Course:PHYS341/Archive/2016wTerm2/ScienceOfMusicalRhythm

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Musical rhythm is the recurring pattern of strong and weak musical elements. It is hypothesized that the enjoyment of music comes from a certain balance of predictability and surprise, and that holds true for the rhythmic timing of elements as well as their melody and harmony. [1]

Fig 1: A man beating a Djembe drum. The timing of hits and rests determine a musical rhythm.

Rhythmic Imperfections

Modern music is primarily produced, mixed, and mastered on a computer using a DAW (Digital Audio Workstation). Thus, computer generated rhythmic patterns are perfect in timing, with each beat or elements occurring exactly on grid (an effect known as quantizing. An example of a quantized drum loop is shown in Fig. 2, along with an audio file.

Fig 2: A 120BPM drum loop that is completely quantized. Note how each drum hit is completely aligned with the grid. Media:QUANTIZED_DRUMS.mp3

This is why computer generated rhythms often sound unnatural and overly synthetic, they lack to the small deviations (which can also be defined as errors) in timings. These deviations in rhythmic timings create a human feel (or groove – cite groove wiki). The deviations are usually 10-20ms earlier or later than the beat, which sees like a minuscule amount of time but the effects it has on music are profound. [2]

Humanization Methods

Computer generated rhythms often sound unnatural, and thus methods are used by producers/composers to add subtle imperfections to the timing of musical events, an effect known as humanization. [3]

White Noise Humanization

The most commonly used (and easiest to implement) is what is known was white noise (WN) humanizing.[4] This usually adds random deviations to all timings – which is quite unlike the imperfections of a human drummer for example, and often results in a jerky rhythm that seems to contradict what the human brain expects. [5] An example of WN humanization is shown in Fig 3, along with an audio example of the same drum loop from Fig 2 (except with WN humanization applied).

Fig 3: A 120BPM drum loop with WN humanization applied. Note the large deviations in timing, which contribute to the jerkiness and synthetic sounding groove. Media:WN_HUMANIZATION_DRUMS.mp3

Long Range Correlation Humanization

An alternate humanization method is to use long-range correlation data, meaning that deviations are not independent events, contrary to how they are treated in WN humanization. [6] This is because the deviations in timing of a professional drummer are not totally random, there is a pattern that follows what is known as a power spectrum – the drummer is usually before the click of the metronome (on average 16ms before), but sometimes perfectly on beat, and sometimes late, in a cyclical or oscillatory pattern. The influence of a certain time-deviation on other beat deviations dies out over time, but they are not independent events. This phenomenon can be modeled as a sum of sines and cosines. [7] An example of LRC humanization is shown in Fig 4, along with an audio example of the same drum loop from Fig 2 (except with LRC humanization applied).

Fig 4: A 120BPM drum loop with LRC (f=50ms) humanization applied. The slight timing deviations are circled, and contribute to the groove. Media:LRC_50MS_HUMANIZATION_DRUMS.mp3


From survey results done to compare different methods of humanization, it is shown clearly that LRC is preferred to WN (survey). Among professional musicians, the preference for LRC was even more drastic than the average listeners'. [8] In fact is has been proposed[9], that perfectly quantized is perceived as music without distinguishable rhythm – and is “weak and inert”. There is evidence of an indistinguishable link between a musical melody or harmony and its rhythm. [10]

Mathematical Reasoning

As early as 1970, scientist and mathematicians have been analyzing music, and have found re-occurring scientific phenomena in modern Western music as well as classical pieces such as Beethoven and Mozart.[11] Musical pitch tends to follow what is known as a 1/f power spectrum, and it has been found that human rhythms also tend to follow the same fluctuations regarding time deviations [12]. Classical compositions, known to follow a 1/f pitch spectra were also found to demonstrate a distinctive 1/f rhythmic deviation spectra as well. [13] For sake of clarity, these classical pieces are written following a 1/f power spectra, which indicates that this phenomenon is not just perceived via slight deviations in timing, but is either written consciously or subconsciously into compositions to manipulate the listener's musical experience. This phenomenon sheds light on the complexity of human imperfections that define musical rhythm: there is a science to making musical rhythm, but it is complex and perhaps entirely subconscious.

Syncopation

Syncopation can be defined as larger deviations of beats being ‘on-time’, where musical elements will sound where unexpected by the listener. Syncopation can be perceived as somewhat of an auditory hallucination/illusion or can be a deliberate rhythm choice by the music producer/composer. Largely syncopated rhythms can lead to listeners inferring unsyncopated rhythms – for example a listener would still hear a 4/4 rhythm and infer the tempo even if all elements were completely syncopated. [14] Studies of syncopation have lead to the insight that the perception of rhythm is an interaction: the presence (or absence) of syncopation will project the presence (or absence) of a strong rhythmic presence. [15]

See Also

References

  1. ↑ Levitina D, Chordiab P, and Menonc V, "Musical rhythm spectra from Bach to Joplin obey a 1/f power law". PNAS Vol. 109, pp.3716-3720 (2012)
  2. ↑ Hennig H, Fleischmann R, and Geisel T, "Musical rhythms: The science of being slightly off". Physics Today Vol. 65 (2012).
  3. ↑ Fitch W and Rosenfeld A, "Perception and Production of Syncopated Rhythms". Music Perception: An Interdisciplinary Journal, Vol. 25 (2007).
  4. ↑ Hennig H, Fleischmann R, Fredebohm A, Hagmayer Y, Nagler J, et al. "The Nature and Perception of Fluctuations in Human Musical Rhythms". PLOS ONE Vol. 6 (2011).
  5. ↑ Hennig H, Fleischmann R, and Geisel T, "Musical rhythms: The science of being slightly off". Physics Today Vol. 65 (2012).
  6. ↑ Hennig H, Fleischmann R, and Geisel T, "Musical rhythms: The science of being slightly off". Physics Today Vol. 65 (2012).
  7. ↑ Hennig H, Fleischmann R, and Geisel T, "Musical rhythms: The science of being slightly off". Physics Today Vol. 65 (2012).
  8. ↑ Hennig H, Fleischmann R, and Geisel T, "Musical rhythms: The science of being slightly off". Physics Today Vol. 65 (2012).
  9. ↑ Ventura, M, "Relations between Melody and Rhythm on Music Analysis: Representations and Algorithms for Symbolic Musical Data". International Journal of Applied Physics and Mathematics, Vol. 3 (2013).
  10. ↑ Ventura, M, "Relations between Melody and Rhythm on Music Analysis: Representations and Algorithms for Symbolic Musical Data". International Journal of Applied Physics and Mathematics, Vol. 3 (2013).
  11. ↑ Voss F, and Clarke J. "1/f Noise in Music and Speech". Nature, Vol. 258 (1975).
  12. ↑ Levitina D, Chordiab P, and Menonc V, "Musical rhythm spectra from Bach to Joplin obey a 1/f power law". PNAS Vol. 109, pp.3716-3720 (2012)
  13. ↑ Levitina D, Chordiab P, and Menonc V, "Musical rhythm spectra from Bach to Joplin obey a 1/f power law". PNAS Vol. 109, pp.3716-3720 (2012)
  14. ↑ Fitch W and Rosenfeld A, "Perception and Production of Syncopated Rhythms". Music Perception: An Interdisciplinary Journal, Vol. 25 (2007).
  15. ↑ Honing, H, "Structure and Interpretation of Rhythm in Music". Psychology of Music, 3rd Edition (2013).
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