![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||
|
![]() | This article may be too technical for most readers to understand.(September 2010) |
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)
My proposed outline for this article:
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)
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." 65.9.15.143 04:28, 28 December 2005 (UTC)
I removed the following:
I couldn't find mention of Love on AllMusicGuide. Hyacinth 10:38, 17 February 2006 (UTC) Hyacinth 10:38, 17 February 2006 (UTC)
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)
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 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@yahoo.co.uk / Certif1ed 21:22, 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)
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.
"Tone"
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)
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)
Does R, I, RI = Retrograde, Inversion, Retro-Inversion? -- CyclePat 03:52, 8 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;
else
return (( 12 + row[index] ) + transpose) % 12;
} // rowOp method
public static void main (String[] args)
{
zeroRow();
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
}
System.out.println("");
}
} // main method
} // TwelveToneMatrix class
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)
Output:
(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)
How is the tone of this article not formal? Hyacinth 19:57, 4 May 2007 (UTC)
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)
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)
![]() |
An image used in this article,
File:Schoenberg - Op. 23, mov. 5.png, has been nominated for deletion at
Wikimedia Commons in the following category: Deletion requests January 2012
Don't panic; a discussion will now take place over on Commons about whether to remove the file. This gives you an opportunity to contest the deletion, although please review Commons guidelines before doing so.
This notification is provided by a Bot -- CommonsNotificationBot ( talk) 20:44, 9 February 2012 (UTC) |
![]() |
An image used in this article,
File:Schoenberg - Op. 23, mov. 5.mid, has been nominated for deletion at
Wikimedia Commons in the following category: Deletion requests January 2012
Don't panic; a discussion will now take place over on Commons about whether to remove the file. This gives you an opportunity to contest the deletion, although please review Commons guidelines before doing so.
This notification is provided by a Bot -- CommonsNotificationBot ( talk) 20:46, 9 February 2012 (UTC) |
The above was removed as uncited. Hyacinth ( talk) 07:08, 9 March 2012 (UTC)
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:
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)
This abstract gives a different number. Hyacinth ( talk) 03:53, 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)
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 71.168.104.144 ( talk) 04:31, 23 February 2015 (UTC)
The general way to solve such problems uses Burnside's lemma. Double sharp ( talk) 12:51, 10 July 2020 (UTC)
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)
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 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)
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. 203.166.241.56 ( talk) 07:02, 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)
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)
Oops, I agree with you, my oversight. Shall I remove this section or do you want to? — Preceding unsigned comment added by Yamex5 ( talk • contribs) 01:36, 30 August 2014 (UTC)
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)
I attempted to add some references concerning Copland's and Stravinsky's history with serial composition, and also a link to an English translation of Hauer's original treatise, but the edits didn't "take". An hour's worth of work lost in the ozone before I even finished adding all the reference links. Don't have time for this. The article is full of "citation needed" and "failed verification" tags, but apparently they can't currently be corrected with citations and verification sources. Give that issue, the article should probably be deleted and rewritten, since as it stands it is full of (apparently uncorrectable) errors. — Preceding unsigned comment added by 74.95.43.253 ( talk) 02:17, 21 March 2024 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||
|
![]() | This article may be too technical for most readers to understand.(September 2010) |
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)
My proposed outline for this article:
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)
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." 65.9.15.143 04:28, 28 December 2005 (UTC)
I removed the following:
I couldn't find mention of Love on AllMusicGuide. Hyacinth 10:38, 17 February 2006 (UTC) Hyacinth 10:38, 17 February 2006 (UTC)
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)
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 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@yahoo.co.uk / Certif1ed 21:22, 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)
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.
"Tone"
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)
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)
Does R, I, RI = Retrograde, Inversion, Retro-Inversion? -- CyclePat 03:52, 8 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;
else
return (( 12 + row[index] ) + transpose) % 12;
} // rowOp method
public static void main (String[] args)
{
zeroRow();
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
}
System.out.println("");
}
} // main method
} // TwelveToneMatrix class
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)
Output:
(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)
How is the tone of this article not formal? Hyacinth 19:57, 4 May 2007 (UTC)
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)
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)
![]() |
An image used in this article,
File:Schoenberg - Op. 23, mov. 5.png, has been nominated for deletion at
Wikimedia Commons in the following category: Deletion requests January 2012
Don't panic; a discussion will now take place over on Commons about whether to remove the file. This gives you an opportunity to contest the deletion, although please review Commons guidelines before doing so.
This notification is provided by a Bot -- CommonsNotificationBot ( talk) 20:44, 9 February 2012 (UTC) |
![]() |
An image used in this article,
File:Schoenberg - Op. 23, mov. 5.mid, has been nominated for deletion at
Wikimedia Commons in the following category: Deletion requests January 2012
Don't panic; a discussion will now take place over on Commons about whether to remove the file. This gives you an opportunity to contest the deletion, although please review Commons guidelines before doing so.
This notification is provided by a Bot -- CommonsNotificationBot ( talk) 20:46, 9 February 2012 (UTC) |
The above was removed as uncited. Hyacinth ( talk) 07:08, 9 March 2012 (UTC)
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:
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)
This abstract gives a different number. Hyacinth ( talk) 03:53, 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)
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 71.168.104.144 ( talk) 04:31, 23 February 2015 (UTC)
The general way to solve such problems uses Burnside's lemma. Double sharp ( talk) 12:51, 10 July 2020 (UTC)
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)
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 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)
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. 203.166.241.56 ( talk) 07:02, 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)
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)
Oops, I agree with you, my oversight. Shall I remove this section or do you want to? — Preceding unsigned comment added by Yamex5 ( talk • contribs) 01:36, 30 August 2014 (UTC)
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)
I attempted to add some references concerning Copland's and Stravinsky's history with serial composition, and also a link to an English translation of Hauer's original treatise, but the edits didn't "take". An hour's worth of work lost in the ozone before I even finished adding all the reference links. Don't have time for this. The article is full of "citation needed" and "failed verification" tags, but apparently they can't currently be corrected with citations and verification sources. Give that issue, the article should probably be deleted and rewritten, since as it stands it is full of (apparently uncorrectable) errors. — Preceding unsigned comment added by 74.95.43.253 ( talk) 02:17, 21 March 2024 (UTC)