Harmony Explained: Building a Scientific Theory of Music
Harmony Explained: Progress Towards a Scientific Theory of Music (2012)
I argue that most music theory books rely on superstition rather than science. By combining physical sound phenomena with how the human brain processes audio, I derive the Major Scale, the Standard Chord Dictionary, and the emotional difference between Major and Minor Triads. This work challenges Hermann Helmholtz's 19th-century theories, showing that his logic would actually make harmony impossible. My goal is to offer a clear, scientific explanation accessible to both researchers and curious musicians.
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases.
- klik99
I read through a lot of this article and it does a good job explaining the ratios and math behind harmonics and how that makes chords, but ideas like lower ratios are more pleasant and minor chords feel like something is missing (from the article "I do not hear the Harmonic Series itself -- something is missing") is just wrong - if it was right, then the happiest music would be entirely octaves. Though it's built on harmonics and overtones which can be explained objectively, you cannot make a fully scientific theory of harmony since cultural expectations factor in just as much (and maybe even more) than the expectations around harmonics. Music is pleasurable when it mostly meets expectations but surprises you as well, IE it sits just outside of what we expect. It then becomes part of what you expect in the future and music evolves.
Ultimately minor sounds sad because it's been used that way for a long time and it's what we expect. I was listening to Trout Mask Replica and my wife said it sounded like her home town funeral music (I later heard some myself and yeah she was right) - Captain Beefheart doesn't sound sad to me, but it does to her. The funeral music uses major 5 note scale.
And on "But I've Been a Musician All My Life / Studied Music In College and I've Never Heard Any of This Before!" - ratios and how chords derive from that was absolutely part of my education at Berklee. This article is good for the objective parts, but really self-congratulating for the subjectiv […]
- simonreiff
I studied harmony and music analysis many years ago as a piano performance major in school. One thing I will say is that harmony really is not an abstract set of symbols on a page representing chords, but rather is a taxonomy of common specific sequences of simultaneously sounding pitches, abstracting away instruments or larger structural considerations and providing a dictionary that defines the most common patterns. Here's an example: Perhaps you're familiar with the idea of major and minor, but you might be unfamiliar with a Picardy third, where a composition is in a minor ("sad") key throughout but ends in that same pitch but on a major ("happy") chord. J.S. Bach used Picardy thirds regularly to end his compositions, but the Picardy third became rarer after Bach's death. Still, it's a beautiful and striking harmonic progression that continues to appear now and then. And now you know EXACTLY why that 1967 song by the Turtles, "Happy Together", has that really nice and memorable ending; that's a modern pop example of a Picardy third. Again, harmony is not abstract; it's the names musicians have given for specific sequential combinations, many of which have been named centuries ago. It's not about nicer or worse; sounds are sounds, but some are combined more often than others and those combined most frequently have well-known names that can be used to explain concisely the "harmonic" aspect of a piece of music.
- TheOtherHobbes
There are much better overviews of this from Sethares and Tymoczko.
Consonance is somewhat frequency-dependent. For more, Google Critical Band and ERB.
The happy/sad idea is pretty much a high-school oversimplification. It's true for beginners, not at all true beyond that.\
It's quite rare to find music with straight major and/or minor triads with no other colours.
- okzgn
The logic that something sounds worse simply by combining dissonant notes is questionable, because music constantly combines elements—notes, chords, even different rhythms—without that necessarily implying displeasure for the listener. Convincing.
- PaulDavisThe1st
I personally consider this to be a better intro, albeit in video form:
https://www.youtube.com/watch?v=tCsl6ZcY9ag
This is a more recent paper (2019) that I think is better constructed and more aware of the in-field work than TFA:
- danbmil99
I think the most fascinating thing about music (from a mathematical/scientific perspective) is the fact that the principal harmonics of equal temperament are so close to the mathematical ideals. Fourths and fifths are so close trained musicians typically cannot hear the difference. Major thirds are farther from the ideal but still are less than 1% off. That can be heard by the trained ear, but in the real world there are chorus effects (multiple voices/instruments at nominal but slightly varied pitch), vibrato, reverb etc. such that in most cases a just major 3rd sounds fine.
Without just temperament, we would never have had "The Well Tempered Clavier", Bobby Daren's "Mac The knife", and basically all of western music from the baroque period on.
- vikramkr
Awfully dismissive of non western tonal harmonic systems for a universal theory of music? The whole idea that musical traditions that use less harmonic structures just haven't unlocked all the structures available is kind of absurd - those musical traditions have been developing for the same amount of time - and there's a pretty huge blind spot for other traditions. The whole microtones just being ornamentations - no that's absolutely not the case. Trying to ignore/hand wave away all the counterexamples and force them into your system is how you get epicycles. If you're gonna do a universal theory of music it would be a good idea to engage deeply with more than one system. As a universal theory of harmonica maybe that's fine but it's sloppy and motivated reasoning
- toolslive
I only skimmed the article. There's a lot of good stuff (debunking a lot of classical harmony) but they miss some important things too.
There's nothing about repetition. Repetition legitimizes.
Our brain is really good at pattern recognition, and as soon as it can predict something you're more than half way there to make it sound good. There's plenty of chromaticism that works because the brain "gets" the sense of direction.