# I can't get to the bottom of this jargon!



## clavichorder (May 2, 2011)

http://en.wikipedia.org/wiki/Tone_row

http://en.wikipedia.org/wiki/Serialism

http://en.wikipedia.org/wiki/Musical_set_theory

What the hell is a tone row exactly? "non repetitive ordering"

What the hell is set theory?

What makes something serial?

I came to wikipedia to learn what makes some music tonal, and other music atonal, and wondering if atonal was necessarily serial or set theory based(whatever the hell that is). I've never gotten a clear understanding. Why is William Schuman's 6th symphony tonal(is it?) and a Roger Sessions Symphony(its serial) or Alan Berg's violin concerto atonal(also serial)? I can't get the the bottom of this esoteric jargon.

I read of examples of Mozart, Bach and Beethoven using tone rows. I can't figure out what makes them tone rows. I have a feeling that a tone row is just a _linear_ succession of chromatic pitches, but I understand that the notes of the tone row can be used out of order? Are serial compositions usually comprised up of many of these tone rows? If so do these tone rows remain isolated, or do they mix up? What prevents things from just becoming one big tone row mess that uses all the notes? I don't get it.


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## Webernite (Sep 4, 2010)

You just take the twelve notes of the chromatic scale and put them in whatever order you like - that's a tone row. Once you've done that, you use the tone row as the motif - the theme - and develop it in basically the same way Beethoven/Brahms would develop a theme. That was Schoenberg's approach, any way. Other composers like Berg were more flexible.


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## violadude (May 2, 2011)

To answer your question, no, atonal does not necessarily make something serial. Atonal music for lack of a better term is any music without a key center, or without a gravitational pull to a tonic. Serial music is any music that orders the 12 chromatic notes, dynamics, phrase types, articulation and other things in a certain set order and uses that order as a bases for the piece. Basically, every serial piece is atonal, but not every atonal piece is serial.

Note: As the article states, something can be considered serial if it is only the notes that are placed in an order (a tone row). But if everything else is as well (dynamics, articulation, phrase structures ect.) it is considered integral or total serialism.


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## Meaghan (Jul 31, 2010)

I wish I had brought my music theory professor's wonderful textbooks to Philadelphia with me so I could quote them here. She makes 20th century theory make so much sense, and I can't explain this stuff half as well as she does. But I can tell you what is meant by non-repetitive ordering: 

If you want to write 12-tone music, you start by constructing a 12-tone row. You do this by taking the 12 tones and arranging them in a sequence of your choosing, in which all of them are used and none of them repeat (non-repetitive ordering). This sequence is your prime row. It is the material you will use to compose your 12-tone piece. You can take your prime row and play it backwards (retrograde), with the intervals turned upside-down (inverted), or transposed, or any combination of these, and make music out of it in that way.

Serialist music does not have to be 12-tone, and can even be tonal. Serialism is often (inaccurately) used as a synonym for 12-tone, but can be applied to any music that uses a sequence as its basic building block. An example of a tonal serialist work would be the theme and variations movement from Stravinsky's Sonata for Two Pianos.


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## violadude (May 2, 2011)

Meaghan said:


> I wish I had brought my music theory professor's wonderful textbooks to Philadelphia with me so I could quote them here. She makes 20th century theory make so much sense, and I can't explain this stuff half as well as she does. But I can tell you what is meant by non-repetitive ordering:
> 
> If you want to write 12-tone music, you start by constructing a 12-tone row. You do this by taking the 12 tones and arranging them in a sequence of your choosing, in which all of them are used and none of them repeat (non-repetitive ordering). This sequence is your prime row. It is the material you will use to compose your 12-tone piece. You can take your prime row and play it backwards (retrograde), with the intervals turned upside-down (inverted), or transposed, and make music out of it in that way.
> 
> Serialist music does not have to be 12-tone, and can even be tonal. Serialism is often (inaccurately) used as a synonym for 12-tone, but can be applied to any music that uses a sequence as its basic building block. An example of a tonal serialist work would be the theme and variations movement from Stravinsky's Sonata for Two Pianos.


Can a serialist piece be tonal? I didn't know that. Are there real examples out there?


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## Meaghan (Jul 31, 2010)

violadude said:


> Can a serialist piece be tonal? I didn't know that. Are there real examples out there?


I guess you could say that serialism became _a thing_ with the advent of dodecaphony, and so it's primarily associated with that. It started off as an alternative to tonality, a different way of having order in music, but later composers experimented with using principles of serialism in tonal music, including, as I said, Stravinsky. The movement I referenced uses a 29-note row and is tonal.

(This, of course, would _not_ qualify as "non-repetitive ordering." But a _series_ doesn't have to refrain from repeating pitches, just a 12-tone row.)


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## Webernite (Sep 4, 2010)

Schoenberg went through three periods:

Chromatic
Atonal
Twelve-tone (i.e. when he used tone rows)

From the brain's point of view, these are essentially just different degrees of chromaticism. You could label them like this:

Chromatic
Very, very Chromatic 
Very, very, very chromatic

A lot of people mistake _Pierrot Lunaire_ for a twelve-tone piece, for example, when in fact it's from his atonal period.


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## Kopachris (May 31, 2010)

Tonality is created when there is a distinct relationship between two or more notes, usually tonic and dominant, which is reinforced by certain harmonic and/or melodic progressions such as your typical perfect authentic cadence (tonic-predominant-dominant-tonic). You can use whatever method you want to make your music atonal as long as it gets rid of that hierarchical relationship. A tone row is simply an ordering of the 12 tones of the chromatic scale so that no note is repeated (e.g. D-C#-F-E-G#-A-G-D#-F#-A#-C-B). When using a tone row, the composer usually only uses inversion, retrograde, and transpositions (and any combinations of those) of that tone row (e.g. inverted, reversed, and transposed by a major second: G-F#-G#-C-D#-B-A-A#-D-C#-F-E). The notes of the tone row can be used in any voice or any register, but they can't be used out of order (i.e. only adjacent notes of the row can be stacked vertically, such as A-G-D# in the above row, but they could be stacked in any order, such as G-D#-A or D#-G-A). Such works are basically written twelve notes at a time. Technically, that's a type of serialism, but "serialism" serialism involves using a similar process with other elements (rhythm, dynamics, etc.). Neither of these are inherently atonal, but it's usually quite difficult to make tonal music while using 12-tone or serial techniques.

I'm sorry I can't explain set theory for you--I'm trying to wrap my head around it still. Could you provide links to those examples of Mozart, Bach, and Beethoven tone rows, though?


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## violadude (May 2, 2011)

Meaghan said:


> I guess you could say that serialism became _a thing_ with the advent of dodecaphony, and so it's primarily associated with that. It started off as an alternative to tonality, a different way of having order in music, but later composers experimented with using principals of serialism in tonal music, including, as I said, Stravinsky. The movement I referenced uses a 29-note row and is tonal.
> 
> (This, of course, would _not_ qualify as "non-repetitive ordering." But a _series_ doesn't have to refrain from repeating pitches, just a 12-tone row.)


Ah, that's interesting. I should listen to that piece.


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## Meaghan (Jul 31, 2010)

violadude said:


> Ah, that's interesting. I should listen to that piece.


Also, the "Serialism and high modernism" section of the wikipedia serialism article talks a bit about Stravinsky's relationship with serialism and illustrates the blurry line between serialist and not. I just read it, it's interesting.


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## violadude (May 2, 2011)

Meaghan said:


> Also, the "Serialism and high modernism" section of the wikipedia serialism article talks a bit about Stravinsky's relationship with serialism and illustrates the blurry line between serialist and not. I just read it, it's interesting.


Now that you mention it, I do remember reading about Rautavaara's 3rd symphony being a serialist piece, even though it sounds completely tonal.


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## Argus (Oct 16, 2009)

Listen and learn.


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## clavichorder (May 2, 2011)

Webernite said:


> You just take the twelve notes of the chromatic scale and put them in whatever order you like - that's a tone row. Once you've done that, you use the tone row as the motif - the theme - and develop it in basically the same way Beethoven/Brahms would develop a theme. That was Schoenberg's approach, any way. Other composers like Berg were more flexible.


I read about Stockhausen using tone rows more freely, the notes were not necessarily played in the same order way every time, and this supposedly erases all trace of themes. I'm not sure I like that idea, but I will listen to some of this music to try and understand how it functions.


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## clavichorder (May 2, 2011)

violadude said:


> To answer your question, no, atonal does not necessarily make something serial. Atonal music for lack of a better term is any music without a key center, or without a gravitational pull to a tonic.


That's what I originally thought. And yet, I've heard people say that The Rite of Spring is tonal, yet in many parts it doesn't seem to gravitate toward any tonic, though it is harmonically a well wrought piece of craftsmanship.

Also, Dutilleux is by this definition, atonal, but his harmonies give the impression of being extremely well thought out.

On the other hand, Hindemith will have a tonic sometimes, but his harmonies sometimes give the impression of being a little less there for the sake of color, and more for the passing of one thing to another. Its like he has a vaguely tonal skeleton with every manner of 'wrong note' thrown in, whereas Dutilleux has an atonal skeleton with beautiful with very carefully selected harmonies. Stravinsky Rite seems somewhere in between.


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## clavichorder (May 2, 2011)

violadude said:


> Note: As the article states, something can be considered serial if it is only the notes that are placed in an order (a tone row). But if everything else is as well (dynamics, articulation, phrase structures ect.) it is considered integral or total serialism.


A helpful clarification. There are varying degrees of 'purity.'


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## clavichorder (May 2, 2011)

Meaghan said:


> If you want to write 12-tone music, you start by constructing a 12-tone row. You do this by taking the 12 tones and arranging them in a sequence of your choosing, in which all of them are used and none of them repeat (non-repetitive ordering). This sequence is your prime row. It is the material you will use to compose your 12-tone piece. You can take your prime row and play it backwards (retrograde), with the intervals turned upside-down (inverted), or transposed, or any combination of these, and make music out of it in that way..


So, am I write in understanding that in a strict serial piece, there are NO notes in the piece that deviate from the notes in the given row? Or that at least a row is kept up and remains 'pure' until its time for a change?

Is non repetitive ordering the 'most extreme' version of serialism? Or is this merely the basic principle? The non repetitive aspect is that each note of the row is only used once in the sequence? Is this a basic requirement?

I suppose I'd have to try to observe this in action. Theory will only get me so far, because certain things that seem crazy in theory, might seem crazy in a totally different way in sound.


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## clavichorder (May 2, 2011)

Meaghan said:


> I guess you could say that serialism became _a thing_ with the advent of dodecaphony, and so it's primarily associated with that. It started off as an alternative to tonality, a different way of having order in music, but later composers experimented with using principles of serialism in tonal music, including, as I said, Stravinsky. The movement I referenced uses a 29-note row and is tonal.
> 
> (This, of course, would _not_ qualify as "non-repetitive ordering." But a _series_ doesn't have to refrain from repeating pitches, just a 12-tone row.)


Hearing you talk about this example gives me a clearer picture.


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## Meaghan (Jul 31, 2010)

clavichorder said:


> So, am I write in understanding that in a strict serial piece, there are NO notes in the piece that deviate from the notes in the given row? Or that at least a row is kept up and remains 'pure' until its time for a change?
> 
> Is non repetitive ordering the 'most extreme' version of serialism? Or is this merely the basic principle? The non repetitive aspect is that each note of the row is only used once in the sequence? Is this a basic requirement?
> 
> I suppose I'd have to try to observe this in action. Theory will only get me so far, because certain things that seem crazy in theory, might seem crazy in a totally different way in sound.


If a piece adheres very strictly to serialism, all notes in it will belong to a row. The row may not sound the same every time, because it may be retrograde, inverted, or transposed. Non-repetitive ordering is a necessary characteristic of a 12-tone row, and yes, the non-repetitive aspect is that each note is used only once within the sequence, though the sequence itself will repeat. Non-repetitive ordering is not a necessary characteristic rows/sequences that are not 12-tone.


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## clavichorder (May 2, 2011)

Kopachris said:


> Tonality is created when there is a distinct relationship between two or more notes, usually tonic and dominant, which is reinforced by certain harmonic and/or melodic progressions such as your typical perfect authentic cadence (tonic-predominant-dominant-tonic). You can use whatever method you want to make your music atonal as long as it gets rid of that hierarchical relationship. A tone row is simply an ordering of the 12 tones of the chromatic scale so that no note is repeated (e.g. D-C#-F-E-G#-A-G-D#-F#-A#-C-B). When using a tone row, the composer usually only uses inversion, retrograde, and *transpositions* (and any combinations of those) of that tone row (e.g. inverted, reversed, and transposed by a major second: G-F#-G#-C-D#-B-A-A#-D-C#-F-E). The notes of the tone row can be used in any voice or any register, but they can't be used out of order (i.e. only adjacent notes of the row can be stacked vertically, such as A-G-D# in the above row, but they could be stacked in any order, such as G-D#-A or D#-G-A). Such works are basically written twelve notes at a time. Technically, that's a type of serialism, but "serialism" serialism involves using a similar process with other elements (rhythm, dynamics, etc.). Neither of these are inherently atonal, but it's usually quite difficult to make tonal music while using 12-tone or serial techniques.
> 
> I'm sorry I can't explain set theory for you--I'm trying to wrap my head around it still. Could you provide links to those examples of Mozart, Bach, and Beethoven tone rows, though?


Sorry, if this seems dense, but the whole tone row can be transposed? And I think I understand what "stacking" vertically means.

As for tone rows by Beethoven, Mozart, and Bach, I can't find the examples, but if you haven't already looked, its under "history and usage" in the wiki tone row article. It would take more understanding of what they are to scout them out in a piece, although I might surprise myself with blind intuition, and in that case you can accuse me of being lazy.


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## Webernite (Sep 4, 2010)

The classic example is the B minor fugue theme from the first book of the _Well-Tempered Clavier_, but that's not strictly a tone row because some notes are repeated.


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## Meaghan (Jul 31, 2010)

There are very interesting similarities between serialism and fugues in general. Composers use the same transformations (retrograde, inversion, transposition) for tone rows and fugue subjects.


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## clavichorder (May 2, 2011)

Meaghan said:


> There are very interesting similarities between serialism and fugues in general. Composers use the same transformations (retrograde, inversion, transposition) for tone rows and fugue subjects.


So the point is, tone rows are very strict, like a fugue, it seems.


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## Jeremy Marchant (Mar 11, 2010)

violadude said:


> Can a serialist piece be tonal? I didn't know that. Are there real examples out there?


Try the second (slow) movement of Andrew Rudin's piano concerto. He assured me when I interviewed him for _Fanfare _ that it was a fully serial work. (It's on Spotify - search for the album "Rudin: celebrations".)


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## Kopachris (May 31, 2010)

clavichorder said:


> Sorry, if this seems dense, but the whole tone row can be transposed? And I think I understand what "stacking" vertically means.


Yes. In fact, when writing 12-tone, the whole row has to be transposed. Can't just transpose the first part of the row and leave the other part untransposed, because that might cause a note to be repeated.

Also, stacking vertically as in harmony.


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## FrankieP (Aug 24, 2011)

You also asked what Set Theory is - don't think it's been responded to yet (sorry if it has!).

Set Theory was developed as a way of classifying pitches in (mainly) atonal music - as the labelling of chords etc as I, IV etc is obviously fairly useless when analysing 12-tone music. There are lots of weird and wonderful rules and quirks, but a few basics:

1. pitches in an octave are referred to working upwards from O-11 (ten and eleven are referred to as 't' and 'e'), so that each individual semitone has a value. 0 is given to the central pitch of the piece, if there is one, or if not I *think* it's C by default.

2. by this logic, a major triad would be [0,4,7]. This type of classification only really works for atonal music though.

3. two note chords are called 'dyads', three note 'trichords', 4 'tetrachords', 5 'pentachords', 6 'hexachords'.. get a bit lost after that!

4. One of the biggest names in the set theory world is Allan Forte, whose book 'The Structure of Atonal Music' outlines his theories and is a very good - if difficult - read. He analysed a lot of music by people like Carter and especially Babbitt in the process.

I hope that's clear-ish? If you want any more info/explanation/alternative explanation because this is unclear then please just ask!


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## violadude (May 2, 2011)

Clavichorder, if you are interested in composing a twelve tone piece. What I advise you to do is just think of your tone row as an alternative scale to the Major or minor scale.


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## PetrB (Feb 28, 2012)

violadude said:


> ... Basically, every serial piece is atonal, but not every atonal piece is serial.


Well, to add to the poor lad's confusion, serial music can be 'just a series' treated in that manner, but not atonal, lol.
Stravinsy, Septet, o.a.
Irving Fine used a twelve-tone row as the basis for all subsequent material in his first (only?) String Quartet, but the work is 'tonal' and 'in C.' Depends upon the tone row, how it is worked, etc.

Working from a series, in the manner of that first Viennese school, is a very near parallel to the earlier construction of the materials of music from other modes or scales. A diatonic scale also 'yields' harmony: in common practice those accords are primarily in thirds. Later in 20th century harmonic context, it came to be 'any three discrete pitches' could be an accord, as long as they were contextually being used as harmonic function similarly as thought of in the past (vs. 'mere coloration.')

Just as in the older manner, both horizontal lines and verticals (accords) are derived from the same material, or scale.

Serial music, strict sense, is very native to contrapuntal procedure, and is easier, (my opinion) to work contrapuntally than as a 'homophonic' procedure.
Not transposing the row would be like staying in one key, and very boring.

Set theory, coming after that first Viennese school of serial approach is where 'sets' of a category, a group of pitches (think 'cell' too) or intervals are set as defining a category. FrankieP has already defined its basics clearly. A dyad -- to be petty academic -- is an interval, i.e. two discrete notes, vs a chord, which by definition is three minimum (or more) discrete pitches. That has not changed 

When you 'go serial' or 'set' theory, they are other ways of generating non-common practice harmonies, and as common practice also considers 'withholding' some of the scale to keep a later area of the composition 'fresh' to the ears in harmony or pitch - content, that same consideration is in play with 'set' theory.

Early serialists soon found if you used all 12 pitches all the time, there was no area to take the music where the ear heard any pitch as 'fresh.' That eliminates surprise or 'newness' and would otherwise be a formula for dulling the listener's ear rather than engaging it. Quickly, they realized by isolating a portion of the row, that could keep one area of a piece in that pitch area: when the other pitches later came into play, there was 'someplace to go.' That, I'm certain was the trigger for thinking of 'sets.'

Elliott Carter's atonal music is based on set theory, where he has 'classified' sets by intervals (and chords of type - which are also 'pitch sets.) That too, leaves more room to keep the music fresh, and a feeling of change for the listener, than a more arbitrary use of all the intervals shuffled like a deck of cards. That manner also allows for pillaging either horizontal (lines) or vertical (chords.)

Series method DOES NOT HAVE TO INCLUDE ALL 12 PITCHES. Stravinsky's In Memoriam Dylan Thomas uses a pitch matrix of five pitches. When he wrote out that matrix, he limited it to five transpositions, at intervals determined by the intervals of the original row. That makes for a very 'clear' and refined vocabulary. "Great art likes chains," as Nadia Boulanger put it.

'Tone rows' of five, six, seven, etc. have all been used somewhere by someone, I'm sure.

If you really want to avoid everyone's sense of archetypical "tonality," not only avoid any honing in on or defining a Tonic, but of course what really defines the 'tonic,' the relationships to it of IV and V. Assiduously avoid a sense of I -V, and I-IV, and you are more likely to succeed.

There. Did any of that help?


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## PetrB (Feb 28, 2012)

"So, am I write in understanding that in a strict serial piece, there are NO notes in the piece that deviate from the notes in the given row? Or that at least a row is kept up and remains 'pure' until its time for a change?"

That is an assumption, based on the 'pure' principle. Its inventor was the first to break each and all of those 'rules' in his own works.

When the composer had moved to Los Angeles, the young newly formed Arnold Schönberg Quartet were enthusiastic young proponents of this composer, and worked directly with him when they were preparing his Quartets for performance. The 'Cellist noticed in his part 'an anomoly' - a B-natural where if the row were 'strict' should not of been there. The player pointed to that B-natural in his part and asked Schönberg, "Shouldn't that be a B-flat?" The composer answered with some irritation, "If I had wanted a B-flat there I would have written one."

So much for the 'rules' of theory. 

Remember, 
ALL THEORY 
~ IS NOT A SET OF RULES 
~ IS ONLY A TECHNICAL PREMISE OF HOW TO CONSTRUCT MUSIC
~ IS A TOOL TO ANALYZE WHAT A COMPOSER HAS DONE, INCLUDING WHAT YOU HAVE DONE, ARE TRYING TO DO.

Non repetitive ordering is the basic principle. 
There are no requirements, just principles: if you 'go back' or rock back and forth on an interval or sequence from the row, it starts, de facto and without regarding the pitch content, to be heard by listeners as 'tonal.' (Think of Vivaldi  

Theory only gets the very best so far, it is the sound, and the ear, always, that is the ultimate guide.


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## PetrB (Feb 28, 2012)

I find comments about 'serialism,' traits of it, or 'tone-rows' in repertoire of the earlier musics gratuitous and very very very very very dodgy.

Best to say the earlier composers once in a while made a construct quite heavy in all or near all of the chromatic scale, because, clearly, they were not 'thinking that way' any more than Bach was thinking 'Tonal Harmony' ala music theory of the 1880's.

The pointing out of 'rows' in earlier repertoire is no more interesting or valid (other than they used an extraordinary number of pitches for the time) than a feminist spin interpretation of Oedipus Rex - that is just not to be extracted from a work written in a time where the ethos was light years away from any form of 'feminism': not even the most forward-thinking radical hetaera of the time was a feminist as we think of it now.

There is that famous chromatic single-line gesture, isolated, to boot, in Mozart's later G-minor symphony, a sequence of 11 of the twelve pitches. Daring, audacious, and 'modern' as can be for its time - in its context it is still breath-taking when heard now. The fact it is a gesture, he did it once, it is a transition and -- has nothing directly to do with the overall organization of the piece, turns, "See, Wolfrl was anticipating or 'onto' serialism." into a beyond skewed 'observation.'


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## mmsbls (Mar 6, 2011)

PetrB said:


> When you 'go serial' or 'set' theory, they are other ways of generating non-common practice harmonies, and as common practice also considers 'withholding' some of the scale to keep a later area of the composition 'fresh' to the ears in harmony or pitch - content, that same consideration is in play with 'set' theory.
> 
> Early serialists soon found if you used all 12 pitches all the time, there was no area to take the music where the ear heard any pitch as 'fresh.' That eliminates surprise or 'newness' and would otherwise be a formula for dulling the listener's ear rather than engaging it. Quickly, they realized by isolating a portion of the row, that could keep one area of a piece in that pitch area: when the other pitches later came into play, there was 'someplace to go.' That, I'm certain was the trigger for thinking of 'sets.'


My limited understanding of musical set theory is that it is more related to mathematical group theory where operators are very important. Examples of operators in music would be transposition (e.g. moving all pitches in a set up a major third), inversion (e.g. instead of increasing pitch by a major third, decrease by a major third), and multiplication (e.g. expanding intervals by a fixed amount). An interesting one is complementation where the complement of a pitch set is all the notes not in that set. The complementation operator would seem to produce what you call "fresh" areas.

Do you believe that these operators are the "important" aspect of music based on set theory?


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## clavichorder (May 2, 2011)

I've gone through serialism today and I think I pretty well grasp it now.

As for set theory, I'll take some time, when I have the energy to review FrankyP, PetrB, and mmslbs's posts to see if anything is illuminated.


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