No, wavelength is just one more dimension along which intensity may vary (in addition to X, and Y, and time), not five or six more dimensions, so a multi-band image is only three-dimensional, regardless of whether there are three wavelength bands (like RGB or YCbCr), four (like RGBA), 8 (like Landsat), or 210 (like HYDICE, AVIRIS, and other imaging spectrometers).
My point is, I am comparing temporal dimension to temporal dimension regardless of how many special dimensions there are. And I don’t understand the argument that an audio sample is more analogous to a pixel that it is a frame on a time line.
In particular, in data processing, all dimensionality is equivalent, since and infinite set S the same cardinality as S^n for any whole number n, and any finite set is smaller than the 1-dimensional set of naturals.
Yeah, at least if Hilbert spaces can fuck off, which is why we can approximate signal processing on digital computers at all. And, because of space-filling curves, in some sense ℝⁿ is equivalent to ℝ. But, to understand signal processing, a much more useful point of view is that ℝⁿ is significantly different for different values of n, but not completely unrelated; and ℤⁿ is a useful approximation of ℝⁿ, as is (ℤ/mℤ)ⁿ.