Phase transitions: The math behind the music

phys.org ^ | May 23, 2019

[BenLurkin]

balance between order and disorder, or entropy, he said.

"We can look at a balance—or a competition—between dissonance and entropy of sound—and see that phase transitions can also occur from disordered sound to the ordered structures of music," he said.

Berezovsky ... he's uncovering the "emergent structures of musical harmony" inherent in the art, just as order comes from disorder in the physical world. He believes that could mean a whole new way of looking at music of the past, present and future.

Berezovsky said his theory is more than just an illustration of how we think about music. Instead, he says the mathematical structure is actually the fundamental underpinning of music itself, making the resultant octaves and other arrangements a foregone conclusion, not an arbitrary invention by humans.

His research, published May 17 in the journal Science Advances, "aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems."

In other words, the same universal principles that guide the arrangement of atoms when they organize into a crystal from a gas or liquid are also behind the fact that "phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music."

The theory also speaks to why we enjoy music—because it is caught in the tension between being too dissonant and too complex.

A single note played continuously would completely lack dissonance (low "energy"), but would be wholly uninteresting to the human ear, while an overly complex piece of music (high entropy) is generally not pleasing to the human ear. Most music—across time and cultures—exists in that tension between the two extremes, Berezovsky said

[Lurkina.n.Learnin]

I like listening to Waylon even without the science.

[thoughtomator]

Consonance and dissonance are literally on the first page of your standard music theory textbook. I guess when you add the flowery language of mysticism that passes for physics these days, reciting something a first-day music student would learn now gets you grant money and press coverage.

[VietVet876]

I usually prefer to listen to Miles Davis’ “Tribute to Jack Johnson” instead of Coltrane’s “Interstellar Space”. Or sometimes to McLaughlin’s “Extrapolation”.

[Da Coyote]

“...flowery language of mysticism that passes for physics these days...”

Heh, good job of saying “I have no clue about math.”

A good many physicists are quite proficient in music. Check out the history of the great ones and you’ll find quite the opposite of Big Bang Theory (which I loved).

[ConservativeDude]

lol

[real saxophonist]

In college, I took an Acoustics class taught by a physicist.

Broke my brain.

[Steely Tom]

His research, published May 17 in the journal Science Advances, "aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems."

Lots of pleasant and useful things involve a balance between opposites.

Coke and Pepsi are a mixture of something sweet (sugar) with something pungent (carbonated water).

So is a Martini. And Worcestershire Sauce.

Many desserts combine something crunchy with something chewy.

A Japanese sword is a balance between hard/brittle and soft/supple.

A photon is stable balance between an electric field and a magnetic field, each locking the other in a little cage.

A negative-feedback loop is a balance between something that produces an action, and something that opposes that action.

The ancient yin-yang symbol captures this concept in a picture.

Certain aspects of love involve the interaction of opposites, both physical and psychological.

'How wonderful that we have met with a paradox. Now we have some hope of making progress.'

— Niels Bohr

[Rebelbase]

"He believes that could mean a whole new way of looking at music of the past, present and future."

For some it becomes the basis of their entire civilzation.

[dhs12345]

An observation while playing with pure sine wave tones — a simple G cord doesn't sound all that great. Actually, it sounds fake and fabricated.

There is a subtly that we all take for granted and enjoy are the very complex sounds that an instrument makes. Especially a nonelectric type — an acoustic instrument.

For example: the frequency distribution of a guitar is very broad and complex. It is the broad spectrum and complexity that makes it appealing.

[Karma_Sherab]

e the opposite of Big Bang Theory (which I loved).

WHAT!!!!
Are you saying that "Thor and Dr. Jones" isn't a classic?

[chajin]

Consonance and dissonance are literally on the first page of your standard music theory textbook. I guess when you add the flowery language of mysticism that passes for physics these days, reciting something a first-day music student would learn now gets you grant money and press coverage.

My first thought as well. I would add that since Euro-American music has been tempered, or intentionally made dissonant, in order to try to shoehorn the square peg of Pythagorean thirds into the not-quite-a-circle of fifths, the man's theory is already suspect. One would have to experience the complexity and true consonance of just intonation to begin to discuss the effects of audio wavelengths.

[BenLurkin]

Saw Miles Davis live in the early 70s. Somebody gave me the ticket. Went straight from work — sitting in my parking-lot uniform amongst nicely dressed jazz aficionados.

Miles Davis’ “Tribute to Jack Johnson”
https://www.youtube.com/watch?v=an7WPGZzStA

John Coltrane - Mars
https://www.youtube.com/watch?v=7MRo-sRmEUY

John Mclaughlin - Arjen’s Bag [Extrapolation (1969)]
https://www.youtube.com/watch?v=YUHhAkhXRSE

[Pride in the USA]

I though you might have something to say about the singer named Dimash in reference to this article.

[Mrs. Don-o]

My knowledge about music theory is scant (read: vanishingly little) but I often wonder about the types of music I like which have a bluesy sound, with the voices sliding up or down, not hitting the standard pitches.

I'm thinking of Amos Lee or Darrell Scott or even Liam O Maonlai doing this bluesy number called "Work Song" (funny to hear these Irish/Scottish singers sounding like they were on Beale Street!)

Very much worth the clicks.

Or anything with a slide guitar/dobro.

What is it that makes it sound --- I don't know. It melts my soul or something.

It sure can't be autotuned, can it!??

[VietVet876]

I was never able to catch Miles. Saw Coltrane in Paris in 1965 and McLaughlin in Philly in ‘73.

[DoodleBob]

While I like the article, it is worth noting that some of the more influential and powerful songs in Rock don't have this battle between consonance and dissonance.

I'm not a huge Beatles fan, but the song Tomorrow Never Knows gives you an indication of just how powerful one note can be. Further, the last 4/9 of Yes' Starship Trooper is basically the same chords over and over again but delivers one of the most powerful outtro in the history of rock (perhaps comparable to Green Grass and High Tides Forever, which interestingly clocks in at 9+ mins like Starship Trooper, and which also has an outtro lasting about 4 mins though with Green Grass there is a slight changup at the 9:04 mark).

I think the broader problem we may be facing as a society, is the advent of robotic-driven music. Labels are investing in 'artificial intelligence' that has taken advanced courses in music theory and what sells and doesn't sell, and this AI is cranking out new music. Will we not only become a society of humans using technology to help clean our kitchens, wake us up, and make our coffee, but also produce our entertainment? Will our favorite songwriter become Collective 0-0009?

[thoughtomator]

> Heh, good job of saying “I have no clue about math.”

Good job of saying that you’re a gullible dunce.

[DoodleBob]

I took some theory in college a LONG time ago, so I'm far from an expert. The ideas behind music theory and counterpoint are that certain approaches to songwriting and melody and harmony produce 'better' music, i.e., a dissonant chord resolving to a consonant chord that is pleasing to the listener.

Part of the problem, nowadays, is what is pleasing to one person is not necessarily pleasing to a different person. Some people love classical but hate punk, some people love punk but hate jazz, some people love jazz but hate country, and some people love country and hate world music, and some people love world music and hate polkas.

All of that said, a study of music theory is (in my opinion) time well-spent insofar as it helps the soul with its unyielding query of "why." Your mileage may vary.

[thoughtomator]

Soul can’t be autotuned, nor can the slight imperfections that distinguish a human performance from a mechanical one.

If you want to understand the physics of music, the place to start is by looking at the overtone series, and the relationships of frequencies produced by it. The relationships between notes on a diatonic scale can be written in whole-number fractions.

A note vs. its octave is a 1:2 relationship. A note vs. its fifth is a 3:2 relationship; vs. its fourth, 4:3; and so on. It is the closeness of the relationships which creates a consonant, or peaceful/at rest sound.

In physical terms, consonance is inverse to the number of times each tone has to cycle before they start at the origin (zero point on the y-axis of their sine waves) together a second time. One cycle = same note. Two cycles = octave. Three cycles = fifth. And so on.

So yes, all the notes on a diatonic scale are multiples of the original frequency, brought down (by halving frequencies repeatedly) to the same octave.