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Is there a study of harmonic implications of an instrument's timbre in western music theory?

For example: If i use an instrument with a "rich" timbre, with lots of overtones, then isn't the sound more prone to "cluster" if i play a set of notes(worst if near each other)?

From this perspective, can we consider a specific timbre to be a unique kind of chord?

Thanks

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    I'm not sure about any other instruments, but this is definitely a factor in electric guitar when effects are used to change the timbre. When you use a distortion effect on electric guitar, you're basically adding a huge number of overtones, and yes, if you play full triads or especially 7th chords with no notes omitted, the sound can get very muddy. That's why "5" chords with only the root and 5th are popular in distorted (and clean) electric guitar parts. Certain distorted timbres can have an almost chord-like sound. – Todd Wilcox Jan 20 '16 at 1:07
  • @ToddWilcox good point - I didn't deal with distortion in my answer, but it makes the maths a lot more complex as it introduces sum and difference frequencies (such that a distorted chord can have frequency components lower than the fundamentals of any of the notes in the chord!) – topo morto Jan 20 '16 at 1:11
  • @topomorto One could question whether electric guitar effects can be properly considered to be contributing to "timbre", depending on one's working definition. – Todd Wilcox Jan 20 '16 at 1:13
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The most commonly-quoted theory on how the timbre of a sound affects consonance/dissonance is Helmhotz' proposition that beat frequencies between the individual partials of notes cause dissonance, and the coincidence of partials resulted in consonance. This was later expanded on by Plomp and Levelt's findings (for example, that dissonance is eliminated when pure tone components are separated by a distance greater than the critical band.)

These findings don't suggest an entirely simple relationship between the harmonic structure of a sound and the amount of perceived dissonance; it depends on the exact shape of the chord played, and the register in which it is played. The temperament of the scale used also has an effect; this can be especially noticeable when using very pure, sinewave-like tones with very few higher harmonics. It's also important to consider that the harmonic structures of notes played on most instruments typically aren't static; The speed with which each harmonic decays also affects the perceived timbre of each note, and hence, the nature of harmonies of chords played with those notes. A newer model of 'roughness' suggested by Vassilakis takes into account fluctuations in the amplitude of individual partials.

http://www.music-cog.ohio-state.edu/Music829B/main.theories.html is a good list of theories for consonance and dissonance (not only relating to harmonic structure).

You ask can we consider a specific timbre to be a unique kind of chord - it's certainly the case that the timbre of the sound used changes the perceived flavour of the chord, sometimes to the point that harmonies that subjectively 'work' with one instrument don't work with another.

Theoretically, it's possible that one note of a certain timbre might have exactly the same frequency spectrum as two notes each with sparser harmonic structures. To this extent, harmony and timbre are not entirely separate studies.

  • Could you refine the statement of critical bandwidth? The dissonance curves that I have seen in publications are much broader than a third, which fits to my own experiments. – Tobias Schlemmer Jan 22 '16 at 0:25
  • @TobiasSchlemmer I guess mpi.nl/world/materials/publications/levelt/… ('Tonal Consonance and Critical bandwidth') would be the more original source. – topo morto Jan 22 '16 at 1:01
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Additional to the answer from topo morto I'd like to mention the book “Tuning, Timbre, Spectrum, Scale” from W. Sethares [1]. Beside others, it describes the construction of scales and tone systems for timbres with inharmonic spectra. Even though it is mainly a place theoretic approach I don't see any reason why it shouldn't work also with a theory based on neural correlation. For the latter Martin Ebeling developed an interesting consonance theory [2,3].

Moreover all studies about tunings relate to the timbre. The old hypothesis of small integers is roughly linked to the timbre of western instruments. It is hard to tell whether the Pythagorian theory of just intonation is the reason that western music is a mainly a on-dimensional thing (I mean the geometry of the sound generating devices: strings, tubes, reeds, …) or if there is a natural background behind that. All instruments of an orchester that have inharmonic spectra belong to the percussion group, which is not covered by western music theory. So there is a strong relationship between the timbre and the music theory.

If you think into the opposite direction, tuning theories are linked to the topic, too. The most prominent feature of a tuning is that it shapes the timbre of chords. The predominant tunings had always an influence on composition and music theory. A well known example is the usage (or avoidance) of the wolf fifth. In the direct comparison a Praetorius piece sounds more vital when played on meantone than on 12tet. This subtile difference may be noticed in a performance even by amateurs, who wouldn't hear any difference in a theoretical demonstration.

[1] Sethares, W. A. Tuning, timbre, spectrum, scale, Springer, 2005

[2] Ebeling, M. Neuronal periodicity detection as a basis for the perception of consonance: A mathematical model of tonal fusion The Journal of the Acoustical Society of America, ASA, 2008, 124, 2320-2329

[3] Ebeling, M. Verschmelzung und neuronale Autokorrelation als Grundlage einer Konsonanztheorie Lang, 2007

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Your question is beautiful and I think there will be more science and research behind it thanks to the advent of the Spectrogram (where you can visualize all the frequencies engaged for a particular sound).

Timbre and harmonic invokation are synonymous to me because when you trigger a string on a guitar or piano, or engage a flute's resonant chamber, you are engaging a whole system which somehow (miraculously) produces sound.

Can we consider timbre to be a specific type of chord?

Certainly. Look at a spectrogram when you play any note and you'll see that many frequencies are engaged.

If i use an instrument with a "rich" timbre, with lots of overtones, then isn't the sound more prone to "cluster" if i play a set of notes(worst if near each other)?`

Well effectively, it's hard to say, some get more pronounced, some frequencies get "buried" in the background. In general, the harmonic engagement of a sound is spaced such that there are many higher (and some lower) octaves engaged. When you start making music that is more than an octave or two apart, the lack of harmony or dissonance that is readily apparent at adjacent notes becomes pretty unnoticeable. Consider a major 7th, it's not even a whole octave away but still sounds pleasing, but if you played a B next to a C, you would hear dissonance. Almost an octave away and it becomes pleasant and beautiful. So the harmonic engagement / distance that they exhibit is a big deal, and that lack-of-same-octave-overlap makes it so that the sounds are just fine.

Could there be lots of clustering? Well yes, consider a piano with the sustain pedal engaged. You start rumbling on a low note and go a few octaves higher.. Eventually the whole resonant body will go wild and you'll get dissonance, but that can also be a desired effect.

So your question,

harmonic implications of an instrument's timbre

Is best examined through a visual representation, like that of a spectrogram. Soon there will be tools to analyze intervals clearly. As far as I know there is no in-depth study of these things, but in the end it comes down to listening.

Just wanted to chime in with my thoughts so far, as it's been a topic of interest for me lately as well.

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