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  #1  
Old 2006-11-02, 15:18
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Unanything Unanything is offline
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Dodecaphonics

The newest thing I've discovered is 20th Century Classical and avant-garde Classical. Love the stuff. There is some amazingly fucked-up stuff there. My Music has just bought a CD of it for me and the department at school. These guys were weird decades before the members of Meshuggah and Gorguts were even born.

One of the great landmarks of this era was the invention of atonality by Arnold Schoenberg. He was the first to go mad and defy melody. Death metal must nod its head to him.

Basically, in atonality, you forget using the minor/major keys or scales and use all 12 notes. After writing some works in a very raw atonal style, most famously Erwartung (1900-ish), which shocked its audiences in performances, Schoenberg disappeared for 11 years to devise a new compositional system for atonal music, called serialism or dodecaphonics, which allows it sound ordered and grounded despite its wild nature. It's an absolutely fascinating way to write, especially for the tech-metal heads out there.
Thus I will lay down the basics.

The composer, when he begins, takes all twelve chromatic notes and arranges them into an order that pleases him. There are around 479 000 000 possibilities (I found the exact figure in an encyclopedia, John Mansley, you could probably calculate it, it something do to with factorials probably), so don't worry too much about accidentally nabbing an already written one, especially with the complexity of rhythm and counterpoint some of the guys like Boulez and Webern used them in.
This order is called your 'note-row'. You must stick to the order of notes you create throughout your piece, and are not allowed to go back to it until you have played the other eleven, although you can play the note any number of times you want before going on to the next. And you can change to other note-rows. I think you are also allowed to have note-rows of less than twleve as your piece gets on. I've seen it in some pieces.

Then certain ways of manipulating it can be employed.

Octave dispersal is popular, and makes the row sound active and jaggy. You can play the notes in any octave, so long as it is that pitch.
Retrograde is allowed, or when you play through your row backwards.
Inversion is allowed, when you play it 'upside-down'. All the intervals go the other way, ascending a perfect fourth becomes DEscending a perfect fourth etc.
Or retrograde inversion.
Transposition is allowed.
Chording is also allowed on how many notes you want, although they must be in order. So you can play the first note, then second, then the third and fourth in a chord, then must follow the fifth, for example.
You are also allowed to change the dynamics and durations of your rows' notes when you repeat it, just so long as that order of notes remains.

Learning to improvise in this style can be difficult, but it is excellent practice, better for coordination than learning your scales, I say, and a very creative way of getting to grips with alternative sounds and melodies.

The advanced composers among you may be further interested in total serialism, where counterpoint is introduced through the use of more than one note-row at once.

The Piano Sonattas, particularly No. 2 and No. 3 by Pierre Boulez are good reference. Try digging around Myspace. And I do warn, it's MAY be quite hard to stomach for even the hardened of ear.

Hope it's of use, Callum.
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Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


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  #2  
Old 2006-11-02, 22:36
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some pretty cool stuff here, i'll screw around with this when i get a chance.
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  #3  
Old 2006-11-03, 00:24
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Sounds pretty cool. looks like a neat element to utilize when writing music. Definitely keep this in the back of my mind next time I write a song.
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Old 2006-11-03, 04:10
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Quote:
Originally Posted by Unanything
The composer, when he begins, takes all twelve chromatic notes and arranges them into an order that pleases him. There are around 479 000 000 possibilities (I found the exact figure in an encyclopedia, John Mansley, you could probably calculate it, it something do to with factorials probably)


Yes it is, that number is just 12! (said "twelve factorial") rounded to three significant figures. The actual number of possibilities is 479,001,600.

[Aside: This figure doesn't allow for repetition of notes, the total number of arrangements - including twelve of the same note - is 12 to the twelfth power, which is 8,916,100,448,256. The total number of arrangements of twelve notes without any note being the same as the previous note is 12 multiplied by 11 to the eleventh power, which is 3,423,740,047,332.]
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Old 2006-11-03, 08:44
Paedophage Paedophage is offline
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Very interesting....Like CompelledToLacerate said, I'll definitly try to utilize this next time i'm writing.
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  #6  
Old 2006-11-03, 14:19
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It has led me to all sorts of heights when writing. I'm also thinking of becoming a straight-up composer, like Luc Lemay, except where he separates his DM and his Classical, I'm going to FUSE them.

Honestly, you need to go hear Boulez or Cage. Boulez' piano stuff is supposed some of the most technical piano in history.

Haha, John! So it is! 12!! Should have at least guessed. I thought it'd be a Combinatoric of sorts, not just the factorial on it's own. And that is awesome, that many? We haven't gotten that far in Maths yet. We started handling the comple numbers today. That was quite fun, how all the formulae can be resolved back to 'a + bi'. But in dodecaphonics, you have to use all twelve notes, and you can't play any one note again until you play the other eleven. But you can play a note as many times as you want before you move on, and for as long as you want.
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Quote:
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Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


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I coated the end of a toothpick with Satan's blood and simply wiped it across the top of an omelet. PERFECT!

Last edited by Unanything : 2006-11-03 at 14:29.
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  #7  
Old 2006-11-05, 10:16
PST 88 PST 88 is offline
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Boulez is a weird guy, but there are many more impressive in 20th century music.

If you want to see some interesting metal writing along these lines, check out Ron Jarzombek's circle of 12 tones. Not just a recapitulation of some old avant-gardism, which is all I'm seeing in this thread. A real cool use of the system.
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  #8  
Old 2006-11-07, 14:10
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Quote:
Originally Posted by PST 88
Boulez is a weird guy, but there are many more impressive in 20th century music.

If you want to see some interesting metal writing along these lines, check out Ron Jarzombek's circle of 12 tones. Not just a recapitulation of some old avant-gardism, which is all I'm seeing in this thread. A real cool use of the system.


I ought to check him out. But the point of it is cycling 12 tones.

Cage is cool, there is this odd sense of melody in some of his stuff, like Bacchanale.
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Quote:
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Also, check out Autopsy, the vocalist sounds like hes about to eat your grandmother while fucking you in the eye. Brutal.


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  #9  
Old 2006-11-17, 15:27
brainiaxe brainiaxe is offline
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Cool Schoenberg was not alone...

"One of the great landmarks of this era was the invention of atonality by Arnold Schoenberg. He was the first to go mad and defy melody. Death metal must nod its head to him."

- Glad to see people paying homage to a great mind! Another pioneer (an American) who was composing and experimenting with atonality during the exact same time period as Schoenberg (both of them born in 1874) but in our own little state of Connecticut (also a pioneer of our mortgage system) was Charles Ives. For a birthday present, his father, a well known high school band leader told his son Charles to sit upon top of the school while he marched two different bands playing entirely different pieces of music from opposite ends of the town eventually to merge together. Imagine hearing that for the first time! Ives's piano rags are quite remarkable for the time in that not only are they tonally deviant like Schoenberg's, but they also indicate to the performer "play this section if you feel like it...or not..." a degree of performance freedom; a concept Schoenberg despised, being raised in the tradition of the symphonic/chamber music instrumentalist much the opposite of an improvisational environment with regard to performance. A good introduction to Ives is his infamous "Unanswered Question". Ives's music career was short lived, ending around 1918 (the time of Debussy's death) where he opted to make a living in a different field, but a tribute was done for him before his death; he made an appearence at one of the rehearsals, but never heard the performance - he was turned off to the industry at that point. Ives as well as Schoenberg opened doors to sounds never heard previously - Schoenberg eventually developed his 12 tone system, realized in 1923 at nearly 50 years old, certainly unmistakable in his expressionist works during the rise of Hitler. Schoenberg was also a distinguished author and master educator (UCLA); a man who was thorough, passionate about reaching the student and of the game tennis where he was consistently given a "schlacking" by an most notable opponent from Brooklyn, New York; George Gerswhin, which of course irritated Schoenberg to no end. Long live the music of these two great men...and to good schlackings in sports.

Last edited by brainiaxe : 2006-11-17 at 16:50.
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  #10  
Old 2006-11-18, 08:49
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Dodecaphonics and atonality kick ass!!

In black metal, some bands use chromatic lines ((which is half one step up or down with every note that is not thesame as the previous, with which they most of the time use every note in the octave. On (bass)guitar and on instruments with a keyboard, the enharmonic equal notes (such as F# and Gb) sound exactly thesame, but for instruments like a violin, they differ and they sound different)). For example: since Ψyvind Mustaparta (a.k.a. Mustis) became part of the line-up in Dimmu Borgir, they use such chromatic lines. Examples are: 'Progenies of the Great Apocalypse', 'Blood Hunger Doctrine', 'Architecture of a Genocidal Nature', 'Blessings upon the Throne of Tyranny' (very high), IndoctriNation (very high) and Absolute Sole Right.
When you do not like a song of which a GP tab is made, you can download it and destroy it with these types of lines and with dischords, like e/f (minor second) or b/f (diminished fifth).
A friend and I for example did this with the song 'Wisemen' of James Blunt (we added loads of diminished fifths, (blocks of) seconds and made the solo a chromatic solo, so it became atonal). Everyone who wants to hear it, mayl me al infernal_purge@hotmail.com with as subject: 'Kill for the Storm'. Note: it is a midi file, so GP is not required.
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  #11  
Old 2006-11-18, 09:23
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Quote:
Originally Posted by johnmansley
Yes it is, that number is just 12! (said "twelve factorial") rounded to three significant figures. The actual number of possibilities is 479,001,600.

This is only for instruments with a fretboard or a keyboard.
Quote:
Originally Posted by johnmansley
[Aside: This figure doesn't allow for repetition of notes, the total number of arrangements - including twelve of the same note - is 12 to the twelfth power, which is 8,916,100,448,256. The total number of arrangements of twelve notes without any note being the same as the previous note is 12 multiplied by 11 to the eleventh power, which is 3,423,740,047,332.]

A C with twelve sharps does still not sound like a C. Phisically, this is quite logic. The proportion between a tone and the chromatic second above is 15/16. When we cound twelve sharps at a note, its proportion is 15 to the twelfth power divided by 16 to the twelfth power, which is 129,746,337,890,625 divided by 281,474,976,710,656 and that is less than 0.5, which means that C############ is higher than a C. Therefore, your maximum is not correct.

There are infinite possibilities for dodecaphonics.
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Old 2006-11-18, 10:06
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Quote:
Originally Posted by USS
A C with twelve sharps does still not sound like a C. Phisically, this is quite logic. The proportion between a tone and the chromatic second above is 15/16. When we cound twelve sharps at a note, its proportion is 15 to the twelfth power divided by 16 to the twelfth power, which is 129,746,337,890,625 divided by 281,474,976,710,656 and that is less than 0.5, which means that C############ is higher than a C. Therefore, your maximum is not correct.


What the fuck are you talking about? A proportion of 15/16? Your post makes no sense.

There are TWELVE distinct notes in western music; forget about butchering music theory and just count them. Ergo, it follows logically that my combinatorical calculations hold.
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Old 2006-11-18, 10:16
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Quote:
Originally Posted by USS
There are infinite possibilities for dodecaphonics.


I shouldn't have to explain why this statement is absurd, given my previous posts in this thread.

I don't know where you learnt this brand of slipshod mathematics, but your analysis of arrangements is very poor to say the least.
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Old 2006-11-18, 13:46
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Quote:
Originally Posted by USS
This is only for instruments with a fretboard or a keyboard.

A C with twelve sharps does still not sound like a C. Phisically, this is quite logic. The proportion between a tone and the chromatic second above is 15/16. When we cound twelve sharps at a note, its proportion is 15 to the twelfth power divided by 16 to the twelfth power, which is 129,746,337,890,625 divided by 281,474,976,710,656 and that is less than 0.5, which means that C############ is higher than a C. Therefore, your maximum is not correct.

There are infinite possibilities for dodecaphonics.
You're speaking about pure intonation, not equal temperament. (I think maybe you didn't make this clear enough.)
As I understand it, dodecaphonics, or 12-tone music, presupposes equal temperament, in which each note relates to the next by the 12th root of 2, not 15/16. That way, C sharped 12 times is exactly C an octave higher.
If it was not based on equal temperament, then - seems to me - one note of the 12 would dominate, inasmuch as others were measured from it in a series of simple ratios. Therefore we would not have a truly atonal music (which I think is how 12-tone music is regarded).

Of course, many other scale and intonation systems are possible. Who says the octave has to have only 12 divisions?.....
http://en.wikipedia.org/wiki/Microtonal_music
http://en.wikipedia.org/wiki/19_tone_equal_temperament
http://en.wikipedia.org/wiki/22_tone_equal_temperament
http://en.wikipedia.org/wiki/31_equal_temperament
...and there's more where they came from...
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Old 2006-11-18, 17:05
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My previous post did not make sense. Then let me say it this way (take some time to understand this logic. Try it out seven hundrets of times and then say I am right.):

If you make a string 2/3 of its length, it will become a perfect fifth. This is one of the axioms of music and intervals.
If you make a string ½ of its length, it will become a perfect octave. Also one of the axioms of music and intervals.
So if the root of a string is F, and we shorten the length of the string by 2/3, then it becomes a C.
C => G
G => D
D => A
A => E
E => B
B => F#
F# => C#
C# => G#
G# => D#
D# => A#
A# => E#

If we take a perfect octave from F, we get an F
After seven times taking a perfect octave, we get an F.
This F is the half of the half of the half of the half of the half of the half of the half of the length of the F we were starting at. So that is ½ to the seventh power of a string's length.

On piano, we are at the F button with both the ways of taking intervals.

According to the twelve times we take a perfect fifth from the root, we get the wave-length that is 2/3 to the twelfth power of the root. This is 4096 divided by 531441, which is nearby 0.0077073.
This is less than the wave-length of the seventh octave, which is ½ to the seventh power, which is 0.0078125.
The frequence of the E# is therefore higher than the frequence of the F. So the E# is higher than the F. This is very logic and easily traceable.

If we take even more perfect fifths and octaves from the F (in total these are 84 perfect fifths and 49 octaves), we get an F with twelve sharps and a custom F. We will see that the F with twelve sharps is definitely not thesame as the F:
The F with twelve sharps is 2/3 to the 84th power which is nearby 1.6156 * 10^-15.
The custom F is now 49 octaves higher than the original F, thus ½ to the 49th power, which is nearby 1.7764 * 10^-15.
These wave-lengths are not thesame.

This proof is simple, clear and perfect. So johnmansley, your theorem is down.


The fifths on a piano are therefore not perfect. There has been lot of discussing about this subject ever before they made the piano and even before the harpsichord was found, and they made a compromis so that the error would be minimal. So on piano, indeed, there are twelve.
For a violin or for other strings, and also for brass instruments and percussion, nevertheless this matters, and you are not about to have the opinion that those are no part of western music.

That passage in which I sayd that a C# is 15/16 of the string of the root, that was indeed not true.


In dodecaphonics, most of the time we do not use a C with twelve sharps or flats. We most of the time use only one sharp or flat at one note. But nevertheless, the number of possible dodecaphonic melodies is INFINITE. We just keep it simple (on piano with 12!, so only 479,001,600 possibilities for a dodecaphonic order - for melody is not really the good word for this).

I am a student of math and music, so this was a subject of some masterclass lessons at a university.
Quote:
Originally Posted by johnmansley
forget about butchering music theory
How can I?
Quote:
Originally Posted by johnmansley
just count them

For once more: how can I count an infinite collection, except for making a calculation?
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Last edited by USS : 2006-11-18 at 17:16.
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Old 2006-11-18, 17:41
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USS, I'm pretty sure everyone here is talking about using equal temperament (as JonR said) and you're off babbling about shit-knows-what and how musical psychics were able to discuss imperfect fifths on a piano before they even fathomed the instrument.
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Old 2006-11-18, 18:03
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That is right, and when they started to add the mathematical part, I did mine. I just replied on what was sayd before.
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Old 2006-11-19, 12:26
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Quote:
Originally Posted by USS
I am a student of math and music, so this was a subject of some masterclass lessons at a university.


I already have my mathematics degree (within which I studied combinatorics) so don't come to me with a holier-than-thou attitude, sunshine.

Quite simply, you're making the error that most pure mathematicians make; you are not applying the mathematics to the real world. Analyse the scenario and the real world in this case is the twelve tones that comprise the basis of western music. This set has a finite number of arrangements, as already shown.

To show this, try and play more than twelve different notes on your guitar. You can't do it. This is the practical world we need to apply the mathematics to, not the theoretical world which you describe.


Quote:
Originally Posted by USS
For once more: how can I count an infinite collection, except for making a calculation?


I'll do it for you:

C
C#
D
D#
E
F
F#
G
G#
A
A#
B

I think you'll find there are twelve notes to be arranged there.

On a final note, my calculations are not theory they are mathematical fact; there is no scope for debate on the number of arrangements of a set with a given number of elements.
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Old 2006-11-20, 04:03
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If you pick twelve random notes (even if they are the most easy notes imaginable), the possibilities are indeed finite. But the notes of which we CAN choose twelve are infinite. Imagine a dodecaphonic with, for example, a B flattened twenty-four times. If we use JonR's scale, this B flat to the 24th power sounds exactly thesame as the B. But then for example a D will not be the usual D. Agreed, we can change this order. But then we cannot play any consonant songs anymore, for we would undermine the music axioms on which the music YOU make is based. So it would tear down your own theory. It simply does not stand.
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forget about butchering music theory
I guess I do not have to explayn why this statement is misplaced, do I?
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Old 2006-11-20, 05:07
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I'm not restating in its entirety what I've already said, but I'll sumarise. In practise, there is a finite number of arrangements ('arrangements' in the mathematical, not the musical sense) of a set containing twelve elements. It looks like you'll just have to take my word for it as you seem incapable of grasping the physical construction and limitations of a fretted guitar.

Final word: the number of arrangements of 12 notes is 479,001,600. Any further posts contradicting the musical practicalities of this mathematical fact will be deleted.
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