Posted by rwf1954 in classical music, harmony, mathematics and music, modes, music, music commentary, nature of music, religion and music, scales, spirituality and music, tonality.
Tags: classical music, harmony, mathematics, modes, music, overtone series, religion, scales, spirituality, tonality
(This is the final post—for now—of a series of commentaries about a series of books about the nature of music. The other commentaries of this series are listed below. This series has been triggered as a result of my rediscovery of the love of creating and performing music. There is definitely a spiritual connection to this rediscovery, evidenced by my recent release of “Issa Music” and my posts about mystical/spiritual aspects of the music of the progressive rock group Yes (The Poetry of (the Progressive Rock Group) Yes: Introduction to “The Revealing Science of God—Dance of the Dawn” from “Tales from Topographic Oceans” and The Poetry of (the Progressive Rock Group) Yes). This further relates to spiritual meditations with the theme of more than one path to God, and the possible coming together of both physics and metaphysics I and II and a discussion of Dr. Eben Alexander’s recent book, Proof of Heaven).
*******
So here I am, at the end of a longer journey than I expected, a journey of exploring music at its most basic level. With this post, I will draw together the comments I have made in posts spanning just over a year about this topic and offer some conclusions—some of these will be personal, as they will be oriented toward what this means for me as I approach my own music. But I also believe there is value in the general conclusions I will draw, conclusions I hope will enrich the music-listening of visitors to these pages.
*******
Well, let’s take a deep breath, because I will start out with the metaphysics/physics/music portion of my conclusions. On the frontiers of physics, we are learning that all matter consists of elementary particles and these particles are points of energy that radiate fields. So, existence is a heavily populated cauldron of overlapping, interacting energy fields. We humans have evolved to sense those energy fields within our finite portions of what we perceive as a three/four dimensional space/time continuum. We ourselves are a complex set of interconnected energy fields interacting with many other complex energy fields, guided through this reality by our senses. Energy—that is existence; that is life.
Music is the only art that involves a direct transmission of energy from one intelligence to another. Painting/visual art is created as imagery and experienced by looking at and absorbing the photons from those images, but not through direct energy. The images undergo a great deal of editing and processing before human beings absorb their content. Story-telling involves transmitting words or actions, again to be witnessed visually, or heard and then translated into ideas in the recipient’s mind. Sculpture/dance/books/poetry are also indirect arts. Music is direct energy. It is a series of vibrations through a medium, but the music is not the medium itself; it is the energy that courses through the medium. The music is not the molecules of the medium that are vibrating, it is the flow of energy generating those vibrations. It can be measured by an oscilloscope as energy waves. Linked with words as song, it can be extraordinarily powerful and affecting. Visual arts (like movies) use music to inject emotion—using the direct energy of music heightens the experience of other arts.
Music takes energy and puts order to it. This musical energy supplies an organized tension and release at a visceral level, a level without words or explanations needed. In a sense, it resembles at a manageable level the occurrence of pain, of pleasure, of longing and longing fulfilled. Music can be said to duplicate the experience of a want or need—fulfilled through tension and release, through a dissonance resolving to a consonance.
So music is energy, sound communication flowing directly into the brain, to be processed by the mind. What is the nature of this energy we call music? What can we say about music—what common denominators can we find for humans, or any other sentient creature? Do all sentient beings experience music the same way? Would Bach make sense to intelligent extraterrestrial creatures? There really isn’t enough information available to us now to answer this question because we have no other intelligent creatures to compare ourselves with. Some thinking is still possible despite this knowledge gap. Again let’s reduce this to the basics. Existence is a set of interacting, overlapping energy fields. Our senses filter the information coming from those fields to allow us, as conscious entities, to function. Our senses evolved for the purposes of survival. The ability to sense sound is one of those senses. The question then becomes whether the phenomenon of sound, energy vibrating through a medium (usually air), would evolve for other conscious intelligent beings, and if so, would it evolve the same way? In looking around at Earth’s life forms, we know other creatures see and hear differently than we do. They might hear a different part of the frequency spectrum. Some senses are more acute for other creatures, and not every creature has every sense. So we can probably conclude that intelligent creatures will vary in the way they experience sound, and Bach will sound different to different intelligences.
However, there is an argument against that idea. Sound appears to have some universal characteristics, characteristics experienced by intelligent creatures in the same or similar ways. Here, at this part of the discussion, we will look at the basics of music, and how those vibrations, that sound energy, appears to humans (and may appear to other sentient creatures).
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Music is sound organized by pitch, or rhythm—usually by both. (If just one is present, the experience may seem musical, but incomplete). Rhythms are built into the human body and into the fabric of existence. In music, rhythm involves patterns of sound focused around a pulse. Rhythm involves the passage of time, the meticulous control of time. Rhythm resonates with humans, and potentially with other conscious creatures, because rhythm is so inherent in life—in the heartbeat, in breathing, in sexual activity, in simple movements of walking or running, in countless other aspects of the universe. Pitch involves sound at a clear frequency. Both rhythm and pitch are discernible enough to be duplicated, making music possible.
There are three inherent characteristics of pitch that give music a universal commonality across human cultures. These are 1) the overtone series, 2) the ratios of vibrating strings and frequencies, and, 3) partials for wind instruments.
All pitches generate an overtone series. That series of overtone pitches is the same for any clear-pitched musical note—first an octave higher; second, a perfect fifth; third, a second octave higher; fourth, a major third (two octaves and a major third higher than the original pitch); fifth, another perfect fifth (two octaves and a perfect fifth higher than the original pitch); sixth, a strange note between a sixth and a flat seventh—like a “blue note” (two octaves from the original pitch plus that strange interval); seventh, three octaves higher than the original pitch. The overtone series gives us a basis for the universally perceived consonant harmonic intervals—the octave and the perfect fifth. It also gives us a basis for the widely accepted as consonant intervals—the third (minor and major), the sixth (minor and major), and the perfect fourth (the distance between the perfect fifth and the original pitch fifth raised an octave). The fundamental notes of the overtone series are more likely to be perceived by a particular musical culture as consonant intervals. The nearly universal pentatonic scale also can be explained as consisting of the pitches from the overtone series. Even the “blue” note, found in some cultures, has some basis for explanation from the overtone series (the note in the overtone series that occurs in between the sixth and the flat seventh of the conventional twelve note scale). So though we aren’t sure if Bach would be comprehensible to all sentient beings, we can see how humans recognize music cross-culturally, and within cultural familiarity, can appreciate music generated cross-culturally. This cross-cultural music appreciation is much easier translated among human beings than different languages.
Another universal aspect to pitch is the characteristics of vibrating strings. The pitch of a vibrating string goes up an octave when the portion of the string vibrating is halved. Intervals can be derived by simple mathematical ratios and the simplest ratios generate the fundamental intervals of the overtone series. (Here are some ratios/these can vary the farther we get from the fundamental intervals of the overtone series—2:1-octave, 3:2-perfect fifth, 4:3-perfect fourth, 5:4-major third, 6:5-minor third, 5:3-major sixth, 8:5-minor sixth, 9:8-major second, 9:5-minor seventh, 15:8-major seventh, 16:15-minor second, 10:7-tritone.) These ratios seem to confer a mathematical rationale for consonant and dissonant intervals. Mathematics is well-established as the vocabulary of physics, of existence. Mathematics would be the best option for communications between us and intelligences from other worlds. Music is wrapped up intimately with mathematics. This is another indication of music intertwined with reality at a very basic level.
Pitch can also be measured with numbers, with the frequencies of a given sound. The number pertains to measurement of the wave of the vibrations. Double a frequency and the pitch moves up an octave. This is equivalent to the vibrating string phenomenon. The ratios between the frequencies operate the same way as the ratios of the vibrating strings. The simplest ratios yield the most consonant intervals.
Earlier I described music as a mini-drama, of controlled longing transitioning to longing fulfilled represented by the resolution of dissonance to consonance. Here, we have evidence of a physics basis for a universal nature of dissonance and consonance, meaning that within cultural variations, there is a universal basis for a given piece of music resulting in a similar music experience for humans and maybe even for other sentient beings.
A third aspect to music that also overlaps with the overtone series and the ratios of frequencies and vibrating strings is the intervals of open notes for wind instruments. Most conventional wind instruments use valves or holes or keys to change the length of the vibrating air column to change the pitch. But wind instruments have natural intervals that occur from bottom to top. A bugle, with no valves, delivers those natural intervals. (Other wind instruments without keys or valves have the same characteristics.) And the intervals are the same as the overtone series! This is clearly not an accident. There is undoubtedly a physics reason for this convergence that I have not come across during my study of these issues. (I invite any reader to offer a comment on this issue if you can bring more insight to it.) For now, I’ll just call this more corroboration of the inherent universal nature of pitched sound, and its mathematical character.
As we continue our look for universal characteristics of music, we come to a characteristic of most music—scales. Scales are a series of pitches, rising (or falling) between octaves that create a “mode” or “key.” They can be found in music all over the world, in locations where they have separate evolution and development. I have mentioned pentatonic scales, the most common scale among the musics of humans. The five tones of a pentatonic scale would likely be considered the minimum number to constitute a scale. What is the maximum number? A diatonic scale has seven tones (not including the repeat of the octave at the end of the scale). A chromatic scale has twelve tones. Western music (and so the music that is my cultural comfort zone) revolves around a twelve-tone chromatic scale. Western composers and musicians have played with quarter tones, but it really hasn’t caught on to Western ears. Other cultures have microtones built into their musics, tones that seem to exist out of the twelve-tone chromatic scale. But in my (admittedly limited) listenings to that music, the microtones seem like either embellishments of one of the twelve chromatic tones, or tones existing out of the equal temperament scale, but still with a twelve-tone feel.
Is this twelve-tone chromatic scale a universal characteristic of music, or are my Western ears accustomed to my own culture’s music? Is there a mathematical explanation/rationale? I believe twelve tones constitute the upper limit on discernible scale pitches, with microtones serving as ornaments to the twelve tones. And there is a mathematical explanation for this upper limit. The first non-octave note of the overtone series, and the simplest non-octave ratio interval of the vibrating strings, is the perfect fifth. The perfect fifth gives us the dominant-tonic move in Western music. The dominant-tonic move, V to I, can be found in almost any music that uses scales. The explanation is easy—we can just look at the overtone series to see how prominent the perfect fifth is, built in to any pitched sound. The V to I move can also be a I to IV move—the I in the first scale becomes V in the next scale, with the IV of the first scale becoming the I in the second scale. This gives us the so-called circle of fifths, or circle of fourths. And if we pursue either one, we derive twelve tones—no more, no less. Taking both from C—Circle of fifths: C-G-D-A-E-B-F#-C#-G#/Ab-Eb-Bb-F-back to C. Circle of fourths: C-F-Bb-Eb-Ab-Db/C#-F#-B-E-A-D-G-back to C. Admittedly, this relies on an equal temperament tuning. Pure cycling through those intervals would lead to some frequency numbers that do not add up. Equal temperament tuning, slight adjustments in the frequencies of the twelve tones, allows the circle of fifths/circle of fourths to work. Equal temperament tuning is technically an innovation recently in Western music. But it is an approach to tuning, to scales, to keys, to harmonies, that I think resonates with nearly every musical culture, and this is because of the universal nature of the twelve-tone scale derived from the circle of fourths/circle of fifths. The microtonal variations found among musical cultures can be explained by the slight adjustments to create the equal temperament scale, and the fact that not all musical cultures make those adjustments.
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Different cultures use the twelve tones of the chromatic scale differently (and approach tuning of their scales differently). Here, we start to drift from a universal music. So the universal aspects of music, to review, appear to be rhythm and pitch, with octaves and perfect fifths as consonant intervals, with scales using some combination of notes from a twelve-note chromatic scale. From here, deviations and varieties occur. Aspects are shared among the musics of the world, but not shared by all. While the use of scales seems universal, scales of five to seven primary tones (from a twelve-tone chromatic scale), the notes in those scales vary extensively. The so-called major scale, a fundamental element of Western music for the last five or so centuries, is not at all universal among human musics. Exotic scales (to my Western ears) with augmented seconds occur cross-culturally. For me personally, the variety of scales and modes is one of the true joys of music, one of the variations among musics that keeps music fresh and exciting. In my own music, I like to look for fresh ways to approach scales, and harmonies deriving from those scales.
Not every musical culture has harmonies, and by harmonies, I mean a deliberate scheme of chords, of sounding different notes simultaneously to create compelling combinations of sounds. We can certainly argue that scales imply harmony, and they do. It is a slight step from scales to harmony. Harmonies are built on scale steps, usually in stacked triads. Contrapuntal schemes, also not found in all musics, but found in many, look at harmonies, how the lines of the counterpoint land at any single point to create chords.
When we speak of harmony, we now come to the concepts of consonance and dissonance. These concepts vary from culture to culture, and vary widely. For Western music, consonance and dissonance have changed within the culture over time. What was considered dissonant last century and the century before has now morphed into acceptable consonance. Octaves and perfect fifths are consonant. Half steps and microtones in clusters are usually considered dissonant. Schemes to design fixed rules for dissonance and consonance have been attempted, using the overtone series or other aspects inherent in music. They generally fail because cultural familiarity and even musical indoctrination contribute significantly to the way we humans evaluate consonance and dissonance. And, music without dissonance would fail miserably. Music plays like a controlled drama (as I mentioned earlier). Dissonance begs for a resolution to consonance. Even a V to I move sets up a feeling of anticipation, of tension as V wants to move to I. This, it can be argued, is dissonance to consonance even though it involves fundamental intervals. So a huge number of choices are available for the sonic dramas that are music. This is another reason that music creators will never “run out of material.” Cultural norms are constantly evolving so new combinations of consonance and dissonance, and of rhythm, are constantly available.
“Tonality” also appears to be universal, despite the efforts of some Twentieth Century Western music composers’ and music theorists’ efforts to render it obsolete. “Tonality” is the idea that music is experienced as revolving around a given pitch. That pitch center can shift. I heard some form of tonality in all the musical examples from around the world in my study as detailed in previous posts. It is true that celebrated Western composers of the Twentieth Century invented schemes that attempted to obliterate any trace of music revolving around a pitch, or key, or tonal center. But when actually listening to the music, the ear gravitates toward a tonal center; the ear searches for a central pitch to orient the musical experience. One of the most successful of the “twelve tone,” “serial” composers, Alban Berg, designed his twelve note “tone rows” around triads and other musical devices of tonality. This gives his “atonal” “serial” music a tonal feel. The “twelve tone” or “serial” composers expanded music, giving music creators another tool in the music-generating toolbox. But they did not, in my opinion, succeed in eliminating tonality because humans naturally look for tonality when they experience music. I suspect this would be part of the musical experience for any sentient creature as well, or the sonic experience would be something other than music.
Another more controversial consideration, controversial in our day and age, is the relationship of music to the religious/the spiritual, to metaphysics. In my opinion, music factors heavily into the human attempts to interact with the Divine, with what humans call God. Music brings order to the world. Religion/spirituality/metaphysics brings an explanation to existence. So music parallels that metaphysical search for spiritual answers. For me, the search for a universal music parallels my search for a universal spirituality, for a convergence of physics and metaphysics.
It is possible that music acts as a conduit to the Divine. Right now, it is difficult to be certain in drawing conclusions on this issue. But I believe as we become more attuned to a convergence of science and the spiritual, we will see more connections between music and the Divine, and perhaps even seek music as a way of communing with the Divine. After all, music is energy, and existence is energy. So it is not a huge jump to relate music to the Divine and consider that it could offer a channel, a route to the Divine.
In reading scientific discussions about music, I was struck by how thinkers seemed to want to avoid the possible metaphysical/spiritual aspect of music. We live in an age when science is supposed to bring us more knowledge of the world, when science is supposed to render faith in God, or consideration of spirituality, as something for less sophisticated thinkers. But when fair-minded music historians and ethnomusicologists discuss the issue, they admit that music was used by early man as a way of interacting with the Divine. Developments in human abilities are often explained by pointing out the evolutionary advantages those developments bring. I think we should consider that there could be an evolutionary advantage for intelligent beings who can access the Divine (though when religious fanaticism becomes destructive we are left to wonder if this evolutionary advantage can have a downside). If we are going to be fair, if we are really going to be scientific, then we shouldn’t be excluding any line of inquiry including the possibility that music, with its affinity for the universal language of mathematics, with its existence as energy and vibrations as a part of our universe of interacting energy fields—that music could be a gift from the God force, whatever it is, a gift aiding human communion with the Divine. So my searches in both of these areas overlap. As I create music, and find myself in a zone where something outside of me seems to take over, I’ll be looking for that spiritual connection to music—that is part of what my music is about.
On the more technical side, this study brings me to some approaches to music that will influence what I will do in this arena with whatever time I have left:
1) I am looking to create accessible music that has a universal feel. It will be unapologetically tonal, though I occasionally will flirt with atonal techniques like tone rows and clusters. (Technology allows me to control the music—time and pitch—in very precise ways. I’d be crazy not to see what can be done with it.)
2) I will look for exotic scales from different cultures and attempt to create exotic harmonies from those scales. This will include combining those with pop and jazz mediums popular today, as well as drawing from the rich heritage of Western “classical” music.
3) I’ll be looking for sounds from different cultures to juxtapose in unique ways. This includes electronically generated sounds that may not sound like any naturally occurring sound.
4) I’ll continue combining different styles—no combination will be out of bounds—multi-cultural sounds and approaches with popular music/rock-pop as well as jazz and even concert music as time and opportunity allow.
I’ve already started this. “Issa Music,” my CD released in late 2011, certainly does all of us. My upcoming CD “The Richard Warren Field Songbook” at this writing consists of thirteen songs with the basic tracks recorded. This CD includes a cover of “Hotel California” with log drum sounds and a flute duet in the instrumental section. The CD also includes a cover of Miles Davis’s “All Blues” with sitar and African flute sounds, as well as a big Fender Rhodes solo. The basic tracks for my original songs on the CD include everything from big strident guitar synthesizer sounds to gentle choral clusters. But this CD barely scratches the surface of the possibilities. Stay tuned at this blog for more on this topic and for details on my upcoming music.
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Previous posts on this topic:
Musicophilia: Tales of Music and the Brain by Oliver Sacks
This is Your Brain on Music by Daniel Levitin
Music, the Brain and Ecstasy by Robert Jourdain
Music and the Mind by Anthony Storr
Good Vibrations/The Physics of Music by Barry Parker
Measured Tones by Ian Johnston
Exploring Music by Charles Taylor
Music and Mathematics: From Pythagoras to Fractals, edited by John Fauvel, Raymond Flood and Robin Wilson
Harmonies of Heaven and Earth: From Antiquity to the Avant-Garde by Joscelyn Godwin
The Study of Ethnomusicology by Bruno Nettl
World Music: A Global Journey by Terry E. Miller and Andrew Shahriari
Part I
Part II
Part III
Part IV
Part V
Part VI
Part VII
Part VIII
Part IX
Part X
The Unanswered Question by Leonard Bernstein
Richard Warren Field's Blog 
Commentary on Music – Conclusions (For Now…) June 1, 2013
Posted by rwf1954 in classical music, harmony, mathematics and music, modes, music, music commentary, nature of music, religion and music, scales, spirituality and music, tonality.Tags: classical music, harmony, mathematics, modes, music, overtone series, religion, scales, spirituality, tonality
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(This is the final post—for now—of a series of commentaries about a series of books about the nature of music. The other commentaries of this series are listed below. This series has been triggered as a result of my rediscovery of the love of creating and performing music. There is definitely a spiritual connection to this rediscovery, evidenced by my recent release of “Issa Music” and my posts about mystical/spiritual aspects of the music of the progressive rock group Yes (The Poetry of (the Progressive Rock Group) Yes: Introduction to “The Revealing Science of God—Dance of the Dawn” from “Tales from Topographic Oceans” and The Poetry of (the Progressive Rock Group) Yes). This further relates to spiritual meditations with the theme of more than one path to God, and the possible coming together of both physics and metaphysics I and II and a discussion of Dr. Eben Alexander’s recent book, Proof of Heaven).
*******
So here I am, at the end of a longer journey than I expected, a journey of exploring music at its most basic level. With this post, I will draw together the comments I have made in posts spanning just over a year about this topic and offer some conclusions—some of these will be personal, as they will be oriented toward what this means for me as I approach my own music. But I also believe there is value in the general conclusions I will draw, conclusions I hope will enrich the music-listening of visitors to these pages.
*******
Well, let’s take a deep breath, because I will start out with the metaphysics/physics/music portion of my conclusions. On the frontiers of physics, we are learning that all matter consists of elementary particles and these particles are points of energy that radiate fields. So, existence is a heavily populated cauldron of overlapping, interacting energy fields. We humans have evolved to sense those energy fields within our finite portions of what we perceive as a three/four dimensional space/time continuum. We ourselves are a complex set of interconnected energy fields interacting with many other complex energy fields, guided through this reality by our senses. Energy—that is existence; that is life.
Music is the only art that involves a direct transmission of energy from one intelligence to another. Painting/visual art is created as imagery and experienced by looking at and absorbing the photons from those images, but not through direct energy. The images undergo a great deal of editing and processing before human beings absorb their content. Story-telling involves transmitting words or actions, again to be witnessed visually, or heard and then translated into ideas in the recipient’s mind. Sculpture/dance/books/poetry are also indirect arts. Music is direct energy. It is a series of vibrations through a medium, but the music is not the medium itself; it is the energy that courses through the medium. The music is not the molecules of the medium that are vibrating, it is the flow of energy generating those vibrations. It can be measured by an oscilloscope as energy waves. Linked with words as song, it can be extraordinarily powerful and affecting. Visual arts (like movies) use music to inject emotion—using the direct energy of music heightens the experience of other arts.
Music takes energy and puts order to it. This musical energy supplies an organized tension and release at a visceral level, a level without words or explanations needed. In a sense, it resembles at a manageable level the occurrence of pain, of pleasure, of longing and longing fulfilled. Music can be said to duplicate the experience of a want or need—fulfilled through tension and release, through a dissonance resolving to a consonance.
So music is energy, sound communication flowing directly into the brain, to be processed by the mind. What is the nature of this energy we call music? What can we say about music—what common denominators can we find for humans, or any other sentient creature? Do all sentient beings experience music the same way? Would Bach make sense to intelligent extraterrestrial creatures? There really isn’t enough information available to us now to answer this question because we have no other intelligent creatures to compare ourselves with. Some thinking is still possible despite this knowledge gap. Again let’s reduce this to the basics. Existence is a set of interacting, overlapping energy fields. Our senses filter the information coming from those fields to allow us, as conscious entities, to function. Our senses evolved for the purposes of survival. The ability to sense sound is one of those senses. The question then becomes whether the phenomenon of sound, energy vibrating through a medium (usually air), would evolve for other conscious intelligent beings, and if so, would it evolve the same way? In looking around at Earth’s life forms, we know other creatures see and hear differently than we do. They might hear a different part of the frequency spectrum. Some senses are more acute for other creatures, and not every creature has every sense. So we can probably conclude that intelligent creatures will vary in the way they experience sound, and Bach will sound different to different intelligences.
However, there is an argument against that idea. Sound appears to have some universal characteristics, characteristics experienced by intelligent creatures in the same or similar ways. Here, at this part of the discussion, we will look at the basics of music, and how those vibrations, that sound energy, appears to humans (and may appear to other sentient creatures).
*******
Music is sound organized by pitch, or rhythm—usually by both. (If just one is present, the experience may seem musical, but incomplete). Rhythms are built into the human body and into the fabric of existence. In music, rhythm involves patterns of sound focused around a pulse. Rhythm involves the passage of time, the meticulous control of time. Rhythm resonates with humans, and potentially with other conscious creatures, because rhythm is so inherent in life—in the heartbeat, in breathing, in sexual activity, in simple movements of walking or running, in countless other aspects of the universe. Pitch involves sound at a clear frequency. Both rhythm and pitch are discernible enough to be duplicated, making music possible.
There are three inherent characteristics of pitch that give music a universal commonality across human cultures. These are 1) the overtone series, 2) the ratios of vibrating strings and frequencies, and, 3) partials for wind instruments.
All pitches generate an overtone series. That series of overtone pitches is the same for any clear-pitched musical note—first an octave higher; second, a perfect fifth; third, a second octave higher; fourth, a major third (two octaves and a major third higher than the original pitch); fifth, another perfect fifth (two octaves and a perfect fifth higher than the original pitch); sixth, a strange note between a sixth and a flat seventh—like a “blue note” (two octaves from the original pitch plus that strange interval); seventh, three octaves higher than the original pitch. The overtone series gives us a basis for the universally perceived consonant harmonic intervals—the octave and the perfect fifth. It also gives us a basis for the widely accepted as consonant intervals—the third (minor and major), the sixth (minor and major), and the perfect fourth (the distance between the perfect fifth and the original pitch fifth raised an octave). The fundamental notes of the overtone series are more likely to be perceived by a particular musical culture as consonant intervals. The nearly universal pentatonic scale also can be explained as consisting of the pitches from the overtone series. Even the “blue” note, found in some cultures, has some basis for explanation from the overtone series (the note in the overtone series that occurs in between the sixth and the flat seventh of the conventional twelve note scale). So though we aren’t sure if Bach would be comprehensible to all sentient beings, we can see how humans recognize music cross-culturally, and within cultural familiarity, can appreciate music generated cross-culturally. This cross-cultural music appreciation is much easier translated among human beings than different languages.
Another universal aspect to pitch is the characteristics of vibrating strings. The pitch of a vibrating string goes up an octave when the portion of the string vibrating is halved. Intervals can be derived by simple mathematical ratios and the simplest ratios generate the fundamental intervals of the overtone series. (Here are some ratios/these can vary the farther we get from the fundamental intervals of the overtone series—2:1-octave, 3:2-perfect fifth, 4:3-perfect fourth, 5:4-major third, 6:5-minor third, 5:3-major sixth, 8:5-minor sixth, 9:8-major second, 9:5-minor seventh, 15:8-major seventh, 16:15-minor second, 10:7-tritone.) These ratios seem to confer a mathematical rationale for consonant and dissonant intervals. Mathematics is well-established as the vocabulary of physics, of existence. Mathematics would be the best option for communications between us and intelligences from other worlds. Music is wrapped up intimately with mathematics. This is another indication of music intertwined with reality at a very basic level.
Pitch can also be measured with numbers, with the frequencies of a given sound. The number pertains to measurement of the wave of the vibrations. Double a frequency and the pitch moves up an octave. This is equivalent to the vibrating string phenomenon. The ratios between the frequencies operate the same way as the ratios of the vibrating strings. The simplest ratios yield the most consonant intervals.
Earlier I described music as a mini-drama, of controlled longing transitioning to longing fulfilled represented by the resolution of dissonance to consonance. Here, we have evidence of a physics basis for a universal nature of dissonance and consonance, meaning that within cultural variations, there is a universal basis for a given piece of music resulting in a similar music experience for humans and maybe even for other sentient beings.
A third aspect to music that also overlaps with the overtone series and the ratios of frequencies and vibrating strings is the intervals of open notes for wind instruments. Most conventional wind instruments use valves or holes or keys to change the length of the vibrating air column to change the pitch. But wind instruments have natural intervals that occur from bottom to top. A bugle, with no valves, delivers those natural intervals. (Other wind instruments without keys or valves have the same characteristics.) And the intervals are the same as the overtone series! This is clearly not an accident. There is undoubtedly a physics reason for this convergence that I have not come across during my study of these issues. (I invite any reader to offer a comment on this issue if you can bring more insight to it.) For now, I’ll just call this more corroboration of the inherent universal nature of pitched sound, and its mathematical character.
As we continue our look for universal characteristics of music, we come to a characteristic of most music—scales. Scales are a series of pitches, rising (or falling) between octaves that create a “mode” or “key.” They can be found in music all over the world, in locations where they have separate evolution and development. I have mentioned pentatonic scales, the most common scale among the musics of humans. The five tones of a pentatonic scale would likely be considered the minimum number to constitute a scale. What is the maximum number? A diatonic scale has seven tones (not including the repeat of the octave at the end of the scale). A chromatic scale has twelve tones. Western music (and so the music that is my cultural comfort zone) revolves around a twelve-tone chromatic scale. Western composers and musicians have played with quarter tones, but it really hasn’t caught on to Western ears. Other cultures have microtones built into their musics, tones that seem to exist out of the twelve-tone chromatic scale. But in my (admittedly limited) listenings to that music, the microtones seem like either embellishments of one of the twelve chromatic tones, or tones existing out of the equal temperament scale, but still with a twelve-tone feel.
Is this twelve-tone chromatic scale a universal characteristic of music, or are my Western ears accustomed to my own culture’s music? Is there a mathematical explanation/rationale? I believe twelve tones constitute the upper limit on discernible scale pitches, with microtones serving as ornaments to the twelve tones. And there is a mathematical explanation for this upper limit. The first non-octave note of the overtone series, and the simplest non-octave ratio interval of the vibrating strings, is the perfect fifth. The perfect fifth gives us the dominant-tonic move in Western music. The dominant-tonic move, V to I, can be found in almost any music that uses scales. The explanation is easy—we can just look at the overtone series to see how prominent the perfect fifth is, built in to any pitched sound. The V to I move can also be a I to IV move—the I in the first scale becomes V in the next scale, with the IV of the first scale becoming the I in the second scale. This gives us the so-called circle of fifths, or circle of fourths. And if we pursue either one, we derive twelve tones—no more, no less. Taking both from C—Circle of fifths: C-G-D-A-E-B-F#-C#-G#/Ab-Eb-Bb-F-back to C. Circle of fourths: C-F-Bb-Eb-Ab-Db/C#-F#-B-E-A-D-G-back to C. Admittedly, this relies on an equal temperament tuning. Pure cycling through those intervals would lead to some frequency numbers that do not add up. Equal temperament tuning, slight adjustments in the frequencies of the twelve tones, allows the circle of fifths/circle of fourths to work. Equal temperament tuning is technically an innovation recently in Western music. But it is an approach to tuning, to scales, to keys, to harmonies, that I think resonates with nearly every musical culture, and this is because of the universal nature of the twelve-tone scale derived from the circle of fourths/circle of fifths. The microtonal variations found among musical cultures can be explained by the slight adjustments to create the equal temperament scale, and the fact that not all musical cultures make those adjustments.
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Different cultures use the twelve tones of the chromatic scale differently (and approach tuning of their scales differently). Here, we start to drift from a universal music. So the universal aspects of music, to review, appear to be rhythm and pitch, with octaves and perfect fifths as consonant intervals, with scales using some combination of notes from a twelve-note chromatic scale. From here, deviations and varieties occur. Aspects are shared among the musics of the world, but not shared by all. While the use of scales seems universal, scales of five to seven primary tones (from a twelve-tone chromatic scale), the notes in those scales vary extensively. The so-called major scale, a fundamental element of Western music for the last five or so centuries, is not at all universal among human musics. Exotic scales (to my Western ears) with augmented seconds occur cross-culturally. For me personally, the variety of scales and modes is one of the true joys of music, one of the variations among musics that keeps music fresh and exciting. In my own music, I like to look for fresh ways to approach scales, and harmonies deriving from those scales.
Not every musical culture has harmonies, and by harmonies, I mean a deliberate scheme of chords, of sounding different notes simultaneously to create compelling combinations of sounds. We can certainly argue that scales imply harmony, and they do. It is a slight step from scales to harmony. Harmonies are built on scale steps, usually in stacked triads. Contrapuntal schemes, also not found in all musics, but found in many, look at harmonies, how the lines of the counterpoint land at any single point to create chords.
When we speak of harmony, we now come to the concepts of consonance and dissonance. These concepts vary from culture to culture, and vary widely. For Western music, consonance and dissonance have changed within the culture over time. What was considered dissonant last century and the century before has now morphed into acceptable consonance. Octaves and perfect fifths are consonant. Half steps and microtones in clusters are usually considered dissonant. Schemes to design fixed rules for dissonance and consonance have been attempted, using the overtone series or other aspects inherent in music. They generally fail because cultural familiarity and even musical indoctrination contribute significantly to the way we humans evaluate consonance and dissonance. And, music without dissonance would fail miserably. Music plays like a controlled drama (as I mentioned earlier). Dissonance begs for a resolution to consonance. Even a V to I move sets up a feeling of anticipation, of tension as V wants to move to I. This, it can be argued, is dissonance to consonance even though it involves fundamental intervals. So a huge number of choices are available for the sonic dramas that are music. This is another reason that music creators will never “run out of material.” Cultural norms are constantly evolving so new combinations of consonance and dissonance, and of rhythm, are constantly available.
“Tonality” also appears to be universal, despite the efforts of some Twentieth Century Western music composers’ and music theorists’ efforts to render it obsolete. “Tonality” is the idea that music is experienced as revolving around a given pitch. That pitch center can shift. I heard some form of tonality in all the musical examples from around the world in my study as detailed in previous posts. It is true that celebrated Western composers of the Twentieth Century invented schemes that attempted to obliterate any trace of music revolving around a pitch, or key, or tonal center. But when actually listening to the music, the ear gravitates toward a tonal center; the ear searches for a central pitch to orient the musical experience. One of the most successful of the “twelve tone,” “serial” composers, Alban Berg, designed his twelve note “tone rows” around triads and other musical devices of tonality. This gives his “atonal” “serial” music a tonal feel. The “twelve tone” or “serial” composers expanded music, giving music creators another tool in the music-generating toolbox. But they did not, in my opinion, succeed in eliminating tonality because humans naturally look for tonality when they experience music. I suspect this would be part of the musical experience for any sentient creature as well, or the sonic experience would be something other than music.
Another more controversial consideration, controversial in our day and age, is the relationship of music to the religious/the spiritual, to metaphysics. In my opinion, music factors heavily into the human attempts to interact with the Divine, with what humans call God. Music brings order to the world. Religion/spirituality/metaphysics brings an explanation to existence. So music parallels that metaphysical search for spiritual answers. For me, the search for a universal music parallels my search for a universal spirituality, for a convergence of physics and metaphysics.
It is possible that music acts as a conduit to the Divine. Right now, it is difficult to be certain in drawing conclusions on this issue. But I believe as we become more attuned to a convergence of science and the spiritual, we will see more connections between music and the Divine, and perhaps even seek music as a way of communing with the Divine. After all, music is energy, and existence is energy. So it is not a huge jump to relate music to the Divine and consider that it could offer a channel, a route to the Divine.
In reading scientific discussions about music, I was struck by how thinkers seemed to want to avoid the possible metaphysical/spiritual aspect of music. We live in an age when science is supposed to bring us more knowledge of the world, when science is supposed to render faith in God, or consideration of spirituality, as something for less sophisticated thinkers. But when fair-minded music historians and ethnomusicologists discuss the issue, they admit that music was used by early man as a way of interacting with the Divine. Developments in human abilities are often explained by pointing out the evolutionary advantages those developments bring. I think we should consider that there could be an evolutionary advantage for intelligent beings who can access the Divine (though when religious fanaticism becomes destructive we are left to wonder if this evolutionary advantage can have a downside). If we are going to be fair, if we are really going to be scientific, then we shouldn’t be excluding any line of inquiry including the possibility that music, with its affinity for the universal language of mathematics, with its existence as energy and vibrations as a part of our universe of interacting energy fields—that music could be a gift from the God force, whatever it is, a gift aiding human communion with the Divine. So my searches in both of these areas overlap. As I create music, and find myself in a zone where something outside of me seems to take over, I’ll be looking for that spiritual connection to music—that is part of what my music is about.
On the more technical side, this study brings me to some approaches to music that will influence what I will do in this arena with whatever time I have left:
1) I am looking to create accessible music that has a universal feel. It will be unapologetically tonal, though I occasionally will flirt with atonal techniques like tone rows and clusters. (Technology allows me to control the music—time and pitch—in very precise ways. I’d be crazy not to see what can be done with it.)
2) I will look for exotic scales from different cultures and attempt to create exotic harmonies from those scales. This will include combining those with pop and jazz mediums popular today, as well as drawing from the rich heritage of Western “classical” music.
3) I’ll be looking for sounds from different cultures to juxtapose in unique ways. This includes electronically generated sounds that may not sound like any naturally occurring sound.
4) I’ll continue combining different styles—no combination will be out of bounds—multi-cultural sounds and approaches with popular music/rock-pop as well as jazz and even concert music as time and opportunity allow.
I’ve already started this. “Issa Music,” my CD released in late 2011, certainly does all of us. My upcoming CD “The Richard Warren Field Songbook” at this writing consists of thirteen songs with the basic tracks recorded. This CD includes a cover of “Hotel California” with log drum sounds and a flute duet in the instrumental section. The CD also includes a cover of Miles Davis’s “All Blues” with sitar and African flute sounds, as well as a big Fender Rhodes solo. The basic tracks for my original songs on the CD include everything from big strident guitar synthesizer sounds to gentle choral clusters. But this CD barely scratches the surface of the possibilities. Stay tuned at this blog for more on this topic and for details on my upcoming music.
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Previous posts on this topic:
Musicophilia: Tales of Music and the Brain by Oliver Sacks
This is Your Brain on Music by Daniel Levitin
Music, the Brain and Ecstasy by Robert Jourdain
Music and the Mind by Anthony Storr
Good Vibrations/The Physics of Music by Barry Parker
Measured Tones by Ian Johnston
Exploring Music by Charles Taylor
Music and Mathematics: From Pythagoras to Fractals, edited by John Fauvel, Raymond Flood and Robin Wilson
Harmonies of Heaven and Earth: From Antiquity to the Avant-Garde by Joscelyn Godwin
The Study of Ethnomusicology by Bruno Nettl
World Music: A Global Journey by Terry E. Miller and Andrew Shahriari
Part I
Part II
Part III
Part IV
Part V
Part VI
Part VII
Part VIII
Part IX
Part X
The Unanswered Question by Leonard Bernstein