Comment by BigTTYGothGF
11 hours ago
I agree that there's a lot to be desired in the pedagogy of music theory, but this is pretty bad. There are so many little things wrong with it that if I started trying to address them all I'd be here forever.
Anybody interested in this stuff would be better off with something like Tuning Timbre Spectrum Scale (https://sethares.engr.wisc.edu/ttss.html) or Music a Mathematical Offering (https://homepages.abdn.ac.uk/d.j.benson/pages/html/maths-mus...)
Responses that say "If I started listing criticisms I would never finish" usually have none. Name 3.
I gave a couple in my other reply, the most damning (imo) was that you completely ignore the cochlea.
My biggest overall critique is that you start with the assumption that everything is an algorithm, that the brain works like a computer, and the world can be derived from that.
"To the intuition of anyone who has seen hardware designed it seems very likely that the brain is halving/doubling frequencies by many different powers of two in parallel and then running all of the results through the frequency recognizer at once. If any one matches, the harmonic has been found. If this were so, then tones (and notes) that differ from each other by a factor of two would sound very much alike. "
I don't see why I should care about a hardware designer's opinion on the matter any more than a clockmaker's or a dog trainer's.
"1.5.1 Timbre: Systematic Distortions from the Ideal Harmonic Series" I don't believe you ever mention how you want the intensities in your "ideal harmonic series" to be distribute, so why does changing the relative intensities to get timbre matter? If I have an ideal harmonic series with peaks at 220Hz, 440Hz, 880Hz, etc, what should its intensities be? Timbre also has to take into account the full ADSR envelope.
"That is, two notes (series-es of overtones) made by the same (kind of) instrument will be distorted from the ideal Harmonic Series in the same (or similar) way. This must be the case in order for an instrument or instrument kind to have a uniform, recognizable timbre"
If you get a guitar in standard tuning and play, say, the 5th fret on the 6th string it sounds different than the open 5th string, despite them both being the same 'A'.
"But The Nasca People Of Peru Use A Linear, Not A Logarithmic, Scale!" "Who knows what is going on with the linear scales of the Nasca. I suspect the following: Linear-scale flutes are easy to make ... This culture was small and isolated and so no one ever noticed harmony"
I checked the cited article (Joerg Haeberli (1979). Twelve Nasca Panpipes: A Study. Ethnomusicology, 23(1), 57–74. doi:10.2307/851338 ). Among the things I learned: (1) At least some of the pipes were ceramic (picture here: https://artmuseum.princeton.edu/art/collections/objects/1374...) (and the Brooklyn Museum claims that "hundreds" have been found: https://www.brooklynmuseum.org/objects/51700), this is not consistent with a culture that is just figuring things out (2) "Intervals close to the fifth, major third, minor third, and major second occur".