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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some pretty cool stuff here, i'll screw around with this when i get a chance.

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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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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Very interesting....Like CompelledToLacerate said, I'll definitly try to utilize this next time i'm writing.

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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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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"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.

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 Øyvind 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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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.

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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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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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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...

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.
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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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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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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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.




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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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.I guess I do not have to explayn why this statement is misplaced, do I?

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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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Very well then. Quite cynical, but so be it then. I can remayn alive with this. The guitar and the piano have their limitations, which makes a Db sound thesame as a C#. Let us define dodecaphonics therefore this way:

ON DODECAPHONICS PLAYED ON PIANO, WE USE THE SEVEN WHITE AND THE FIVE BLACK KEYS OF THE OCTAVE, NO MATTER WHERE, NO MATTER HOW LONG, NO MATTER HOW HARD, NO MATTER HOW FREQUENTLY. AS LONG AS THEY ARE USED IN A CERTAYN ORDER.

This way, we can both agree.

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^True.

The point here is that all western instruments have been set to equal temperament for at least 200 years (very approximately ). That's the system we work with.
Technically (in "pure" terms) every note is "out of tune" (except octaves), but it's the only temperament that allows our functional harmony system (keys, chords, modulations, etc) to work. We need all 12 semitones to be equal so that all keys are equivalent and we can modulate freely without retuning. We put up with the impurities.

It's true that instruments capable of sliding pitches (violins etc, the human voice) can perform in pure temperaments if they want - adjusting intonation for different keys. Unaccompanied choirs, for example, can sing (quite naturally) in pure intonation by ear. Most wind instruments can adjust their intonation too. (In fact, some wind players need to use certain lip or finger techniques to play exactly in ET anyway.)
But if they play with fixed pitch instruments like pianos, organs or guitars, then they will either be out of tune. or will need to tune to the ET instruments.

IOW, the point you are (were) making is not wrong, in theory, it's just not applicable in practice. (which is what the others were saying.)

In any case, IMO, the whole mathematical argument is a red herring. Who cares how many permutations there are? Musicians don't...

I do, johnmansley does and Unanything does, so that is three already. Perhaps you too I am a mathematician in ecudation (still at university), johnmansley is graduated and Unanything was interested in the number. And we are all musicians (are we?).
So this problem is solved I guess. We are both right, but we meant something different.

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True, the number of arrangements is irrelevant - just an interesting aside.

OK, now that this is sorted out, it'd be interesting to hear people's views on using dodecaphonics and/or any contemporary examples. I think Anata have used this technique in one or two of their songs.

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I've actually never really used the technique to compose. I find it a good technical exercise and a great insight into the workings of melody, but other than that, note-rows seem too systematic for me. I prefer to compose for melody rather than systematic rule. Atonality can be controlled without it, if what is written is truly felt by the composer. I've recently started writing on the piano, and I've worked out proper sheet music.

My band, Transcension's next song wil haev some piano on it.

I like studying music like this, it gives one a universal insight into music. It allows one to listen and analyse anything. And the avant-gardiers have it even better, because they can tolerate anything.

On John's point above, I first came across dodecaphonics in the magazine Guitar Techniques. It was in the Creative Rock section. The note-row they had in the example piece was cool.

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Guess you never heard of Scriabin's music? Of course, he had some help with his insane writing. He had synesthesia, where every sound you hear also triggers the visualization of colors, so each note that he hears makes him see a specific color related to that note. How crazy would it be to compose music that way??

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You then just make music by coincidence. It will certaynly become atonal that way.

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That's not a strictly correct tone row. The 2nd note is the same as the first (octave up); two notes repeat (C and F#) before all the others have been used; F and C#/Db have not been used.

This is the point about the 12-tone system. It may seem too "systematic" to you, but if you don't follow those rules, you slip back into tonal music. If you "compose for melody" (which is also my favourite method), without an imposed system, you will be following your ear and intuition, which is likely to lead you down tonal paths, because we (all of us) are so used to hearing tonal music and its melodic intervals.
That's fine of course, but it's not really dodecaphonic music - it's a mish-mash of tonal with maybe some atonal suggestions - chromaticism, IOW.

IMO, music is aither tonal or atonal - it can't be both. If strict tone-row rules aren't applied, then tonal values will creep in: one note will start to dominate, or groups of notes will suggest a scale.
Of course, what matters is how it sounds in the end! We don't have to apply any kind of rules. But when defining it, it's important to distinguish true "atonal" music from "tonal-plus-chromaticism". We need to be clear what our goals are, IOW. "Tonal-plus-chromaticism" is great (my favourite type of music!), but it isn't atonal, or "dodecaphonic" as I understand it.

The fact that a piece uses all 12 tones doesn't make it atonal. There must be 100s of jazz tunes (all firmly tonal) that use all 12 tones. There's simply a hierarchy between a diatonic set of 7 and the other 5. Can that be called "dodecaphonic"? If so, what's the point of the term?
That's why Schoenberg imposed his tone-row rules, to prevent tonal bias happening.

OT: JonR from JS? What are you doing here? :P

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Just passing through...

how about you?

I think it can be. Like you have a melody as the first theme and a dodecaphonic row as the second theme. It is both. But I agree, it cannot be at thesame time.

This is a good dodecaphonic:

|-----------------------------------------------------------------------------------------------------|
|-----------------------------------------------------------------------------------------------------|
|-----------------------------------------------------------------------------------------------------|
|------44---------------3-------------------555555555555555555555555555555555555555555555555555555555-|
|----------------6666-----7-1111-33-22-4444-----------------------------------------------------------|
|-2222----334455------1-------------------------------------------------------------------------------|

No argue about this. A note may be repeated (within one octave or not) until the next is played.

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I think you're right about the repetition of a note. But as I understand it, you can't come back to that note before the full tone-row is completed.
I'm not an expert, and maybe "dodecaphonic" is different (a broader term) from Schoenbergian 12-tone serialism.
There's good reference here...
http://en.wikipedia.org/wiki/Serialism
... but no specifics as to the restrictions on note repetition. (But clearly it's a lot more complicated than just how you use the 12 pitches, eg, rules on use of intervals, and other musical aspects to which serialism can be applied. )

You cannot come back to the note indeed, but as you have completed the row, you can turn the row, so for example C F# G E A B Bb Db Eb G# D F can then after the F turn to F D G# Eb Db Bb B A E G F# C and can then from the C agayn three times be repeated. That is also possible in dodecaphonics. I call it the lobster technique, I do not know whether it is the official name for such composing technique or not.

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What you sayd about the repeating of notes: it is stated. It may very well be thesame, I cannot tell you. I will ask to my music theory teachers one day soon.

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I doubt if "lobster" technique is an official name...

I realise the tone-row is subject to all kinds of manipulation once established, but you found the quote in wiki that confirmed my understanding of it.

However, we now have 3 terms to contend with, which are interconnected but may or may not be identical: "serialism", "dodecaphonics", "atonality"
(You gotta love this theory stuff... )

Actually, the 4 should be where the 3 is. And I agree with you in that dodecaphonics is systematic. It compromises on expressiveness, and the reason Beethoven and Mozart are so huge is because they balanced formal structure with expressiveness prefectly. And you get very tonal rows as well. They just sound like they are constantly modulating. I just use dodecaphonics for finding rows that actually sound good, I don't stick by it for anything. What you are saying is very true, I understand perfectly. But you've made me realise that perhaps we should probably stop distinguishing between atonality and tonality. Every row is just lots of mini-tonalities thrown together and inaudible due to their rapid modulation.
And considering melody in DM sometimes, I think you can be far out of tonality and still not be doecaphonic.

There needs to be a new tonal system I think. I've had ideas about constructing one for a while now. This major/minor thing is annoying. I hate it. I always use modes, I only use the key sig' to show the set of notes the thing's in. Who dare declare the obsoletion of modes!

I've more or less given up with dodecaphonics (already). I've found that the height of all this modern stuff came and ended with Debussy. He wrote for sound rather than system or philosophy. If I hear a piece, I don't hear it's philosophy or it's sytematics. I externally read or find out about it's sound. I hear it's sound, it's rhythms and it's pitches and it's textures and timbres. Debussy did the weird stuff for the weird sound. I do similar. I actually like Cage and Boulez for the SOUND rather than the philospshy. And guys like Takemitsu did it probably for the weirdness of sound anyway. I mean, what's with getting flute players to speak French translations of Japanese poetry down the flute?

Oh, and Scriabin's music sounds awesome. I would like to hear an insight into the world of a synaesthetic. I bet he was like one of these pointillist composers.

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Note at this statement: There are atonal melodies that are not dodecaphonic. For example: try on the piano to play some random white keys. It will be atonal.
But indeed, dodecaphonic guarantees atonality (as long as you choose the order of the notes randomly).

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Not at all. It will be in the key of C major, or A minor, or one of the modes. The white keys give a pre-prepared 7-note tonal set. That's the point of them.
It may not sound very musical - but it will sound tonal, because (if you play truly randomly) we'll eventually hear C as the home note, because of the familiarity of that usage of those 7 notes.

My main point here is that our ears are attuned to tonality, over centuries. We struggle to find it in any music we hear - we can't help it. It's one of the main ways we make sense of music. This is why Schoenberg expended so much effort on establishing rules about how to avoid it - by not making any selection from the 12 tones, but using them all equally.
I suspect you don't need to choose the notes at random. (Indeed, random might mean you end up with a tonal set by accident.)
You can (and maybe should) plan the order, but you must use all 12 without going back to any of them before all 12 have been used.

IOW, atonality doesn't come from randomness (most of the time, maybe it does, but not guaranteed every time). It comes from strictly avoiding accidental suggestions of or tendencies towards tonality.

John Cage used random principles ("aleatory" music), but he incorporated untuned percussion and other non-musical noises. In any case, his aim was not to produce atonality, but to remove the composer's control, to produce music as contemplative sounds, in which any sound was valid and worth listening to.

Maybe the example of using the seven white keys was a bad example, but it is still true that an atonal piece of music can be composed without using all twelve keys. For example: leave the D and play the rest in any order, using them all. Or try a hexatonic scale. It has no real root, for you can start at any note. Or try an octotonic scale. That one has eight tones that all can be used as root. I know a piece of music for violoncello and piano, which was written in a KZ. Except for no measure, you cannot hear any melody, or tonality.

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I did not say this within the last group of posts in this topic anywhere. I sayd the order of the notes matters, not the number of notes, which was set to twelve.

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Yes, you're right - symmetrical scales like the octatonic (diminished) or hexatonic (wholetone) would qualify as atonal, IMO.
And I guess an 11-note scale would be as near-as-dammit atonal in effect.

I think you're misunderstanding me. You said (which I quoted):My point was that if you choose from 12 notes at random - random order - you may end up repeating a note before you've used up all 12. Which is (a) not true serialism, and (b) might just possibly (tho admittedly unlikely) result in a tonal sound.
IOW, to make sure you use each of the 12 notes once only (even if it repeats itself) you can't make the order random - you have to take note of what notes you've already played to make sure you don't play it again before the other 11 have been used.
IOW, you have to impose a structure, a judgement. You can BEGIN with a random choice, but you need to remove any note that has been used before.
Or to put it another way, you can choose a random order, but only from the remaining (unused) notes. Every time you play a note, it's removed from the pool.

I'm not reading all three pages of this, so if someone didn't mention Boyd Rice, Edgard Varèse, John Cage and George Antheil you should check out their work.

Schoenberg and Stravinsky were what got men into noise in the first place (well, them and Merzbow).

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The way you pick random notes (which indeed should be explayned earlier) is like a vase with twelve balls with on each of those balls a note name. Each ball you take out of the vase, you lay aside. (It is like the lottery, or like the way the UEFA orders the clubs for the first round in the Champions League.) You cannot get a ball agayn that way. This way we choose the random order. Only on this way we will get a row we want.

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Exactly. Good simile.

Else we get a pool of four clubs: Man U, Chelsea, Barcelona and Man U. Will be quite strange. Can you imagine?

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I can't say I'm the biggest fan of aleatoric music, although I love the sound Cage's music. I like his Sonatas And Interludes For Prepared Piano. Music is about sounds to me, rather than philosophies. You can't hear philosophies in music, only sounds. So that's what I focus on. Even all the avant-garde-heads that I've met thought I was nuts. This composer called Graham Fitkins told me about when he performed this piece where he had to push a piano through a wall at university.

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Some chick told me about this in high school, how it can be used totally blows my mind.

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It is only a theoretical fact. But you can write a piece of music using a scale with all notes sharpened twelve times for strings and brass, which will definitely sound different than a piece with all notes 'clean'. I think the first piece with that scale is still to be written.
But that calculation was not the one that you should read. The one in which I use the 2/3 (distance to the perfect fifth) as the mayn part of the calculation should be read.

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Er, I think you must be talking about football (soccer)... Not one of my areas of interest or expertise unfortunately...

How would such a piece be "written"?
I presume you'd need to specify a tuning standard (whatever the calculation is for 2/3 x12 from concert pitch). And then use ordinary notation?
And in any case, if every note was sharpened the same amount, surely you'd end up with the same (equal tempered) note inter-relationships? Just based on a different concert standard pitch. This would sound the same as normal music, just a little higher in pitch.

Or do you mean every note should be calculated in Pythagorean perfect 5ths (so you end up with pure intonation rather than equal temperament)? Many pieces have been written that way of course, it's just that they are mostly several centuries old...

Or some combination of equal tempered pitches and pure ratio ones?

(Perhaps I'm just not clear what you mean... )

It would be written at the clef with xxxxxx at every note (guess you know what x means).
It will sound thesame as a clean modal scale (for it is pure intonation), but abit higher. It is like having a piano tuned too high for this age. Perhaps the Cxxxxxx will be the clean C in three centuries

Note: I was indeed talking about soccer: the European Champions League. It was just an example to illustrate the fact that we take different notes and lay aside.

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OK! Enough temperament pedantry!

I opened the thread to discuss dodecaphonics! Anyone come up with anything good?! I have a serial work on the way. So far, it has three note-rows in it.

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AHAHAHHAHAHAHHAHHA!!!!! Go back to your studies, because you are so fucking flawed in grammar.

That is impractical for now. Why do you keep implying that enharmonic notes don't exist? I suggest that for the purposes of this thread and the ones involved here, you should keep in mind--for their sakes--that C5 is herein the same exact pitch as C6. In the real world C6 may be a few cents higher, but it complicates things to bring that up. Leave it up to the basis of enharmonic tones.

It would also be a lot easier if you guys explained yourselves with diagrams of your own matrises to prove points.

Stravinsky's Dance of the Adolescent Girls is a good one.
And I'm sure all of you have heard the App. Spring Ballet, the orchestration from '45. That's actually not so much like university music and likable by general audiences.
....I usually dislike post-modern music for the reason that it isn't usually intended for people to listen to.

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Because for strings and brass (which I mentioned in the very same line) they DO not exist. They do exist on a piano, a guitar and other limited instruments, yes (look at the calculation in which I showed that a B# is higher than the C. Theoretical experts have been thinking about this while creating the spinet (the precursor of the harpsichord (which is precursor of the piano)) and they made a compromis that we still use, named 'enharmonic equality', which is made to make the instruments play at nearly the right tone with a minimal distance, so you do not have to retune while playing a piece with modulation), but not for these types of instruments, that do not have to retune while playing modulations at all. These instruments play with pure intonation. If they use enharmonic equality, they play false.

I do not know if you have read through all the posts, but it is very clearly mentioned already (for example in the first twenty posts).
It may indeed be not very practical, but what is this forum's name?

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Well, depends what you mean by "false".
In contemporary music (I mean all music from the last 200 years or so), every instrument strives for equal temperament, at least when playing in ensembles with other instruments.
Pianos are of course fixed in equal temperament (B# is identical to C), as are guitars, vibraphones, accordions, etc.
Horns are problematic, it's true, as players often have to "lip" notes into tune. (I'm not familiar enough with all wind instruments to know how much this affects them, or whether it's easier or harder to play in equal temperament than in a "pure" key.) Presumably their own key is easiest.) But "in tune" means in equal temperament (to match a piano).
Same with strings. They CAN play in pure intonation - in one key at a time - if they want; but that would only make sense in string ensembles.
In any case, orchestral string players use vibrato which would mask any "out-of-tuneness". Pitches oscillate in excess of any differences between ET and pure intonations.

In any case, on topic, 12-tone serialism depends on equal temperament. Otherwise the note relationships would not be equal in value.
IOW, in a sense you have a point (about an infinity of possibilities), but in practice it's irrelevant.

No shit, but you're missing the contradiction that Jon just said, again, that you all are talking about atonality, serialism, and the twelve-tone system. There MUST be enharmonic notes for that.

If you want to discuss pitch in the real world, I'd suggest making a new thread because you keep debating this off-topic in a thread about Schoenberg.

You must be blind if you haven't noticed that everyone so far has disagreed with everything you say because of this....

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By 'false' I mean that only the octave on that instrument is perfect.
But in dodecaphonics indeed you do not need any consonant intervals except for the octave, because indeed else the relationship between the notes is not anymore equal, and we will hear some notes being superior to others.
The point I was making was indeed off-topic (which could be a reason to delete every post about this subject; also the only reason everyone was disagreeing about it), but not wrong.
So I agree with the fact that there are 479 001 600 possibilities if we use the notes on the piano and make every instrument play in these ET notes. Pure intonation is used on other pieces of music, but not in dodecaphonics.


So now this problem is solved, we can turn our faces back to Schoenberg and leave this off-topic discussion behind us.

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OK, I think I see what you're getting at. You're saying that there is (or could be) a type of music which uses 12 tones in non-equal temperament. IOW, 12 unequal divisions of an octave.
This would be pretty interesting. How it sounded would depend (of course) on how much - if at all - any of the intervals approximated familiar pure or equal tempered intervals. There would - certainly - be some intervals that sounded more dissonant than others (including intervals of the same number of steps), and it would be hard to write in this system and ignore these effects. And it seems to me the less you ignored such effects, the more you would be writing a kind of tonal music - if a highly dissonant kind.
Even so, I'd guess there's some potential here. (I've no idea if any composer has researched this concept, but I'd be surprised if none have.)
But are you still saying that there is (at least potentially) a form of dodecaphonics that doesn't use 12-TET? This seems to be the sense of the rest of your posts (but not clearly of that last sentence).
I mean, seems to me there could be 12-TET dodecaphonics (as in Schoenberg and serialism); or there could be dodecaphonics starting from some kind of pure intervals (eg 4ths and 5ths), leading to uneven semitones (but with octaves corrected); or there could be dodecaphonics based on some other kinds of irregular 12-step division of the octave, including random ones?
Fine with me! (Apologies if I've misunderstood you.)

hahahha.


Well, I just gave a listen to a schoenberg fugue that was pretty weird.

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I need to hear more Schoenberg, I've heard some key stuff, but I need more. I'll be looking out for those fugues.

Has anyone come up with anything? I've got one piece going. I'm taking time to develop the textures carefully though.

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That would be a quite funny experience. But I think you nevertheless should ignore the superiority of some notes, because (as we did in Schoenberg's music) we choose a random tone row in the 'lottery manner' (take and do not put back).
A second of C and a D-flat will be indeed more dischord than the second D-flat and D, because the distance between C and D-flat is (relatively and absolutely) smaller than between D-flat and D. Same for C, C# and D, but then it is the opposite way.

There can be such dodecaphonic indeed. I do not think any of that kind of music has been composed thus far, but you can see a challenge in it. Take for example the tone row C, C#, Cx, Cx#, Cxx, Cxx#, Cxxx, Cxxx#, Cxxxx, Cxxxx#, Cxxxxx, Cxxxxx# using pure intonation (first problem is: how to write this on sheet?). The distance between the Cxxxxx# and the C will therefore be the smallest distance here.
(We of course can also change some notes, but the point is clear.) This tone row (we will change the order of the notes of course) is based on other distance. It will probably give us a quite strange feeling, but 'clean' dodecaphonics (ET) (in another way) also do. So it may be an interesting update of our music knowledge:
PURE INTONATION DODECAPHONY

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Wow some cool stuff you got there.

Seriously, fuck off about the temperament thing.

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For my next composition at school, my teacher has actually requested that I do a serial piece. I had some stuff in the works already, so I'm gonna work on developing it.

I got a few note rows going on in it (about 5, 3/4 unused so far, and 2 in development), and it will include piano.

So far, it's only got pitch serialism, but I'm really considering getting all total serialism crawling going. I was even thinking of using some mathematics going. The only thing though is that it's quite difficult making an entire piece out of it, and at times I feel it is killing my ideas, in the near exact words of Boulez himself. Fortunately I like all the stuff I've come up with.

And one final thing, it sounds real fucked up! I'm loving it. I'll post my progress when I get more done.

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Yeah I'd like to hear that.

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Here's a start. I can play the upward sliding bit in 6/8 so far. I came up with it a while ago. Give me your thoughts!

Attached Files

Intro.gp5 (18.9 KB, 105 views)

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I had to compose a serialism piece for college two years ago.

This video describes it pretty well...

http://www.youtube.com/watch?v=u5dOI2MtvbA

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Shit, I'd like to listen to your compo Unanything, but i don't have GP5 5.1, and don't want it.Any way of posting a simple GP5, or even GP4?

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Sorry man. I could e-mail you a midi. I don't think you can attach midis here.

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Hey, e-mail me one if you could. I wanted to hear it but couldn't.

jimharas@yahoo.com

Thanks

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Sent one!

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That's fucking awesome. Did you have a simple structure and just throw in a bunch of notes randomly, or did you plan out the entire thing note-by-note.

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Note by note, of course. It's incomplete as of yet though, as it may have sounded.

Some of the rows came from calculation, some from jamming and improvising. Most of the verse came from using symmetrical scale type stuff and filling in the gaps.

There are around 10 rows in there, probably more, if you discount the retrogrades, the inversions, the retrograde inversions and the alternate ways they are played.

And thanks, Shunt.

Anyone else want a copy?

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Me!!Send me one!

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I'll need your e-mail address then. I can't attach midis here.

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hated_gg_allin at hotmail.com

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Glad you enjoyed it!

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Then put it in a zip file and attach it.

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