# 12 tone rows



## Tikoo Tuba

How many are possible ? May you present just one ?


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## mbhaub

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =* 479,001,600*. More than enough to keep Schoenbergians busy for the foreseeable future.


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## SanAntone

Here is a tone row generator:

https://www.bigcomposer.com/data/utilitydata/random.html

And here is a matrix calculator

https://www.musictheory.net/calculators/matrix

The matrix presents all permutations of the tone row, in a handy format for composers to use. BUt you have to create your own row from scratch.


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## ArtMusic

mbhaub said:


> 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =* 479,001,600*. More than enough to keep Schoenbergians busy for the foreseeable future.


Theoretically correct but incredibly difficult outside of academia to write something.


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## Bwv 1080

mbhaub said:


> 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =* 479,001,600*. More than enough to keep Schoenbergians busy for the foreseeable future.


No, 479,001,600/4

R, I and RI equivalence


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## Phil loves classical

Bwv 1080 said:


> No, 479,001,600/4
> 
> R, I and RI equivalence


I believe it's either the 479,001,600 possible row instances, or 479,001,600 / 48 for unique rows that are not transpositions, R, I, and RI. You're kind of alluding to unique rows.


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## Roger Knox

Phil loves classical said:


> I believe it's either the 479,001,600 possible row instances, or 479,001,600 / 48 for unique rows that are not transpositions, R, I, and RI. You're kind of alluding to unique rows.


Ihe original row (O) in the context of a musical composition has a certain status, at least in the first period of twelve-tone composition. (In post-WW2 serialism that would be seen differently.) So I would agree with counting possible row instances, as they are possible O's.

Anyway, having only the 479,001,600/48 unique rows to choose from would crimp my style!


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## Bwv 1080

Phil loves classical said:


> I believe it's either the 479,001,600 possible row instances, or 479,001,600 / 48 for unique rows that are not transpositions, R, I, and RI. You're kind of alluding to unique rows.


No, 12! does not include transpositions, it's just the number of permutations of 12 objects. If you included transpositions it would be 12!*12


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## Bwv 1080

if you go the total serialism route and to keep things simple likewise assume 12 rhythmic durations and 12 dynamics/articulations
then you get 12!^3 or ~10^26

but is like saying the 10^10^6 books in Borges' Library of Babel encompasses all of writing?


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## SanAntone

I doesn't matter how many rows are possible. At least one composer (can't think of his name) used the same row throughout his career, some used fewer than 12 pitches, Stravinsky for example. 

The 12-tone row's importance is put into perspective if you think of it as no more important than the diatonic scale in tonal music.


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## Gargamel

Babbitt only used four or five. (There are only six all-partition rows, and one of them is pretty useless since it's just the ordered total chromatic.)


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## Tikoo Tuba

Bb C A F# E B Eb D Ab Db F G


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## Bwv 1080

Tikoo Tuba said:


> Bb C A F# E B Eb D Ab Db F G


Use base-12 numbers (0 to B), not letters


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## Phil loves classical

Bwv 1080 said:


> No, 12! does not include transpositions, it's just the number of permutations of 12 objects. If you included transpositions it would be 12!*12


Yes, 12! is the number of permutations of 12 objects, but that does include transpositions, which are still arrangements of those 12 objects, unless you're going into microtones.


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## Bwv 1080

Phil loves classical said:


> Yes, 12! is the number of permutations of 12 objects, but that does include transpositions, which are still arrangements of those 12 objects, unless you're going into microtones.


No - to see this look at the '3 tone row' of A B C. There are 3! = 6 permutations, ABC,ACB,BAC,BCA,CAB,CBA but still 12 transpositions.


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## Phil loves classical

Bwv 1080 said:


> No - to see this look at the '3 tone row' of A B C. There are 3! = 6 permutations, ABC,ACB,BAC,BCA,CAB,CBA but still 12 transpositions.


But it's different for a 12 tone row, you have the same number of states as tones/objects. In the 3 tone row, you still have 12 possible states, but only 3 tones/objects, so you have more choice or combinations available. The 12 tone row is analogous to a 3 tone row with only 3 possible states, where you use up all the available states in the row.


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## Bwv 1080

Phil loves classical said:


> But it's different for a 12 tone row, you have the same number of states as tones/objects. In the 3 tone row, you have 12 possible states, but only 3 tones/objects, so you have more choice. The 12 tone row is analogous to a 3 tone row with only 3 possible states.


you have some tranpositional equivalence, but not complete. for example this has 6 unique transpositions, but is invariant under R










But simplistically even <0123456789AB> has 12 transpositions if you were following strict serial procedures


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## Tikoo Tuba

Bwv 1080 said:


> Use base-12 numbers (0 to B), not letters


no thanks ....... anyway , I won't be posting another tone row .

I present to my student as the first lesson in composition 12 pennies . Upon each is written a tone-name . Blindly they are chosen from a pouch . This is your first 12-tone row . You may play it . The intervals are the content .


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## BabyGiraffe

We can classify them using Gauss diagrams (called also chord diagrams). There are only 554 of them for 12 equal. 
For example:


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## Bwv 1080

BabyGiraffe said:


> We can classify them using Gauss diagrams (called also chord diagrams). There are only 554 of them for 12 equal.
> For example:
> View attachment 154521


even simpler, there are 50 6-note PC sets / chords. Each has its unique 6-note complement (either the same or another member of the set). So only 50 rows with unique intervallic content


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## Tikoo Tuba

mbhaub said:


> 12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =* 479,001,600*. More than enough to keep Schoenbergians busy for the foreseeable future.


I happily accept your number , and so very gleefully will divide it by 12 - the measure of a transposition set . Here goes ... ah , this shall be my favorite number forever .


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## Tikoo Tuba

That number is 11! . 

Since there is a finite set of original interval sequences , you can choose though not invent a 12-tone row . I'll suppose if choosing just one it will represent your personality . Are you orderly chromatic or what ? This thread requests your participation , and please present a 12-tone row of your free and instinctive choice . No ? ok , whatever


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## Barbebleu

Is the word row in twelve tone row pronounced as in sew or as in cow? Asking for a friend!


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## Tikoo Tuba

Bi-polar ? Choose 12 woo .


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## Symphonic

Tikoo Tuba said:


> How many are possible ? May you present just one ?


One is already one too many.


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## SONNET CLV

Reading through this thread has made me incredibly hungry, so I just called Dunkin'® and ordered a dozen donuts, an assortment of 12 different varieties with no duplications.

Now ... in what order will I eat them?

How many possible selections do I have again?

Yikes! I'm getting even more hungry just thinking about the possibilities.


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## Roger Knox

SONNET CLV said:


> Reading through this thread has made me incredibly hungry, so I just called Dunkin'® and ordered a dozen donuts, an assortment of 12 different varieties with no duplications.
> 
> Now ... in what order will I eat them?
> 
> How many possible selections do I have again?
> 
> Yikes! I'm getting even more hungry just thinking about the possibilities.


I also associate serialism with food. At graduate school, wrestling with such gnarly topics I developed cravings for beer, cola, and hamburgers. Donuts are of the same ilk. In the face of cravings, such concerns as the combinatorial or invariant properties of a row of donuts will wither into insignificance.

I hope they have mini-donuts!


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