What Makes Music Sound Good? (2010) [pdf]
dmitri.mycpanel.princeton.edu
dmitri.mycpanel.princeton.edu
And he counts rhythms starting with zero. If you did this with any group of musicians, they would shout you out of the room. Imagine Mick Jagger yelling, "Zero, one, two, three!"
I'm not saying he doesn't have his reasons, but these sorts of things incline me to think he's not in the mainstream of musical culture. Which is fine, of course, but may be misleading to readers who think they're getting traditional musical information.
See his work on orbifolds: https://en.wikipedia.org/wiki/Orbifold#Music_theory
Does he mean two notes played at the same time?
Potentially they are useful in discussing theory in writing, potentially they are relevant when tuning using non-equal temperament. But knowing this distinction doesn't help you make music that sounds good. An ear trained pianist, for example, would not distinguish these two intervals, and I would argue that would not be a limiting factor to the quality of music they could produce.
or, perhaps to keep it within the artistic sphere, they're like https://en.wikipedia.org/wiki/Checker_shadow_illusion and other "same color" illusions -- they are technically the same, but taken in context they signify different things.
you would build different chords around them, you would play different melodies around them, etc. in other words, it's not just when writing them out in english that we treat those two intervals differently -- we treat them differently while using them during music
you are, of course, correct that many very competent musicians would not correctly name this distinction using the official theory terms. but that doesn't mean that they don't understand the distinction when using them in musical contexts, or that the distinction is not meaningful. plenty of professionals are experts at something without being able to describe it perfectly in words
Strictly speaking, you can't actually know the name of the interval until you see the written notes, although obviously you can make some educated guesses based on the standard practice of the music style.
He's being (purposely?)confusing here, but in context what he's saying is that you can't determine the names of intervals just by listening: i.e., you can't distinguish between an augmented fifth and a minor sixth just by listening to the two pitches.
> If you did this with any group of musicians
I think you mean any group of musicians in the modern western tradition. Not all traditions count the same way, or even treat numbers as a standard way of marking rhythm. I suspect that if you counted 1-2-3-4 to Sappho she'd just look at you funny and throw her lyre at you or something.
I'd like to be gracious and assume the author is using this weird phrasing to emphasize this universality of his points, but I honestly suspect he's being purposely obscure to emphasize his professorship.
Of course this makes way more sense because it drives home the connection between rhythm and modular arithmetic.
I think he means that when you hear a tritone you cannot say for sure whether it's an augmented fourth or a diminished fifth - the notation could technically be written either way. But usually, the "set of common conventions" that he mentions will make one "more correct" than the other.
According to his website, he's a Harvard and Oxford grad that's studied music. He's also a prof at Princeton in their music department (which is no small feat).
It's likely that he's using terminology that's more common in certain circles. If you get into music theory at the top-tier music schools and other high-end educational institutions, the way they talk about music is going to be different than how most practicing musicians talk.
I've always had problems with existing consonance theories along these lines, probably out of ignorance. I believe that consonance probably has something to do with partial relationships. But it always has seemed the existing theory regarding consonance and partials is half baked at best.
Harmonic sounds have partials at f, 2f, 3f, 4f, and so on. So let's take C and G, a perfect fifth. Will say f = C. So C's sawtooth has partials of
f 2f 3f 4f 5f 6f ...
G, at a perfect fifth, is 3/2 the frequency of C. So it has partials at
3/2f 3f 9/2f 6f 15/2f 9f 21/2f 12f ...
The only overlaps are 3f, 6f, 9f, 12f. That's pretty thin gruel given how fast these partials drop of in amplitude (for a sawtooth, a partial at xf drops off as 1/x)
Now consider E, a major 3 and also considered highly consonant. This is 5/4. So we have
5/4 5/2 15/4 5 25/4 15/2 35/4 10 ...
That's an overlap of just 5, 10, ... with a super fast dropoff.
Now consider Eb, a minor 3 and also consonant. This is, wait, Eb can't be approximated in rational values at all, um....
And if you just have sine waves, rather than sawtooth or whatnot, they consist of a single partial so there's never any overlap -- you're back to the pythagorean square 1.
For example, on a piano if you undamp but don't sound one C, by setting the key down gently and holding it, then strike the C an octave below, the higher C will start ringing quite audibly and add its own partials, the same happens also of course to a lesser degree if you say undamp the G an octave + 5th above the C you're striking. This happens all the time during normal piano playing, because pianists purposefully hold long-duration keys down, and the sustain pedal keeps undamped the notes already played.
It can also work in the "downward" direction for example on the violin where the open strings are E A D G with E the highest, the well known Vivaldi A minor concerto (eg Suzuki book 4) opens with shifting on that E string to eg 3rd position to play the A which is an octave higher than the open A string. To the extent you get this perfectly in tune, presuming a properly tuned violin of sufficient quality, the open A string ie an octave lower will start "ringing" as will the D below that to a lesser degree; and if you then subsequently damp those open strings, it changes the sound significantly. This "ringing" effect is quite important to violinists in developing their sense of tuning and calibrating exactly where to set their fingers.
The ratio of the partials creates waves of differing complexity and periodicity.
This makes the wave easier or harder to comprehend by the auditory system.
On speakers play a sine wave in the left channel and a sine wave of a slightly different frequency in the right channel. You'll hear a beat frequency due to the actual physical interaction of the two waves in the air.
Then do the same thing except using headphones with good isolation so each ear only hears one of the sine waves. You still hear a beat frequency even though the two waves are no longer interacting in their air.
Local Consonance and the Relationship Between Timbre and Scale
https://sethares.engr.wisc.edu/paperspdf/consonance.pdf
Informal explanation of the paper:
I wonder about this. Many folk musics have independently arrived at the pentatonic, and music in pentatonic is really quite jumpy. Listen to some jigs or reels and you'll be startled by how much the melody jumps around. In contrast, if you want to find very smooth melodic motion with long scale passages, approaches by semitone and so on, you'll find it much more in Bach than in folk or modern pop. So smooth melody might be more of a minority taste.
Or consider the song Axel F. It's pretty much the perfect pop hook, all producers dream of creating something like it and all listeners can instantly latch onto it. Yet it consists mostly of jumps, including a third, a fourth, a fifth, a sixth, and an octave.
The way I had the pentatonic scale explained to me (embarassingly recently) explains why this is so.
If you take all the chords of a given key, and then examine all the notes, and remove any note that sounds discordant with any chord of the key, the notes that remain are the notes of the pentatonic scale. (That's not 100% true, but it's close enough to true for rock 'n' roll.) What this means is, if you have a backing track that sticks to chords within the key, you can kind of noodle around in the pentatonic scale however you like, and it'll sound alright. For guitarists, this is like adding training wheels to your bike... suddenly, you're effortlessly making music, without crashing and burning, and all you're doing is sticking to the pentatonic scale. (Yeah, there's targeting chord tones, and following the changes, etc. but for a beginner/intermediate guitarist, the pentatonic scale is magic.)
Before youtube, the above information was rather hard to come by, I found. I played guitar for approximately 30 years before figuring it out via to youtube. I made a youtube video[1] covering what I deemed to be the salient points... I'm not aware of another single youtube video covering all these points, (though all the points are covered by many combinations of other multiple youtube videos).
Any property, in this case the rewarding effect of acoustic stimuli in humans, can be powerfully maximized. There must exist patterns in music-space that would have profoundly greater impact on human minds than those our low-wattage brains can find. So through a really powerful search and optimization process that can more efficiently explore remote, undiscovered regions of music-space, we could get musical stimuli more intense than anything previously imagined.
What these songs would sound like is the real mystery. Would they sound anything like the music we're familiar with? Would they lead to musical wireheading?
It also seems a bad idea to measure musical goodness by, say, how many times humans will replay a certain audio file. If you use this measure, I don't think you'll end up with what you want at all.
Because people listen to music for words and other sounds that are added to music.
Though he talks about the five properties, I tend to disagree with this generalisation - what I like at the moment really depends on my state of mind, mood, time of the day, and what I want to feel like after listening to a few songs. Sometimes I really get into songs with complex patterns and interesting time-signature changes, and at other times I simply settle with some Wes Montgomery. What sounded good to me this morning doesn't work for me now. What I disliked five years ago is something I keep coming back to today.
Age contributes as a very significant factor to what sounds good. Speed metal or power metal was "good" in my teens and twenties, but these days I need to be in a very specific mood with specific energy levels to even consider some Pantera or Megadeth. On the other hand, I can easily get into Sepultura ("Ratamahatta", "Roots bloody roots", etc.) even though they are often much heavier, because there's a kind of easy coexistence with their type of music that I find curious. There are other musicians I liked way back then, but you couldn't pay me money to listen to them today - even the same songs I had on repeat.
Perhaps the prof is on theoretically sound footing, I'm a layman in this field, but I can't experience what he describes.
https://eev.ee/blog/2016/09/15/music-theory-for-nerds/
(posted to hn 7 years ago https://news.ycombinator.com/item?id=12528144 )
Speaking as someone totally new to music theory, I found it quite interesting to arrive at this question.
Any examples of this? Amazing if true.