Your blog is inspiring, articulate and profound. It should be read by every music student and every composer!
With thanks and warmest regards, Joel
Friday, January 15, 2010
Wednesday, January 13, 2010
Infinite Permutation as a Creative Principle
Consider the following process as a manner of invention for musical material. A medieval composer takes a melodic fragment from plainchant, sets it in longer note values as a cantus firmus, and composes polyphony against the cantus firmus according to the contemporary practice. The new music sounds like medieval polyphony instead of plainchant. A bebop musician in the 1940’s takes the chord changes of a standard popular song and composes a new melody using the same harmonic structure. The new tune sounds like bebop instead of a standard pop song.
Now consider that the medieval composer takes a line of the new music and makes it the basis for new polyphonic composition using the same process. Or the bebopper makes substitute chord changes for the new tune and then composes a new melody over the substitute changes. These processes can continue ad infinitum, and the new music will always retain a seed of the original, but it will not necessarily be recognizable to the causal listener. Furthermore, the new work may sound radically different from the original or the most recent creation and the composer can create a new musical language in this manner. There is no end to the different directions this process can take, and there is no reason why the new creative work may not deal with any of the parameters of music (besides melody, harmony and counterpoint) and reframe the old model with, for example, new tuning systems, structural principles, rhythmic systems, instrumental, vocal or electronic settings, etc.
Now consider that the medieval composer takes a line of the new music and makes it the basis for new polyphonic composition using the same process. Or the bebopper makes substitute chord changes for the new tune and then composes a new melody over the substitute changes. These processes can continue ad infinitum, and the new music will always retain a seed of the original, but it will not necessarily be recognizable to the causal listener. Furthermore, the new work may sound radically different from the original or the most recent creation and the composer can create a new musical language in this manner. There is no end to the different directions this process can take, and there is no reason why the new creative work may not deal with any of the parameters of music (besides melody, harmony and counterpoint) and reframe the old model with, for example, new tuning systems, structural principles, rhythmic systems, instrumental, vocal or electronic settings, etc.
Friday, January 8, 2010
Artistic Vision and Craft
I define artistic vision as: the generating ideas for works of art; and craft as the power and technique to carry out the artistic vision. Much of our training as musicians consists of mastering the techniques and skills used to execute musical ideas. Less training is spent on the development of artistic vision. People who earn graduate degrees in music are not generally expected to do original research until they reach the doctoral level; even then, their topics of research are often suggested and always approved by their graduate advisers. Contrast that with the musical originality of the giants of music history: Machaut, Josquin, Monteverdi, Bach, Beethoven, Berlioz, Wagner, Schoenberg, Stravinsky, Ives, Parker, Cage, Ellington, Partch, Monk, Stockhausen, Xenakis, and Gaburo, some of whom were self-taught or didn’t earn graduate degrees. Many composers with advanced degrees have superior craft, but lack original vision. Many musical visionaries possess original artistic visions, but lack the technique to completely realize their ideas; they either limit their musical visions to match their technique--or else they eventually master the craft necessary to realize their visions.
The ideal, of course, is to develop an original vision and possess the craft to realize that vision. Vision and craft go hand in hand. I have sometimes been criticized by performers for composing music which is technically difficult if not impossible. Of course, the technique is necessary to realize my ideas completely and distinctly. If performers approach my music with a sincere desire to understand the artistic vision, and they dedicate themselves to realizing that vision, the technical mastery follows naturally. Good musicians who work hard make great performances with an intensity which is excellent and rare.
The ideal, of course, is to develop an original vision and possess the craft to realize that vision. Vision and craft go hand in hand. I have sometimes been criticized by performers for composing music which is technically difficult if not impossible. Of course, the technique is necessary to realize my ideas completely and distinctly. If performers approach my music with a sincere desire to understand the artistic vision, and they dedicate themselves to realizing that vision, the technical mastery follows naturally. Good musicians who work hard make great performances with an intensity which is excellent and rare.
Thursday, January 7, 2010
My Music Is For Everyone
My music is for everyone. Those who listen with open minds will find their hearts opening and feel love for every lving being. Those who listen with open hearts will find their minds opening to infinite possibilities. Those who listen with open hearts and minds will find their bodies responding to the deepest rhythms of the universe.
Friday, January 16, 2009
America's Pathological Obsession with Celebrity
1.16.09
America’s Pathological Obsession with Celebrity
To watch the news media transform Barak Obama from Democratic presidential candidate to celebrity-in-chief after the election is to be reminded of the deeply pathological obsession Americans have with the hero worship which negates the validity of the individual and represents an anti-democratic spirit. I am not criticizing Obama, I voted for him. He seems like a very good man; it is good to have a president elect who doesn’t brag about the fact that he doesn’t read newspapers, like his anti-intellectual predecessor. He seems to have the motivation of wanting to serve rather than to amass personal power and money; and he has inherited a shambles of Bush’s legacy of war, torture, spying on citizens, profiteering, economic and ethical collapse. I wish him all the best in his task of running the country.
Unfortunately, the people who create media celebrity not just of politicians, but also film and television stars, rock stars and celebrity businessmen, scientists and yes, composers don’t understand the true nature of artistic creation and research but focus on the symbolic nature of image and its dissemination in an effort to cater to vicarious pleasure in their clients and profit from them. As soon as the election was over the hawking of memorabilia began. Democracy resides in individuals not the leaders; they are only elected to serve the people. My deep concern is that hero worship of celebrity leaders leads to imperial thinking and makes a mockery of democracy. Our last leader thought of himself as above the law and look at what it resulted in. My prayer is that Barak Obama will be able to see through the hype and live up to his fine words.
America’s Pathological Obsession with Celebrity
To watch the news media transform Barak Obama from Democratic presidential candidate to celebrity-in-chief after the election is to be reminded of the deeply pathological obsession Americans have with the hero worship which negates the validity of the individual and represents an anti-democratic spirit. I am not criticizing Obama, I voted for him. He seems like a very good man; it is good to have a president elect who doesn’t brag about the fact that he doesn’t read newspapers, like his anti-intellectual predecessor. He seems to have the motivation of wanting to serve rather than to amass personal power and money; and he has inherited a shambles of Bush’s legacy of war, torture, spying on citizens, profiteering, economic and ethical collapse. I wish him all the best in his task of running the country.
Unfortunately, the people who create media celebrity not just of politicians, but also film and television stars, rock stars and celebrity businessmen, scientists and yes, composers don’t understand the true nature of artistic creation and research but focus on the symbolic nature of image and its dissemination in an effort to cater to vicarious pleasure in their clients and profit from them. As soon as the election was over the hawking of memorabilia began. Democracy resides in individuals not the leaders; they are only elected to serve the people. My deep concern is that hero worship of celebrity leaders leads to imperial thinking and makes a mockery of democracy. Our last leader thought of himself as above the law and look at what it resulted in. My prayer is that Barak Obama will be able to see through the hype and live up to his fine words.
Sunday, November 30, 2008
In Defense of Modernism
In Defense of Modernism
Nowadays it is common to hear people say things like: “the death of modernism” and “discredited modernist attitudes of the past” or “humans have a congenital inability to understand anything but tonal music” or “music should be entertainment first”. In contrast, consider the life and work of Anton Webern, who labored in obscurity during an era of chauvinist nationalism in his native Austria and quietly rebuilt the foundations of European concert music by developing the contrapuntal practice and timbral implications of previous work along with serial technique. The extreme brevity of his middle period work was unprecedented in concert music history. The extreme concentration of his musical thought led Stravinsky to call him a “miner of diamonds”. That the importance of his work was almost universally recognized after the Second World War testifies to the truth that modernist music is not impossible to understand.
Music with an experimental consciousness bespeaks a fresh outlook on life and an ongoing development of knowledge. People who appreciate experimental music and other avant garde arts have a kind of openness of mind which comes as a breath of fresh air in a world of hardened attitudes and political positions.
I have come to the conclusion that the current prejudice against experimental music is a result of confusion between music and music theory. Music theories come and go as musicians attempt to explain the musical languages of their times or former times, yet great music of any culture or era has the power to outlast the fashions of the day regardless of which theoretical construct or musical language was used in its composition. That is why we still listen to great music of the past. It speaks to us regardless of the theory the composer knew and practiced, because of the compositional excellence of the composer’s technique and the honesty of his artistic voice.
We deeply respect the poetic art of Shakespeare, but wouldn’t dream of recommending that contemporary poetry should be written in Elizabethan English or use classical forms. Yet a similar attitude prevails among reactionary critics and musicologists who insist on the primacy of earlier musical languages and the impossibility of understanding music conceived with experimental principles. (It is a bit like saying that poetry written in a foreign language couldn’t be any good because it is written in a foreign language.) There is nothing particularly universal about any music theory or language as many pedagogues claim (they are generally repeating the same mistakes they were taught). If any theory were universal, we would see the same musical language used in every culture in every age. Nothing could be farther from the truth. Musical languages are as various as spoken and written languages and they evolve continuously just as the meanings of words keep changing as language is used.
Music theories are not only the result of analysis of past or current practice; some new theories are the result of composers’ need to organize new musical ideas or may make use of conceptual models borrowed from other disciplines. An example of this is Xenakis’ use of probability concepts in the development of his theory of stochastic music.
Music is much more than a form of sonic entertainment; it is also a form of knowledge and wisdom capable of touching humans at the very deepest levels of consciousness. This knowledge aspect of music is continually developing as a kind of scientific understanding, and the aesthetic aspect is timeless, as a conception of beauty. The interaction between these two aspects is the nexus of artistic creation in music. Composition, performance and listening all take part in this creation.
The primary message of a musical composition (from the smallest details of its sound world to the design of its macrostructure) is realized according to the intention of its creator. This is so true as to seem tautological, but what does it mean? As with any human endeavor the creator’s intention is coded into the creative act and its tangible result. If a person designs and builds an ultra fast racecar, the car will be a result of this intention and will be built accordingly, with special internal parts and racing tires, etc. It will be substantially different from a family sedan or a limousine. This is obvious to a casual observer even though she may be unskilled in the appreciation of the technical details of its construction.
Music that is a part if an historical tradition also embodies the ideas and attitudes attached to its genre. If the composer develops some of those ideas or rejects some, the knowledgeable listener will understand this. The case of experimental music is special. Since Beethoven, there is a tradition of musical experimentation, in which innovation has become a kind of normal expectation of musical genius. (In a certain sense, this is oxymoronic, since innovation and tradition are generally contradictory.) The composer is expected to invent some new sounds, sound combinations, or musical ideas as a normal part of the creative process, and many composers continue this tradition, even though some critics and listeners consider the tradition to be dead or irrelevant.
The experimental work of John Cage represents a high water mark in this respect, since he expanded the notion of music making to include chance operations, nonintentional sound and incorporated silence into music as an essential element. He also introduced the listening strategy of appreciating all sounds (even environmental sounds) for their own sake, quite apart from any musical ideas in the conventional sense. He also incorporated a kind of theatre (different from staged drama and more related to real life) into the process of music making. He regarded the avant garde to be an attitude of mental flexibility.
Some listeners consider the avant garde not to be an attitude of mental flexibility, but a musical language and treat it as just another historical style, which has passed its heyday. The idea of postmodern music as somehow “newer than new” reflects this notion. The ironic detachment of considering the incorporation of older musical ideas to be somehow innovative bespeaks a consideration of musical style above musical substance. Keeping up with the latest trends in musical fashion has become more important than invention of musical ideas and techniques.
Music seems to be unique as an art form in which traditional work is passed off as somehow innovative, or an acceptable practice of performance. Or unusual mixtures of different styles are called new. This attitude would be laughable in the sciences and other arts, but it is the convention in music. Can anyone imagine a visual artist who only painted in the style of Leonardo or a scientist who only reworked the theories of Newton? Our symphony orchestras and opera companies routinely program only the works of past masters or commission new works from composers who use “accessible” (read conservative) musical language, in the hopes of not alienating their moneyed patrons by challenging their unspoken assumptions.
Nowadays it is common to hear people say things like: “the death of modernism” and “discredited modernist attitudes of the past” or “humans have a congenital inability to understand anything but tonal music” or “music should be entertainment first”. In contrast, consider the life and work of Anton Webern, who labored in obscurity during an era of chauvinist nationalism in his native Austria and quietly rebuilt the foundations of European concert music by developing the contrapuntal practice and timbral implications of previous work along with serial technique. The extreme brevity of his middle period work was unprecedented in concert music history. The extreme concentration of his musical thought led Stravinsky to call him a “miner of diamonds”. That the importance of his work was almost universally recognized after the Second World War testifies to the truth that modernist music is not impossible to understand.
Music with an experimental consciousness bespeaks a fresh outlook on life and an ongoing development of knowledge. People who appreciate experimental music and other avant garde arts have a kind of openness of mind which comes as a breath of fresh air in a world of hardened attitudes and political positions.
I have come to the conclusion that the current prejudice against experimental music is a result of confusion between music and music theory. Music theories come and go as musicians attempt to explain the musical languages of their times or former times, yet great music of any culture or era has the power to outlast the fashions of the day regardless of which theoretical construct or musical language was used in its composition. That is why we still listen to great music of the past. It speaks to us regardless of the theory the composer knew and practiced, because of the compositional excellence of the composer’s technique and the honesty of his artistic voice.
We deeply respect the poetic art of Shakespeare, but wouldn’t dream of recommending that contemporary poetry should be written in Elizabethan English or use classical forms. Yet a similar attitude prevails among reactionary critics and musicologists who insist on the primacy of earlier musical languages and the impossibility of understanding music conceived with experimental principles. (It is a bit like saying that poetry written in a foreign language couldn’t be any good because it is written in a foreign language.) There is nothing particularly universal about any music theory or language as many pedagogues claim (they are generally repeating the same mistakes they were taught). If any theory were universal, we would see the same musical language used in every culture in every age. Nothing could be farther from the truth. Musical languages are as various as spoken and written languages and they evolve continuously just as the meanings of words keep changing as language is used.
Music theories are not only the result of analysis of past or current practice; some new theories are the result of composers’ need to organize new musical ideas or may make use of conceptual models borrowed from other disciplines. An example of this is Xenakis’ use of probability concepts in the development of his theory of stochastic music.
Music is much more than a form of sonic entertainment; it is also a form of knowledge and wisdom capable of touching humans at the very deepest levels of consciousness. This knowledge aspect of music is continually developing as a kind of scientific understanding, and the aesthetic aspect is timeless, as a conception of beauty. The interaction between these two aspects is the nexus of artistic creation in music. Composition, performance and listening all take part in this creation.
The primary message of a musical composition (from the smallest details of its sound world to the design of its macrostructure) is realized according to the intention of its creator. This is so true as to seem tautological, but what does it mean? As with any human endeavor the creator’s intention is coded into the creative act and its tangible result. If a person designs and builds an ultra fast racecar, the car will be a result of this intention and will be built accordingly, with special internal parts and racing tires, etc. It will be substantially different from a family sedan or a limousine. This is obvious to a casual observer even though she may be unskilled in the appreciation of the technical details of its construction.
Music that is a part if an historical tradition also embodies the ideas and attitudes attached to its genre. If the composer develops some of those ideas or rejects some, the knowledgeable listener will understand this. The case of experimental music is special. Since Beethoven, there is a tradition of musical experimentation, in which innovation has become a kind of normal expectation of musical genius. (In a certain sense, this is oxymoronic, since innovation and tradition are generally contradictory.) The composer is expected to invent some new sounds, sound combinations, or musical ideas as a normal part of the creative process, and many composers continue this tradition, even though some critics and listeners consider the tradition to be dead or irrelevant.
The experimental work of John Cage represents a high water mark in this respect, since he expanded the notion of music making to include chance operations, nonintentional sound and incorporated silence into music as an essential element. He also introduced the listening strategy of appreciating all sounds (even environmental sounds) for their own sake, quite apart from any musical ideas in the conventional sense. He also incorporated a kind of theatre (different from staged drama and more related to real life) into the process of music making. He regarded the avant garde to be an attitude of mental flexibility.
Some listeners consider the avant garde not to be an attitude of mental flexibility, but a musical language and treat it as just another historical style, which has passed its heyday. The idea of postmodern music as somehow “newer than new” reflects this notion. The ironic detachment of considering the incorporation of older musical ideas to be somehow innovative bespeaks a consideration of musical style above musical substance. Keeping up with the latest trends in musical fashion has become more important than invention of musical ideas and techniques.
Music seems to be unique as an art form in which traditional work is passed off as somehow innovative, or an acceptable practice of performance. Or unusual mixtures of different styles are called new. This attitude would be laughable in the sciences and other arts, but it is the convention in music. Can anyone imagine a visual artist who only painted in the style of Leonardo or a scientist who only reworked the theories of Newton? Our symphony orchestras and opera companies routinely program only the works of past masters or commission new works from composers who use “accessible” (read conservative) musical language, in the hopes of not alienating their moneyed patrons by challenging their unspoken assumptions.
Wednesday, July 23, 2008
The Nature of Musical Time and SPANDA
The Nature of Musical Time and the Composition of SPANDA
Structure in my music follows a model borrowed from physics. I apply this system to the structuring of both time and sound. There are up to 12 hierarchical levels of structure in this system. They are from smallest to largest:
1.) particle/wave, 2.) atom, 3.) element, 4.) cell, 5.) field, 6.) subzone, 7.) zone, 8.) world, 9.) system, 10.) galaxy, 11.) cluster, and 12.) superstring. Each level of structure is at least one order of magnitude larger than the previous level, and will contain several elements from the next lower level.
Musical time exists in at least three domains of perception. In the audio spectrum (roughly 20 Hz. to 20 kHz.) we may perceive the qualities of pitch, timbre, noise, loudness, etc. I will call this the domain of pitch and timbre. In the next domain of time (roughly 20 Hz. to about 10 seconds) we perceive the rhythmic aspects (durations and patterns of relative duration between sounds) and internal changes in the pitch, timbre and loudness envelopes (growth and decay aspects) of sounds, as well as the shorter aspects of musical ideas (motives, melodies, short phrases, harmonic successions, motion of sound in space and accents of various kinds). I call this the domain of musical rhythm. In the next time domain (from about 10 seconds to about one hour) we perceive the larger structural aspects of music (longer phrases, periods, sections, movements, etc.) in which the musical forms and the development of ideas take place. I call this the domain of musical form.
Stockhausen has pointed out* that each of these domains is about eight to ten “octaves” in size. (An octave being a 2 to 1 ratio of time duration, whether measured in frequency (cycles per second or Hertz) or in duration (micro seconds, milliseconds, seconds, minutes, hours, etc.). For example, the interval between pitches with the fundamental frequencies of 220 Hz. to 440 Hz. constitutes an octave in the pitch domain; the difference between the two tempi MM 60 and MM 120 constitute an “octave” in the rhythmic domain, and the durations 30 seconds and one minute have the ratio of an “octave” in the structural domain of musical time.) Different perceptions of time (pitch, timbre, rhythm and duration) take place in these different domains because our nervous systems process the temporal data differently as the sound materials cross the perceptual thresholds between each phenomenon. Musical composition consists mainly of the ordering of sonic configurations of the different musical elements in these three different temporal domains. So the composer must master the configuration of time in several different ways. Within each domain there are many different parameters of sound to be ordered and configured.
I conceived the complex of 198 compositions titled SPANDA in 1989 using this understanding of musical time. SPANDA is a Sanskrit word borrowed from the yogic philosophy of Kashmir Shaivism, which means the ‘creative throb of Consciousness’ (which creates the entire universe and everything in it). The duration of the entire complex was derived from the pitch of the first sound of the first composition in the complex. That pitch is a Bb with the fundamental frequency of 116.54 Hz. When this frequency is transposed downwards by 27 octaves, it passes out of the domain of pitch and timbre, through the domains of rhythm and musical form, and into the next domain of time in which we live our lives and experience our education and life experience. The former Bb now forms a “wave” one cycle of which has the duration of 13 days and almost eight hours. (See table one below.)
116.5409…Hz. Bb
58.27947…Hz. Bb (one octave lower)
29.13523…Hz. Bb lowest Bb on the conventional piano keyboard
14.56761…Hz. below the audio spectrum
Into the domain of musical rhythm
7.2838……Hz. (four octaves lower)
3.6419……Hz. (3.6 cycles a second or .2745 seconds per
cycle)
.5491” (duration of one cycle measured in seconds)
1.098…”
2.196…” (eight octaves lower)
4.393…”
8.786…”
17.573…” (no longer short enough to be perceived as rhythm)
35.146…” (12 octaves lower)
70.292…” (1minute 10.29” per cycle)
2’ 20.58…”
4’ 41.17…”
9’ 22.34…” (16 octaves lower)
18’ 44.68…”
37’ 29.372…”
1 hr. 14’ 58.745…” (out of the domain of musical form
into the temporal realm of education and life experience)
2 hrs. 29’ 57.49…” (20 octaves lower)
4 hrs. 59’ 54.98…”
9 hrs. 59’ 49.961…”
19 hrs. 59’ 39.92…”
1 day 15 hrs. 59’ 19.84…” (24 octaves lower)
3 days 7 hrs. 58’ 39.694…”
6 days 15 hrs. 57’ 19.898”
13 days 7 hrs. 54’ 38.77” (27 octaves lower)
Table One
The full theoretical duration of SPANDA is thirteen days, seven hours, 54 minutes and 38.77 seconds. (In reality this duration will vary somewhat with individual interpretations of tempo and rubato interpretations of different performers.) Each day of the cycle was subdivided according to different principles of division, and embodies a different “rhythm” of durations based on the principles of each day of the cycle. The collective proportions (of the durations of the 198 pieces) constitute the coherent macrostructure of the complex. I proceeded in this fashion according to my understanding that a numinous world of hyperspace exists under the aspect of patterned relations,** in this case the pattern of relative durations of the compositions in the complex, a kind of higher order of temporal macrostructure. I sometimes refer to this as the architecture of the complex.
SPANDA Macrostructure
13 days 7 Hours 54' 38.77" = Bb 116.54Hz / 2 27 times ( = a wave one cycle of which is 13 days 7hrs 54' 38.77")
Day principal sound structural principle # of time zones Title
1 Bb noise entropic 27 Symphonies of Sound
2 F logarithmic spiral 19 Symphonies of Time
3 Ab spatial 8 Symphonies of Space
4 E exponential 11 Symphonies of Energy
5 D polyphonic overlapping 7 Symphonies of Earth
6 G expansion from a point 5 Symphonies of the
Light of Consciousness
7 F# linguistic, microcosmic 13 Symphonies of the Word
8 A aperiodic different speeds 7 Symphonies of Love
9 D# biomorphic 10 Symphonies of the Seed
10 B games and play 15 Symphonies of the Children
11 Db linear growth and decay 11 Symphonies of the Vine of
Life and Death
12 C isomorphic with inversion 26 Symphonies of the
Universe
13 Bb serial 37 Symphonies of
Transmutation and Metamorphosis
14 Bb silence seamless Postlude (7 hrs. 54’ 38.77”)
Each composition of the 198 constitutes an individual “time zone” of a specific duration whose internal structure is subdivided according to different numerical principles into “time fields” which are in turn subdivided into different “time cells” with specific internal structure which contain the sonic materials. These different levels of temporal hierarchy constitute the macrostructural, middle level, rhythmic, and microstructural forms of the compositions. In this way of working, the fundamental dichotomy between form and content disappears since the content is determined by the form and the form may be determined by an analysis of the content. Furthermore, the principles which determine the rhythm may also be used to determine the melodic, harmonic and timbral materials.
Structure in my music follows a model borrowed from physics. I apply this system to the structuring of both time and sound. There are up to 12 hierarchical levels of structure in this system. They are from smallest to largest:
1.) particle/wave, 2.) atom, 3.) element, 4.) cell, 5.) field, 6.) subzone, 7.) zone, 8.) world, 9.) system, 10.) galaxy, 11.) cluster, and 12.) superstring. Each level of structure is at least one order of magnitude larger than the previous level, and will contain several elements from the next lower level.
Musical time exists in at least three domains of perception. In the audio spectrum (roughly 20 Hz. to 20 kHz.) we may perceive the qualities of pitch, timbre, noise, loudness, etc. I will call this the domain of pitch and timbre. In the next domain of time (roughly 20 Hz. to about 10 seconds) we perceive the rhythmic aspects (durations and patterns of relative duration between sounds) and internal changes in the pitch, timbre and loudness envelopes (growth and decay aspects) of sounds, as well as the shorter aspects of musical ideas (motives, melodies, short phrases, harmonic successions, motion of sound in space and accents of various kinds). I call this the domain of musical rhythm. In the next time domain (from about 10 seconds to about one hour) we perceive the larger structural aspects of music (longer phrases, periods, sections, movements, etc.) in which the musical forms and the development of ideas take place. I call this the domain of musical form.
Stockhausen has pointed out* that each of these domains is about eight to ten “octaves” in size. (An octave being a 2 to 1 ratio of time duration, whether measured in frequency (cycles per second or Hertz) or in duration (micro seconds, milliseconds, seconds, minutes, hours, etc.). For example, the interval between pitches with the fundamental frequencies of 220 Hz. to 440 Hz. constitutes an octave in the pitch domain; the difference between the two tempi MM 60 and MM 120 constitute an “octave” in the rhythmic domain, and the durations 30 seconds and one minute have the ratio of an “octave” in the structural domain of musical time.) Different perceptions of time (pitch, timbre, rhythm and duration) take place in these different domains because our nervous systems process the temporal data differently as the sound materials cross the perceptual thresholds between each phenomenon. Musical composition consists mainly of the ordering of sonic configurations of the different musical elements in these three different temporal domains. So the composer must master the configuration of time in several different ways. Within each domain there are many different parameters of sound to be ordered and configured.
I conceived the complex of 198 compositions titled SPANDA in 1989 using this understanding of musical time. SPANDA is a Sanskrit word borrowed from the yogic philosophy of Kashmir Shaivism, which means the ‘creative throb of Consciousness’ (which creates the entire universe and everything in it). The duration of the entire complex was derived from the pitch of the first sound of the first composition in the complex. That pitch is a Bb with the fundamental frequency of 116.54 Hz. When this frequency is transposed downwards by 27 octaves, it passes out of the domain of pitch and timbre, through the domains of rhythm and musical form, and into the next domain of time in which we live our lives and experience our education and life experience. The former Bb now forms a “wave” one cycle of which has the duration of 13 days and almost eight hours. (See table one below.)
116.5409…Hz. Bb
58.27947…Hz. Bb (one octave lower)
29.13523…Hz. Bb lowest Bb on the conventional piano keyboard
14.56761…Hz. below the audio spectrum
Into the domain of musical rhythm
7.2838……Hz. (four octaves lower)
3.6419……Hz. (3.6 cycles a second or .2745 seconds per
cycle)
.5491” (duration of one cycle measured in seconds)
1.098…”
2.196…” (eight octaves lower)
4.393…”
8.786…”
17.573…” (no longer short enough to be perceived as rhythm)
35.146…” (12 octaves lower)
70.292…” (1minute 10.29” per cycle)
2’ 20.58…”
4’ 41.17…”
9’ 22.34…” (16 octaves lower)
18’ 44.68…”
37’ 29.372…”
1 hr. 14’ 58.745…” (out of the domain of musical form
into the temporal realm of education and life experience)
2 hrs. 29’ 57.49…” (20 octaves lower)
4 hrs. 59’ 54.98…”
9 hrs. 59’ 49.961…”
19 hrs. 59’ 39.92…”
1 day 15 hrs. 59’ 19.84…” (24 octaves lower)
3 days 7 hrs. 58’ 39.694…”
6 days 15 hrs. 57’ 19.898”
13 days 7 hrs. 54’ 38.77” (27 octaves lower)
Table One
The full theoretical duration of SPANDA is thirteen days, seven hours, 54 minutes and 38.77 seconds. (In reality this duration will vary somewhat with individual interpretations of tempo and rubato interpretations of different performers.) Each day of the cycle was subdivided according to different principles of division, and embodies a different “rhythm” of durations based on the principles of each day of the cycle. The collective proportions (of the durations of the 198 pieces) constitute the coherent macrostructure of the complex. I proceeded in this fashion according to my understanding that a numinous world of hyperspace exists under the aspect of patterned relations,** in this case the pattern of relative durations of the compositions in the complex, a kind of higher order of temporal macrostructure. I sometimes refer to this as the architecture of the complex.
SPANDA Macrostructure
13 days 7 Hours 54' 38.77" = Bb 116.54Hz / 2 27 times ( = a wave one cycle of which is 13 days 7hrs 54' 38.77")
Day principal sound structural principle # of time zones Title
1 Bb noise entropic 27 Symphonies of Sound
2 F logarithmic spiral 19 Symphonies of Time
3 Ab spatial 8 Symphonies of Space
4 E exponential 11 Symphonies of Energy
5 D polyphonic overlapping 7 Symphonies of Earth
6 G expansion from a point 5 Symphonies of the
Light of Consciousness
7 F# linguistic, microcosmic 13 Symphonies of the Word
8 A aperiodic different speeds 7 Symphonies of Love
9 D# biomorphic 10 Symphonies of the Seed
10 B games and play 15 Symphonies of the Children
11 Db linear growth and decay 11 Symphonies of the Vine of
Life and Death
12 C isomorphic with inversion 26 Symphonies of the
Universe
13 Bb serial 37 Symphonies of
Transmutation and Metamorphosis
14 Bb silence seamless Postlude (7 hrs. 54’ 38.77”)
Each composition of the 198 constitutes an individual “time zone” of a specific duration whose internal structure is subdivided according to different numerical principles into “time fields” which are in turn subdivided into different “time cells” with specific internal structure which contain the sonic materials. These different levels of temporal hierarchy constitute the macrostructural, middle level, rhythmic, and microstructural forms of the compositions. In this way of working, the fundamental dichotomy between form and content disappears since the content is determined by the form and the form may be determined by an analysis of the content. Furthermore, the principles which determine the rhythm may also be used to determine the melodic, harmonic and timbral materials.
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