Talk:Twelve-tone technique

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Retrograde is a redirect page to an article about astronomy. Invariance is a page that lists various mathematical and physical concepts. Where those links should go instead, if anywhere, is something that those who care about this page should think about. Michael Hardy 17:55, 24 Dec 2003 (UTC)

The retrograde page did, however, include a link to Musical terminology, which previously discussed retrograde. I just changed that link to Counterpoint, which discusses "Contrapuntal derivations" including retrograde. Invariance (which redirects to Invariant), also discusses invariance as it relates to twelve tone music. Hyacinth 18:22, 24 Dec 2003 (UTC)


My proposed outline for this article:

  1. Intro
  2. Antecedents (Scriabin & others using transposed pitch class sets such as the magic chord)
  3. Schoenberg's invention, rules, and suggestions; Hauer's system
  4. Description of basic techniques
    1. Integer notation of row
    2. Mod 12
    3. Matrices: An I-Matrix shows the prime form from left to right, retrograde from right to left, inverse from top to bottom, and retrograde-inverse from bottom to top, being named for the integer on the top or left rows.
  5. Historical summary of Schoenberg's and others uses including more advanced techniques
    1. Derivation
      1. trichord
      2. tetrachord
    2. Partitioning
    3. Combinatoriality
      1. Semi-combinatorial sets are sets whose hexachords are capable of forming an aggregate with one of its basic transformations transposed.
      2. All-combinatorial sets, Six basic hexachordally all-combinatorial sets
    4. Invariance
  6. Final



a free leson website that you can learn more about this subject go to [1] thanks bye!


We should create a page called "dodecaphonism" that redirects to this article. --Pat 02:30, 3 December 2005 (UTC)

Only if we think readers are really going to look for this subject under that term. Hyacinth 01:30, 26 April 2006 (UTC)

Additions to the outline[edit]

The combinatoriality section should also include first, second, third, and sixth order all-combinatorial hexachords. In addition to the definition of these orders, there applications to various theorems could be included. (For example, the pattern of M5-symmetrical and TnM5, TnM7 mappings in first order all-combinatorial hexachords.) In order to arrive at a complete explanation of basic combinatoriality, aspects such as complementation, Tn, TnI operations, and most of Rahn's common-tone theorem should be used as a primer. Inclusion of the combinatorial matrix would also be a good introduction to the topic. I would also include a section on the use of the set-complex to construct a 12-tone row. For this to be effectively achieved, perhaps a seperate article that covers the second part of Forte's "The Structure of Atonal Music" is needed. For a strong introduction to combinatoriality, the section would basically summarize chapter 5.6 of Rahn's "Basic Atonal Theory," as well as some of Perle's text and Babbitt's articles in "Perspectives of New Music." 04:28, 28 December 2005 (UTC)

See Combinatoriality. Hyacinth 01:32, 26 April 2006 (UTC)


I removed the following:

  • "In modern music, noted electronic innovator, Tobi Love, used the technique applied to dance music and classical, allowing songs of either genre to switch back in genre comfortably."

I couldn't find mention of Love on AllMusicGuide. Hyacinth 10:38, 17 February 2006 (UTC) Hyacinth 10:38, 17 February 2006 (UTC)

A confusing topic[edit]

The twelve-tone technique is a confusing topic, but that doesn't mean the article needs to be confusing. I think that there's some language in the article that would make it impossible to decipher for someone who isn't educated in the subject, so I added the template at the top of this talk page. Smedley Hirkum 18:54, 27 February 2006 (UTC)

Which language is confusing? Hyacinth 01:26, 26 April 2006 (UTC)

The title of this article is a travesty[edit]

By my count it is closer to 11.66666...(etc) not quite twelve, given that A flat can only be written in less than three forms.

"Twelve-Tone System", as a musical term, is flawed and misleading. The compositional system invented by Schoenberg is correctly termed "Twelve-Note System", and this is the phrase that is most often used in Britain. "Twelve-Tone" is a direct translation of the German “zwölf Töne” or “zwölftönig”, and musical Germanisms such as this have been infecting English, especially American English, for over a hundred years, and should be purged from the language.

The terminology may be acceptable in German, but it is not in English. We are really dealing with "notes" here, and not "tones", and it should not be necessary to explain the difference to anyone with a modicum of musical knowledge.

I strogely urge that this article be re-titled.

Cbrodersen 12:34, 25 November 2006 (UTC)

I disagree. I have seen the term "twelve-tone" used extensively throughout english writing. I have encountered "twelve-note", but only as a rarity. Perhaps this is a matter or regional dialect, but I think you'll find the majority of English speakers use "twelve-tone" (offhand, it wins by a landslide in a googlefight). Also, if you want to look at the music of Schoenberg, the 12-thing groups are only sometimes twelve notes in length, they often stretch on as he repeats small cycles of pitches within the row, but they always have the twelve pitches. I'm not sure where you're going with "infection" of "Germanisms", but whatever their means of introduction into the English lanaugage, the article should reflect the terms people actually use, not one person's personal ethics about what belongs in the English language. I've added a small note at the top about the use of this alternative name for the technique. - Rainwarrior 19:54, 25 November 2006 (UTC)

I completely agree that the music is called 12-note music, and in most of the literature I have read on the matter, that is what it is called - but then, I live in England.

The accuracy of describing the atomic units as notes is as irrefutable as the use of the word "tone" is confusing to anyone, let alone those to whom this subject matter is new.

Encyclopaedias are not here to recycle urban myths, show the results of straw-man polls (like that "Google-fight" - do as many as 300,000 internet users really know or even care about this enough to vote?) or prolong misconceptions held by common usage. Encyclopaedias are here to educate by using facts in their articles and make the subject matter as transparent as possible, not maintain a degree of opacity so that only those who already understand it can grasp the subject.

The "12 pitches" used in a note row are just notes - the pitch is yet to be determined, and there is no indication of their tonal colouration.

Tones are realised and fully coloured sounds - notes are written indications of what the tones will be. Each performer will produce a different tone.

Tones are also steps in musical scales. The twelve-note scale contains 12 semitones - the greatest number of steps in a scale using whole tones is 6.

In German, the word Ton depends on its context - a luxury that is not afforded by the English language.

Note is therefore the term to use in English to avoid confusion between the notation itself, as used in composition, the step in the scale and the finally produced sound.

I hope this finally clarifies the matter - but realise there are those stuck with the abstract notion that "tone" somehow means the same as "note".

User: / Certif1ed 21:22, 6 January 2007 (UTC)

I personally think twelve-tone is a more accurate term, but this argument aside (Wikipedia needs to reflect actual usage, not the descriptive accuracy of a term), if this is really just a regional dialect issue, I would reccomend you read Wikipedia:Manual of Style#National varieties of English before you make more edits to change the dialect of pages involving twelve-"stuff". - Rainwarrior 22:03, 6 January 2007 (UTC)

Did you read the post above? twelve tone is not accurate at all for the reasons given. It is also not true that an encyclopaedia should reflect actual usage - maybe comment on the inaccuracy of it, but not perpetuate fallacies. This has nothing to do with dialect, and everything to do with facts. MarkCertif1ed 23:04, 6 January 2007 (UTC)
After a couple curse words I still can't believe someone even brought this issue up. Twelve-tone music... in french: Musique à douze tons. All linked with dodécaphonism, Schoneberg, etc... etc... etc... sad... I am gravely disappointed. --CyclePat 22:21, 6 January 2007 (UTC)
French also clarifies the usage through context. The English language has two words "tone" and "note", which have different meanings. Why would anyone be gravely disappointed about this? It's only a reference in an encyclopaedia that few outside of musical studies would ever read. And currently, it's obviously wrong. MarkCertif1ed 23:04, 6 January 2007 (UTC)
Yes, I did read it. I don't agree with it. Did you read mine from earlier? Anyhow, please sign your posts. Just type ~~~~ (it's in the top left corner of your keyboard) at the end of your post and it will automatically be tagged for you. - Rainwarrior 22:38, 6 January 2007 (UTC)

I don't understand why you don't agree, because you don't clarify your position - you just say it's what you think.

You seem to be saying that consensus, or what you think, wins over facts.

I imagine Darwin experienced the same thing :o)

BTW, in the top left corner of my keyboard is the Esc key. (fixed!) MarkCertif1ed 23:02, 6 January 2007 (UTC)

Here is my observations and inferences (with proper sources) (feel free to use it in the main article). As per A History of Western Music, a music history book by Palisca which is highly regarded by recent music scholars in University, "Twelve-tone music" is the proper terminology to describe this type of serial music. (Palisca, Fifth Ed., 860) An interesting point of history describes that Schoenberg formulated a "method of composing with twelve tones which are related only with one another" by 1923. As per Palisca, this "twelve-tone" music or "dodecaphonic technique" may be sumarized as follows:
"...the basis of each compostion is a row or series consisting of twelve tones or pitch classes of the octave arranged in an order the composer chooses."(Palisca 736)
We (The composers) are using all twelve "pitches" of the series before going on to the next. Notice that during Palisca's definition he/she is very careful not to say "twelve-note." Now earlier, I also mentioned that Schoenberg formulated this treaty by 1923 (several years after he took a break in composing).(Palisca 736) If you take a look at the etymology of tone and in particular atonal, you will notice that the term atonal is first attested in 1922. [2] Given the close relationship not only in date but in musical époque(History of the twentieth century) I would support the term "twelve-tone music" or "twelve-tone technic." Atonal music and serialism where created during this time and go hand in hand with the twelve-tone music. Furthermore, I would also support the idea that "twelve-tone" is a lot more "popular" than twelve-note (which may have been used to describe the technic itself).(as I believe Rainwarrior indicated). Essentially you have the tonal period (1899 - 1907),atonal period(1908 - 1921) and docecaphonic period(1912 - 1951). (Ulrich, Michels.Guide Illustré de la musique, 1990, p.525). All theses periodes themes deal with tone and not necessarilly notes (which would be secondary material). --CyclePat 00:44, 7 January 2007 (UTC)
Well, other than the usage, I don't agree that "note" is more appropriate than "tone" because the most fundamental part of the technique is that all twelve tones (in this case, meaning pitch-class) are in continual and regulated use. In some serial music, there is one note per pitch-class per use of a row, but this usage is in the minority. Schoenberg rarely uses up the whole row in just twelve notes. Berg almost never. Webern does quite often (it fits his concise style of writing). It's also a minority in postwar dodecaphony as well. The thing common to them all is not by any means twelve notes. It is twelve pitches. But for further exercise, imagine writing for a whole orchestra but being limited to twelve notes per row. Every beat would be the same 12-tone chord. Study a few dodecaphonic scores and you'll see what I'm talking about.
As for context resolving the meaning, we do that in English too. I don't know why you think context belongs only to French or German or whatever. Tone can mean many things. I can mean timbre, it can mean pitch, it can mean note, it can mean sound. If we wanted to be as unambiguous as possible the correct term would probably be "twelve-pitch-class", but this term, while probably more accurate, doesn't do any better job helping the uninitiated understand what it means (and of course, no one calls it that). Similarly, substituting "note" for "tone" clears up the ambiguity, yes, but as I've said, "note" doesn't describe what the composers are actually doing with the technique. - Rainwarrior 01:32, 7 January 2007 (UTC)
As for "concensus over facts", well, this is about language. In language the concensus is the fact. A word has a meaning only because a bunch of people think it means the same thing. Maybe you want a clearer definition for it, but we are no making the term here, we are describing it; explaining it. The only thing important here about the name is that we use the names people use and understand. If people are unclear about what the name means, they read the article. That's what they came here for, actually. They already knew the name. - Rainwarrior 01:39, 7 January 2007 (UTC)

I never cease to be amazed at the passion created over this matter of musical terminology, a passion perhaps exceeded only over the terms "bar" and "measure". It is true that the preferred British usage is "twelve note". However, many British publications employ "twelve tone" rather than "twelve note". Just pulling a few books off of my shelf, I find this is the case with M. J. Grant's Serial Music, Serial Aesthetics (Cambridge University Press, 2001), Robin Maconie's The Works of Karlheinz Stockhausen, 2nd ed. (Oxford University Press, 1990), and Patricia Hall and Friedemann Sallis, A Handbook to Twentieth-Century Musical Sketches (Cambridge University Press, 2004). American usage, on the other hand, universally uses "twelve-tone" and, as Richard Toop notes in his translation of Stockhausen’s Texte vol 2 (in press):

The familiar term "twelve-tone" is American (tone = note), and dates from Schönberg's teaching in Los Angeles.

FWIW, the OED offers some pertinent definitions:

"Note" 7. a. A single tone of definite pitch, as produced by a musical instrument, the human voice, etc. Cf. TONE n. 2a.

8. A written character or sign expressing the duration and (usually) pitch of a musical sound. Sometimes in pl.: (gen.) musical notation; music in notated form.


2. a. Mus. and Acoustics. A sound of definite pitch and character produced by regular vibration of a sounding body; a musical note.

from which it may be seen that the words are often used interchangeably, in British as well as American practice.--Jerome Kohl 02:33, 7 January 2007 (UTC)

What is gravely saddening is that there are people in this world who consider themselves knowledgable about music, and yet cannot understand that there is a difference between "note" and "tone" - the words are not interchangeable.
Notes are unrealised sounds.
Tones are realised ones.
We say "He cannot sing a note" - that means he cannot realise the notes in the piece.
We say "She has a great tone" - that means she can realise the notes in the piece.
We say "His muscles have great tone" - we can see and experience "tone".
We say "She took notes" - but the notes are probably only meaningful to her until they have been realised.
A pitch is a note that has its approximate frequency defined - the note C is not a pitch until you define the octave it resides in.
When you write a note row, you are more concerned about the order of the notes than the pitches of those notes.
There is no need to cite sources - especially from Wikipedia - if you don't understand that there is a difference between note and tone, you cannot fundamentally understand music.
To use the terms interchangeably is unnecessary obfuscation.
MarkCertif1ed 21:10, 7 January 2007 (UTC)
When a technical distinction between "note" and "tone" is to be made, you are of course correct (though the illustration with "He cannot sing a note" is not well-chosen, since this might mean that he has a terrible cold and is therefore unable to produce a tone, despite his complete competence under healthy conditions). In ordinary language, however, I refer to the OED definitions quoted above, and this still has no real bearing on whether the American/British "twelve tone" should be replaced by the insular British "twelve note". I find it extremely ironic in the context of a plea to split (unnecessarily, in my view, since failing to make this distinction obfuscates nothing at all in the context of Schoenberg's technique) a technical hair, that immediately below this discussion appears the marker: "Category:Wikipedia articles that are too technical".--Jerome Kohl 22:25, 7 January 2007 (UTC)

Almost two months after this heated exchange, I have taken the cautious step of adding the alternative British term (in the form found in the New Grove), alongside "dodecaphony".--Jerome Kohl 20:34, 27 February 2007 (UTC)

It was actually removed very recently, apparently. - Rainwarrior 04:09, 28 February 2007 (UTC)
Erm, what? From the New Grove, or from the Wikipedia article? I just checked New Grove today, and it was still "Twelve-note composition". Your link to the history of Wikipedia doesn't seem to show removal of a reference to this British variant term. Sorry if I am being thick.--Jerome Kohl 06:53, 28 February 2007 (UTC)
Ah! Wait! I see! (I guess I really am thick!) I recall seeing that edit a few days ago, which considerably improved the tone of the initial paragraph, but I didn't notice the removal of "twelve-note technique" from the parenthetical addendum. However, the term as used in New Grove is "twelve-note composition", and the previous version did not specify this is a specifically British usage.--Jerome Kohl 16:29, 28 February 2007 (UTC)
I wasn't being very useful anyway, but I meant the article. The link I mentioned shows someone removing the bolded "twelve-note technique" from the lead. Anyhow, the edit you made was good, my comment didn't really mean anything. - 16:29, 28 February 2007 (UTC)
Twelve tone, or twelve note, what matters most is that so-called music sounds like shit. As such, it doesn't deserve all this fuss. The subject matter of this article is a travesty, not its title. :) —Preceding unsigned comment added by (talk) 23:03, 15 January 2008 (UTC)
Please see Wikipedia:Talk page guidelines. This page is for discussing the improvement of the article. If you want to vent go somewhere else. Hyacinth (talk) 01:02, 16 January 2008 (UTC)

Computer program generating R, I, RI[edit]

Does R, I, RI = Retrograde, Inversion, Retro-Inversion? --CyclePat 03:52, 8 January 2007 (UTC)

Yes, though I think this section of the article should be removed. There is at least one external link to a row-form generator (if that's what the user needs), but even without that the kind of calculation these things do is more or less trivial even by hand (with a little practice a person can easily hand-calculate an entire twelve-tone matrix in about five minutes). This isn't even a computer related topic, and scheme isn't really one of the more widely used programming languages. Who is going to find this useful? - Rainwarrior 06:45, 8 January 2007 (UTC)
Usefullness is in the eye of the beholder. I personally find that the computer matrix generator that I used online was an excellent education tool to learn about 12-tone music. Furthermore, generally historians are pre-occupied with every detail. At wikipedia however, many wikipedian fail to realize the historical significance. Take for example Electric bicycle laws. In october the laws changed and someone decided... "hey! that information is no longer... usefull... or accurate." In fact, the information that this editor removed (and I placed back with a little reformating for historical purposes) was accurate (for that time). Information that is well sourced, and that meets our requirements of wiki rules, should rarely be removed. "usefulness" is a not a wikirule for exclusion. I do not believe we should exclude information because based on our short citedness of "usefullness". (Our "future" generations depend on it...) Back to the law example, we sourced the information but it changed. Though the source might no longer be valide it was at the time and History has a record of this somewhere. I object to the removal. I recomend a re-write. Finally, many tragedies in histories are often linked to the removal or anialition or control of certain information. Take for example the CF-105 Arrow. Unfortunatelly it is difficult to find scematics of this airplane because the program was entirelly scraped (with a conspiracy twist). Let us not kill "the matrix" computer generator. --CyclePat 19:21, 8 January 2007 (UTC)
So, already having two external links to ready-to-go matrix generators, you think we should keep the computer code written in an obscure language that does this as well? Do you think we should have code in other languages too? - Rainwarrior 22:57, 8 January 2007 (UTC)
Yes to the first question! And yes to the second! If we have code in other languages (such as Java, or C++ or musical "notes", or numbers, or scribbles etc...) and it is part of the core subject, obviously, it should be in the article. The programming language Java etc... or whatever programming language is used I believe would be external to the subject, however, 12-tone should point to it. If we are placing code in other languages (music is another language!) then we should try to reference it to a main article. For matrix software I would suggest that if we actually manage to get to the point of discussing the program language, it should be split from this article and place within its own. (Perhaps the article being Matrix Software Generator (Music).) For the code, in reference to the matrix, it should be directly referenced because it is inherently part of the representation of (just like a musical note (which is according to Wikipedia a symbol drawing)) the musical form 12-tone. --CyclePat 00:10, 9 January 2007 (UTC)
I still think it's trivial information, but if it stays I do like the idea of putting these things into a different article. Here's a java matrix generator that's basically about the same functionality as the scheme program. It took about fifteen minutes to write. - Rainwarrior 04:00, 9 January 2007 (UTC)
 // The "TwelveToneMatrix" class.
 public class TwelveToneMatrix
     // row data
     static int row[] = { 8, 7, 5, 10, 4, 11, 3, 2, 1, 0, 6, 9 };

     public static void zeroRow()
       // transpose the row to start at C
       for(int i=0;i<12;++i)
         row[i] = (row[i] + 12 - row[0] ) % 12;
     } // zeroRow  method

     public static int rowOp( boolean inverted, int transpose, int index )
       // returns an element of the row after inversion and transposition
       if( inverted )
         return (( 12 - row[index] ) + transpose) % 12;
         return (( 12 + row[index] ) + transpose) % 12;
     } // rowOp method

     public static void main (String[] args)

       for(int i=0;i<12;++i)
         for(int j=0;j<12;++j)
           // print element j of the row transposed to element i of the inverted row
           int x = rowOp( false, rowOp( true, 0, i ), j );
           System.out.print( x );
           if( x < 10 ) System.out.print(" "); // more space for small numbers
           if( j != 11) System.out.print(" "); // space between numbers

     } // main method
 } // TwelveToneMatrix class

Okay! I've though about it... that code is related to the subject but it's so far out that it doesn't need to be in our article. (We have enough as it is with people probably trying to understand the concept of the matrix that we don't need to bombard them with how to make a program for it. I would place it in it's own article... as perhaps the afformentioned suggestion. Code should leave the article and be placed in a seperate article. --CyclePat 05:26, 10 January 2007 (UTC)
I definitely agree with that. For now, how about we just keep it safe here on the talk page? The following material was added by SteloKim (talk · contribs) in this edit. - Rainwarrior 06:14, 10 January 2007 (UTC)

Computer program generating R, I, RI[edit]

You can get R, I, RI easily using computer programming.

A Scheme program:

 (define (retro l) (reverse l))
 (define (inverse l) (map (lambda (x) (remainder (- 12 x) 12)) l))

 (define prime-row1 '(8 7 5 10 4 11 3 2 1 0 6 9))

 (display prime-row1) (newline)
 (display (retro prime-row1)) (newline)
 (display (inverse prime-row1)) (newline)
 (display (retro (inverse prime-row1))) (newline)


 (8 7 5 10 4 11 3 2 1 0 6 9)
 (9 6 0 1 2 3 11 4 10 5 7 8)
 (4 5 7 2 8 1 9 10 11 0 6 3)
 (3 6 0 11 10 9 1 8 2 7 5 4)

What does this have to do with the article? Hyacinth (talk) 01:06, 16 January 2008 (UTC)
I didn't think it had much at all to do with the article. That's why I moved it here for discussion. - Rainwarrior (talk) 05:47, 17 January 2008 (UTC)


How is the tone of this article not formal? Hyacinth 19:57, 4 May 2007 (UTC)

It's not not formal. The tag was added by Joeyramoney in this edit, with no accompanying explanation. I've removed it. - Nunh-huh 20:05, 4 May 2007 (UTC)

Citation style[edit]

What citation style is used in this article? Hyacinth (talk) 00:27, 13 July 2008 (UTC)

Or when did a citation style become established on Wikipedia and what is that citation style? Hyacinth (talk) 04:09, 22 June 2009 (UTC)

The citation style used here is called "author-date style" in the Chicago Manual of Style, and elsewhere is called Harvard Style. In this particular case, the citations are displayed in footnotes. Both Chicago Style and the footnote variant are accepted styles according to Wikipedia:Manual of style. Many other styles are also acceptable. If you are referring more specifically to the question of whether footnote numbers in the text are to be placed before or after closing punctuation, the Wikipedia position is here : Wikipedia:Manual_of_style#Punctuation_and_inline_citations.—Jerome Kohl (talk) 04:39, 22 June 2009 (UTC)

New Category?[edit]

I propose a new category: "Dead-ends in Composition". This article would be the main article of the category. InFairness (talk) 08:28, 10 May 2009 (UTC)

See WP:NPOV. Hyacinth (talk) 09:00, 10 May 2009 (UTC)

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Removed: Uncited[edit]

  • In 1971 jazz pianist Bill Evans – who played on the landmark modal jazz album Kind Of Blue by Miles Davis – recorded a Grammy Award-winning album called The Bill Evans Album, which included a composition called "T.T.T. (Twelve Tone Tune)" where his trio explored the jazz implications of using the twelve-tone compositional technique.{{Citation needed|date=September 2010}}
  • More recently progressive metal guitarist Ron Jarzombek (Watchtower, Spastic Ink, Blotted Science) used the technique almost exclusively on the track "Oscillation Cycles" off of Blotted Science's album "The Machinations of Dementia". Ron also released a DVD titled "12 Tone Variations" in which similar techniques are explained.{{Citation needed|date=September 2010}}

The above was removed as uncited. Hyacinth (talk) 07:08, 9 March 2012 (UTC)

Number of unique tone rows[edit]

Currently the article states that there are 9,985,920 unique tone rows. This is dubious: 9,985,920 does not divide 12!. I think the correct statement should be:

although 469,022,400 of these are merely transformations of other rows. There are 9,979,200 truly unique twelve-tone rows.

The numbers come from the fact that each equivalence class has 48 elements (12 transpositions, times 2 for inversion, times 2 for retrograde). Choosing one representative from each equivalence class gives 12!/48=9,979,200 representatives. Subtracting this from the total number of tone rows leaves 469,022,400 remaining which are "merely transformations".

--Leo C Stein (talk) 16:11, 20 July 2012 (UTC)

You are probably right. However, what is needed is a reliable source that gives this figure.—Jerome Kohl (talk) 19:09, 20 July 2012 (UTC)
Not knowing the music theory literature, I will update the figure and change the tag to Citation needed. --Leo C Stein (talk) 21:47, 20 July 2012 (UTC)
I have made a cursory search of some of the more likely candidates in the music theory literature, with no result. However, I'm afraid I have never been very interested in the mathematical properties of twelve-tone rows (like Schoenberg, I am more interested in twelve-tone music than twelve-tone music), so other hands may be able more quickly to find the relevant literature. Part of the problem here, of course, is what the criteria are to define "unique forms" of a 12-tone row. The canonic operations of course include transposition, inversion, retrograde, and retrograde-inversion, but do they also include, for example, rotation? What about cycle-of-fourths (M5) and cycle-of-fifths (M7) transformations? If these are included, then various combinatorial properties of certain rows would ensure that the total number could not be an integer division of 12!.—Jerome Kohl (talk) 22:15, 20 July 2012 (UTC)
This is getting slightly off-topic, but I don't believe you can rig up some well-defined equivalence relationship where you'll end up with a number of equivalence classes which does not divide 12!. Including time-rotations is division by another 12, giving 831,600 which is still an integer. Cycle-of-fifths and cycle-of-fourths are inverses so we only need to consider one of them; I believe that is also another factor of 12, giving 69,300 which is again an integer. You can't use any intervals besides fifths and fourths for that type of transformation since otherwise you'll violate the condition of being a tone row. --Leo C Stein (talk) 00:14, 21 July 2012 (UTC)
Sorry, I mis-spoke. What I meant to say was: a number that divides 12! evenly. As I said, I'm not much interested in the maths of twelve-tone technique (though the maths can be very useful to analysis), but if just one particular confluence of transposition, rotation and M5 transform happens to coincide with (for example) one TnRI form, I'm not at all sure that there will be a symmetrical set of similar forms that will add up to such an even division of 12!. If you knock out just one row form as a duplicate, then you have got an extra 11 forms floating around in there.—Jerome Kohl (talk) 00:53, 21 July 2012 (UTC)

This abstract gives a different number. Hyacinth (talk) 03:53, 21 July 2012 (UTC)

Hardly surprising, since there are multiple ways of defining what constitutes a "unique form" of a twelve-tone row.—Jerome Kohl (talk) 03:59, 21 July 2012 (UTC)

Hunter, David J. (2010). Essentials of Discrete Mathematics, p.426. ISBN 9781449604424, brings up the number of distinct rows available through transformation once one has chosen a row. Hyacinth (talk) 04:01, 21 July 2012 (UTC)

Thanks, Hyacinth. One assumes that Hunter specifies the canonic operations within which a "distinct row" is regarded to exist.—Jerome Kohl (talk) 04:15, 21 July 2012 (UTC)

I am very happy that you are all thinking mathematically about this! The idea that the number must divide 12! is a good idea, but unfortunately it is not correct. The reason is that a tone row may be invariant under non-trivial transformations, which will lower the number of tone rows it's equivalent to. For example, the tone row 0123456789AB (just the ascending chromatic scale) is invariant under retrograde inversion, so there are only 24 tone rows in its class: twelve of them are 0123456789AB, 123456789AB0, 23456789AB01, and so on; and the other twelve are their reverses, i.e. BA9876543210, and so on. As you can see, not all equivalence classes are the same size, so the problem is more complicated than just dividing 12! by 48. The original number from a few years ago was correct, and I have found an academic source for it. — Preceding unsigned comment added by (talk) 04:31, 23 February 2015 (UTC)

Template and category[edit]

Composers have been added to Template:Twelve-tone technique and Category:Twelve-tone and serial composers has been created. However, many of the composers added to the template were not originally in Category:Twelve-tone technique and are not in Category:Twelve-tone and serial composers. Hyacinth (talk) 10:19, 14 November 2012 (UTC)

Shall I add those cats, then? Or did you have something else in mind? FWIW, the names came from the beginning of the list of serial and twelve-tone composers in the serialism article. There are still quite a lot more to be added, if that line of action is desirable.—Jerome Kohl (talk) 16:41, 14 November 2012 (UTC)
What is the criteria for inclusion of the composers in the list and template? For example, Louis Andriessen mentions one serial piece. Hyacinth (talk) 06:33, 17 November 2012 (UTC)
A good question. For my part, the sole criterion for adding a name to the list of serial and twelve-tone composers in the Serialism article is that they are identified as such in at least one reliable source. However, such sources are not supplied in that list (as they are for a very few of the entries in the List of dodecaphonic and serial compositions), and I cannot vouch for the other editors who have added names to it. Should we demand references for each composer named? As for the example of Andriessen, what should be the threshold for the numbers of pieces composed in either twelve-tone or serial technique, before a composer may be admitted to this list? (For what it's worth, I can easily come up with another three or four serial pieces by Andriessen, though documenting their seriality may be a little more difficult.) I do not mean this facetiously—it is a serious question that also should be asked about a great many other trivia lists around Wikipedia. In addition, while twelve-tone technique is fairly straightforward, what exactly is to be construed as serialism, anyway? Aren't we obliged to accept the word of reliable sources that this piece or that is serial, or that this composer or that has used serial techniques, even if no particular works are named?—Jerome Kohl (talk) 07:33, 17 November 2012 (UTC)
It seems like there should be a criteria more strict than having composed at least one 12T or serial piece. The huge majority of (all) people have drawn something in their life, but a very small minority are called (visual) artists (almost all people regularly add and subtract, but are not mathematicians).
The listing or categorization of some composers as 12T or serial composers seems very clear. For example, Schoenberg. Once he invented the technique almost all of his compositions where 12T, and he is famous for it. Similarly, the exclusion of some composers seem very clear. For example, Philip Glass wrote 12T/serial pieces as a teenager, but withdrew those compositions, never wrote 12T/serial pieces again, and is famous for non-12T/serial pieces.
I would say being well known for 12T/serial compositions, and primarily writing 12T/serial should be the criteria (I assume, but haven't checked, that this would exclude Aaron Copland, for example). However, I'm not sure how clear or easy this criteria would be to apply. Hyacinth (talk) 08:44, 17 November 2012 (UTC)
Now we are getting somewhere although, as you say, applying these criteria may not be very easy. There is that problematic phrase "well-known", for example, which immediately raises the question, "well-known to whom?" For example, in the circles in which I move, Copland is quite well-known as a twelve-tone composer, even if only for a handful of early and late works (e.g., Poet's Song of 1925, the Piano Quartet of 1950), and perhaps not quite as well-known as a non-twelve-tone serial composer of some middle-period work, such as Vitebsk (1928) and the Piano Variations (1930). (All of this, by the way, is at least "well-known" enough to be found in Howard Pollack's New Grove article on Copland.) On the other hand, if you were to survey the audience at a Boston Pops concert where they had just played Fanfare for the Common Man, with the question "was Aaron Copland a serial composer?" I'm sure you would get quite a different answer. As for "primarily writing 12T/serial", I suppose some sort of quantitative measure could be established, but Schoenberg could easily fail such a measure (if the bar were set, say, at a minimum of 40% of total mature output), given the large number of compositions preceding the Suite, op. 25, and the Wind Quintet, as well as the substantial number of non-twelve-tone pieces he composed after that point (e.g., the Variations for Band and the Second Chamber Symphony). On the other hand, George Rochberg would certainly fail on a statistical basis, and on grounds that he is most famous for having repudiated twelve-tone composition, and yet he surely should be included for the fact that up to about 1962 he was regarded as a leading light of American twelve-tone music. It is also true that he never withdrew his important works using that medium, and why should he have done? The Second Symphony and the Serenata d'estate, to name just two pieces, are amongst the finest he ever composed (and I am not altogether convinced he completely abandoned 12T devices anyway, based on the sound of the Fifth Symphony, even if he only used it as one amongst a variety of techniques). The same problem, only several orders of magnitude larger, applies to the category "serial" which, like "post-modern", seems to mean whatever the author using the word wants it to mean at the moment—a bit like Humpty Dumpty in Through the Looking-Glass. In this case, we really are reduced to the argument of main force: if a sufficient number of writers declare a composer to be a serialist for a long enough time, then he must be one, regardless of how he actually composed his music.—Jerome Kohl (talk) 21:26, 17 November 2012 (UTC)
(Chamber Symphony No. 2 (Schoenberg) was begun in 1906.)
There are many categories which seem highly unclear, such as "Category:Composers for piano". Debussy may clearly be included, but should anyone who ever wrote a piece for piano be included? ("Cat:Opera composers" seems more clear. Having even a single opera performed seems notable.)
I don't think the circles we run in should count. If I where to ask my friends, "Is Copland a serialist?" they very well may ask, "Copland who?" and "What's a serialist?", neither of which seem to prove anything. Further, did you mean Copland is well known, among your circles, as a serialist composer, or as a composer who wrote serial pieces? Hyacinth (talk) 04:59, 19 November 2012 (UTC)
Reading this it seems strange that I didn't mention self-identification as a criteria. Hyacinth (talk) 04:53, 19 November 2012 (UTC)
Schoenberg's Chamber Symphony No. 2 was completed in 1939. Was there a point to your mentioning its earlier beginning?
I agree about clear and unclear categories. Is this one of the former, or one of the latter? If the latter, what can we do to improve matters?
There are circles and then there are circles. Of course you are perfectly right that many people would say, "Copland who?" How does this help us in our present task? If by your follow-on question do I think these people think Copland was a twelve-tone composer or a twelve-tone composer (to cite Schoenberg's distinction), I am very much afraid that some of them see him as the former.
Self-identification is one possible criterion, of course, though we have to keep in mind that people change, and may change their minds about what they identify with (as in politics). Rochberg is one good example; Stravinsky is another. Another difficulty with self-identification, with particular reference to "serialism" (as opposed to twelve-tone technique), has to do with what we mean by that word. Berio, for example, famously renounced serialism, but in words that make clear what he meant was twelve-tone technique. He went right on using tone rows, usually in a free form (e.g., Sequenza V), and remarkably similar to the way in which Stockhausen used them later, in the 1970s (e.g., Tierkreis). Stockhausen self-identified as a serialist, but Berio did not. How do we resolve this conundrum?—Jerome Kohl (talk) 07:31, 19 November 2012 (UTC)

I would assume that most people think that there is a difference between being French, living in France, and having visited France. However, it would seem that you don't or that our rhetorical arguments are becoming too complicated to sort out. Hyacinth (talk) 11:50, 19 November 2012 (UTC)

I thought you were making a reference to Schoenberg's distinction, that is all. So let's stop with the rhetorical arguments, already, and get down to some concrete proposals for dealing with this problem of the thresholds for inclusion or exclusion. One obvious requirement for inclusion is that there must be a reliable source verifying that a composer has either used twelve-tone-technique, or has been a serial composer. I think it would be unreasonable to require any source to verify that any composer has composed 100% of his or her works in this way. This is more or less the way things currently stand. Now, how can we reasonably narrow this down?—Jerome Kohl (talk) 16:51, 19 November 2012 (UTC)
Another thought: It seems to me that the navbox template is a more critical problem than the categories. When we are dealing with a subject like "Beethoven Symphonies" or "States of Brazil", we have a well-defined and reasonably small set of elements, and its purpose is self-evident. One problem with the "Twelve-tone and serial composers" navbox is that it is so open-ended. After all, twelve-tone technique is just a compositional procedure that may be adopted by any number of composers, for a single work or for many—like fugue, polytonality, isorhythm, or even such narrower devices as the cambiata figure or the suspension. Serialism is a much more difficult idea to pin down. Then there is the question of what it is meant to help the reader to do. Does the navbox itself really need a more narrow definition?—Jerome Kohl (talk) 03:25, 20 November 2012 (UTC)

Hauer and Steinbauer[edit]

I am surprised there is no reference to Joseph Mathias Hauer or Othmar Steinbauer in this article, or that wikipedia does not have wiki articles on them yet. One of the books cited in this article is all about Hauer and Steinbauer and their contribution to 12-tone and serialism.4meter4 (talk) 16:14, 26 January 2014 (UTC)

Assuming that you meant Josef Matthias Hauer, there has been a wiki article on him now for a very long time. He should undoubtedly be mentioned in the present article (in fact, he is: see the third paragraph of the lede). Although of course his "twelve-tone method" does not correspond to Schoenberg's twelve-tone technique, it is sometimes confused with it (for example in connection with Roger Sessions's music), and historically there has been some dissension over whether Schoenberg or Hauer had the best claim on the "invention" of "twelve-tone music".—Jerome Kohl (talk) 21:05, 26 January 2014 (UTC)
Thanks. :-) I'm not sure how I missed that. Steinbauer and his school in Vienna would be a nice addition as well.4meter4 (talk) 23:53, 26 January 2014 (UTC)
I am not at all familiar with Steinbauer. From what I read on his article in the German Wikipedia, he appears to have been a follower of both Hauer and Schoenberg (not to mention being a pupil of Webern). Just where he fits into the history of twelve-tone technique, and how notable he is in this context (whether a leader or a follower, for example), I am not yet sure about.—Jerome Kohl (talk) 03:11, 27 January 2014 (UTC)
I just discovered his contributions are covered in part in the last paragraph in the combinatoriality article. I do recall reading somewhere that his school in Vienna produced some notable 12-tone composers. I'll see what I can dig up in google books.4meter4 (talk) 04:58, 27 January 2014 (UTC)
It sounds like you are looking for a teacher of notable students. That's a good goal, but I would prioritize the question of his importance as either a composer (compared with, say Apostel, Jelinek, Heiß, or Krenek) or a theorist (compared again with Krenek, but also Eimert in Europe, or Babbitt, Perle, and Martino in the US).—Jerome Kohl (talk) 05:20, 27 January 2014 (UTC)

No Criticism or Reception??[edit]

Nobody has bothered to list the reactions? The fact that 12-tone is in violation of all of the principles Bach spent decades discovering and that, along with atonal music, is pretty much unlistenable? John Cage revisted all of this stuff in the 60's and came out the other end with very little change - even he concluded most of it just covered old, empty ground. A criticism section would be highly appropriate, particularly considering this kind of 'research' did not escape scot-free. (talk) 07:02, 31 July 2014 (UTC)

Agreed that a reception and/or criticism section would be a good idea, but I hope you have got some really good sources about Bach and his decades-long invention of whatever it is that "the 12-tone" violates, and why that makes any difference at all. I have no doubt you will be able to find sources (though just how reliable remains to be seen) claiming that atonal music is "unlistenable". There is a lot of this sort of thing about. It will be especially interesting to see what you can produce from John Cage concerning his conclusions about twelve-tone technique. Have at it. Everyone is an editor on Wikipedia.—Jerome Kohl (talk) 16:53, 31 July 2014 (UTC)

While J.S.Bach did not employ serialism, in Book I of the Well Tempered Clavier, fugue 12 uses 11 of the 12 notes, and fugue 24 in B minor uses all 12 notes, though some are repeated.Yamex5 (talk) 01:31, 30 August 2014 (UTC)

A melodic minor scale, plus its dominant and subdominant, will cover all 12 notes. That's... not hard nor rare. And that's not related to the 12-note technique here. Ahyangyi (talk) 11:25, 11 January 2015 (UTC)
Indeed not, and neither is the presence of twelve pitch classes necessary for serial composition, though it is difficult to imagine how twelve-tone technique could exist without this precondition. Hans Keller makes the distinction between chromatic saturation and serial techniques very clearly in his 1955 article, "Strict Serial Technique in Classical Music", Tempo (new series) no. 37 (Autumn): 12–16, 21–24. Significantly, Keller does not include any of Bach's many chromatic compositions in his discussion.—Jerome Kohl (talk) 03:51, 12 January 2015 (UTC)

Tone Row Postulates[edit]

The second postulate, "No note is repeated within the row" as stated, is misleading. The immediate repetition of a note is permitted. What the twelve tone method prohibits is returning to a note, call it 'n', after one or more notes following 'n' in the row have been heard, and before the remaining notes of the row have all been heard. As an example, consider the row { c, d, bb, eb, db, f, f# g#, e, a, g, b }. When the note f# is played for the first time, it may be repeated as often as the composer wishes, but once g# is played, the f# cannot be played again until e, a, g and b have been played.

Also, the rule above only applies to monophonic lines. If the music consists of two or more voices, nothing prohibits one voice from progressing through the tone row while the other voice(s) sustain or repeat their current note. Yamex5 (talk) 23:43, 29 August 2014 (UTC)

I think if you read this article a little more carefully, you will notice that the passage to which you are referring concerns the construction of tone rows. A little further down is a section on "Application in composition", which points out this distinction, and goes on to say "Thus, for example, postulate 2 does not mean, contrary to common belief, that no note in a twelve-tone work can be repeated until all twelve have been sounded". Similarly, a twelve-tone row does not have "other voices"—in fact, it could be argued that it is not even a "monophonic line" in fact, but rather a theoretical abstraction that may be manifested in a variety of ways, including monophonic lines.—Jerome Kohl (talk) 23:52, 29 August 2014 (UTC)

Oops, I agree with you, my oversight. Shall I remove this section or do you want to? — Preceding unsigned comment added by Yamex5 (talkcontribs) 01:36, 30 August 2014 (UTC)

It is usually best to leave discussions in place, even if they may cause some slight embarrassment. In this case, it may serve as a suggestion for something that might be made clearer in future, or at least a caution not to make that section less clear.—Jerome Kohl (talk) 02:56, 30 August 2014 (UTC)

Criticism by (J.N.) Straus[edit]

Joseph Nathan Straus (Twelve-tone music in America, chapter 8, pp.177 et seq) makes the point (which I agree with, but - irrelevant) that no music (aside from exercises for theory classes, obviously, etc etc- one makes certain assumptions and means no music actually and intentionally composed, not just to contradict this point...) - is "Twelve-tone" in any strict way, nor does this matter. (Nor is it a form of serialism; you can repeat notes without repeating them indefinitely without their being based on any finite tone-row, and vice versa, etc; the concepts are orthogonal.) Many a composer has, it seems, apologized for writing insufficiently non-repetitive, non-twelve-tone music without realizing that's not the point... (I should put apologize in silly-quotes; who cares what kind of music one writes, so long as it's not boring... but I hope what I really mean is - well, will edit later; no time.) Schissel | Sound the Note! 21:44, 8 August 2015 (UTC)

This sounds like a point that is worth developing. Joe certainly knows his beans when it comes to twelve-tone music (in contradistinction to twelve-tone music, as Schoenberg so aptly put it). In this connection, you may be interested in taking a look at the edit history of Piano Concerto (Schoenberg), where certain former claims about "strict" twelve-tone practice have been adjusted quite a bit recently. Nearly a century after Schoenberg first devised the technique very few people really understand how it works in practice, though many, having read about it in a book, think they know what it is supposed to be. Joe is one of the rare exceptions.—Jerome Kohl (talk) 22:22, 8 August 2015 (UTC)