I hear the term get thrown around a lot, and it seems pretty nebulous. Usually, it's invoked under the heading of tone, but I've heard it linked to intonation and a handful of other categories. At the physical level, though, how do the waves of a "bright" tone differ from those of a "dark" tone? Does a unit exist(or can an existing unit be re-appropriated) to describe brightness? Thanks for the help.
Brightness is somewhat subjective but relates to the harmonic content of the tone. Tones having strong higher harmonics tend to be perceived as brighter. This is easy to demonstrate at the organ using our various octaves, superoctaves, mixtures, and so forth.
Note that what is important is the relative strength of the harmonics, not merely the presence of a large number of noticeable harmonics. When you examine spectra, look not for a great number of harmonics but for the relation of their amplitude to the fundamental. For example, at the organ, we have string pipes whose spectra show that harmonic content is significant up to at least thirty harmonics. However, these stops are not perceived as especially bright because the strength (relative amplitude) of the harmonics is not dominating the fundamental.
Intuitively I would answered units of brightness are the pitch, the loudness, the amount of treble in a sound opposite to the bass, overtones or harmonics of an instrument and the envelope and timbre. These units can be objectively measured.
I would agree that that therefore also aspects as the istrumentation, the speed, the gestures of the conductor, the interpretation of the orchestra, the tune and its elements are influencing our subjective concept of brightness.
To find evidence for my answer I looked up terms as tone, Klang, timbre and found that brightness is an aspect of tone quality but it is not clearly defind.
So a spongy term is defined by another spongy term, however you find physical formulas that most people can’t understand.
In a German link about Klang it is said that this term has ti be differentiated of sound.
Theres an ASA of timbre saying:
The Acoustical Society of America (ASA) Acoustical Terminology definition 12.09 of timbre describes it as "that attribute of auditory sensation which enables a listener to judge that two nonidentical sounds, similarly presented and having the same loudness and pitch, are dissimilar", adding, "Timbre depends primarily upon the frequency spectrum, although it also depends upon the sound pressure and the temporal characteristics of the sound" (Acoustical Society of America Standards Secretariat 1994).
This link is quoting Erickson (1975, 6) who gives a table of subjective experiences and related physical phenomena based on Schouten's five attributes:
Other answers have missed that brightness is completely objective.
(But it usually doesn't need to be precisely measured, so we speak of it rather imprecisely)
Ultimately, in every sense of the word, "brightness" is higher frequency. A sound that is brighter than another is higher in frequency in some way, whether the description is literally of a higher fundamental frequency, or whether the timbre of the sound is more concentrated in upper harmonics, or the chord has one note raised, or whatever. Adam Neely has a great video on this subject,
in which he notes brightness of chord qualities. He argues that an augmented chord is objectively brighter than a major chord, and from that he makes the case that brightness has nothing to do with consonance or dissonance. In terms of chords and scales, when a note is raised in comparison to a standard, it is brighter, and the other way around is darker.
When modulating to new keys, adding sharps is brighter, paying attention to enharmonics (E-F is a whole 7 sharps brighter, as every note moves up).
The unit for brightness would depend on the context; when modulating to a new key, obviously one would talk of a "3-flat modulation" or "2-sharp modulation". In timbre, one commenter mentioned the Centroid frequency, which I imagine is a measure of central tendency of intensity at different harmonics. (Basically, average of overtones)
It's important to note the importance of this quantification of "brightness"; namely, it's limited. It's never very important to measure exactly how bright something is, it's usually much better to just say something is brighter than something else.