so many abstract transformations both on the microscopic pitch levels and the structural levels of the whole piece.

However, if music is a way to convey ideas, then this is a new and exciting way to do that. Every major serial piece is its own world, built on a protocol that is unique to the piece, as opposed to traditional tonal music, which is all built on the same protocols. It is a way of creating a musical object or stating an idea, and then developing it in profound ways. It's just that unfortunately most of these things can't be detected by listening and requires analysis of the score. It's a way of creating and manipulating patterns, kind of like codebreaking. That can be a rewarding experience itself. Yes, the current way in which we are conditioned to listen to music is incompatible with serialism, but I believe our listening abilities will evolve and advance to accept atonality. And the evolution of classical music made the development of serialism inevitable. Like any science, it develops at a rate much faster than the layman can understand, but eventually we will come to a point where the theoretical and the practical meets.

...modes and scales are still useless.


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#24
Quote by Xiaoxi
Almost but not quite.

Transformations are any operations involving altering the series. The example you mentioned specifically is transposition up 2 (or up a whole step). But other transformations include inversion, retrograde, and retrograde inversion.


Okay, yes. I should have been more clear that a transformation didn't have to be quite so specific and that my example was a very simple one.

Quote by Xiaoxi

The aggregate specifically refers to the set of all 12 chromatic pitch classes and no less. Anything less would be considered diads/decachords, trichords/nonachords, tetrachords/octochords, etc. Collection refers to the original set of unique pitch classes that are used, so the collection would not be 1 2 2 3 3 4 4 5 5 6, etc. It would still be 1,2,3,4,5,6.


I stand corrected.

Quote by Xiaoxi

Yep, but transformations are essential techniques used by all serial composers. Berg, Webern, Stravinsky, Babbitt, Crumb, Crawford, Feldman, Boulez, list goes on and on...


Yes. It is to modern composition almost what harmonizing things in thirds is to conventional composition.

CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
#25
Quote by Xiaoxi
I don't disagree, and have mixed feelings about serialism. But keep in mind that I just explained it in is an oversimplified, "lite" version of a microscopic concept that skips a lot of fundamentals which are harder to comprehend. There is a useful purpose for why concepts like these exist and are presented in this way. You could express the act of kicking a soccer ball in a mathematical formula, or you can describe the physical act of it with plain words. The latter is obviously easier, but the former belongs to the larger concepts of physical science, which most would agree is important and necessary.

On the surface and considering the practicality of writing this kind of music for the general audience, there is no doubt in my mind that most of the developments in serial music will bypass just about everyone's ears. Straus suggests that by organizing a set class through these mathematical concepts, the music will retain a sense of unity and pattern that the listeners will pick up on, ultimately making for a satisfying listening experience. I disagree, I think the atonal nature of 12 tone serialism is too disorienting for anyone in the present to hear the patterns given so many abstract transformations both on the microscopic pitch levels and the structural levels of the whole piece.

However, if music is a way to convey ideas, then this is a new and exciting way to do that. Every major serial piece is its own world, built on a protocol that is unique to the piece, as opposed to traditional tonal music, which is all built on the same protocols. It is a way of creating a musical object or stating an idea, and then developing it in profound ways. It's just that unfortunately most of these things can't be detected by listening and requires analysis of the score. It's a way of creating and manipulating patterns, kind of like codebreaking. That can be a rewarding experience itself. Yes, the current way in which we are conditioned to listen to music is incompatible with serialism, but I believe our listening abilities will evolve and advance to accept atonality. And the evolution of classical music made the development of serialism inevitable. Like any science, it develops at a rate much faster than the layman can understand, but eventually we will come to a point where the theoretical and the practical meets.
Well, personally I feel like a layman listens to music for relatability and beauty. I think for someone to appreciate something like serialism it takes not only the ability to hear what's going on but the fundamental retraining of enjoying music to appreciate the elegance and cleverness of what's going on like a scientist. There will always be some of us who dig the ideas and stuff circulating about.