I have one request: if you are going to comment on the paper, please actually read it first. Here is a little test to check that you read it: did you notice the points below?
(1) This is a paper in the field of Computer Science. Having studied music all of your life, even at Berklee, does not qualify you in Computer Science, so be open to learning what Computer Science is. In science we have a practice of making the simplest model we can from which emerge the observed measurements. Hence the remark by Feynman quoted near the top of the paper on how to know when you are right:
"When you get it right, it is obvious that it is right -- at least if you have any experience -- because usually what happens is that more comes out than goes in. Your guess is, in fact, that something is very simple. If you cannot see immediately that it is wrong, and it is simpler than it was before, then it is right. The inexperienced, and crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought."
Many of you seem to like very complex explanations of harmony. Note that Feynman is saying that is not an indication of a theory being right.
(2) This problem has not really been solved before. Even someone like Daniel Levitin was convinced (the last time I spoke to him) that Helmholtz had the correct theory of harmony. However, as I point out in the paper:
* The American Acoustical Society has a collection of experiments, one of which they say (not just me), proves Helmholtz's theory is wrong.
* If Helmholtz is right, playing multiple notes always sounds either a little worse or a lot worse, but never better, and so we would never play two notes at the same time at all; harmony would not exist and there would be nothing to explain.
(3) There is strong evidence for the absolute nature of auditory processing that is not only cross-cultural, but cross-species. In the paper, there is a quotation from Daniel Levitin's book "This is your Brain on Music", where he discusses an experiment he witnessed in graduate school where music was played through wiring directly into the brain of an owl. The music was played into the brain with the root removed; when coming out of the brain of the owl, brain had restored the root (see the paper for details).
That means that virtual pitch (1) is created by the structure of the brain, not by a cultural expectation, and (2) further, that it is created by the brain of, not just a human, but of an owl! This is a very strong argument for the assertion that the processing of sound and the artifacts thereof are quite universal.
(4) The explanation of the experience of the minor triad in "Harmony Explained" requires the concept of an inconsistency arising from a redundant recognizer algorithm. Being a musician does not make you an expert in recognizer algorithms and their emergent artifacts, so read what that is before you comment.
The theory of the minor goes like this: two redundant recognizers exist in the brain. When hearing a minor triad:
* one recognizer fires, that of the conjunction of three pairwise intervals of tones,
* whereas another recognizer does not fire, that of the triple of tones in order.
This combination of firings is inconsistent because it is not possible for it to occur by playing any single normal harmonic series on, say, a flute. To generate it, one must play multiple notes and then use the effect of the recognizer of intervals pairing up tones from across the notes. That is, this is a new kind of auditory perception that can be created as an artifact of the auditory recognizer algorithms of the brain, but cannot be heard otherwise.
If you object to my assertion that minor triad is well-described as "I recognize it, but something is wrong", try reading the explanation in the paper of the same phenomenon in visual perception called cubism. Say what you will about the minor triad, when you look at Picasso's "Head of Woman" (provided in the paper), does it not disturb you? Would not not describe it as "I recognize it, but something is wrong"? Does your objection to the analysis of the minor still stand in the context of visual art?