Music 29

pitch space

A PITCH SPACE describes the organization of a group of pitches/notes/tones. A tonal pitch space (see Fred Lerdahl) is one where the pitches are organized in hierarchies around a central tone, with the other tones sharing varying degrees of affiliation with the primary tone. Pitch space theory accepts the notion of octave equivalence and reduces the grouping of tones to a single octave. In traditional western music theory, tones are organized into scales with the tones arranged in ascending order. This is a pitch space, but one that does not give any special accounting for the relationships that exists between the tones in the space. A tonal pitch space might use a multi-dimensional representation to better show relationships. It is also possible to have non-tonal pitch spaces, or non-western micro-tonal pitch spaces.

sound source

A SOUND SOURCE is the physical object that accounts for a single stream in an auditory scene (e.g. a violin in a string quartet, a single loudspeaker in a stereo pair, the single human voice in a choir, a frog in a pond, etc.). To answer the question "what is the sound source?" identify the physics of the object that causes the vibration. Objects produce signature sounds and can be classed into a small number of categories: wood, metal, stretched skin or fabric, string, electronic, etc.

voice

A VOICE is defined as a single thread of sound that might be made of just one sound source or multiple sound sources working in tandem. All music features a number of identifiable voices. A source is a sound that has a single cause, as in someone hitting a drum, or playing a violin, or starting a car. In music, sources are combined in ways to form a voice. For example, if a full choir of human singers were all singing the same melody, we would say there was only one "voice". Typically, composers writing for western style choirs write for four "voices" categorized by register and human voice type: the sopranos, the altos, the tenors, and the basses. It makes sense that the term voice is related to the human body. It turns out that we can use the human body to take account for many things musical. For example, in the sound example of the solo saxophonist, the player uses her mouth to force a reed to buzz and cause the air column in the saxophone tube to produce specific tones. This technique is very similar to the way our actual vocal chords work to produce tone. Can you agree that the saxophone sound is an extension of the human voice process? The saxophone is external to the body but remains close because the energy source is the human breath. The connection is undeniable and we infer the human connection even if we have no actual knowledge of the source.

interval

A music interval is defined by the frequency ratio between any given pair of tones where both tones feature a clearly audible fundamental frequency. Tones can be understood as simple (single sine tone), complex (many sine tones), harmonic (many sine tines in multiples of the fundamental), or inharmonic (many sine tones not related to the fundamental frequency as a whole-number multiple). Any two fundamental frequencies that share the same ratio, regardless of the pitch level (high or low), also share the same interval class name. We perceive these interval classes as similar in character even when they appear to our ears as higher or lower in pitch. The low-order, whole number ratios (1:1, 1:2, 2:3, etc.), comprise the primary building blocks for western tuning systems and all pitch space dependent music(s). The most common interval names are: The unison with a ratio of 1:1, the two frequencies are identical: The octave with a ratio of 1:2; see also "octave equivalence": The fifth with a ratio of 2:3; see also "drone": The major third with a ratio of 4:5: The minor third with a ratio of 5:6: An easy way to understand how multiple tones relate to one another is to compare their interval ratios. The harmonic series is defined by the numeric counting numbers with 1 representing the first partial/fundamental (frequency X), 2 representing the second partial (X times 2), 3 representing the third partial (X times 3), etc. Using the harmonic series as a gauge we can see that the interval of an octave, with a ratio of 1:2, occurs between the 1st and 2nd partial (the fundamental and first overtone), the 2nd and 4th, the 4th and 8th, and so on. The interval of a fifth occurs between the 2nd and 3rd partial, the 4th and 6th, the 8th and 12th etc... The next example presents the first six partials in a harmonic series. Notice that when the first six are combined into a common fate event, that the result is what western music theory calls a major chord. Low order ratios forming a major chord: It is understandable that the octave (1:1), the fifth (2:3), the third (5:6), are considered strongly in the construction of a pitch space -- especially a tonal pitch space. As the ratio climbs into the higher numeric range, the perceptual relationship of the tones can become quite complex. A ratio of 29:31 (not present in western tuning systems) can be heard as a more complex interaction of sounds, where the interval 32:64 will be reduced to 1:2 and be perceived as a far more simple interaction (the octave).

noise

A signal/waveform entering the ear and having roughly equal energy present at all audible frequencies is called NOISE. Examples include: electroacoustic hiss, flowing water, sand pouring into a bucket. Many varieties of noise exist dependent on frequency content. The science of acoustics has assigned very specific names to different kinds of noise. The most common names are white, pink, and brown.

melodic profile

MELODIC PROFILE is concerned with the shape and direction of melodies (melodic tones); how they move across time -- step motion, skip motion, and directionality. David Huron in his book Sweet Anticipation summarizes several organizational elements of Melodies in terms of simple profile rules that have been studied and confirmed by researchers in music cognition. 1) Pitch proximity -- successive pitches tend to be near to one another. 2) Central pitch tendency -- the most frequently occurring pitches in melodies tend to lie near the center of some distribution. 3) Ascending leap tendency/descending step tendency -- melodies tend to exhibit relatively rapid upward movements (ascending leaps) and relatively leisurely downward movements (descending steps). 4) Arch phrase tendency -- Western melodies tend to exhibit arch-shaped pitch contours. The lowest pitches in the phrase tend to occur near the first and last positions while the highest pitches tend to occur near the middle of the phrase.

meter

METER arises when beats in a clock-time/grid-time structure are grouped into larger cyclic patterns called measures. Measures typically contain 2, 3, 4, 6, or 8 beats, but can also be irregular in number. A measure presents combinations of strong and weak beats that create patterns of duple or triple meter. Most measures in western music use simple duple or triple meters, or a combination of both called compound meter. Meter is not a "given", it must be established and maintained. The following sound example, is a pulse train with no metric indication. Any sense of grouping you have when listening to this example is an illusion and is due to our perception systems (our natural tendency to sense and group things into larger and larger units). Unaccented Pulse: In the next sound example, the same pulse train is heard with a loudness accent; the only change is that every fourth occurrence of the pulse is louder. This establishes a rudimentary meter -- STRONG, weak, weak, weak -- STRONG, weak, weak, weak. The beat falls on every 4th sub-divisions and it establishes a tempo at around 78 beats per minute. It is the beat that establishes the tempo, not the sub-division. Accented Pulse: One way to transform this model into a duple meter (two beats with an alternating strong and weak feel), is to lower the loudness accent on each second beat. This should create a two-beat pattern without having added any other level of accent, no frequency domain accent, nor agogic accent. Duple Meter: Another way to maintain the feel of the duple meter, is to add a frequency domain accent (change the pitch) on the off-beat. The next sound example is the same duple meter with a frequency domain accent to keep the duple meter strongly present. In addition, there is an added line which is higher in pitch than all the rest. Notice that the durations in the added line are all drawn from the tatum duration, and the line is a subset of the 24 tatums, which all together form a section of music. Duple Meter, with added higher pitched line: Here is the same example with the newly added line turned into a melodic line by pitch changes (i.e. different pitches are assigned to each event in the line). Duple Meter, with melody: Here is the same example with several changes: 1) the tatum which has been present at every pulse is now reduced and turned into a lower accompanying part, 2) a second level of melodic line is introduced. Duple Meter, with 2nd melody added: The next example shifts the beat accents to establish a triple meter -- STRONG, weak, weak -- STRONG, weak, weak. All other parts remain unchanged. Notice how the change from duple meter to triple meter affects perception of the other parts. Again, the only change here is that the accents created at the beat level are shifted from STRONG/weak, to STRONG/weak/weak.

microtiming

MICROTIMING is concerned with the minute grid-time deformations/deviations that create special feel without destroying the impression of the beat/meter/tempo relationships. From Jazz pianist Vijay Iyer: "I have experienced one of the most interesting musical revelations of my life, gradually over the last several years, in studying West African dance-drumming and in playing jazz, hip-hop and funk. The revelation was that the simplest repetitive musical patterns could be imbued with a universe of expression. I have often witnessed the Ghanaian percussionist and teacher C. K. Ladzekpo stopping the music to chide his students for playing their parts with no emotion. One might wonder how much emotion one can convey on a single drum whose pitch range, timbral range, and discrete rhythmic delineations are so narrow, when the only two elements at one's disposal are intensity and timing. Yet I have become convinced that a great deal can be conveyed with just those two elements. "

microtonal

MICROTONAL refers to systems of tone organization and individual tones that use the frequency space existing between the smallest western music interval of a semi-tone. We speak of alternate tuning systems and non-western tone organization as microtonal. We also speak of ornamental frequency deviation applied to more standard tunings as microtonal inflection. Traditional western tonal spaces presents 12 tones per octave, each equally divided across the octave. Of course, audible frequency space is capable of producing many more tone per octave, and human hearing is perfectly capable of sensing divisions of the octave upwards to 40 tones per octave or more. Many composers have explored developing new tuning systems that propose pitch spaces that involve different arrangements of tones across the octave, or more than 12 tones per octave. Composer Harry Parch (1901-1974) created his own microtonal instruments and then composed music for those instruments. Many musical cultures feature pitch spaces that are microtonal and/or have microtonal inflections -- frequency deviations as a kind of expressive tool. In the next example, a classical singer from Pakistan (Shafqat Ali Kahn) sings a monophonic phrase that involves microtonal inflection as well as recognizable intervals typical of much western music

monophony

MONOPHONY is one of four archetypal design models used to describe musical texture in terms of how the various "voices" or agents behave in a musical setting. A monophonic sound example features a single strand or stream of musical activity. A single human singing is the simplest example of a monophonic texture. A single solo instrument would be monophonic, and a full choir of men and women all singing the same line would be monophonic. Most music features combinations of all of the various archetypes which, include Monophony, Heterophony, Homophony, and Polyphony.

pitch

ONE, PITCH, and NOTE are three distinct terms that are closely linked and are often used synonymously. Each term denotes a sound that contains an audible fundamental frequency with or without overtones or partials. As long as there is an audible fundamental frequency, the individual partials can be harmonic, inharmonic, or a combination of the two. TONES can range from complex tones involving many partials, to simple tones involving only a single sinewave component. If a tone is very complex and very inharmonic, it no longer is perceived as a tone and is characterized as some type of noise signal. Noise is not considered a tone. In the next example, a repeating harmonic tone begins as a complex tone, and progresses toward a simple tone. The fundamental frequency of the tone never changes. This is also a good example of a timbral transition from bright-->dull. Bright to dull: In the next example, a series of complex harmonic tones are heard, and the fundamental frequencies change or repeat over time. Complex tones moving: In the next example, a series of simple tones are heard, and the fundamental frequencies change or repeat over time. Simple tones moving: In the next example, a series of complex inharmonic tones are heard and the fundamental frequencies change over time. Inharmonic tones with changing fundamental frequencies: PITCH refers to a psychoacoustic phenomenon whereby our auditory system situates tones as pitches in some "high" and "low" sounding region. In most cases, the perception of pitch for complex harmonic tones will be the same as the perception of the fundamental frequency, as all the partials will support and emphasize the fundamental. But it is not unusual for certain instruments to be perceived in pitch as one octave higher than their actual frequency components show. In the case of complex inharmonic tones, the perception of pitch can be very different for different ears and situations. In the next example, a series of complex inharmonic tones are heard with all the tones sharing the same fundamental frequency. Although they have the same fundamental, the tones sound like they are shifting in PITCH (i.e. the perceived central pitch is not the necessarily the same as the root fundamental of the tone) Inharmonic tones with the same fundamental frequency: A NOTE refers to a harmonic pitch or tone. As most western instruments produce harmonic tones, they can all play the same "note" and be in tune with one another. Below is a sound example featuring different instruments/sources playing the note "A-440". The timbres of the various sources are quite different from one another, but we perceptually group the sounds together because of the solid and shared fundamental frequency. Each sound has a different overtone structure which is the chief factor determining the timbre of the sound. Tones with different timbres, all playing A-440:

room effect

Once sound is released into a room or open space, the acoustic characteristics of the space will operate on the sound and alter our perception of that sound. Consider three elements: The position of the listener, the location of the source, and the size and acoustic characteristics of the room. Most commercially engineered audio has been processed with some form of room effect or other spatial processing. Composers and performers often record live performances in spaces that have unique room acoustics. The following sound example initially features a human voice heard in a dry non-resonant space, followed by the same voice modified by room simulation techniques so it sounds like it is in a reverberant resonant room.

overtone

Overtones are components of a complex waveform existing above a fundamental frequency -- they can be harmonic or inharmonic in relation to the fundamental frequency. A vibrating string produces overtones, as do most resonating systems -- bells, wind instruments, etc. Extraordinary Sound prefers to use the term "partials" to describe the various components of a complex sound. The first "partial" is the fundamental frequency and the second "partial" will be the frequency nearest to the fundamental. When we use the term overtone, the frequency nearest the fundamental frequency is called the first overtone. In the next example, several string instruments play a fundamental frequency. Other instruments touch lightly on the strings to isolate particular overtones of the fundamental.

periodic

PERIODIC refers to anything that has a noticeable repeating cycle. The term can be applied on different scales of time. On the micro level (milliseconds), periodic waveforms create complex sounds involving the perception of pitch/note/tone. On the macro level (seconds/minutes), one can speak of periodic cycles of events like a repetitive drum beat. In the frequency domain (c. 12Hz-20,000Hz), periodic waveforms generate harmonic spectra. In contrast, aperiodic waveforms exhibit limited periodicity or no periodicity at all, and generate varying degrees of inharmonic waveforms or noise. When viewing an amplitude representation of a complex wave, it is often easy to spot a periodic beat in the time domain. waveform-periodic In the "Periodic Beat" visual and sound example below, a periodic beat is continually divided into halves to create smaller and smaller sub-divisions of the master beat. The smallest sub-division would be an example of the tatum for this example. clock-time-beat-clock Periodic Beat: The duration of the timing cycle must not be too large or the periodic quality will not be perceived -- think of traffic lights - or astronomical events -- both periodic but not easily predicted. In the following sound example, four acoustic instruments begin playing a pattern with a periodic structure. After a short time, each instrumentalist begins to speed up or slow down slightly causing the pattern to break apart into an aperiodic event structure. Keep in mind that the basic 4-event note pattern remains in place for each player without alteration, only the speed changes. Periodic pattern becoming an aperiodic pattern:

predictability

PREDICTABILITY in music is concerned with our ability to anticipate possible futures for a piece of music, based on the current behavior of the music. In his book, Sweet Anticipation, David Huron sites four modes of prediction in music. 1) Schematic predictability: the music is constructed so that it conforms to what ever existing schemas listeners are likely to bring to the listening experience. 2) Dynamic predictability: the music is constructed so that the work itself will evoke accurate work-specific expectations. 3) Veridical familiarity: the music becomes predictable because you listen to it over and over again (veridical -- corresponding to the truth -- what actually is). 4) Conscious predictability: music is organized so that observant or knowledgeable listeners will be able to infer future musical events through conscious thought as the music progresses.

proportion

PROPORTION in music is concerned with our ability to hear temporal relationships in terms of proportional durations. At the beat level, we can easily comprehend sub-divisions as proportional to a beat. Beat sub-divisions: clock-time-beat-clock This perceptual effect can be extended to a tempo level, where we can comprehend larger groups of beats as measures. Most popular music sticks to temporal proportions that fit a power of two series (i.e. 2, 4, 8, 16, 32). Irregular medium size time spans are quickly noticed. The larger the span of time, the more difficult it is us for us to comprehend proportions. A typical large section of popular music might have 32 measures broken into two sections of 16 measures, with each 16 measure section broken into 4 measure sections, and each 4 measure section broken into to 2 measure groups (i.e. all proportionally symmetrical with no irregularities). Many composers have explored using proportions to govern large scale durational structures. For example, the Golden Section is a proportional ratio that occurs often in music.

repetition

Repetition is a key characteristic of all music. When a fragment or section of music is replayed and recognized by the listener, we hear musical form. Repetition can happen on all possible time scales related to music, including both small bits of music, or large sections of music. Repetition is an important consideration of form and perception, particularly when a grid-time space is used. Repetition of small fragments or phrases of music are common features of most music, but live musicians will never play the repeated pattern exactly in the same way. In that sense, there is no true repetition. Each repetition offers a chance to hear and experience the passage with slight changes. This effect where repetition is really understood as a constantly varied repeated pattern, is lost in the electronic world, where a sample -- a fixed recorded fragment -- might be repeated verbatim. With fixed electronic sound, the repetition is real and precise and always the same. Music that does not feature any form of repetition does exist and can be considered special. Removing repetition as a forming principle in music poses special problems, and challenges, and causes the listener to ask the question "how does it holds itself together?"

schematic expectations

SCHEMATIC EXPECTATIONS, as described by David Huron, might arise from general knowledge of how events typically unfold, and are linked to processes involving long-term memory. For example, a familiarity with the common traditional patterns of jazz music would provide a listener a schema. Relying solely on the schematic expectations of traditional jazz might cause someone to reject more adventurous jazz music as it conflicts with expectations that come with the schema.

soundscape

SOUNDSCAPE is a term coined by composer and environmentalist, R. Murray Schafer. Soundscape treats all the sound in the world as a macrocosmic musical composition. Soundscape recording involves capturing sound from the natural world "as is". Soundscape recordings must not be confused with the natural soundscapes we experience in the real world. When natural soundscapes are captured by microphones and recording technology something akin to a film is created. the soundscape recording is mediated through technology. In many instances, we respond to the quality and ingenuity of the recording, not just the source material. It is very difficult to capture the sound of a thunderstorm or ocean waves in a digital format. Spatial aspects are all but lost, and often must be simulated. A bad recording of a beautiful soundscape is akin to a poor recording of a great piece of music. Think of the sounds produced by natural world phenomenon. Water Sounds: ocean, rain, flowing rivers, waterfalls, melting ice Wind Sounds: breeze, gusts, tornado, hurricane Fire Sounds: small wood fire, forest fire, house burning Animal Sounds: insects, mammals Ecosystem Sounds: rainforest

partials

Sound waves enter the ear as amplitude varying sound pressure waves. All complex waveforms can be broken down into a discrete number of amplitude varying fixed frequencies (sine tones). The individual components are called PARTIALS (i.e. small bits of the overall sound). A harmonic partial is one that is (roughly) a whole number multiple of a common fundamental frequency. We speak of the 1st partial as the fundamental. The 2nd partial then is two times the fundamental and this forms the ratio of 2 to 1. An inharmonic partial is one that is not a whole number multiple of a common fundamental frequency. Bells and Gongs typically have inharmonic partials. For example, in a bell sound we might discover a partial that is in the ratio 4.32453 to 1, a more complex relationship to the fundamental frequency. Below is a sound example of a bell struck several times in a row. Each time the bell is struck, the energy in the partials is reinvigorated and the composite of all the partials rings loudly again. A sinetone has been added to the beginning, and it rises and matches the various partials of the bell. This demonstrates how tones, harmonic or inharmonic, can be related to one another spectrally. Partial listening with a bell and sinetone: Even though many partials are present in the bell sound, we still perceive the sound as a single sonic event. This effect of fusion is partially due to something called common fate. The terms overtone, harmonic, and partial, all refer to the same idea; they refer to components of a complex sound. Extraordinary Sound prefers the term partial as it is always clear which component is being referenced. The first partials is always the fundamental frequency, and the second is always the frequency closest to the fundamental, etc.

temperament

TEMPERAMENT refers to the practice of making slight tuning adjustments to musical intervals that are pure ratio intervals (2:1, 4:3, etc.) in order to fit a number of notes into a workable pitch space. The most common example of this practice is equal temperament, the accepted tuning system for most western music practices. Each occurrence of the interval of a fifth in western music tuning is actually slightly detuned. To create the interval of a perfect fifth we need a frequency ratio of 3:2 between two tones. If we then begin with the higher tone and create a new perfect fifth interval, a third tone is generated. If we continue this process for twelve steps, we coincidentally find a frequency that is very close to a power of two when compared to the original tone in the first interval. This suggests that the system can be closed and circular with twelve pitch classes, just as we find on the twelve keys to an octave on the piano. In order for this system to actually work, each interval must be tempered by a very small amount. This means that the actual ratio of the frequencies are not pure, but for psychoacoustic reasons our ears are able to accept these small deviations and accept the interval as a fifth. As the tempering is spread out across the twelve tones, the actual interval distance between tones is the same, and thus we call the result equal temperament.

texture

TEXTURE refers to the structure of a weave of fiber or cloth. In music, texture can be categorized into different types of individual streams of musical activity over time. Textures in music often change and overlap, so it is sometimes difficult to pinpoint a single texture for a single section of music. Traditional music theory defines four general types of musical textures: Monophony Heterophony Homophony Polyphony monophonic <-> heterophonic <-> homophonic <-> polyphonic

timbre

TIMBRE (pronounced tahm-ber) is the standard term that recognizes awareness of frequency material in the event domain. Mostly, the term refers to the specific tone color that various musical instruments emit. Timbre has been one of the most illusive and abused terms in music. It has often been called a trashcan term that holds everything that cannot otherwise be categorized. In many ways, timbre is everything in music. But with our emerging understanding of the frequency domain and the note to noise continuum, the term timbre begins to be a useful, audible, and practical concept.

tone

TONE, PITCH, and NOTE are three distinct terms that are closely linked and are often used synonymously. Each term denotes a sound that contains an audible fundamental frequency with or without overtones or partials. As long as there is an audible fundamental frequency, the individual partials can be harmonic, inharmonic, or a combination of the two. TONES can range from complex tones involving many partials, to simple tones involving only a single sinewave component. If a tone is very complex and very inharmonic, it no longer is perceived as a tone and is characterized as some type of noise signal. Noise is not considered a tone. In the next example, a repeating harmonic tone begins as a complex tone, and progresses toward a simple tone. The fundamental frequency of the tone never changes. This is also a good example of a timbral transition from bright-->dull. Bright to dull: In the next example, a series of complex harmonic tones are heard, and the fundamental frequencies change or repeat over time. Complex tones moving: In the next example, a series of simple tones are heard, and the fundamental frequencies change or repeat over time. Simple tones moving: In the next example, a series of complex inharmonic tones are heard and the fundamental frequencies change over time. Inharmonic tones with changing fundamental frequencies: PITCH refers to a psychoacoustic phenomenon whereby our auditory system situates tones as pitches in some "high" and "low" sounding region. In most cases, the perception of pitch for complex harmonic tones will be the same as the perception of the fundamental frequency, as all the partials will support and emphasize the fundamental. But it is not unusual for certain instruments to be perceived in pitch as one octave higher than their actual frequency components show. In the case of complex inharmonic tones, the perception of pitch can be very different for different ears and situations. In the next example, a series of complex inharmonic tones are heard with all the tones sharing the same fundamental frequency. Although they have the same fundamental, the tones sound like they are shifting in PITCH (i.e. the perceived central pitch is not the necessarily the same as the root fundamental of the tone) Inharmonic tones with the same fundamental frequency: A NOTE refers to a harmonic pitch or tone. As most western instruments produce harmonic tones, they can all play the same "note" and be in tune with one another. Below is a sound example featuring different instruments/sources playing the note "A-440". The timbres of the various sources are quite different from one another, but we perceptually group the sounds together because of the solid and shared fundamental frequency. Each sound has a different overtone structure which is the chief factor determining the timbre of the sound. Tones with different timbres, all playing A-440:

note

TONE, PITCH, and NOTE are three distinct terms that are closely linked and are often used synonymously. Each term denotes a sound that contains an audible fundamental frequency with or without overtones or partials. As long as there is an audible fundamental frequency, the individual partials can be harmonic, inharmonic, or a combination of the two. Tones can range from complex tones involving many partials, to simple tones involving only a single sinewave component. If a tone is very complex and very inharmonic, it no longer is perceived as a tone and is characterized as some type of noise signal. Noise is not considered a tone. In the next example, a repeating harmonic tone begins as a complex tone, and progresses toward a simple tone. The fundamental frequency of the tone never changes. This is also a good example of a timbral transition from bright-->dull. PITCH refers to a psychoacoustic phenomenon whereby our auditory system situates tones as pitches in some "high" and "low" sounding region. In most cases, the perception of pitch for complex harmonic tones will be the same as the perception of the fundamental frequency, as all the partials will support and emphasize the fundamental. But it is not unusual for certain instruments to be perceived in pitch as one octave higher than their actual frequency components show. In the case of complex inharmonic tones, the perception of pitch can be very different for different ears and situations. In the next example, a series of complex inharmonic tones are heard with all the tones sharing the same fundamental frequency. Although they have the same fundamental, the tones sound like they are shifting in PITCH (i.e. the perceived central pitch is not the necessarily the same as the root fundamental of the tone) A NOTE refers to a harmonic pitch or tone. As most western instruments produce harmonic tones, they can all play the same "note" and be in tune with one another. Below is a sound example featuring different instruments/sources playing the note "A-440". The timbres of the various sources are quite different from one another, but we perceptually group the sounds together because of the solid and shared fundamental frequency. Each sound has a different overtone structure which is the chief factor determining the timbre of the sound.

onset

The beginning of an event or sound is called the ONSET. At the moment of impact, the initial point of contact between an activator and a source is called the onset of the sound. Onsets last for only a brief instant (20-100 milliseconds). The onset or initial point of contact is often the richest moment in the life of a sonic event. It can be full of sonic complexity and rich in variation, and it is often the primary cue for our ears in helping determine the nature of the source. In the following example, a string of sonic events are placed closely together in time. Hearing with our ears, we are able distinguish and identify most of the individual events. Meanwhile, our brain interprets the events as ordered and grouped in certain ways; the sonic events are actually overlapping in terms of their total duration. Our hearing/ear focuses on the onsets; we hear the sharp attacks and mostly ignore the remaining tale or resonance of the various events.

octave equivalence

The idea of OCTAVE EQUIVALENCE proposes that tones, which share power-of-two frequency relationships, will also share very close audible similarity; they can be considered belonging to the same class of tone, regardless of where they appear in the overall pitch space. The musical interval formed when two tones have a frequency ratio of 2:1 is called the octave (two octaves of frequency distance would be 4:1). Doubling, or quadrupling a given frequency at the octave will have the effect of mostly reinforcing the fundamental pitch. Western music theory accepts "octave equivalence" and classes all these tones by the same note name. Earst Terhardt defines octave equivalence this way: "tones may be perceived as similar in certain aspects, that in some respect a tone may be replaced by another one or that one tone may even be confused with another one. These criteria apply practically only to two musical intervals, namely, the octave, and, to a lesser degree, the fifth. At least within the framework of tonal music, the affinity of tones being in an octave interval is so pronounced that this relationship is termed octave equivalence." Why do octaves have such affinity? Some experts in cognition say it is hardwired in our brain and auditory systems and that all human beings regardless of cultural background experience the effect. And there are some solid psychoacoustic reasons to support an octave equivalence theory. For example, the difference between the fundamental frequency and the first overtone or partial (Ratio 1:2, called the octave) is the smallest whole number ratio in comparison with all the other partials. This means that the second partial contains half the frequency information of the first partial or fundamental frequency (see the diagram below). The fundamental has 1, 2, 3, 4, etc. partials and the second partial has 2, 4, 6, 8, etc. (i.e. all the even number partials). Acoustics show that the second partial in a complex harmonic tone has roughly one-half the amplitude of the fundamental.

sustain

The term sustain is different from resonance, but complimentary. Sustain involves keeping energy moving into the object being excited. When a bow sits on a string and is pulled across the string, it vibrates and generates a harmonic spectrum. All resonant potential is damped the instant the bow stops pushing. The bow is sitting on the string and prevents it from ringing further. The bow must be continually moved to produce sound. The following image shows a very noisy sound. Fourrier analysis of the image (sonogram) shows that the frequency space is saturated with energy; we hear and perceive the signal as noise (i.e. frequency saturation of one sort or another). The next sound example tests the limit of a violinist to play one long note without changing the direction of the bow, thus introducing a slight bump in the sound. The violinist must play the note softly because a loud dynamic would force the player to move the bow faster and with more bow pressure. By playing softly and slowly, the violinist continues to put energy into the sound over time.

phrase

A PHRASE is a complete musical statement usually involving several events or tones. Phrases can be broken down into smaller motivic phrase fragments, but are perceptually grouped into a complete musical statement. Typical phrases last anywhere from 2-15 seconds and are analogous to a single sentence.

octave

A musical interval is defined by the frequency ratio between the fundamental frequencies for any pair of tones. In western music theory the common low-order ratios are given names (Octave, Fifth, Third etc.), with the intervals being recognized as closer or further apart in terms of frequency. When any two tones share the same fundamental frequency ratio, they share the same interval class name. The two tones in an OCTAVE have a fundamental frequency ratio of 1:2 (i.e. the upper tone has a fundamental frequency that vibrates two times faster than the lower tone). In the sonogram of the sound example, the successive octave for each complex harmonic tone contains exactly half the number partials as its lower octave neighbor.

section

A portion of a larger piece of music that might last from approximately 15-20 seconds to up to several minutes, is called a SECTION.

inharmonic

Any combination of frequencies (partials, overtones) in the frequency domain that cannot be reduced to a set of roughly whole number ratios which relate to a real or virtual fundamental frequency, are said to be inharmonic (contrast harmonic). When a waveform is complex and seriously inharmonic, it is identified as a form of noise. Bell sounds have distinct partials, which are often inharmonic (i.e. the majority of overtones or partials cannot be related to the fundamental frequency of the bell with whole number ratios). Bell: Since our ears combine all the sounds into a composite image of "bell" we are not always aware of the individual frequency components (partials) that may be very strongly present in the sound. In the case of a bell, the strongest partials are always those that ring out the longest and this is most often, but not always, the fundamental. Listen carefully to the resonant elements in final seconds of the next bell. One can hear clearly that certain simple tones continue on to the end as all the other components die away. Bells are frequently used as a metaphor for cleansing and clarifying processes -- the very thing that happens when we ring bells. Bell, listen for the strongest and longest partials: In the next sound example, a single bell is struck several times -- each time the bell is struck the energy in the partials is reinvigorated and the composite of all the partials rings loudly again just as they begin to die away again (a process of constant renewal). In this example, a sinetone has been added to the beginning which rises and matches the various partials of the bell. This demonstration begins to uncover how tones produced by objects or electronics can be related to one another and form harmony or consonance. Bell with a sinetone: Here is one of the Sather Bells on the campus at UC Berkeley, with a fundamental of G. Sather Bells, fundamental G: We hear a fundamental, but it is not as defined and as clear sounding as one that has all the supporting cast of harmonic partials. Contrast the sound of the Sather Bells, with a vibraphone playing a G fundamental. All the partials are harmonic, but there are very few of them. Vibraphone, fundamental G: Contrast the sound of the vibraphone, with a saxophone playing the G -- all the partials are harmonic and there are lots more of them. Saxophone, fundamental G: The sax is much more complex harmonically, then the vibraphone, but both are harmonic. Listen to both the sax and the vibraphone at the same time. Notice how well they harmonize together. Mix of Saxophone and Vibraphone, fundamental G: Here is the bell, the sax, and the vibraphone all together. Compare this example, with the bell alone and notice how the strong harmonicity of the sax and vibraphone emphasizes the fundamental of the bell -- leaving the weaker inharmonic partials drifting about and adding complexity to the overall sound. Mix or Bell, Saxophone and Vibraphone, fundamental G: Balinese Gamelan ensembles feature many musicians playing with an orchestra of inharmonic gongs, bells, metal bars, and drums. As the instruments themselves are most often inharmonic, each Gamelan is unique and will be tuned with itself, making it impractical to exchange one instrument in one Gamelan with another. The tradition of composing with this kind of sound recognizes the existence of the fundamental frequencies -- but the resonance heard in the Gamelan is inharmonic, is in strong contrast to the resonance of the western ensembles were harmonic resonances are the rule.

order-disorder continuum

Composer Gérard Grisey (1946-1998) defined musical time along an order to disorder continuum. Order (Clocks, Grid-Time) ----Periodic (maximum predictability) ---------Continuous-dynamic (average predictability) -----------------continuous acceleration -----------------continuous deceleration ---------Discontinuous-dynamic (slight predictability) -----------------acceleration or deceleration by stages, polyphonic time structures Disorder (Clouds, Open-Time) ----aperiodic (zero predictability) ---------------unpredictability of durations

gesture

Denis Smalley defines gesture this way: "sound-making gesture is concerned with human, physical activity which has spectromorphological consequences: a chain of activity links a cause to a source. A human agent produces spectromorphologies via the motion of gesture, using the sense of touch or an implement to apply energy to a sounding body. A gesture is therefore an energy-motion trajectory which excites the sounding body, creating spectromorphological life" The perception of tones and the grouping of tones into gestural shapes is something to consider. Listen to the next example and track the gesture according to tone shape, and the motion from low tones to high tones. The pianist is not reading any music, and has been instructed only to play a quick "gesture" from the low end of the piano upwards to the high end.

note to noise continuum

Denis Smalley, in his article Spectromorphology: explaining sound-shapes, describes a "note to noise" continuum. The diagram below presents an expanded variation of this concept.

global morphology

GLOBAL MORPHOLOGY is concerned with the large-scale temporal unfolding of all the events that occur while listening to a piece of music. If we consider a piece of music as an "Auditory Scene" full of detail and levels and streams of activity, then the global morphological view is something like an aerial view of a city from the sky looking down. Rather than focus on specific event morphologies, the goal is to capture the whole, the gestalt. The listener is both autonomous and connected to the frame of the on-going sound. We can choose to gather information about the individual localized events, or to allow ourselves to be carried on the wave of the global morphology -- the large-scale unfolding of all things happening as they sum to an "it" moving through time.

graduated continuant

GRADUATED CONTINUANT is one of three archetypal amplitude envelope shapes, alongside attack-impulse, and attack-decay. Graduated continuants are sounds that are continually fueled with energy and involve the continual imposition of gesture. As this type of amplitude shape involves varying amounts of energy, it can have any kind of dynamic shape over time. Graduated continuant it is fundamentally different from the attack-impulse model and the attack-decay model.

grid-time

GRID-TIME is linear measured time with the added features of temporal flexibility and malleability. Grid-time has its own duration continuum. tatum<->beat sub-division<->beat<->meter/measure<->phrase<->section<-entire piece> David Huron, in his book Sweet Anticipation, describes how grid-time provides a predictive template, a model where future events are easily anticipated, can be delivered or denied, ruptured, or create surprise.

heterophony

HETEROPHONY is one of four archetypal design models used to describe musical texture in terms of how the various "voices" or agents behave in a musical setting. Heterophony features one predominant "voice" with all other streams ornamenting and roughly following along with the primary voice. This texture is more common in non-western musics, particularly Persian, Turkish and middle-eastern musics. Most music features combinations of all of the various archetypes, which include Monophony, Heterophony, Homophony, and Polyphony.

homophony

HOMOPHONY is one of four archetypal design models used to describe musical texture in terms of how the various "voices" or agents behave in a musical setting. Homophony is a very common music texture that features one central melodic stream of musical activity with all other musical activity providing harmonic support. Most commercial pop and rock music is homophonic in texture as it features a solo singer with all the other instruments supporting the singer with chords that harmonize and support the melodic line. Most music features combinations of all of the various archetypes, which includes Monophony, Heterophony, Homophony, and Polyphony.

open-time

In contrast to clock-time/grid-time, open-time has no precise time-point measurement or guide. One metaphor is that of the hour glass, where sand moves with a continuous flow (shh........), as compared to a clock, where times flows with each clock-tick (tick...tick...tick...). Another view of open-time considers each "voice" in a musical setting to be temporally independent from the others; a kind of polyphony of time, with multiple voices moving in their own independent time space. The next two sound examples are demonstrations of open-time. The overall effect is one of temporal freedom, a space not governed by a strict grid.

loudness

Loudness is concerned with how we perceive amplitude. The perception of relative loudness is not always directly correlated with amplitude (the technical term that deals with the amount of air pressure being displaced). Many factors can influence our perception of loudness: frequency, amplitude, timbre, and distance from the source. Loudness is a term that belongs to psychoacoustics. Simply put, it is how loud something appears to be at any given moment. Almost Inaudible <-> Quiet <-> Normal Listening Level <-> Loud <-> Extremely Loud The diagram below demonstrates with scientific accuracy that it requires more amplitude to perceive low and very high frequencies at the same loudness level as frequencies located in our human hearing "sweet spot".

modes of excitation

Modes of excitation categorize physical acts or gesture that result in energy being transferred into another object to produce vibration and sound. The various modes of excitation are: strike, pluck, bow, blow, shake, rub

morphology of sound

Morphology is the study of the form and structure of things. MORPHOLOGY OF SOUND is the careful tracking of how a piece of music or sound evolves through time. R. Murray Schafer defines sonic morphology as "the study of changing forms of sound across time or space". Morphology of sound involves a dissection of sound into related parts -- parts that can then be compared to similar parts in other sounds even when the other sounds are seemingly very different in nature and origin. The technique implies close examination of the sound and finite understanding of key sonic components over time. This is done to inform our brains of special attributes belonging to a sound event -- attributes that we might otherwise group into larger auditory scenes and thereby miss entirely. ExSound separates morphology of sound into two distinct spaces bounded by time, Global Morphology (large-scale structures) and Event Morphology (instant to instant structures).

glissando

Moving from a start frequency toward a target destination frequency by smoothly increasing or decreasing the frequency rather than leaping. Consider a complex harmonic tone in a glissando passage. When the fundamental frequency moves, all the associated partials will move accordingly to maintain the proper ratios between harmonics.

musical state or moment

Music can give the impression of being in a particular STATE, or MOMENT -- not moving forward and holding in space like a mobile. The moment might be frozen, static, or mobile-like, but it is happening and perceived as a continuous "now". In these states there is a global perception of a musical space without beginning middle or end. This is contrasted with music that has motion -- that is changing or morphing over time into something else.

phasing

PHASING refers to a rhythmic process involving two or more parts where one or more parts begin to deviate in temporal phase relationship with an isochronous pulse. Most tempo in music is steady and governed by a common temporal measure. In phasing, one or more parts speeds up gradually, or slows down to pull the basic pulse out of phase. A common phasing situation is that created by a set of church bells.

polyphony

POLYPHONY is one of four archetypal design models used to describe musical texture in terms of how the various "voices" or agents behave in a musical setting. With polyphony, simultaneous but complimentary streams of musical activity work independently, but also function together as a unified whole. Most music features combinations of all of the various textural archetypes, which include Monophony, Heterophony, Homophony, and Polyphony. Western classical music was obsessed with polyphony for hundreds of years, and most Baroque, Classical and Romantic music is rooted in polyphonic practices.

resonance

RESONANCE is the physical phenomenon that occurs when objects continue to sound after they have been excited and are no longer receiving energy from an external source. Resonance happens in the aftermath of excitation. Certain objects like bells and cymbals have exceptional resonant properties and can ring for a long time after being excited. See chapter "The Frequency Domain" for extensive details about Resonance.

rupture

RUPTURE in music indicates a clear and abrupt break in a musical continuity. In certain musics, classical western music for example, rupture is an error, as things need to be brought to proper closure before continuing onward. But in other musics, Hip-Hop for example, rupture is always possible and considered playful. As Hip-Hop is strongly connected to audio and digital culture, it stands to reason that rupture, the ability to break something, to change channels, to turn 180 degrees in an instant, would be a valued component. Both musics, western classical and hip-hop, can use or deny-the-use of rupture to excellent effect!

rhythm

Rhythm spaces emerge from clock-time, and grid-time temporal structures. A pulse with no accent does not occupy a rhythm space. A pulse may be periodic and isochronous, but when duration, pitch, timbre, and loudness are unchanging, no rhythmic profile is created. The following sound example is a pulse train with no accent. If you hear any rhythmic grouping, it is an illusion; it is due to a natural tendency to group things into larger and larger units. Pulse Train, no accent: To create a rhythm space we must use accent. Here is the same pulse train with a loudness accent, the only change is that every fourth occurrence of the pulse is louder. The accent establishes introduces the beat. The beat falls every 4 sub-divisions and this creates a new rhythmic layer that is four times longer than the pulse. Pulse Train, accented: Once a beat is established, the tempo in beats per minute can be identified. In the last example, the beat falls every 4 sub-divisions and this establishes a tempo at around 78 beats per minute. It is the beat that establishes the tempo, not the sub-division. When the tempo is steady and on the grid space, then groups of beats can be further distinguished with periodic strong and weak accent. This higher level oscillation between strong and weak beats is called meter. In 1913, the young composer Igor Stravinsky shocked the musical world when he created the Rite of Spring. One famous section of the piece explores the effects that can be created from an unpredictable accented pulse. The pulse is steady and even, but the accents arrive without a clear pattern. Stravinsky is able to create tension by confusing our sense of anticipation as to when the next accent will occur.

sonic event

SONIC EVENT is a single audible event that belongs to a larger auditory scene. Sonic events can be made from one or more sound sources (i.e. several sources might fuse together to form one sonic event), and will have varying degrees of auditory salience. In a piece of audio or live music, sonic events stand out as a single feature usually lasting only an instant or extending to many seconds. The next two examples features several different sources combined into single sound sources with the classic archetypal amplitude envelope

spectrum

SPECTRUM in music refers to the distribution of energy across the frequency space of human hearing produced by any sound source. Human hearing can be modeled in a frequency space that extends from approx. 16-20 Hertz (cycles per second) to roughly 20,000 Hertz. Fourier Transform analysis results in a data set that shows the amount of energy (amplitude) present at each frequency level in the human hearing range. In the image below, time is represented on the horizontal axis and frequency on the vertical. We see a stable tone with a rich set of evenly spaced partials -- the darker the area, the greater the amplitude of the partial.

tempo

TEMPO is defined as the number of beats per minute. In most music, the tempo varies from 60-120 beats per minute, roughly mirroring the range of the human pulse rate. Tempo is an essential element in all grid-based musics. Tempi can slow down gradually or accelerate, vacillate, or break down completely into open-time. slow <-> fast

temporal polyphony

TEMPORAL POLYPHONY is a term coined by the author of this text. Temporal polyphony involves different performers working with microtiming and flexible differences of grid-time tempi to create special states, grooves or feels. In these cases, each member of the group operates on the grid of time in slightly different ways. The result can be a magical temporal state that often requires years of practice and understanding to achieve.

tatum

The TATUM is the smallest common durational sub-division in any piece of music that depends on clock-time. The term was coined at CNMAT (Center for New Music and Audio Technologies) and is not in common use. The duration of a tatum is much faster than that of a beat; in many musical circumstances, the tatum is never actually heard as it can be much smaller in duration than any sub-division used in a piece of music. Any duration in a particular work must be a whole-number multiple of the tatum. For commercial software, sequencers divide a beat into 480 or 960 tatums. This large number allows for complex durations to be represented in whole numbers -- i.e. to create five sub-divisions in a 480 tatum world, each sub-division will need 96 tatums. For most western music, the tatum duration is much longer; it is usually no smaller then a sub-division of the beat by 3 or 4.

music notation

The most common type of MUSIC NOTATION is a reduction of the fundamental frequencies (pitch, note, tone) with indications for duration, temporal placement and loudness. These traditional western music scores are used by musicians to recreate musical performances, but they depend on something called performance practice -- the various traditions of performance that are handed down from musician to musician through practice, writing, and speaking.