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 noteworthy. A set of great musicians can play a single note for minutes and get it to sound amazing, this has always fascinated me more.

Music theory IMO has historically a too strong focus on the harmony (or the lack thereof) between notes. Not that it isn't important, but with some texts you get the feeling it wouldn't matter to the authors whether the piece was heard expressively played on a grand piano or cut together from equal leveled sine waves.

In my experience harmonies are greatly influenced by the relative levels of the notes and the overtone content within each note, to a degree you can make a supposed "harmonic" chord sound bad and a supposed disharmonic one sound good.

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diydsp 3 hours ago | parent | next [-]

A professor taught us genre is defined by how you resolve dissonance...

And dissonance has cultural and physiological components...

And other traditions focus on rhythm over harmony...

That said this looks like a good introduction.

	▲	PaulDavisThe1st 3 hours ago \| parent [-]
		That's a great line from the professor. Really great. Also, other traditions focus on melody over harmony (e.g. Carnatic and Hindustani), although they have to consider harmony as a by-product of polyphonic music (i.e. more than 1 instrument).

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antonyt 3 hours ago | parent | prev | next [-]

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.

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dgellow 3 hours ago | parent | next [-]

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)

	▲	nwatson 2 hours ago \| parent \| next [-]
		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.
	▲	IAmGraydon 2 hours ago \| parent \| prev [-]
		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.

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NobodyNada 2 hours ago | parent | prev | next [-]

Adam Neely has an interesting video about one-note muisc, with some good (and bad) examples: https://www.youtube.com/watch?v=eSuK_5zW2iM

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klaff 2 hours ago | parent | prev | next [-]

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.

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brudgers 2 hours ago | parent | prev [-]

I'm finding this difficult to imagine

Maybe go on Youtube and listen to music that you might not be familiar with?

Cage, Schaffer, Stockhousen, Boulez are some composers in the tradition of European classical music.

If you go outside that tradition, there’s even more. Endlessly more.

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klaff 2 hours ago | parent | prev | next [-]

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.

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IAmGraydon 2 hours ago | parent | prev [-]

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.

Someone already asked, but give me an example.

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klaff 2 hours ago | parent | next [-]

>Timbre itself is meaningless without a note to carry it

I suppose that is literally true but I think of timbre (especially after reading Sethares who I mentioned earlier) as telling me about the notes that are brought along for the ride but aren't shown on the sheet music. It's well known that a distorted powerchord introduces a major 3rd (and not the 12TET major third) as well as a phantom or missing bass note and other higher notes which may or may not be perceptible in a given piece. Quite a bit different from what two flutes playing a root and fifth will give you.

	▲	IAmGraydon an hour ago \| parent [-]
		That makes some sense, but if you look at a spectrum analysis of any signal that isn't a sine wave (and specially for highly clipped signals like you mention here), they consist of many tens or hundreds of even and odd harmonics, which is what you're referring to here when you say a root/fifth chord under distortion produces a major third phantom note. In truth, it creates many, many phantom notes, and pretty much any instrument, even a flute, does as well. Yes, that's the timbre - the relationship of the harmonics that result from a waveform. That's the very idea behind additive synthesis, where the harmonic nodes are individually created from a series of sine waves. So I guess it could be said that a single non-sine note would produce a harmony (multiple notes with a harmonic relationship), but this is not the same thing as a harmonic progression, where that relationship would change.

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toolslive 2 hours ago | parent | prev [-]

Not a one-note solo, but Miles Davis's solo on So What is really minimalistic.