Although the beginnings of its development date back to the late 17th century (Harding 1938: 2), the metronome saw many prototypes before Dietrik Winkel's adjustable double pendulum found its way into Johann Maelzel's metronome in 1815. Since the breakthrough of this successful design, the metronome has played an increasingly significant role as a tool for musicians and composers. Performers playing along with a metronome listen to the equivalent of a temporal mirror which illuminates their tendencies to drag or rush in musical passages. One doesn’t follow a metronome due to the biological latency of perception, thought and action, but instead creates an inner pulse which runs concurrent to the sounding pulse of the metronome, making adjustments as needed.
For composers, the metronome serves the score, communicating intended tempo. Notated tempos in scores however, remain somewhat problematic as variations in performance conditions (e.g. space acoustics, the performer’s mood in the moment, audience reaction) can lead to quite different speeds. As we will further see, emotion and speed are directly linked and perceived tempos are often different than measured tempos.
The pendulum metronomes started out mostly reproducing tempos with the specific range of 50 to 160 beats per minute (Bingham and Turner 2017: 27). By the 20th century, that range standardized at 40 to 208 bpm, although scaled somewhat unevenly.[1] Musical tempo in European classical music from the early 19th century until the late 20th century seemed to be encapsulated by this range, particularly when one takes into account the possibility to double and halve tempos in duple and triple meters. Undoubtedly the range of metronome markings reflected the range of musical tempos needed at the time. The mechanical states of technology of both traditional acoustic instruments and the pendulum metronome were comparable, suited for each other. With the discovery of electricity however, new technologies created possibilities to reveal other speeds, as seen above in chapter 3. Further, as rhythmic approaches continue to rapidly expand since the 20th century, for example in the areas of meter and subdivisions of the beat, the doubling or halving of 19th century tempos to reach other speeds is no longer sufficient.
In the late 1970’s the pendulum metronome began to be superseded by quartz metronomes. Based on counting the vibrations of a quartz crystal when stimulated by electricity, these new metronomes had superior accuracy and evenness. Shockingly, despite the new technological possibility to greatly expand the range of tempo, the quartz metronomes preserved the traditional 40 to 208 bpm scaling. The barrier of traditional tempo ranges was finally broken open in the late 20th century with specialized software and then made ubiquitous around the turn of the 21st century with the creation of software platforms for apps on smart phones. Many different metronome apps are currently available on the ever-present smart-phone, creating easy-access to tempos in the range of 10 to 400 bpm and allowing us to explore their musical possibilities. With this expansion of musical tempo our imaginations of musical possibility also expand.
Since tapping one’s foot is frowned upon in live performance, direction is given to not visibly move during the exercise, both for control and to not distract others. This leads to the following question: can one accurately keep track of the passing of time only in the brain, just with cognition, or is the involvement of the other senses necessary, such as a kinesthetic movement? Must we tap our feet in order to maintain a steady pulse, as is commonly done when first learning music?
Experience has taught me that physical movement is indeed an extremely advantageous ingredient for maintaining a steady pulse. Through a gentle nodding of the head, a rocking of the torso or by moving a foot, toe or finger, one can create a physical sensation which is compared each time the movement is repeated, enabling exact copies and ensuring regularity. Additionally, audible sounds can also help for steadiness, either in the music, such as in a percussive part, or in the player through a soft clicking of the tongue or a quick inhalation, a technique often used for cues among musicians. Created sounds by the player, however, are not always practical since they may interfere with the (sounding) music. When rhythmical cues occur in the music, aligning is similar to playing with a metronome: reaction has a latency so we must set up, synchronize and follow our own physical internal pulse (see chapter 4).
1. From 40 to 60 bpm in increments of 2, from 60 to 72 in increments of 3, from 72 to 120 in increments of 4, from 120 until 144 in increments of 6 and from 144 until 208 in increments of 8. The percentage of change ranges from 3.33% to 5,26%. From 120 until 208 can be seen as a doubling of the tempos from 60 onwards.
During the tempo 10 exercise most people have the tendency to clap early, before the metronome click. Even when one is consistently synchronized as the beat goes around the circle, they often clap too soon when it comes time to put their own pulse into sound. Apparently, some part of our timing mechanism undergoes a change during the last beat.
There are likely several potential causes, but 10 years of exploration on this exercise in classrooms has taught me that often it has to do with simply becoming nervous. The tempo 10 exercise is very difficult; in fact, one could call it a ‘machine for failing’. It occurs regularly that quite some time will pass after a clap before the correcting click of the metronome sounds, showing 'failure' and creating a feeling of disappointment. On the other hand, occasionally one does get it perfectly correct, making a very strong positive impression. This exercise is chosen to be carried out in a social situation and the likelihood of failure in front of one’s peers can create a situation of tension to some degree, having an exceptional influence on our sense of speed.
The speed of thoughts in the brain, on the other hand, seems to be constantly in flux, as if it is a function of the continually changing environment and personal conditions. This can be simply demonstrated by a familiar experience: at some moments tempo 60 bpm, or the speed of seconds on our watches or clocks, feels very fast. We are surprised to see the ticks move so quickly. At other moments, it can seem as though there is heaviness to the second, each one thudding forward in slow motion. Only when we utilize a spoken sound, such as “one one-thousand, two one-thousand, three one-thousand” can we reliably recreate the correct speed. We know the sound of those words in normal speed and also the feeling of the movement made by our muscles to speak them.
This supports the idea that when a musician is gaging time to play music, count rests, and play together with other musicians, he or she is measuring durations largely against feelings in the body and available sounds around them. Certainly the brain is also active, listening, counting, interpreting, and thinking, but without the connection to the body, the speed of time lacks grounding. This corresponds with my experiences: we need to (mostly) use feeling through movement to keep track of speed correctly.
Not unrelated, time in general is always measured by movement, whether considering the age of the universe by observing the motion of galaxies or the length of one second by counting atomic vibrations.
Most musicians or public speakers can also attest to this effect. In public, we often perform or speak faster than practiced, even despite a recollection of not having sped up. This discrepancy demonstrates the fluidity of our perception of speed. It is as if there is an ‘inner clock’ to which we relate our actions, giving us our sense of duration; when the clock speeds up so do our actions. Because the relationship between the two remains consistent our impression of elapsed time remains the same. However, since the clock is running faster, less time has passed.
To understand this ‘inner clock’ model more clearly, let’s take a look at recent neurobiological research.
"1. Experience of duration in the present: the more events in the present, the shorter our experience of duration for that moment in the present; the fewer events, the longer our experience of duration." (Delaere 2009: 31)
Craig states that our sense of time passing emerges from a cinemascopic series of ‘global emotional moments.’ Unlike film which has a fixed frame rate, our own internal frame rate of perception seems to be flexible, as suggested above. In addition to emotions, the density of music can shape our experience of speed. Take for example the first of Messiaen's three laws of experienced duration:
Put otherwise: a short empty time interval is experienced in the present as longer than a filled time interval. When there are many events occurring, our attention can be filled with experiences and we lose track of time. If there are fewer events, we have more attention for time and we can feel it stretching or slowing down.
The movement Telescopic Ladder from the piece Tools (McGowan 2003) utilizes several compositional and performative approaches to explore organized and chaotic speeds, and achieve its goal for a multi-layered richness.
After a brief repetitive introduction, the work sequentially builds up a four voice temporal canon, where each added layer is proportioned at 4:3 speed to the immediate underlying layer. The entrances of the layers are timed so that they all end at the same point, a process which is intended to be evident to the listener. In effect this sets up a polypulse situation with four different pulses. Performing the movement with a conductor or common pulse would be extremely difficult or very approximated, but each successive player executing a 4 against 3 speed ratio of the previous player’s pulse is perfectly practical. The result is a musical phrase with a transparent form, focussing on the convergent moment of the same line in different speeds.
Computers and modern chronometers have high temporal resolutions and can divide lengths into trillions of subdivisions per second. For example, the current definition of a single second is 9,192,631,770 vibrations of a caesium atom and there are atomic clocks which fastidiously count this away all day, helping to coordinate time throughout the planet.
While our brains are also very fast in all the things they do, there are both physical limits to the speed of our senses and psychological limits to the speed of our perception, as mentioned above. Craig (2015: 232) determined that the maximum speed for ‘global emotional moments’ is 100-125 milliseconds. In musical terms this is the equivalent of sixteenth notes at tempo 150 bpm, sounding like this:
Personally, I would describe this speed only as moderately fast, certainly not at the limits of my perception. When I was a student flutist, for example, our goal for double tonguing articulation was sixteenth notes at tempo 160, while playing the allegro from J.S. Bach’s Sonata in C Major for flute and basso continuo. This tempo translates to notes of 94 ms per note and is regularly achieved by flutists all over the world. Further, this example points not to just perception, but also action: moving and coordinating fingers, tonguing and breathing.
How fast are our own 'global emotional moments'? If we equate Craig's unit with individual notes, then we can test ourselves. Below is a serialized musical passage at various speeds to give one the opportunity to test their own ability to clearly perceive individual notes. As the speed increases with each new version, the reader can check for herself at which speed the notes start to blur together, where their individuality is lost.
150 ms per note (100 bpm)
100 ms per note (150 bpm)
Here below are two pieces of music. Without looking at a time keeping device, listen to each one and write down your estimate of its length. The answer is in the next section.
The next 'Random Speed' section (page 24) utilizes structured improvisations by the players. Each player chooses ad libitum a pitch and a tempo to repeat which are different than any other tempo/pitch combination already being played in the ensemble. The players then switch to new pitches and speeds at will and the result is a cacophonic texture of multiple layers and multiple speeds. It ends in an tutti accelerando from each player’s current speed to as fast as possible. This section is a quite simple approach to create a complexity of speeds (and pitches) that would be very difficult to notate or execute correctly. Additionally, cementing such a music into standard notation would strip it of its improvisational freshness.
With the return thereafter of the temporal canon, each iteration is at a faster tempo, making use of the quintuplet line to springboard to the new speed at the ratio of 5:4 via an explicit tempo modulation (four quintuplets become the new 16ths notes).
Further testing and exploration of this subject was made by bassist, composer and music educator Adam Neely (2017), providing additional musical examples which also break the 100 ms barrier. He maintains that the threshold is actually near to 50 ms, which is the point at which individual notes start to become pitch because they are repeating at 20 hz, approximately the lowest pitch our ears are setup to perceive. This indeed is true with repeated notes, i.e. the same sound repeated over and over 20 times a second, or more. In the current test above, the pitches are chosen to not repeat, nor with any perceptible pattern. This lack of repetition prevents the transition to pitch and the sequence morphs into a sea of fast notes. Even though the notes are faster than 50 ms per note and no longer individually perceptible, the passage has not become a single pitch. Only through repetition does this effect take place, as is shown below through repeating Beethoven's entire Ninth Symphony fast enough that it itself transforms into a straight tone.
Finally, speeds faster than those explored here do play a role in the perception of sound, as excavated in detail in the excellent book Microsound, by Curtis Roads (2001). The Micro Time Scale is at the edge of auditory perception where timbre and transients are perceived. Faster still are the Sampled Time Scale, the Subsample Time Scale and the Infinitesimal Time Scale. The musical speeds explored in most detail in this essay, however, lie in the realm of the Sound Object Time Scale, or in traditional compositional terms, musical notes.
Despite the ubiquitous role of time in most everything we do there is still much to understand about its essence as a function of human perception. One way to learn about the cognisance of time is simply by listening to music. The rhythms, sounds, and silences of music are jacketed by the human condition and we learn about the possibilities of existence through listening to music made by others.
Organic to all cultures, music is likely an emergent property of our biological existence, a manifestation of who we are, how we think,and how we feel (Craig 2009: 6). Organic to music, on the other hand, is time, because without duration, there is no music. Nonetheless, the expansive identity of time with its major implications in the realms of science, philosophy, and religion, tells little about our immediate experiences in music. The concept of speed, though, is full of enlightening character. Take some common terms to describe tempo in European classical music:
largo = broadly
adagio = slow and stately
allegro = fast, quickly and bright
vivacissimo = very fast and lively
Speed is relational and it reveals aspects about how we think and feel. Formulated by humans, speeds have character.
Time in music is often credited as having a dual identity. Pierre Boulez (1990: 87) described the two characters as smooth, or amorphous time, and striated, or subdivided time. Another composer/conductor, David Epstein (1995: 7), classifies the duality similarly with chronometric, or subdivided time, but his integral time points rather to perceived experience, inclusive of the unique context of each piece of music. Both claim that all music exists in some combination of the two.
Although a unified agreement among researchers is still lacking about the existence of an ‘inner clock’ controlling our speed of action, in some respects our behaviour matches such a mechanism (Hammond 2013: 56). The time dilation effect mentioned above could be a result of the inner clock moving at a faster rate. When in a nervous situation, for example caused by the fear of failure, the ticks of our inner clock speed up and the actual durations of experienced time become shorter as we fail to notice. We don’t realize that we have sped up because our actions remain relative to the inner clock, regardless of its speed. To reiterate the antidote for this effect, by remaining in contact with movements in the body we can prevent rushing because actions can feel different when sped up.
While the circadian clock in mammals (our daily patterns of sleeping, eating, bodily temperatures, etc…) has been localized to a specific part of the brain (the suprachiasmatic nucleus), no such single concentration has been found for the perception of time on the scale of seconds to minutes (Wittmann 2017: 31). Neither is there a specific organ to sense time as there is for the senses (hearing, sight, smell, touch, taste). However, we do indeed experience the passing of time and current theories posit that perception as an emergent sense based on the neurophysiological operating of the brain.
In this direction, relevant research has been carried out by the neurobiologist A.D. (Bud) Craig, who has singled out the anterior insular cortex (AIC) as a key part of the brain involved in our sense of time (Craig 2015: 223). The AIC is a central collection point for signals from the body, which includes information from our sensory organs, our autonomic processes, our cognitive processes, and our emotions. According to Craig, the total accumulation of these signals at each immediate instant comprises a ‘global emotional moment’ (Craig 2015: 49), an image of ‘the material me’.
Each ‘global emotional moment’ represents a snapshot of our self-awareness and as we move to the next, the previous snapshot is stored into memory. The series of snapshots in memory creates a cinemascopic representation of ourselves, similar to the way film functions: a series of static moments passing at a certain speed creates the illusion of fluid motion. In our case, the existence of memory allows us to experience a progression of ‘global emotional moments’ across time, thus giving us our perception that time is passing. Interpreting this model through the lens of duality, one could say that rapid subdivided time creates a sensation of smoothness.
The dilation, or the perceived slowing down of time is a commonly experienced phenomenon. Here follow some examples of this effect.
Stressful situations can lead to the dilation of time in all human beings. Take for example falling off of a bicycle. In a moment of potential danger such as this, our brains kick into high gear, intensely focusing on the situation. The result is the creation of a series of very strong impressions which are stored into memory as fast as possible (Eagleman 2015: 90).
When recalling the event, it seems as if it occurred in slow motion. We built up a large number of strong memories in a relatively short period of time. Usually one takes more time to create so many strong memories, hence it seems in retrospect as if the accident took much longer. Of course, the event didn’t take place in slow motion, as any observer will attest to.
Another example of fear causing an overestimation of time involves eight-legged creatures. Test subjects who suffer from arachnophobia demonstrated that they estimated time intervals to be longer when looking at photos of spiders (Watts and Sharrock 1984: 597-589). To relate this to the effect of nerves during the tempo 10 exercise, it is as if the subjects believe that six seconds has passed when only 4 or 5 seconds have passed. Since time is being subdivided, possibly the compression effect is taking place within the smaller subdivisions, equating to an overall increase in tempo.
Musical speed has many more facets than presented here, each an opportunity for in-depth study. The tempo 10 bpm exercise, for example, contains many more musical and extra-musical angles to explore than presented here, such as topics related to tempo curves while speeding up and slowing down, communicating pulse among musicians, preparatory movements for articulating sound, and the development of temporal conviction. Further, notation is always a topic ripe for refinement and advancement, to create new ways to write down contemporary performance practices, such as in Chapter 2.
A. D. Craig's model of how we keep track of time explains two key points which I know to be true as a musician, and which are directly relevant to this research into musical speed:
1. we use the senses of our body, our interoceptive awareness, to feel time passing, and
2. our emotions influence our perception of the speed of time.
Researcher Marc Wittmann writes: “Temporal experience, self-consciousness, and the perception of bodily states and feelings are tightly bound to each other; they cannot be experienced separately.” (2017: 135)
From moment to moment the perception of speed in the mind can change remarkably, as most can attest to who have experienced an accident, a strong cup of coffee or an exciting piece of music. While the key instruments the mind has for reliably measuring speed are the body’s physical feelings, and most musicians are intuitively in-tune with those sensations, there is still much to understand about exactly how these mechanisms work. How do musicians develop physical mechanisms to keep track of time? How can they be used to control speed under various emotional situations?
David Eagleman writes, “you don’t perceive objects as they are. You perceive them as you are,” referring to the inherent subjectivity of how we conceive reality. (2017: 79) Every human brain is unique and will have its own understanding of time. Music, created by the brain and the body, emerges from its velocities, physiologies, capabilities, identities, and creativities. For instance, all the musical examples in this essay, whether art compositions or speed and duration tests, have come forth out of possibilities imagined by a brain, and their existence communicates the possibility for that conception to others. Instead of studying the brain to learn about music, study music to learn about the brain.
The current essay takes a look at both types of time through the lens of musical speed. The examples, created from my perspective as a composer, performer and teacher, are focussed on various velocities of events, their characters and how one might conceive of them. While the related elements of rhythm and meter are common in music, this essay takes a more generalized approach to speed and its directly related cousin, tempo.
In order to explore the identity of speed I present here a multitude of perspectives revealing numerous properties, hoping to provide a clear concept for the reader to experience, interpret and conceptualize for herself. First there will be an explication of musical speed with examples exploring various qualities. The next section will delve into topics related to a specific tempo, weaving historical, practical and conceptual approaches to the sense of inner pulse. This leads directly to an exploration of neurobiological issues such as how we keep track of time, the relationship between emotions and perception, and the different effects of present moment and retrospective experiences.
The final two sections contain further musical examples, including a composition inspired by several topics in this essay, an exploration of the full range of speed, and quizzes of duration and maximum speed perception. While some of these examples could be used for generalized testing via the scientific method, my intention to create them was rather to test myself; i.e. instead of examining for what the ‘average’ person might think, I am curious about what I can learn from these examples that can be used in a future composition, performance or lesson.
We begin with several demonstrations of speed in music.
One natural conclusion of an increased clock speed would be that our mental and physical perceptions also speed up, however this has been demonstrated to not be the case. In a death-defying experiment led by neuroscientist David Eagleman, volunteers were dropped free-fall backwards into a net (Eagleman 2009: 90). A watch on their wrists flashed numbers just faster than possible to read at a relaxed state. Despite the occurrence of the well-known time dilation effect of dangerous situations, the perceptual apparatus of the volunteers failed to be able to read the numbers. In other words, they weren’t able to see things any faster than before, despite the retrospective impression that the free-fall took place in slow motion. Although this study may not be entirely conclusive, it remains entirely plausible that the bodily mechanisms have physical limits which cannot be surpassed.
Although Eagleman has shown that our perceptual apparatus does not speed up during moments of high emotional salience, we are certainly more acutely aware and that can also create dilation, according to the attention effect, mentioned in chapter 10.
There are other theories that specify the role of the AIC merely as a hub for signals to travel to other parts of the brain, and not per se the central location of our self-awareness (van den Heuvel and Sporns, 2013). While there is still clearly much to be understood about the exact functioning of the brain, there are two ways to interpret this situation in relation to this research. First of all, 40 years of musical experience has taught me that the body and emotions clearly play significant roles in how we perceive the speed of time. No scientific proof is needed, however the models can stimulate a broader understanding of this process, which can lead to new artistic ideas. Secondly, experiential knowledge can, in turn, provide justification for scientific models which may have yet been difficult to prove.
Craig’s model is largely driven by interoceptive awareness, which is the ability to detect changes in our physiology (Craig 2015: xiii). In other words, by feeling how our body moves we create moments which, in sequence, add up to the sense of time passing. This matches my own experience performing and teaching rhythm: we must feel ourselves moving to have the ability to track time accurately. Since 2015 there is a new type of metronome which makes use of this fact. Instead of making a click sound to be listened to, the Soundbrenner Pulse vibrates short pulses which can be felt. An interesting development, I feel it creates a physical sensation which can be close to how musicians experience their inner pulse.
Next, let’s explore how our perception of the speed of time is flexible.
Attention also plays a role in our perception of time. According to psychologist Amelia Hunt, when we focus our attention to an event it creates the impression that it lasts longer than it did (Hunt 2008: 125-136). One example is the telephone illusion: while waiting in anticipation (or attention) for a call to be answered, the initial silence between rings can seem so long that one begins to wonder if the phone is dead or has been answered.
A variation of this, known as Chronostasis demonstrates that novelty can also cause us to stretch time. A common example takes place when we look at the second-hand of an analogue clock. Upon first glance, it seems as though the hand has frozen. We feel that time has stopped (and it literally appears that way) but merely our perception of that moment has stretched.
Finally, when we focus our attention to the passing of time itself, it seems to slow down (Hammond 2013: 44). All of these effects demonstrate how our perception of the speed of time is a fluid variable.
The speeds occurring in music, then, should reveal truths about the general technical specifications of the brain. What are our fastest and slowest speeds? The discrepancy briefly explored here between scientific testing and empirical practice regarding maximum performance speeds needs to be clarified. Furthermore, how far can the human apparatus adapt to new speeds shown through technology?
Does our speed of thought follow the density of music? Messiaen and likely our experiences concur, yet more specificity is needed about the effects of different characters and different speeds of music. If we take note of the varieties of flow in music, not just velocities of sounds, but the totality of the timing relationships of all the musical elements, what can we learn? Are the rules universal or are they invented by each piece of music, in an integral manner as mentioned by Epstein? If it is a combination of the two, how does that work? How do they differ from culture to culture, from person to person?
How do the well-known temporal illusions such as chronostasis, the kappa effect and the oddball effect function in music? When we understand more about the effects of musical speed in these contexts, we will know more about the brain and how it creates, experiences, and interprets time. This information will in turn inspire more creation of musical works.
This essay is an artist’s response to theory, creating musical exercises and examples for his own testing and curiosity, a personal science. It is clear that science has much truth to determine and art has much undiscovered territory to explore. Each cannot postpone its work, however, until the other is complete. Art and science must inspire each other in their current states, no matter the stage nor speed of progression.
Finally, I would like to present a demonstration of one perspective on the range of speed in music. Taking Beethoven’s Ninth Symphony as source material, here are 25 versions of the same recording in different speeds, beginning from a couple of notes taken from the symphony stretched to 24 hours, to ending with the entire symphony repeated at a frequency beyond the range of human hearing.
As the scale of speed increases, the identity of the music transforms and we hear different aspects of the material. Some shifts indeed sound merely as a faster version of the previous iteration, while other shifts reveal very different qualities in the music. The normal elements of our immediate attention reduce beyond detection while other elements, normally too slow to perceive, speed up into range. As the versions become faster, the detailed level of our hearing goes from a single note, to a motive, to a phrase, to a block of phrases, to a section, to a movement, and finally to the entire piece.
From there, if we keep increasing the speed, an important transition takes place when the entire Symphony is compressed to 1/20th of a second and then looped. We stop perceiving the music as a sequence of sounds as our hearing apparatus translates the repetitions into pitch. They start out as a complex low tone at the bottom of our frequency range of hearing and simplify into a clean pitch as they speed up. Doubling the speed creates octave transpositions of the tone until it has risen in frequency beyond our perception.
1. Excerpt, 1/24th speed (full symphony stretched to 24 hours)
The ecstatic sound of the symphony orchestra is almost in stasis, frozen in time.
2. Excerpt, 1/8th speed
We start to hear a melody move in slow motion.
3. Excerpt, 1/2 speed
The theme becomes recognisable, although far under tempo.
4. Excerpt, 1x (original speed)
This is the original intended speed. Joy and majesty are in full splendour.
5. Excerpt, 2x faster
A faster version of the original, perhaps slightly comic. The musical information of the original speed is still intact.
6. Excerpt, 4x faster
The theme is now at the speed of motives.
7. Excerpt, 8x faster
Phrases have become blocks; the theme is barely recognisable.
8. Excerpt, 16x faster
At this speed we have left all thematic material in a blur and the harmonic movements of the section become apparent.
9. Full symphony, in 60 seconds
This speed has rendered all melody and harmony inaudible. Block dynamics of large sections are apparent.
10. Full symphony, in 5 seconds
At this speed, only larger blocks of dynamics and entire movements can be distinguished.
The following two pieces investigate a technological revolution of the increase of speed, from the Industrial Age to the Digital Age.
The tape part of Workshop (McGowan 2004), for recorder and tape, consists solely of recorded samples of industrial machines. These machines click, scrape, start, stop, stutter, rotate, dig, pump, brake, crank, drill, step, hammer, hook, lift, wipe, paddle, mangle, sew, toggle, stamp, shear, saw, ratchet, punch, shuttle, and warp. The speeds are largely similar to speeds carried out by human bodies. We also have lungs which expand and contract, fingers that go up and down, muscles that form embouchures and tongues that flicker back and forth. While the recorder is sonically very different than most industrial machines, the moving parts of the player are in sync.
With Volt (McGowan 2015), for violin and tape, the tape part is comprised of sounds by computers and circuit-bent electronics. Instead of computer sounds originating from an express tone generator function, the tape part is made up largely from the extraneous sounds emitted by circuits running various sorts of data manipulations (programs). These sounds reflect the speed, complexity, variety and subtlety of electronic movements, which are very far away from the mechanical movements humans undertake to play an instrument.
Both pieces, taken from Guy Livingston's DVD, One Minute More (2008), are the same length: one minute.
Likely the first piece seemed longer than the second due to two factors: a higher density of events and a constantly changing musical style. The goal of For Crying Out Loud (McGowan 2004) was to create as much musical change as possible within one minute. Most parameters change every second or two: tempo, harmony, melody, register, dynamic, musical style, etc….
The second piece La Serenissima by Hillary Zipper (2009), contains fewer events and the musical style remains more or less consistent throughout. Due to these qualities, our inner clock slows down and we estimate the duration as shorter than the first piece. Despite this explanation though, I feel its beauty can create a feeling of timelessness.
11. Full symphony, in 1 second
Simply a faster version of the previous iteration, with same elements audible.
12. Full symphony, in 0.1 seconds (10th of a sec)
Has become one sound.
13. Full symphony, in 0.05 seconds (20th of a sec)
Now one short sound.
14. Loop, 20 Hz
Through repetition, it starts to make the transition to a pitch at the lowest part of our hearing.
15. Loop, 40 Hz
A low tone is audible.
16. Loop, 80 Hz
Octave higher.
17. Loop, 160 Hz
Octave higher.
18. Loop, 320 Hz
Octave higher.
19. Loop, 640 Hz
Octave higher.
20. Loop, 1280 Hz
Octave higher.
21. Loop, 2560 Hz
Octave higher.
22. Loop, 5120 Hz
Octave higher.
23. Loop, 10240 Hz
Octave higher. Peak hearing of middle aged adult.
24. Loop, 15360 Hz
Peak of young person.
25. Loop, 20480 Hz
Beyond typical human hearing range.
While the main dissimilarity between these two works could be boiled down to the difference between large moving machines (with relatively large masses) and small moving electrons (with very small masses), the relationship to the human body of the soloists is fundamentally different, as is demonstrated in the speed. While the recorder can easily keep up with the industrial machine speed in duet-like musical dances or by playing the role of a cog in the machine, the computer speed is more difficult for the violinist to match. The asynchrony creates a tension in the music which ultimately led to a different approach to the composition to take advantage of that contrast, either by exploring complimentary voices, for example by each taking its own sound and speed to express a similar idea, or by expressly highlighting the differences in imitation games.
The next section takes a look at music’s own speed keeping device: the metronome.
2. Retrospective evaluation of time passed: the more events in the past, the longer our experience of duration for that moment in the past; the fewer events in the past, the shorter our experience of duration for that moment in the past now." (Delaere 2009: 31)
The estimations of this quiz are made in retrospect, or recalling from memory after the fact. This is covered by the second of Messiaen's three laws of experienced duration:
Contrary to the present moment experience, the relationship between density and estimated duration is flipped. Time intervals in the past containing more changes are perceived as longer than similar intervals with fewer changes. As described in chapter 10, when an above average number of memories are created we recall the experience as longer than it was.
In the piano etude below, titled The Speed of Time (McGowan, 2014), I explore a number of topics previously investigated: 1. the tempo 10 speed, 2. changing relationship between the density of events and the perception of duration, and 3. the relationship between emotions and our sense of inner pulse.
The etude is written in tempo 10 bpm with each bar throughout the entire piece lasting exactly six seconds as given by the metronome clicks. As the rhythms develop and the density increases, the immutable periodic clicks feel as if they are getting farther and farther apart. Our consciousness of flow allows itself to be guided by the music and as the etude explores an increasing temporal resolution our experience of the length of six seconds dilates.
The performance notes specify for the audible metronome click to be a part of the live performance, so that both the performer and audience can hear it as the piece progresses. Some musicians (most often in popular music) perform with a click track, but it is not customary in live performance of classical European music, nor have any pieces come to attention that explore an express juxtaposition of human and machine speeds in order to highlight their differences for the audience.
There are four basic ingredients necessary to bridge six seconds correctly: a steadfast concentration, a subdivided counting system, a physical movement to regulate the counting speed, and a sense of the whole.
Through a well-controlled movement which remains steady, one can get very close to clapping on the next beat, but maintaining a constant focus is a must to pull it off. Even small distractions (cognitive interruptions or a movement such as a quick look to the side and back) can cause one’s timing to slip.[3]
Further, my experience has taught that an attention to the entire six seconds indeed as one unit, separate from the subdivisions, can help to pinpoint the exact length. At one nears the end of the duration, before it is time to clap on the beat, shifting attention to the whole can give a perspective that leads to adjustments that achieve better results.
The challenge for the pianist to perform the etude live with the metronome clicks showing only each downbeat, is herculean. While the performance below by Laurens de Boer is excellent, we can witness some effects of time distortion in various spots. On the surface it may seem that this piece is about success and failure, but there are many more elements being explored. For example, the contrast of silence and flow, the use of increasing tuplets to create more notes per measure, the rhythmic, melodic and harmonic stories of the piece, the difference between human timing and machine timing, etc... While the metronome explicitly articulates the meter, the player also has to keep track of all of these elements in the live performance also adding to the difficulty.
There are of course, many other factors which influence our sense of speed such as our emotions, body temperature, age, and if we have enough oxygen (Hammond 2013: 43). As a woodwind player I have become acutely aware of how running out of air during a long phrase can create a sense of urgency and unknowingly increase the musical speed.
Through practice and combining the four techniques mentioned above, the confidence can emerge that it will be correct.
I began to experiment in my music and teaching with tempo ranges under 40 bpm and found some interesting possibilities in tempo 10. 10 beats per minute equals a pulse every six seconds and I created the following exercise: students in a circle, clapping one after the other on the beat, together with the metronome.[2] While many people can do this reasonably well, it turns out to be a very difficult exercise to do perfectly, even for trained musicians. Perfect is when the metronome is rendered inaudible by clapping exactly in sync.
In order to do the tempo 10 exercise one must traverse the six seconds by breaking it up. It is not possible to feel such a long duration accurately as a single unit. According to Marc Wittmann, "the brain's capacity for temporal integration, which is what combines stimuli from the environment into units, has a maximum duration of three seconds." (Wittmann 2017: 39-58)
3. Neuroscientist David Eagleman demonstrates small timing slips with this exercise: “Go look in a mirror. Now move your eyes back and forth, so that you're looking at your left eye, then at your right eye, then at your left eye again. When your eyes shift from one position to the other, they take time to move and land on the other location. But here's the kicker: you never see your eyes move. What is happening to the time gaps during which your eyes are moving? Why do you feel as though there is no break in time while you're changing your eye position? (Remember that it's easy to detect someone else's eyes moving, so the answer cannot be that eye movements are too fast to see.)” (Eagleman 2009: 155-169)
In the context of the dual nature of time, this means that an exact six second interval cannot be embodied as a single smooth whole, but must be subdivided. To do this, we create a grid in our minds of six (one per second: 60 bpm), eight (80 bpm) or other number of equal divisions in order to traverse the temporal distance. Indeed, without explaining this in the classroom, students almost always subdivide on their own accord when encountering this exercise for the first time.
The task is then twofold: 1. adjust the speed of the subdivisions so that the grid exactly fills up six seconds and 2. reliably maintain it. Performing these tasks accurately requires a mastery of one’s internal mechanisms for keeping track of time, known in music as one’s inner pulse. Developing the skills needed to do this exercise greatly enhances a musician's general rhythmic abilities for other musical situations.
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Delaere, Mark. "Tempo, Metre, Rhythm. Time in Twentieth-Century Music." Unfolding Time. Leuven: Leuven University Press, 2009. Print.
Eagleman, David. Brain Time, Edge (2009, June 23), retrieved from
https://www.edge.org/conversation/brain-time.
Eagleman, David. The Brain, Pantheon Books, 2015.
Eagleman, David. "Who Am I?" Brain: The Story of You. Vintage, 2017. Page 79.
Eagleman, D. M. “Brain Time.” What's Next? Dispatches on the Future of Science: Original Essays from a New Generation of Scientists. Ed. Max Brockman. Vintage, 2009. Print.
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Hammond, Claudia. "The Time Illusion." Time Warped: Unlocking the Mysteries of Time Perception. New York: Harper Perennial, 2013.
Human Speed in Music
Research, concept, text and media by Ned McGowan.
Technical realization of Beethoven's Ninth Symphony expanded & compressed by Bas Bouma.
Title drawing by Bas Bouma. Layout and design by Bas Bouma and Ned McGowan.
2. This exercise was inspired by exercises in Dalcroze eurhythmics classes at the Cleveland Institute of Music with David Brown.
Harding, Rosamond E. M. The Metronome and it's precursors. Gresham Books, 1938. Print.
Hunt, A.R. “Taking a long look at action and time perception.” Journal of Experimental Psychology, Human Perception and Performance, 34(I) 125-136. 2008
McGowan, Ned. "For Crying Out Loud". One Minute More. Guy Livingston, piano. Transatlantic DVD 001; 2009. Track 60. Audiovisual recording.
McGowan, Ned. Tools. 2003. Ensemble Hexnut. The Netherlands: Donemus. Print.
McGowan, Ned. Workshop. 2004. Susanna Borsch, recorder. The Netherlands: Donemus. Print.
McGowan, Ned. Volt. 2015. Diamanda Dramm, violin. The Netherlands: Donemus. Print.
Neely, Adam. "What is the fastest music humanly possible?" Online video clip. https://youtu.be/h3kqBX1j7f8. Accessed 11 July, 2018.
Roads, Curtis. Microsound. MIT Press, 2001. Print.
van den Heuvel, Martijn P. And Olaf Sporns. “Network hubs in the human brain”. Trends in Cognitive Sciences, Volume 17 , Issue 12 , 683 – 696. Elsevier. 2013
Watts, Fraser N., and Robert Sharrock. “Fear and Time Estimation,” Perception and Motor Skills 59. SAGE Publications, 1984. https://doi.org/10.2466/pms.1984.59.2.597
Wittmann, Marc. "Felt Time: The Psychology of How We Perceive Time." Trans. Erik Butler. Cambridge, MA: MIT, 2016.
Zipper, Hillary. "La Serenissima." One Minute More. Guy Livingston, piano. Transatlantic DVD 001; 2009. Track 10. Audiovisual recording.