Hey Kristopher. This is very atmospheric and eerie stuff. One easily gets lost in there. Got about 10 minutes in, but this isn't for me a daytime listening piece, better suited to the wee hours. It sets a unique and compelling mood-space where thoughts freely float. Im going to throw it on the big speakers this evening. (Im reminded a bit of the feeling when I listen to Morton Feldman.)
Thanks Gx. The irony can't be overlooked that an object whose form is governed entirely by explicit functions of time would ultmately evoke the diametrically opposite attributes of indeterminacy, or even stochasticity. Sufficiently obscure algorithms appear to be chaotic, or perhaps even magic, to paraphrase (and perhaps mar) some famous quote by some person of notoriety unrecalled by me at the moment. (Huxley?)
This approach is in some indirect sense a repudiation of Schoenberg's serialism, because in my opinion, and mine only perhaps, the twelve tone method was destined to fail in its avowed mission of obliterating tonal hierarchy. No such objective is feasible in 12 EDO, because its intervals nearly approximate the fundamental sonorities of fifths, fourths, thirds, and sixths (minor thirds), ie, 3/2, 4/3, 5/4. etc. These sonorities are anchored to our physical reality in such a fundamental manner that, given a cloud of random semitones, and a sufficient number of unbiased composers with no inherited aesthetic predisposition and a sufficient amount of time, they would eventually arrive at the same modal system, and through contraction, eventually probably diatonicism. What I posit here is the notion that harmony itself, a spectrum from unison to the most dissonant utterance possible (white noise, perhaps?), is inherently hierarchical,and can only be liberated within a system in which the tonal hierarchy itself is not disregarded, but unmoored.
In short, the effort of serialists to obliterate tonal heirarchy sought to do so by eschewing fundamental harmony, whereas perhaps the more fruitful, and meaningful, endeavor might have been not to liberate music from harmony (in the hierarchical sense), but rather to liberate harmony from the constraint of fixed, discrete scales.
The homage to fundamental harmony is present here, but the notion of tonal center has been eradicated, at least across any substantive interval in time. The sense of a tonal center, or "key" is instantaneously present, but in constant flux throughout.
I'll reserve my commentary on structure for HS's remarks, because I have to go for now. Thanks for listening.
HS Teoh > Kristofer EmerigOctober 1, 2023 at 8:13pm
Was in the middle of posting and the machine ate my message. Short paraphrase: to be free from tonal hierarchy, get rid of the tone (in the sense of a note with a constant, fixed pitch). Look to human languages for inspiration: "tonal" languages show two interesting characteristics: (1) pitch is not absolute (it differs by person); (2) the pitch contour is more important than the exact pitch itself.
IOW, pitch relationships don't have to be exact. The shape of the pitch contour is more important than the pitch itself. Varying pitch should be the norm rather than the exception.
Ah, yes. I've lost many a massive missive to Ning's voracious appetite for bytes of bloviation. Now come on, you acknowledged your love of silly puns;)
Put practically, in a pantonal setting, we can have an instantaneous sense of tonicity (in the sense of a "home" pitch), that varies across time. Therefore, if you listen to the above example and pause it at a certain point, you can probably imagine or sing a pitch that 'feels like' the tonic. Now if you play another section, separated in time, and perform the same exercise, you will find that those two pitches bear no diatonic relationship; neither is likely to be shared in the same 12 EDO scale, unless by dumb luck. This is the sufficient and necessary condition for making music mathematically transformable with respect to the parameters of pitch and time, viewed as the basis of a frequency-time vector space.
If one attempts to, for instance, tranform a discrete melody through a orthogonal rotation, as you suggested, the result is a series of frequency spectra of zero duration. The width of the continuum of frequencies corresponds to the duration of the mapped note, The temporal spacing of those objects correspond to the pitch of the mapped notes, with higher pitches being mapped backward or forward in time, depending on the direction of the rotation. In short, the mapping results in discrete continua of pitches (whose frequencies are bound by the order and duration of the mapped notes) of zero duration, arranged in time according to their pitch.
Take the image of a melody in a piano roll editor, and rotate it, to visualize what I'm saying, and observe that this is not true of a continuous curvilinear 'melody'..
HS Teoh > Kristofer EmerigOctober 2, 2023 at 10:54am
I wouldn't be dismissive of massive missives, but yes, I do love silly puns. :-D
Now, if you rotate the midi roll in the literal sense, then a 45° rotation of a single note for example would yield an upward glissando, because the start and end of the note, being at different points in time, would correspond to different pitches. But I daresay this isn't the sense in which fugue devices work: consider the retrograde, for example. Played on a piano, a note of the theme would start with an attack, decay, then a period of sustain, and a final release. If we were to retrograde the theme in the literal sense, the corresponding note in our retrograde theme would have to start with the final release in reverse, then a sustain, and end with an attack (a reversed decay) followed by a decay (a reversed attack). The result is easy to construct in any audio editor -- just take any piano piece and retrograde the audio file. It's an interesting sound, certainly, but arguably not what "retrograde" means as a fugue device. We still expect notes to sound in the usual manner -- attack, decay, sustain, release, except that the order of pitches (and note durations) is reversed.
Thus one may argue that in applying a fugue device what matters is the start of the note, rather than the rest of it. This is why in my charts I used single points in time ("events") rather than the entire note in performing the various transformations. You'd transform these starting points, and then use them to fill out the actual notes to be played after the fact. (If you're a stickler for mathematical notation, this would be notated as UAU-1 where U transforms notes into single points in pitch/time space, and A is the actual transformation.)
Of course, if you're talking about a literal transformation of a continuous, curvilinear melody, then that's something else. In that case you'd be dealing directly with the transform A over the continuum of pitch/time space. That also has its own interesting characteristics. A sufficiently-rotated curve, for example, may turn into chords. Consider an arc-shaped pitch/time "melody", for example. If you rotate it 90°, you'd end up with a single starting point (corresponding to the peak of the arc) that bifurcates into two simultaneous curves.
This sort of thing actually jives with my idea of dispensing altogether with the concept of a "note" ("anotal" music? :-P). Instead, the "music" would be like drawing curves on the pitch/time continuum. And one could postulate drawing actual 2D shapes on the continuum, with "themes" corresponding to specific figures, which can then be treated to various transformations: rotations, scalings, shearings, stretchings, you name it. Indeed, one could envision a picture-to-sound translator that takes any 2D black-and-white image as input, and outputting the corresponding audio. Then your "score" would literally be a series of hieroglyphic-like scribbles, each representing some kind of musical theme, appearing in various orderings and transformations over the course of the music. A very interesting avenue to explore, I must say.
Of course, we again have to take care not to do this too literally -- because unless you're dealing with pure sine waves, there will be harmonics with any natural-sounding note, and I wouldn't propose to rotate the harmonics along with the note as well -- then every note would result in an infinitude of new notes, each corresponding with a harmonic. To make any sense of such a scheme, we still have to operate at some level of abstraction, where the 2D curves are mapped to notes that generate their own harmonics, but these harmonics are not considered when performing our theme transformations.
"one could envision a picture-to-sound translator that takes any 2D black-and-white image as input, and outputting the corresponding audio. Then your "score" would literally be a series of hieroglyphic-like scribbles, each representing some kind of musical theme, appearing in various orderings and transformations over the course of the music. A very interesting avenue to explore, I must say."
The tool you describe is precisely what's needed to explore this avenue efficiently, and its present unavailability is precisely the reason I will not be spending another months-long period of toil to construct another object like this. The user interface should work similarly to Geogebra, but produce not only the graph, but a corresponding midi output that maps the domain and range of funcions to time and frequency repectively. In fact, I've used Geogebra extensively to obtain pitch contours, but this sort of patchwork drawing approach is inefficient and tedious. The proper tool could be easily coded within the span required to produce the example above. Didn't Lincoln say that, if he had eight hours to cut down a tree, he'd spend six hours sharpening the axe?
HS Teoh > Kristofer EmerigOctober 4, 2023 at 1:04pm
Didn't Lincoln say that, if he had eight hours to cut down a tree, he'd spend six hours sharpening the axe?
Spoken like a true programmer. :-P It's what drives programmers to spend months constructing elaborate pieces of software instead of computing the answer by hand in 2 hours.
On further thoughts, this tool should support free-hand curve drawing (either with mouse or touchpad), because most melodic shapes of interest aren't going to be ideal geometric objects like circles and rectangles. Also, since pitch needs to vary over time, and most humans aren't going to be able to think on the timescale of sound wavelengths, the software will have to interpolate between the quantized coordinates generated by mouse movement / touchpad sensors. Preferably quadratic or cubic interpolation, since connecting the points with linear segment would likely introduce unwanted artifacts in the resulting sound. So the objects will have to be some kind of interpolated splines, and the program will have to infer them from user input using quadratic or cubic curve-fitting algorithms.
Furthermore, we'd like to perform geometric operations on our themes, so of course things like rotation, scaling, shearing, reflecting, will all have to be basic operations.
Finally, to help the unwary audience (well, and the composer :-D) understand what's going on, the program ought to be able to generate a simple video showing the "score" (i.e., the 2D layout of curves) scrolling past a vertical line representing the current point in time of the audio. Which of course includes generating the audio itself, which isn't going to be trivial because just about all current audio synthesis tools are designed with discrete fixed pitches in mind. So things like vocoding on an organ patch, say, isn't going to be a simple thing to implement. I suppose the lazy way out is to go all-out synthetizer-from-scratch, i.e., generate the waveforms programmatically, optionally overlaid with harmonics and what-not as needed.
Wow. That's already quite a hefty list of requirements... with my copious amounts of non-existent free time, I'm not sure when any of this will come to fruition. :-/
gregrorio j > Kristofer EmerigOctober 4, 2023 at 1:12pm
"In short, the effort of serialists to obliterate tonal hierarchy sought to do so by eschewing fundamental harmony, whereas perhaps the more fruitful, and meaningful, endeavor might have been not to liberate music from harmony (in the hierarchical sense), but rather to liberate harmony from the constraint of fixed, discrete scales.
The homage to fundamental harmony is present here, but the notion of tonal center has been eradicated, at least across any substantive interval in time. The sense of a tonal center, or "key" is instantaneously present, but in constant flux throughout."
Yes, beautifully said. When working in 12 tone, I also see it as an extension of the harmonic possibilities with tonal center in constant flux, as you say. (Obliteration of tonal heir-achy is not what Im trying to achieve.) My thinking is pretty much the same, whether it be 12 tone (though more restrictive) or other.
Stravinsky says something about this in the book 'Conversations with Stravinsky' by Robert Craft - (an illuminating, provocative and hilarious read - 1959):
"R.C. Do you think of the intervals in your series as tonal intervals; that is, do your intervals always exert tonal
pull?
I.S. The intervals of my series are attracted by tonality;
I compose vertically and that is, in one sense at least,
to compose tonally.
R.C. How has composing with a series affected your own
harmonic thinking? Do you work in the same way—
that is, hear relationships and then compose them?
I.S. I hear certain possibilities and I choose. I can create
my choice in serial composition just as I can in any
tonal contrapuntal form. I hear harmonically, of
course, and I compose in the same way I always have.
R.C. Nevertheless, the Gigue from your Septet and the
choral canons in the Canticum Sacrum are much
more difficult to hear harmonically than any earlier
music of yours. Hasn't composing with a series there-
fore affected your harmonic scope?
I.S. It is certainly more difficult to hear harmonically
the music you speak of than my earlier music; but any
serial music intended to be heard vertically is more
difficult to hear. The rules and restrictions of serial
writing differ little from the rigidity of the great con-
trapuntal schools of old. At the same time they widen
and enrich harmonic scope; one starts to hear more
things and differently than before. The serial tech-
nique I use impels me to greater discipline than ever
My reaction to the 2 minutes or so: this sounds like one of those mystery soundtracks when the protagonists find themselves aboard a derelict alien spaceship, surrounded by strange things they can't even begin to comprehend, and not knowing what to expect next. Loved the microtonal shifting and meandering that nevertheless pretend that they sound like consonant or semi-consonant intervals.
Only thing is, the tones are so continuously blended that it's hard to pick out any specific theme: everything is simply melded into one. As a result, after about 16 mins it's all starting to sound more-or-less the same, and I'm starting to wonder where the music is heading, if anywhere at all. The alien ship continues to fascinate, but we appear to have lost our way in its twisting, incomprehensible hallways, and no longer know where we are headed. We are wondering whether it's time to head back, but are compelled to go on because the captain's orders were clear: thoroughly explore this ship in case there is something to be found therein. The tension is rising, the soundtrack is having a (very) poco a poco crescendo, but we have still not discerned any identifying characteristics of our strange surroundings.
At 31 minutes, we are completely lost on board the alien ship, and no longer know the way back. The dark cavernous halls surround us, offering strange constructs that we are unable to comprehend and dare not touch. There is a lull at 32:20: we seem to have reach an empty hall in the middle of the ship. But there is nothing else to do but the press on deeper into the darker passages. We are now deep in the bowels of the ship, and still do not understand a thing. The halls are all different, yet more-or-less of the same incomprehensible alien architecture. Ostensibly each one has a specific purpose, but lacking any information on the former occupants and what must be their totally alien physiology, we cannot even begin to guess what this purpose might be.
At 45 mins there's a lull -- we seem to be passing from one section of the ship to another. But still no understanding of our surroundings whatsoever. The architecture in this new section is different, yet as far as we could tell all of the same incomprehensible style and construction.
And then, after an hour of aimless wandering through the belly of the alien ship, we suddenly find ourselves at the far end. There was no indication whatsoever (none that we could discern anyway) that beyond that last hallway the ship would come to an end. We just came up against a final wall, and that was it. Nowhere else to go but back to our captain to report our disappointing findings that, despite great hopes along the way, we did not actually discover anything that stood out in particular, that might be of interest to him. The alien architecture and the wealth of twisty, incomprehensible shapes were, of course, vital and interesting data for our analysts; but any hopes the captain may have had of specific artifacts that might be of interest to us were, unfortunately, unfounded.
Comments
Hey Kristopher. This is very atmospheric and eerie stuff. One easily gets lost in there. Got about 10 minutes in, but this isn't for me a daytime listening piece, better suited to the wee hours. It sets a unique and compelling mood-space where thoughts freely float. Im going to throw it on the big speakers this evening. (Im reminded a bit of the feeling when I listen to Morton Feldman.)
Thanks Gx. The irony can't be overlooked that an object whose form is governed entirely by explicit functions of time would ultmately evoke the diametrically opposite attributes of indeterminacy, or even stochasticity. Sufficiently obscure algorithms appear to be chaotic, or perhaps even magic, to paraphrase (and perhaps mar) some famous quote by some person of notoriety unrecalled by me at the moment. (Huxley?)
This approach is in some indirect sense a repudiation of Schoenberg's serialism, because in my opinion, and mine only perhaps, the twelve tone method was destined to fail in its avowed mission of obliterating tonal hierarchy. No such objective is feasible in 12 EDO, because its intervals nearly approximate the fundamental sonorities of fifths, fourths, thirds, and sixths (minor thirds), ie, 3/2, 4/3, 5/4. etc. These sonorities are anchored to our physical reality in such a fundamental manner that, given a cloud of random semitones, and a sufficient number of unbiased composers with no inherited aesthetic predisposition and a sufficient amount of time, they would eventually arrive at the same modal system, and through contraction, eventually probably diatonicism. What I posit here is the notion that harmony itself, a spectrum from unison to the most dissonant utterance possible (white noise, perhaps?), is inherently hierarchical, and can only be liberated within a system in which the tonal hierarchy itself is not disregarded, but unmoored.
In short, the effort of serialists to obliterate tonal heirarchy sought to do so by eschewing fundamental harmony, whereas perhaps the more fruitful, and meaningful, endeavor might have been not to liberate music from harmony (in the hierarchical sense), but rather to liberate harmony from the constraint of fixed, discrete scales.
The homage to fundamental harmony is present here, but the notion of tonal center has been eradicated, at least across any substantive interval in time. The sense of a tonal center, or "key" is instantaneously present, but in constant flux throughout.
I'll reserve my commentary on structure for HS's remarks, because I have to go for now. Thanks for listening.
Was in the middle of posting and the machine ate my message. Short paraphrase: to be free from tonal hierarchy, get rid of the tone (in the sense of a note with a constant, fixed pitch). Look to human languages for inspiration: "tonal" languages show two interesting characteristics: (1) pitch is not absolute (it differs by person); (2) the pitch contour is more important than the exact pitch itself.
IOW, pitch relationships don't have to be exact. The shape of the pitch contour is more important than the pitch itself. Varying pitch should be the norm rather than the exception.
Ah, yes. I've lost many a massive missive to Ning's voracious appetite for bytes of bloviation. Now come on, you acknowledged your love of silly puns;)
Put practically, in a pantonal setting, we can have an instantaneous sense of tonicity (in the sense of a "home" pitch), that varies across time. Therefore, if you listen to the above example and pause it at a certain point, you can probably imagine or sing a pitch that 'feels like' the tonic. Now if you play another section, separated in time, and perform the same exercise, you will find that those two pitches bear no diatonic relationship; neither is likely to be shared in the same 12 EDO scale, unless by dumb luck. This is the sufficient and necessary condition for making music mathematically transformable with respect to the parameters of pitch and time, viewed as the basis of a frequency-time vector space.
If one attempts to, for instance, tranform a discrete melody through a orthogonal rotation, as you suggested, the result is a series of frequency spectra of zero duration. The width of the continuum of frequencies corresponds to the duration of the mapped note, The temporal spacing of those objects correspond to the pitch of the mapped notes, with higher pitches being mapped backward or forward in time, depending on the direction of the rotation. In short, the mapping results in discrete continua of pitches (whose frequencies are bound by the order and duration of the mapped notes) of zero duration, arranged in time according to their pitch.
Take the image of a melody in a piano roll editor, and rotate it, to visualize what I'm saying, and observe that this is not true of a continuous curvilinear 'melody'..
I wouldn't be dismissive of massive missives, but yes, I do love silly puns. :-D
Now, if you rotate the midi roll in the literal sense, then a 45° rotation of a single note for example would yield an upward glissando, because the start and end of the note, being at different points in time, would correspond to different pitches. But I daresay this isn't the sense in which fugue devices work: consider the retrograde, for example. Played on a piano, a note of the theme would start with an attack, decay, then a period of sustain, and a final release. If we were to retrograde the theme in the literal sense, the corresponding note in our retrograde theme would have to start with the final release in reverse, then a sustain, and end with an attack (a reversed decay) followed by a decay (a reversed attack). The result is easy to construct in any audio editor -- just take any piano piece and retrograde the audio file. It's an interesting sound, certainly, but arguably not what "retrograde" means as a fugue device. We still expect notes to sound in the usual manner -- attack, decay, sustain, release, except that the order of pitches (and note durations) is reversed.
Thus one may argue that in applying a fugue device what matters is the start of the note, rather than the rest of it. This is why in my charts I used single points in time ("events") rather than the entire note in performing the various transformations. You'd transform these starting points, and then use them to fill out the actual notes to be played after the fact. (If you're a stickler for mathematical notation, this would be notated as UAU-1 where U transforms notes into single points in pitch/time space, and A is the actual transformation.)
Of course, if you're talking about a literal transformation of a continuous, curvilinear melody, then that's something else. In that case you'd be dealing directly with the transform A over the continuum of pitch/time space. That also has its own interesting characteristics. A sufficiently-rotated curve, for example, may turn into chords. Consider an arc-shaped pitch/time "melody", for example. If you rotate it 90°, you'd end up with a single starting point (corresponding to the peak of the arc) that bifurcates into two simultaneous curves.
This sort of thing actually jives with my idea of dispensing altogether with the concept of a "note" ("anotal" music? :-P). Instead, the "music" would be like drawing curves on the pitch/time continuum. And one could postulate drawing actual 2D shapes on the continuum, with "themes" corresponding to specific figures, which can then be treated to various transformations: rotations, scalings, shearings, stretchings, you name it. Indeed, one could envision a picture-to-sound translator that takes any 2D black-and-white image as input, and outputting the corresponding audio. Then your "score" would literally be a series of hieroglyphic-like scribbles, each representing some kind of musical theme, appearing in various orderings and transformations over the course of the music. A very interesting avenue to explore, I must say.
Of course, we again have to take care not to do this too literally -- because unless you're dealing with pure sine waves, there will be harmonics with any natural-sounding note, and I wouldn't propose to rotate the harmonics along with the note as well -- then every note would result in an infinitude of new notes, each corresponding with a harmonic. To make any sense of such a scheme, we still have to operate at some level of abstraction, where the 2D curves are mapped to notes that generate their own harmonics, but these harmonics are not considered when performing our theme transformations.
Argh, Ning ate my superscript. It should be UAU⁻¹ (take that, Ning!).
"one could envision a picture-to-sound translator that takes any 2D black-and-white image as input, and outputting the corresponding audio. Then your "score" would literally be a series of hieroglyphic-like scribbles, each representing some kind of musical theme, appearing in various orderings and transformations over the course of the music. A very interesting avenue to explore, I must say."
The tool you describe is precisely what's needed to explore this avenue efficiently, and its present unavailability is precisely the reason I will not be spending another months-long period of toil to construct another object like this. The user interface should work similarly to Geogebra, but produce not only the graph, but a corresponding midi output that maps the domain and range of funcions to time and frequency repectively. In fact, I've used Geogebra extensively to obtain pitch contours, but this sort of patchwork drawing approach is inefficient and tedious. The proper tool could be easily coded within the span required to produce the example above. Didn't Lincoln say that, if he had eight hours to cut down a tree, he'd spend six hours sharpening the axe?
Spoken like a true programmer. :-P It's what drives programmers to spend months constructing elaborate pieces of software instead of computing the answer by hand in 2 hours.
On further thoughts, this tool should support free-hand curve drawing (either with mouse or touchpad), because most melodic shapes of interest aren't going to be ideal geometric objects like circles and rectangles. Also, since pitch needs to vary over time, and most humans aren't going to be able to think on the timescale of sound wavelengths, the software will have to interpolate between the quantized coordinates generated by mouse movement / touchpad sensors. Preferably quadratic or cubic interpolation, since connecting the points with linear segment would likely introduce unwanted artifacts in the resulting sound. So the objects will have to be some kind of interpolated splines, and the program will have to infer them from user input using quadratic or cubic curve-fitting algorithms.
Furthermore, we'd like to perform geometric operations on our themes, so of course things like rotation, scaling, shearing, reflecting, will all have to be basic operations.
Finally, to help the unwary audience (well, and the composer :-D) understand what's going on, the program ought to be able to generate a simple video showing the "score" (i.e., the 2D layout of curves) scrolling past a vertical line representing the current point in time of the audio. Which of course includes generating the audio itself, which isn't going to be trivial because just about all current audio synthesis tools are designed with discrete fixed pitches in mind. So things like vocoding on an organ patch, say, isn't going to be a simple thing to implement. I suppose the lazy way out is to go all-out synthetizer-from-scratch, i.e., generate the waveforms programmatically, optionally overlaid with harmonics and what-not as needed.
Wow. That's already quite a hefty list of requirements... with my copious amounts of non-existent free time, I'm not sure when any of this will come to fruition. :-/
"In short, the effort of serialists to obliterate tonal hierarchy sought to do so by eschewing fundamental harmony, whereas perhaps the more fruitful, and meaningful, endeavor might have been not to liberate music from harmony (in the hierarchical sense), but rather to liberate harmony from the constraint of fixed, discrete scales.
The homage to fundamental harmony is present here, but the notion of tonal center has been eradicated, at least across any substantive interval in time. The sense of a tonal center, or "key" is instantaneously present, but in constant flux throughout."
Yes, beautifully said. When working in 12 tone, I also see it as an extension of the harmonic possibilities with tonal center in constant flux, as you say. (Obliteration of tonal heir-achy is not what Im trying to achieve.) My thinking is pretty much the same, whether it be 12 tone (though more restrictive) or other.
Stravinsky says something about this in the book 'Conversations with Stravinsky' by Robert Craft - (an illuminating, provocative and hilarious read - 1959):
"R.C. Do you think of the intervals in your series as tonal intervals; that is, do your intervals always exert tonal
pull?
I.S. The intervals of my series are attracted by tonality;
I compose vertically and that is, in one sense at least,
to compose tonally.
R.C. How has composing with a series affected your own
harmonic thinking? Do you work in the same way—
that is, hear relationships and then compose them?
I.S. I hear certain possibilities and I choose. I can create
my choice in serial composition just as I can in any
tonal contrapuntal form. I hear harmonically, of
course, and I compose in the same way I always have.
R.C. Nevertheless, the Gigue from your Septet and the
choral canons in the Canticum Sacrum are much
more difficult to hear harmonically than any earlier
music of yours. Hasn't composing with a series there-
fore affected your harmonic scope?
I.S. It is certainly more difficult to hear harmonically
the music you speak of than my earlier music; but any
serial music intended to be heard vertically is more
difficult to hear. The rules and restrictions of serial
writing differ little from the rigidity of the great con-
trapuntal schools of old. At the same time they widen
and enrich harmonic scope; one starts to hear more
things and differently than before. The serial tech-
nique I use impels me to greater discipline than ever
before.
My reaction to the 2 minutes or so: this sounds like one of those mystery soundtracks when the protagonists find themselves aboard a derelict alien spaceship, surrounded by strange things they can't even begin to comprehend, and not knowing what to expect next. Loved the microtonal shifting and meandering that nevertheless pretend that they sound like consonant or semi-consonant intervals.
Only thing is, the tones are so continuously blended that it's hard to pick out any specific theme: everything is simply melded into one. As a result, after about 16 mins it's all starting to sound more-or-less the same, and I'm starting to wonder where the music is heading, if anywhere at all. The alien ship continues to fascinate, but we appear to have lost our way in its twisting, incomprehensible hallways, and no longer know where we are headed. We are wondering whether it's time to head back, but are compelled to go on because the captain's orders were clear: thoroughly explore this ship in case there is something to be found therein. The tension is rising, the soundtrack is having a (very) poco a poco crescendo, but we have still not discerned any identifying characteristics of our strange surroundings.
At 31 minutes, we are completely lost on board the alien ship, and no longer know the way back. The dark cavernous halls surround us, offering strange constructs that we are unable to comprehend and dare not touch. There is a lull at 32:20: we seem to have reach an empty hall in the middle of the ship. But there is nothing else to do but the press on deeper into the darker passages. We are now deep in the bowels of the ship, and still do not understand a thing. The halls are all different, yet more-or-less of the same incomprehensible alien architecture. Ostensibly each one has a specific purpose, but lacking any information on the former occupants and what must be their totally alien physiology, we cannot even begin to guess what this purpose might be.
At 45 mins there's a lull -- we seem to be passing from one section of the ship to another. But still no understanding of our surroundings whatsoever. The architecture in this new section is different, yet as far as we could tell all of the same incomprehensible style and construction.
And then, after an hour of aimless wandering through the belly of the alien ship, we suddenly find ourselves at the far end. There was no indication whatsoever (none that we could discern anyway) that beyond that last hallway the ship would come to an end. We just came up against a final wall, and that was it. Nowhere else to go but back to our captain to report our disappointing findings that, despite great hopes along the way, we did not actually discover anything that stood out in particular, that might be of interest to him. The alien architecture and the wealth of twisty, incomprehensible shapes were, of course, vital and interesting data for our analysts; but any hopes the captain may have had of specific artifacts that might be of interest to us were, unfortunately, unfounded.
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