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This 50 message thread spans 4 pages:  < <   1   2  [3]  4  > >  
  Re: Algebraic complexity in music  MartinY at 11:20 on 13 January 2010
 

I thought I would update people with what I think about this subject. I have not done all I thought I would because I have been deeply involved with something incredibly time and commitment consuming and the 2nd half of 2009 has not provided much time for creative thought though I have been able to continue to do editing of early music.

I was thinking at one stage that algebraic complexity as regards music was an inapplicable dead end but I have now realised it is more of a side street. Even models which do not fit reality very well still generate out of the box thinking which can lead to an idea for a piece which can then be subjected to the best mathematical algorithm of all - trial and error. (It does not matter if there is plenty of error if nobody else sees it.)

One area where complexity theory is very applicable is however the representation of scores in computer files. I have been changing computers and was thinking about the importance of digital preservation. What is going to happen when your music typesetter goes obsolete and you can't alter your scores anymore? Will MUSIC-XML be a route to the future? Will Sibelius / Finale / LilyPond etc. give us decades of future compatability and stability.

The simplest and most practical thing I can suggest, which we should all do, is scan all your scores, (including the handwritten stuff), into pdfs and make loads of DVDs of the resulting directories and spread them about geographically a bit so if your house burns down you still have them. (I have seen the aftermath of a fire in a library and the books only get charred around the edges but I think my chaotic piles of manuscripts might not be so lucky.)

Before I even think anymore about digital preservation I must do some spring cleaning so the whole place is safer and less of a tip!

  Re: Algebraic complexity in music  Misuc at 11:04 on 14 January 2010
 

This is aa really fascinating subject. I have been looking through the pages of this discussion. I realise that it is possible I didn't make my case clearly enough. This, basically, is that you don't need numbers to trace out (what is interesting or relevant about) the complexity of a piece of music. I repeat my conviction that fractals - and more particularly the concepts of 'emergent systems' etc. - have something to do with the issue. But it is in the music itself where the complexity lies and not in the numerical 'facts' about the music. The parallel is with, say, biological complexity and evolution. The mathematics is of only peripheral value in understanding the issue.

I put forward Bach's 1st 2-part invention as an example of a pretty straightforward 'mathematical' (i.e. 'clever', rigid, formalistic, limited....) invention. Sometimes I compare this with, say, a pretty idiotic/simplistic Sonatina by Clementi (No. 1) and ask which is the more complex? the answer has to be the Clementi, since, even in so dumb a piece, the effect of the parts on the whole and vice-versa is so much more involved and all-encompassing (the mere change of a note - F to F sharp - trebles the length of the piece - whereas even in the most complex structure of a piece of Bach you can always bring the piece to an end within about 4 bars wherever you are.

This is not to say that Clementi is tha deeper composer! But it is to say that the evolutionary development of the musical language itself is a factor whih has to be taken into account.

  Re: Algebraic complexity in music  scott_good at 22:07 on 24 January 2010
 

Hi Martin, Misuc

" The parallel is with, say, biological complexity and evolution. The mathematics is of only peripheral value in understanding the issue."

Yes - makes sense.

"I put forward Bach's 1st 2-part invention as an example of a pretty straightforward 'mathematical' (i.e. 'clever', rigid, formalistic, limited....) invention. Sometimes I compare this with, say, a pretty idiotic/simplistic Sonatina by Clementi (No. 1) and ask which is the more complex? the answer has to be the Clementi, since, even in so dumb a piece, the effect of the parts on the whole and vice-versa is so much more involved and all-encompassing (the mere change of a note - F to F sharp - trebles the length of the piece - whereas even in the most complex structure of a piece of Bach you can always bring the piece to an end within about 4 bars wherever you are."

This is very interesting. I'm worried about the use of the word complex, though. Seems the opposite in that the Clementi has so little power to have variation - cause and effect are more concrete. Whereas in Bach, his use of clever, ridgid, and formalistic technique implies a kind of order within chaos. The various techniques he uses can work on a multitude of time scales, in exclusion or tandem of each other.

That is why I think Bach is more "complex" - each "effect" on the line, tonality, rhythm etc can lead to a multitude of possible outcomes, rather than only a few. But, it is certainly an interesting way of looking at it.

I guess the question is chaos more complex than order? Maybe it isn't mathematics that is the issue, but the very concept of complexity.

A circle is not a complex object to identify and understand. But to measure it perfectly is next to impossible - what is that pi? So, is a circle complex or simple?

Just throwing it out there. But there does seem to be some kind of discontinuity going on within the language of math, that it can so accurately describe certain objects or phenomenon, and not others that are similarly related.

"But it is to say that the evolutionary development of the musical language itself is a factor whih has to be taken into account."

For sure...but, it does reek a little of "moral relativity"..."complexity relativity". Important to take into account, but possibly distracting from the big picture.

I am getting so very interested in this subject. It is of such importance for a composer to think about this now.

How did we get to this point, and what does it mean.

Indeed, what does complexity mean in today's music? Is timbre the "new complexity" over harmony? I'm even starting to think that timbre and harmony are the same thing, or more precisely, harmony is a subset of timbre.

What about meter, tempo, and rhythm? Where does this fit onto the complexity scale.

????????

  Re: Algebraic complexity in music  Zak at 00:15 on 25 January 2010
 

I don't have much of a mind for math, but I do find it interesting--espescially in musical applications. You say, Martin, that use of the Fibonacci numbers is as old as Bartok, but according one theory textbook I read (The Musician's Guide to Theory and Analysis) use of the Fibonacci numbers goes back even farther. As you may know, this fascinating series of numbers converges on the ratio known as the "golden ratio" (or "section"), 1.618033..., denoted by the Greek letter phi; according to this book, the recapitulation of some classical sonata form movements has been observed to occur approximatley 62% of the way through, thus coming near to the inverse of phi, .618033.... How truthful this is I don't know, I haven't bothered to check it out myself, primarily because the text doesn't specify whether this includes exposition repeats or the repeats of the development and recapitulation as in Mozart's Sonata, K. 533--that is the right Koechel number, right? C Major?-- and other, earlier sonatas (i.e., whether that's calculating by time length or number of measures).

As to digital preservation, that seems like a good idea, though keeping original [u]manu[/u]scripts in fire-proof safes would also be a good idea, if you can. (As a student just starting my formal education in composition--though I have educated myself over the past few years--, both a fire-proof safe and Sibelius, etc. are out of my price range, however--not that I have much of anything I feel worthy of preserving in my manuscript books yet.)

<Added>

Ignore the 's in manuscripts, I meant for it to underline "manu" but obviously it won't just underline a part of a word.

<Added>

Now why'd it do that? Just put a "u" in brackets ([]) before "'s".

  Re: Algebraic complexity in music  MartinY at 20:48 on 25 January 2010
 

Scott has spotted two things which are very important and need a longer considered post... One is that combining chaos and complexity theories is going to generate paradoxes, sugesting to me that there is a limit to how complex you can get without it becoming chaos. I think these paradoxes can be expressed as relatively comprehensible real world situations.

Also regarding pi, (and e), transcendental and Boreal numbers are going to have some very bizarre properties. Pi is simply arccos (-1) and there are series which give pi but none of this apparant simplicity helps.

  Re: Algebraic complexity in music  Zak at 23:09 on 26 January 2010
 

I would say that Bach and Clementi each have their own kind of "complexity". Bach has an intellectual profundity which Clementi lacks, but the Clementi sonantina (if you're talking about the one I think you are) has a certain delightfulness, if you will--there must be a complexity behind that; of course, Bach is the better composer, but what exactly does that mean? (What is it that makes him better?) A different kind complexity must be involved there. But they do share a complexity: the complexity behind the system of functional tonality.

An interesting idea about the relationship of timbre and harmony; what exactly are you thinking? I can see two general points here: first, that timbre is the result of what overtones an instrument produces, and aren't overtones also a generating force of harmony? Second, timbre does have an effect upon harmony: a chord in low brass would sound quite different in high strings or woodwinds. (A probably idiotic idea: What would be the possibility of composing a piece drawing harmonies strictly from the overtones produced by the instruments it is written for? Not having an extensive knowledge of accoustics I can't answer that question, but I thought I'd share that thought.)

  Re: Algebraic complexity in music  scott_good at 23:22 on 26 January 2010
 

"What would be the possibility of composing a piece drawing harmonies strictly from the overtones produced by the instruments it is written for?"

Voila! Killer piece based on the overtones of a low E of the trombone! Great explanation in the video as the music moves along.

http://www.youtube.com/watch?v=kX77MC5oXDY

I'll respond to the rest when I have some time. Now have date to do some gardening with my son.

...oh ya...welcome Zac!

  Re: Algebraic complexity in music  Zak at 00:25 on 27 January 2010
 

Interesting... Not such an idiotic idea after all, I guess. Thanks.

  Re: Algebraic complexity in music  MartinY at 09:26 on 27 January 2010
 

Where do I start? Well lets consider just the notation of a piece without considering all that implies. (For instance there is performance practice which modifies how we read the notation, and also when we see a Bach invention images are generated of men wearing wigs sat at keyboards and cold German winters etc. which are generated from the interaction of the notation with ourselves and are not present in the information being stored.)

So we define a virtual machine which generates a printed score from code. The machine knows all about symmetry, repetition, style, transposition, inversion etc. and so can store the score as an efficient sequence of zeros and ones. The complexity is a single number: the smallest number of zeros and ones required to store the piece.

Highly structured pieces clearly will be smaller than unstructured pieces by this definition even though the structure may well be aesthetically the most appealing part of the piece. (We could have a really basic virtual machine which knew nothing about structure but then the complexity would just be the aggregate number of notes and their attributes. Not very interesting.)

Now because the machine knows all about structure the most complex pieces will be the ones with the least structure. As the sequence of notes becomes more random it becomes more complex by this definition. Ah but once we have a random sequence, one random sequence is supposed to be as good as another. (If you run a simulation to produce a physical observable like the polarizability of water it should give the same answer whatever random sequence of numbers you use provided they are true random numbers.)

So we are in the metaphorical contest with the skunk (too rude to explain) saying to other composers my music is more complex than yours, we win by generating random numbers which have no structure and therefore make a longer encoding. But my complexity is meaningless because no random sequence is better than any other. Here is the first paradox. My random sequence only has meaning in an iconographic sense. It is meaningful because it is my randomness therefore very important because I am a very important person..... nonsense! So this is my first paradox.....

An observation. The encoding for the Bach invention will be a relatively short sequence of numbers. Pi to infinite digits continues to generate random numbers in its decimal tail. Therefore the encoding for the Bach invention must occur an infinite number of times in pi..... Interesting.... but of course this applies to any infinite random sequence.

Any motto from this... do not write new complexity pieces unless you know when to stop......

  Re: Algebraic complexity in music  Misuc at 14:08 on 28 February 2010
 

Many thanks to Scott for that link to Grisey - which led me on to others, Murail, Radulesco Lachenmann, which we, shamefully, never hear in the UK. COMPOSITION TODAY would do much better featuring such clips etc. rather than removing the forum themes from the front page and, on our behalf, but without consultation, offering up our communication-space to yet more self-confessed "self-serving blog entries" from forgettable would-be momentary semicelebrities who

" feel like I should have something to say about something, but any ideas I have had recently seem to be a little self-serving or just plain dull.......(see, a self-serving blog entry)...."

CT admin would do better to listen to Emily Dickinson:

"i'm nobody! Who are you?
Are you nobody, too?
Then there's a pair of us don't tell!
They'd banish us, you know.

How dreary to be somebody!
How public, like a frog
To tell your name the livelong day
To an admiring bog!"

Meanwhile, back to that rather amazing piece by Grisey most of it based on the harmonics of a single note: what imagination and what an acute ear, to hear all those possibilities! - even if it's not quite music yet. (Taking apart a watch will not tell us much about the nature of time, and taking apart sounds doesn't tell us that much about whatever it is that music does)

And this takes me back to what I originally wanted to write about- this complexity thing. I think music's most valuable complexity can often be attained only through the greatest 'simplicity'.

Going back to the Bach example: the 1st 2-part invention is complex in the sense that there is a 'schema' for it which is complete and self-sufficient, and could be filled out with different actual pitches. In this respect the music is subject a sort of 'imposed' form. [In this respect it is similar to a whole class of tunes (e.g. the British National Anthem) which can similarly - on whatever scale - be broken down into patterns of O[riginal] and I[nversion] units etc. In most cases, what is interesting is not so much - or not only - the abstract pattern, but how the demands of this pattern can be reconciled with the demands of the tonal (key-) structure - all sorts of compromises have to be negotiated.

To demonstrate this point, I often fold up pieces of paper in a fairly irregular way and tear out holes. You are left with a paper-cut with many contradictory symmetries and broken symmetries, which can be very attractive.

But is "God Save the King(Queen)' a more interesting tune than 'La Marseillaise' [where there is no such 'schema'] ? There is no comparison between the staid and constipated anthem of stuffy Imperialists and the elan and brave, optimistic fervour of the greatest of national anthems, with its bold gestures and much more pregnant, unpredictable phrase-structure.

Less can be more. Compare the 1st 2-part invention with another Bach piece. My wife, who is not musically trained at all, but has an uncanny ear for the emotional complexities of music, asked me to play 'that wierd piece of Bach with all the repeats...[?]....the one that's so mysterious and scary......[?]....' -then I realised what she meant: the 1st prelude from the '48' - which has no 'O' and 'I' structure, and actually no motifs which could be turned upside down, sequenced etc. Provided that the player conscientiously and consistently refuses any attempt to 'interpret' the music, this allows the listener to continually regroup the phrase-lengths, and to lose himself and the beat and thus to let contending hidden currents to vie with one another in all their complexity.

In the same way, harmonising a folk song must usually destroy its complexity.

Listen to the late great Phil Tanner http://digital.othermusic.com/playlist/?TRACK_ID=264424 for the creative intonation and measure. Any accompaniment or orchestration would define the mode/tonality, fix the metre etc. and thus not allow the many contradictory meanings that are there in the performance.

Or what about this? FW04468_102 DEATH OF DIGENES.aup
[ The Death of Digenes 15:03 n.a. Modern Greek Heroic Oral Poetry
Story: Zeus sends an angel to Byzantine hero Digenes, to tell im it is time to die. D says: but stay and drink and eat first. The meal over the angel reminds him: D says I'll fight you first. They fight. D is about to win - which would overturn the eternal order - so Zeus turns the angel into an eagle who carries D into the air. D's wife calls out"If you're going to kill D kill me too" She dies too, and out of their graves grow twining grape vines ]

While I'm at it I can't resist giving you this part of the DIgenes epic too: The Abduction of Digenes' Bride 5:14 n.a. Modern Greek Heroic Oral Poetry

or to Almeda Riddle http://www.last.fm/listen/artist/Almeda%2BRiddle/similarartists#pane=webRadioPlayer&station=%252Flisten%252Fartist%252FAlmeda%252BRiddle%252Fsimilarartists

Once you are attuned you will find more and more of the layers of meaning to a piece of music many more than there are notes. The fetishism of the written note (and its whole associated paraphernalia of intonation, metre, 'tonality' etc.) is what prevents both minimalists and 'maximalists' {the 'new complexity school'] from attaining the same subtlety and meaningful complexity.

To take the most elementary case possible, listen to this naive nursery tune: http://www.last.fm/user/misuc2/library/music/Almeda+Riddle/_/Go+Tell+Aunt+Nancy
You cannot separate the notes from the basic 'gesture' - the element of what the performance is for: she is telling a joke to amuse children: she is at the same time giving you a perspective of the round of life and death: a poignant but unsentimental picture of the dependence of animals on humans and humans on animals: this is spiritually far richer and more subtle and complex than can even any longer be recognised when it is heard by classical music in general.




  Re: Algebraic complexity in music  Misuc at 14:12 on 28 February 2010
 

Many thanks to Scott for that link to Grisey - which led me on to others, Murail, Radulesco Lachenmann, which we, shamefully, never hear in the UK. COMPOSITION TODAY would do much better featuring such clips etc. rather than removing the forum themes from the front page and, on our behalf, but without consultation, offering up our communication-space to yet more self-confessed "self-serving blog entries" from forgettable would-be momentary semicelebrities who

" feel like I should have something to say about something, but any ideas I have had recently seem to be a little self-serving or just plain dull.......(see, a self-serving blog entry)...."

CT admin would do better to listen to Emily Dickinson:

"i'm nobody! Who are you?
Are you nobody, too?
Then there's a pair of us don't tell!
They'd banish us, you know.

How dreary to be somebody!
How public, like a frog
To tell your name the livelong day
To an admiring bog!"

Meanwhile, back to that rather amazing piece by Grisey most of it based on the harmonics of a single note: what imagination and what an acute ear, to hear all those possibilities! - even if it's not quite music yet. (Taking apart a watch will not tell us much about the nature of time, and taking apart sounds doesn't tell us that much about whatever it is that music does)

And this takes me back to what I originally wanted to write about- this complexity thing. I think music's most valuable complexity can often be attained only through the greatest 'simplicity'.

Going back to the Bach example: the 1st 2-part invention is complex in the sense that there is a 'schema' for it which is complete and self-sufficient, and could be filled out with different actual pitches. In this respect the music is subject a sort of 'imposed' form. [In this respect it is similar to a whole class of tunes (e.g. the British National Anthem) which can similarly - on whatever scale - be broken down into patterns of O[riginal] and I[nversion] units etc. In most cases, what is interesting is not so much - or not only - the abstract pattern, but how the demands of this pattern can be reconciled with the demands of the tonal (key-) structure - all sorts of compromises have to be negotiated.

To demonstrate this point, I often fold up pieces of paper in a fairly irregular way and tear out holes. You are left with a paper-cut with many contradictory symmetries and broken symmetries, which can be very attractive.

But is "God Save the King(Queen)' a more interesting tune than 'La Marseillaise' [where there is no such 'schema'] ? There is no comparison between the staid and constipated anthem of stuffy Imperialists and the elan and brave, optimistic fervour of the greatest of national anthems, with its bold gestures and much more pregnant, unpredictable phrase-structure.

Less can be more. Compare the 1st 2-part invention with another Bach piece. My wife, who is not musically trained at all, but has an uncanny ear for the emotional complexities of music, asked me to play 'that wierd piece of Bach with all the repeats...[?]....the one that's so mysterious and scary......[?]....' -then I realised what she meant: the 1st prelude from the '48' - which has no 'O' and 'I' structure, and actually no motifs which could be turned upside down, sequenced etc. Provided that the player conscientiously and consistently refuses any attempt to 'interpret' the music, this allows the listener to continually regroup the phrase-lengths, and to lose himself and the beat and thus to let contending hidden currents to vie with one another in all their complexity.

In the same way, harmonising a folk song must usually destroy its complexity.

Listen to the late great Phil Tanner http://digital.othermusic.com/playlist/?TRACK_ID=264424 for the creative intonation and measure. Any accompaniment or orchestration would define the mode/tonality, fix the metre etc. and thus not allow the many contradictory meanings that are there in the performance.

Or what about this? FW04468_102 DEATH OF DIGENES.aup
[ The Death of Digenes 15:03 n.a. Modern Greek Heroic Oral Poetry
Story: Zeus sends an angel to Byzantine hero Digenes, to tell im it is time to die. D says: but stay and drink and eat first. The meal over the angel reminds him: D says I'll fight you first. They fight. D is about to win - which would overturn the eternal order - so Zeus turns the angel into an eagle who carries D into the air. D's wife calls out"If you're going to kill D kill me too" She dies too, and out of their graves grow twining grape vines ]

While I'm at it I can't resist giving you this part of the DIgenes epic too: The Abduction of Digenes' Bride 5:14 n.a. Modern Greek Heroic Oral Poetry

or to Almeda Riddle http://www.last.fm/listen/artist/Almeda%2BRiddle/similarartists#pane=webRadioPlayer&station=%252Flisten%252Fartist%252FAlmeda%252BRiddle%252Fsimilarartists

Once you are attuned you will find more and more of the layers of meaning to a piece of music many more than there are notes. The fetishism of the written note (and its whole associated paraphernalia of intonation, metre, 'tonality' etc.) is what prevents both minimalists and 'maximalists' {the 'new complexity school'] from attaining the same subtlety and meaningful complexity.

To take the most elementary case possible, listen to this naive nursery tune: http://www.last.fm/user/misuc2/library/music/Almeda+Riddle/_/Go+Tell+Aunt+Nancy
You cannot separate the notes from the basic 'gesture' - the element of what the performance is for: she is telling a joke to amuse children: she is at the same time giving you a perspective of the round of life and death: a poignant but unsentimental picture of the dependence of animals on humans and humans on animals: this is spiritually far richer and more subtle and complex than can even any longer be recognised when it is heard by classical music in general.




<Added>

Sorry about waiting months and then sending this rambling piece TWICE. I was struggling to achieve some simple complexity in my own music this is taking time. And just now I was trying to upload mp3 links. It still does not appear that i have done so correctly.

  Re: Algebraic complexity in music  Misuc at 20:02 on 02 March 2010
 

I am sorry to bother you good folks again, but I have to apologise yet again. I just can't manage to get my computer to upload mp3s etc. and I just don't understand how these audio and video clips work. I thought I downloaded various recordings and then posted them as links on tis forum. Some didn't upload at all and none of them came out as they were intended. I would like to try again when I get time - if anyone is interested. (At least one should appeal to Scott's kids). If I get to learn how to do it, I'd like to send in much more. There is so very, very much - a whole 'undiscovered' second world of artistry..........

  Re: Algebraic complexity in music  scott_good at 21:59 on 02 March 2010
 

"Many thanks to Scott for that link to Grisey - which led me on to others, Murail, Radulesco Lachenmann, which we, shamefully, never hear in the UK. "

My pleasure.

"Meanwhile, back to that rather amazing piece by Grisey most of it based on the harmonics of a single note: what imagination and what an acute ear, to hear all those possibilities! - even if it's not quite music yet."

Funny, I am with you on this. I'm slightly addicted to this piece (Partiels), but agree that it in some ways doesn't feel like "music"...even though it is beautiful, but more like a sculpture. I mean, it is music, but I think I understand your point. (http://www.youtube.com/watch?v=kX77MC5oXDY)

BUT, please find time to listen to Vortex Temporum to hear Grisey at his most musical. There are clips on youtube but the sound quality is just not good enough. Take the time to listen all the way through - I really do think you will appreciate the scope of this work (about 40min)

It was the first piece of his I experienced, and was able to hear it live. Amazing.

"Going back to the Bach example: the 1st 2-part invention is complex in the sense that there is a 'schema' for it which is complete and self-sufficient, and could be filled out with different actual pitches."

Funny, but you are very correct, once again! Well, at least I should say from the perspective of Gustav Ciamagga (who is, btw, one of my absolute favourite electro-acoustic composers). I attended a lecture of his entitled "Algorhythmic Composition" quite a few years ago. To demonstrate a simple set of procedures, he took this invention and multiplied the intervals by various intervals - M2nds you get "Debussy", P4th, you get "Hindemith" etc. It was very convincing.

aside: He also showed us how Porgy and Bess was structured around various algorhythmic principals! Gershwin studied the Schillinger system (http://www.schillingersystem.com/whatis.htm), for which I know very little, but would be curious to hear if anyone else has studied these ideas.

"In this respect the music is subject a sort of 'imposed' form. . . In most cases, what is interesting is not so much - or not only - the abstract pattern, but how the demands of this pattern can be reconciled with the demands of the tonal (key-) structure - all sorts of compromises have to be negotiated. "

Yes, this is interesting. And is why for me I'm happy to be composing in this time - one can choose or not choose to impose these sorts of compromises. There is no "Uber" system to be negotiated, only music, sound, and emotion.

"But is "God Save the King(Queen)' a more interesting tune than 'La Marseillaise' [where there is no such 'schema'] ? There is no comparison between the staid and constipated anthem of stuffy Imperialists and the elan and brave, optimistic fervour of the greatest of national anthems, with its bold gestures and much more pregnant, unpredictable phrase-structure."

Humm...not so sure I'm with you on this. I would hate to have to sing "La Marseillaise", it is overtly violent and racist. But then, God Save the *insert bloodline of choice* is also a bit much - ha ha - happy and glorious and reigning dominions and all that. I still like the tune, though. And does work well with harmony, no? In fact, hardly works without. Just like the Bach invention sounds terrible with only one voice.

"Less can be more. Compare the 1st 2-part invention with another Bach piece. . . the 1st prelude from the '48' - which has no 'O' and 'I' structure, and actually no motifs which could be turned upside down, sequenced etc. Provided that the player conscientiously and consistently refuses any attempt to 'interpret' the music, this allows the listener to continually regroup the phrase-lengths, and to lose himself and the beat and thus to let contending hidden currents to vie with one another in all their complexity."

Yes, this is a "riff" song. Just let the riff be, and the fluxing of harmony becomes interesting, especially with the extended peddle point at the end. Lovely piece - astounding really.

"In the same way, harmonising a folk song must usually destroy its complexity. "

Yes, this is a good point. But sometimes harmony can BE the interpretation, rather than the kind of interpretation that Mr. Tanner provides (it isn't THE way to sing the music, but rather His way, which is part of the reason folk music is so special). Here is a harmony that I think is quite beautiful, and seems to me essential in the interpretation (phrasing, tempo, intonation, vocal shaping etc). Not sure if you like barber shop (gotta dig the common tone diminished chords!) - if you don't just pass over it. But this is certainly a melody that does not need harmony.

Tura Lura Lura

http://www.youtube.com/watch?v=4LcoMfVQHGw

"The fetishism of the written note (and its whole associated paraphernalia of intonation, metre, 'tonality' etc.) is what prevents both minimalists and 'maximalists' {the 'new complexity school'] from attaining the same subtlety and meaningful complexity. "

A very interesting point.


  Re: Algebraic complexity in music  MartinY at 07:48 on 03 March 2010
 

There are lots of things I would like to comment on but I would like to update a little question related to effectiveness of music and ornamentation....... I have been doing lots of admin and editing baroque music, only writing a couple of hundred bars of a little recorder piece recently. It is interesting how the limitations of the type-setting have influenced the baroque music. Quantz has used a rather sophisticated engraving system which allows him to put more or less all the ornamentation and articulation marks he wanted into the print, (Quantz comments that some composers leave to the performer lots of things which the composer ought to be writing.) When Gottfried Finger is published in London by Walsh the moveable type cannot do much more than give the notes and there is a massive sense of something lacking if you play this music plain without adding anything.


We can see the connection with complexity now... when you add ornamentation, even in a totally mechanical way, the music comes to life, even though you have not done anything creating information or being creative, because you are just following a system... I thought this was interesting but do not know what it means.... Though we can see that in earlier music ornamentation is necessary, though now it is composed into the music, grace notes fast events, too fast for the brain to register as individual points but nevertheless necessary for the music.

I was thinking what would happen if you tried to put the Empfindsamer Stil into a modern context. You might get something not a million miles away from Boulez' chamber music.

I need to think a little bit more to write something on style and the little notes / colouring events etc which are part of modern styles. I also wonder what would happen if you applied mindlessly a modern Hotteterre-like schema mechanically to a piece in a modern style?

I have found writing music for pure recorders that some things do not work because there is a lack of varied instrumental colour, but articulation and fiddly ornaments might be able to make up for that..... Of course I am limited in what I can do because I do not want to write a 7 page preface on techniques to learn before you can play the piece because though some people would love that, many would throw the music out at the sight of it.....

  Re: Algebraic complexity in music  IanTipping at 12:37 on 03 March 2010
 

"the fetishism of the written note...."

A very interesting point indeed. I think that Misuc makes some really valid points on this and just as an aside, I'd like to refer to the compositions of Duke Ellington. Many of you will know this but due to some, ahem, tax irregularities, Ellington's music actually entered the public domain on his death rather than after the usual 70 years. In spite of this, remarkably little of his music has been published in its original arrangements. In order to see these, one has to visit the Smithsonian and although I've not made the trip myself, a very good friend of mine recently completed a PhD which was in part devoted to Ellington's composition and method of working. As a result I have seen photocopies of the original manuscripts and it is an enlightening experience.

How this relates to Misuc's points about notation and complexity is that, looking at the scores, virtually all the solos are notated (which surprised me), yet when you listen to the recordings, they sound improvised. In terms of interpretation of the written note, it is clear that a HUGE amount of license is being taken and consequential complexity added to the bones of what appears in the score - and that this is intended by Ellington (or Strayhorn, depending who wrote that particular section). The notation of the solos becomes purely a guide, where the swoops of Johnny Hodges Alto or the Gutbucket wah of Tricky Sam's Trombone, whilst intrinsic to the performance (and clearly intended by the composers) would be either impossible or incredibly difficult to notate (and more to the point imitate, hence the reason for numbers being dropped when the soloist featured left the band).

I have occasionally tried to do things along these lines myself, but I've generally found that a) I write things that are not idiomatic, or that become so in performance or b) the players are either too conservative or go too far away from the sketch (I'm not giving up on it, mind you!) I suppose that Ellington and Strayhorn had an advantage in that most of the featured soloists stayed with the band for many years, and so they learned what the guys could do and how they would interpret the notes presented to them. When questioned about how he hung on to players for so long, Ellington said "Well, you have to have a gimmick... my gimmick is I pay them."

This whole (slightly rambling) post relates to Martin's points about published scores from the Baroque. I wonder if the reason for the lack of ornamental detail comes (in part, at least) from the publishers knowing that competent performers of the time would simply know the language and add the necessary without being cued, much like the Ellington band soloists? I suspect that the afforementioned 'Fetishism of the written note' simply became so pervasive in the 18th and 19th centuries that those kind of spontaneous additions became eradicated as composers sought more and more control of their output.

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