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Here is an excerpt from Introduction to the Study of Musical Scales by Alain Danielou. The important part is in bold. I included the rest of the passage only to provide context:

It is the loss of this pedal point of the tonic, somewhere in the course of ages, which renders the modes of plain-chant so vague and so weak. They lack a basis, and their classification becomes a rather abstract game, like the system of the Greek Doris! i in the unreal form generally attributed to it. It is by an artificial conception that a mode can be assimilated to the plagal 9 form of another mode. The melody remains unaffected and in the tone of C (Sa), because, to determine a tone, a permanent element is required, and habit can, up to a certain point, create this permanence in favor of C (Sa): that is, in favor of the western major mode, supposing that we are still using only the white keys of the piano. Another mode can be determined only by constantly imposing its tonic. Percussion instruments, such as drums, cymbals, etc., can be sufficient to determine this tonic. This is why, in ancient music, the problem did not arise, as such instruments were always present in a musical performance. The accurate tuning of the different notes of the scale should, of course, be sufficient to define the tonic, but, as the differences in intervals are very small, rare indeed are the musicians who can maintain this accuracy without referring constantly to the tonic.

Do cymbals as well as other “unpitched” drums actually have a pitch?

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There's no debate, there's a whole spectrum from almost unpitched to clearly pitched (e.g. timpani, marimba). There are a lot of weakly pitched instruments in the the middle (e.g. tomtoms: there are high and low toms even if the exact pitch is not clear). There's probably no such thing as a completely unpitched percussion instrument: even with an instrument like a snare drum, some instruments will have more high frequency components than others.

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Many percussion instruments either produce many harmonically unrelated frequencies simultaneously (such as a snare drum) or produce frequencies that change significantly with time (e.g. a tom tom). It's possible for a set of such instruments to have frequency spectra which seem to have a definite intervals between them, but not have pitches that can be compared with instruments that produce a steady set of harmonically related frequencies. One could, for example, have a set of tom toms that were tuned and could play recognizable melodies, but be incapable of establishing a key center that would be applicable to another instrument such as a flute.

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    Y'all'd better be watching me for the changes.
    – Mazura
    Oct 12, 2023 at 2:44

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