| Rick Mealey wrote:
>
> By my reckoning (and I think Slonimsky did the math before me), when
> we consider the octave subdivided into 12 pitch classes, we have
> thousands of ways to combine the twelve:
>
> 12 pitch classes sounded singly
> 66 two-voice chords (not counting inversions)
> 220 three-voice chords (" " ")
> 495 four-voice
> 792 five-voice
> 924 six-voice
> 792 seven-voice
> 495 eight-voice
> 220 nine-voice
> 66 ten-voice
> 12 eleven-voice
> 1 twelve-voice uberchord
> ----
> 3434 distinct sonorities
Some years ago I wrote a LISP program that calculated all the possible
relationships between all 12 notes. The 'World Vector', an extension of the
concept of the Interval Vector, was a large document detailing relationships
for every possible n-voice set, using Forte notation. Thus you could select,
say a 012456, and look up the population of all the constituent intervals,
trichords, tetrachords and pentachords which could be formed from it
(subsets). Similarly, you could look up how often it occurred within all the
sets of order 7 or greater (supersets).
Then I found an amazing book called 'Composition with Pitch Classes' by Robert
D. Morris, which takes Pitch Set Theory well into the realms of mathematics,
and is well worth a look if you wish to navigate far and wide within pitch
space - but it's not exactly bedtime reading!
> Some of these will be more musically useful than others: the composer
> decides that, and this (I believe) is the fundamental decision
> he/she/it makes. Theoretically, and here I'm paraphrasing
> Persichetti's text, any one of these permutations let's call them
> chords for sake of argument may follow another, or even follow
> itself. And likewise the composer will find some progressions between
> chords found to be more sonically useful than others.
True, however I believe that it is possible for any composer to become
disoriented in pitch space and to misjudge the significance of some not so
obvious properties of sets with which she/he/it is working, unless they have
an understanding of how to navigate accurately within the pitch space
universe. Only then can she/he/it make informed decisions about whether a
pitch set is as useful as they think it is, by being aware of its full
potential.
> The trick that composers face is to narrow all those choices down to a
> subset about which they feel strongly, whether it be for the length of
> one piece or for his/her/its entire body of work.
It is important to fully understand, either by intuition, or by objective
analysis, the ramifications of a set about which a composer feels strongly -
both its internal character, and its relationships to the remainder of the
pitch universe ; for example, its complement, its invariant behaviour under
various modes of transformation, ways in which it resembles other sets and
ways in which it differs, its capacity for variation etc.
> Several people here have hinted that the medium plays a role in
> determining the appropriate chords to use the question of the sort of
> piece one would write for an orchestra versus that which one would
> write for a computer versus that written for a combination of carbon-
> and silicon-based lifeforms/musicians. Someone somewhere is using
> Csound to render the blues using granular synthesis, and somewhere
> else another Csounder would never dream of using Csound for that
> purpose. Taste does play a role.
If a composer's sound world is defined in part by a bunch of chords that they
keep coming back to, I don't see why the medium should influence that. Set
theory doesn't talk explicitly about "chords" as such. It uses the term
'simultaneity' to refer to a collection of notes that have a predominantly
vertical incarnation. The concept of the set is one where the constituent
pitch classes are not committed in time, register, articulation or any other
compositional sense. The decision to distribute the set amongst the
instruments of an orchestra, the registers of a solo flute, or as boundaries
of noise bands in a Csound piece, is one which, in principle, does not have
any bearing on the set theoretical properties of the pitch collection(s) in
question.
Even for those rendering the blues via granular synthesis, there would be a
compositional phase space with its obscure deep structure underpinning a more
obvious surface quality. Depending on how well one knows this region, it would
be possible to turn such an unlikely exercise into something magical. One
thing is for sure though - the granular synthesis would be the easy bit ....
> For me personally, medium is not so much of an issue. Yeah, I'm
> interested in coming up with textures that most people haven't heard
> before; this is my primary reason for experimenting with Csound. But
> still speaking for myself, timbre means nothing if I don't have a
> composition underlying. There are plenty of pieces out there that
> consist of seemingly randomly-placed found sounds-- works by Varese
> and Stockhausen come to mind-- but that's not where I personally
> choose to work. I cling to the belief that we haven't yet exhausted
> all possibilities with the equal-tempered 12-tone octave regarding
> harmony, melody, or rhythm (and don't get me started on those
> permutations).
Varese and Stockhausen - an unfortunate choice, because they took great care
to structure their pieces, in both the electronic and acoustic domains. Ok if
you don't want to work where they went, but randomly placing sounds is one of
the few things neither of them did - at least not in the implied perjorative sense.
I agree about the need for an underlying sense of composition. However, I
believe that the idea of music relying upon the mining of some rich,
undiscovered harmonic mother-lode has had its day. This harks back to Liszt's
statement that ".. every new piece should have a new chord..." - or words to
that effect. It's not that there are no unexhausted possibilities left. But
the position we find ourselves in today is that music no longer depends so
heavily upon discrete pitch relationships, in the way it did in the past.
Harmonic evolution is not a backwater either, but it is now one of a number of
possible contenders in a composer's palet, and it can be rejected like any
other under certain circumstances.
Bob Douglas
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From: Paul
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Subject: Re: Higher numerical precission in Csound
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Job M. van Zuijlen wrote:
>
> I have been following the professional audio industry for 30 years and
> there is hype, occasionally.
I'm glad someone else pointed this out. I am no expert on pro audio (I'm
a bit chagrined that M. Gogins has refuted some of my ignorant claims
about pro audio gear... well, you live and learn). But I have done
quite a bit of lurking on rec.audio.pro (though not in the last six
months or so) and it's worth noting that the resident gurus over there
do not always agree with each other about these things. There is no
reason to assume that the pro audio industry is immune to faddism and
hype; with the current level of technology and the much-lamented lack of
blind testing, I think it is entirely possible that there is quite a bit
of gear currently being sold on merits that people are taking on faith.
I think I can hear the difference between sampling rates of 44.1 kHz and
48 kHz, at least in some cases, but I can't eliminate the possibility of
placebo effect; and I have yet to hear about a blind test that
demonstrates that 96 kHz has any merits over 48 kHz.
I've read some arguments that 96 kHz was a big mistake because it is not
trivial to smoothly convert 96 kHz to 44.1 kHz (which will, like it or
not, remain the primary delivery format for some years yet); 88.2 kHz
would have given almost the same amount of (presumed) improvement in
sound while greatly reducing that problem. This makes very good
intuitive sense to me, and I have not seen a single counter-argument.
Yet 96 kHz gear, not 88.2, is being advertised like crazy in all the
studio-gear magazines.
And then there's the _real_ lone nuts in the wilderness, who claim that
PCM was a mistake from the get-go, and we should be converting
everything to some sort of 1-bit, extremely-high-sampling-rate
technology that Sony is now using for archival masters; they claim that
this blows the pants off of every other format currently in use (in part
by eliminating the anti-aliasing filters). Who knows. I don't even
understand how this system works. Too bad it's completely incompatible
with all existing software and hardware... I wonder if those guys are
right, and I wonder if we'll ever get to find out; or if we're now stuck
with PCM regardless.
But it's all kind of an academic point for me anyway since I'll be
working with a sub-$100 16-bit soundcard for the foreseeable future
(maybe that's why I'm more concerned with keeping csound speedy than
with increasing its precision.. I feel the speed limits every time I use
csound, but I have never noticed problems with lack of resolution
(except in cases where I really needed an interpolating loscil and there
wasn't one... I think this has been added recently)).
--PW
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Date: Thu, 10 Jun 1999 02:26:31 -0400
From: Paul
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Mike Berry wrote:
>
> In the float/double question, everybody is making it a real-time vs.
> file-time comparison, which I don't think is totally fair. CSound,
> however you use it now, was designed as a file-time program.
I'm afraid I have to turn this on its head and say that csound, however
it was designed, is now used both real-time and file-time. Why should
the intended limited scope of a tool outweigh the actual uses people
find for it? I don't think it should. So I disagree with your statement
that:
> .... Any improvements should be judged first on whether they improve
> file generation (e.g. sound quality) and then on how they impact compile
> times.
I think we should rather, whenever possible, take both into account. If
there is a way to provide options so the user can push csound further in
either direction, then that is what I'm in favor of. A compile-time flag
would do fine for me (I could just have two binaries: a speedier one and
a "better" one).
This is assuming that there is significant speed loss in the actual
performance of the proposed double-precision version, which several
folks have pointed out might not be the case (or at least might not be
that bad). I'm now quite curious to see what actually happens in
practice. It would be pretty funny if all this talk were shown to be
completely irrelevant.
--PW
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Subject: Re: Higher numerical precission in Csound
From: Nathan Day
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----------
>From: Paul
>To: zuijlen@ibm.net
>Subject: Re: Higher numerical precission in Csound
>Date: Thu, 10 Jun 1999 3:33 PM
>
Your talking about sigma delta modulation, instead of recording the abosulte
voltage, it simply records whether it went up or down. The theory says if
you record at 16 times the sample rate of 16 bit audio with sigma delta
modulation you'll get the same quality. But it's actually easier and cheeper
to go to an even high sample rate than it is to increase the sample rate of
PCM. Sigma delta modulation can easily be convert to PCM and vice versa and
so a lot of companies use with say 128x oversampling, they can then use very
gentle analogue filters on the inputs and then use digital filters to
convert the sigma delta modulation data into a PCM.
> And then there's the _real_ lone nuts in the wilderness, who claim that
> PCM was a mistake from the get-go, and we should be converting
> everything to some sort of 1-bit, extremely-high-sampling-rate |