A good overview on the topic. My general issue with things like these is the simple fact, that as a lifelong musician I find the "less worse" harmonic combinations (to quote the abstract) often very boring. Aside from great composers like Bach et al I find the harmonic relationship of the notes played one of the least interesting aspects of the music, and expression, timbre, rhythm, phrasing much more important and n…
Have you read Sethares' Tuning Timbre Spectrum Scale book or the shorter paper? It gets right in on the topic of the interrelationship between timbre and dissonance. As you say, the timbres of the instruments are very important to how dissonance is or isn't experienced by the listener.
I have to highly recommend the book 'Fundamentals of Musical Acoustics' for mathematical/physical explanations of sound and music. Bells having multiple resonant modes, tuning kettle drums, how string materials and plucking methods changes harmonic profiles, why having lots of high frequency harmonics sounds bright (and electric guitars, pianos optimise for this), why sounds without high frequency harmonics sound hol…
Are you talking about "Fundamentals of Musical Acoustics" by Arthur H. Benade? I'm interested in buying the book, but I'm not sure which one you mean. Do you perhaps even have the ISBN?
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 subjective/experiential part of it.
A good overview on the topic. My general issue with things like these is the simple fact, that as a lifelong musician I find the "less worse" harmonic combinations (to quote the abstract) often very boring. Aside from great composers like Bach et al I find the harmonic relationship of the notes played one of the least interesting aspects of the music, and expression, timbre, rhythm, phrasing much more important and n…
Also a lifelong musician here, and I think you're completely wrong about harmony. Western music (assuming that's what we're talking about here) IS directly derived from harmonic progression. It is truly the core of the music. The underlying chords are the obvious harmonic progression. Melody is just an expression of underlying harmonic structure. Rhythm is meant to emphasize the changes and movement of harmonic structure. Timbre itself is meaningless without a note to carry it, and a note is meaningless without the harmony it implies.
All of the many parts of western music serve the harmonic progression. This is because human emotion attaches itself most strongly to harmonic progression, and music is the art of manipulating human emotion through sound.
>A set of great musicians can play a single note for minutes and get it to sound amazing, this has always fascinated me more.
Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
Half joking, but Berlin techno :) You can have a whole set developing motifs, then multiple minutes of a single note being played in the middle, and somehow that sounds awesome (if you’re into it)
A long hold of one note doesn't mean there isn't harmonic progression. It just means the progression is slow in that part of the song. It's often done to create a massive contrast that occurs when the progression finally...progresses. In electronic music, this often comes as the drop or some similar kind of break.
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.
A good overview on the topic. My general issue with things like these is the simple fact, that as a lifelong musician I find the "less worse" harmonic combinations (to quote the abstract) often very boring. Aside from great composers like Bach et al I find the harmonic relationship of the notes played one of the least interesting aspects of the music, and expression, timbre, rhythm, phrasing much more important and n…
Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
I can only think of examples which as you describe have accompaniment moving underneath. Neil Young's solo in Cinnamon Girl is one example. Another is Bob Dylan's Like a Rolling Stone in which he sings one note as the chords run up C Dm Em F and only breaks on the G.
Do you have any examples of "a single note for minutes and get it to sound amazing"? I'm finding this difficult to imagine. A lead voice doing this while some accompaniment is changing chords underneath makes sense to me, but then you're back to harmonic relationships.
Half joking, but Berlin techno :) You can have a whole set developing motifs, then multiple minutes of a single note being played in the middle, and somehow that sounds awesome (if you’re into it)
Not quite one note, but "Open Eye Signal" (2023 remaster) by Jon Hopkins has wide spectrum background and heavy rhythms, but once the song gets going the main instrument moves between fifth -> seventh-flat -> sixth -> fifth on repeat, and that's the melody for the song. And yet, to me, it's captivating.
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.
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.
"Worse" is definitely a subjective appreciation influenced by culture and personal taste.
In the 00s, I sang in the Holy Name Cathedral choir and we did a lot of 20th/21st century choral works with harmonies that strayed very far from the classical tonal vocabulary to the point where when I was doing my own composition work, I realized that I didn’t hear dissonance any more.