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I was wondering if there is some kind of music instruments taxonomy or quantitative/qualitative sorting based on richness of sound or other comparable timbre characteristics. I realize that timbre quality of an instrument varies according to register, articulation, and other performing parameters (and as such it is quite complex to define or measure), however I was wondering whether a rough and generalized "tabular" arrangement still exists.

FYI: I am not interested in literature on MIR classification algorithms, only in a (pre-existing) arrangement of music instruments based on such characteristics.

Thank you in advance for any feedback you could provide! Best, Ilias

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    I wonder if the title could say "...based on timbre" rather than specifically "richness"; richness sounds like rather a subjective word and isn't often used for precise description of timbre. – topo morto Dec 24 '17 at 9:14
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    I'd have to agree with you topo. There is no taxonomy based on richness, and in fact there can't be one because richness is not defined. – Doktor Mayhem Dec 25 '17 at 0:18
  • Thank you for your comments! I am approaching the topic from a high-level perspective, and I was wondering whether someone has attempted to categorize richness, even from his/her own "subjective" perspective. If you are aware of another taxonomy on timbre in general, I would be happy to know. – Ilias Kyriazis Dec 27 '17 at 9:43
  • There is probably some sort of trade-off between precision and usefulness. The most precise way to differentiate timbres is by looking at the full overtone spectrum, but this is not very useful. More realistically, if you compose for traditional orchestra (say), you learn enough about the timbres of the individual instruments to make well-informed decisions. What exactly is it that you want to use this classification for? – Remy Jan 6 '18 at 2:24
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Researchers like Grey, Moorer, Strawn, Gordon, pioneered this kind of stuff. I forget the exact source but I recall an article where they placed all orchestral instruments on a 3-d graph, linked together by certain timbral features. This article is probably a good place to start... work backwards from the bibliography at the end.

http://cnmat.berkeley.edu/sites/default/files/attachments/Timbre-Space.pdf

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Sounds like you might actually be looking for a reference on orchestration. This deals with how the sounds that an orchestra has at its disposal can be put to use to express any aspect of a composition. As an example of an orchestrational choice, if you want to express something more introspective, you might want to give the solo to a flute instead of a trombone.

What you're asking might also not really be worth doing, since "richness" is often achieved with instrument combinations. This video might be an interesting watch, as one of the goals the creator is going for is richness:

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