Posted on 05/24/2019 6:24:48 AM PDT by 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
(Excerpt) Read more at phys.org ...
Baroque music had strong links to mathmatics.
(old joke)
Music moves so many parts at once, different layers of brain and neural net I suppose, but also the beat of the heart, sweat and memory, smells --- could be tobacco or lavender ---the heat that comes up from the belly. All these cultures have all these quirky kinds of music, but they all have music.
I would be afraid of a world where all the music comes from AI. I would rather hear a squeaky little girl with an off-pitch banjo, than all the algorithm-produced perfection which, seems to me, comes from the deceiver and the seducer.
Math is not my thing, I'll admit. The most perplexing job of work I ever did was Algebra II --- I got good grades, but I never "got" what I was going. I did well-enough on the tests, stupidly.
I once had a knock-me-down experience, though, that "revealed" to me that way before Greek or Hebrew, God spoke Trigonometry.
Sang it, probably. HA.
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The math in music theory is not hard at all!
It’s all about the frequencies.
Every time a note rings out, a plethora of other notes ring out alongside it - all the multiples of the note’s frequency.
So if you hear a note with frequency of 400Hz, you will ALSO hear “overtones” at 800Hz (x2), 1200Hz (x3), 1600Hz (x4), 2000Hz (x5), etc.
The first overtone is the octave, which will sound the same as the original note, but higher - as does every doubling of the original note. So octaves for 400Hz are at 800, 1600, 3200, 6400, etc.
This means you can go down an octave as well, by halving the frequency.
So the 2nd overtone of our example note is at 1200Hz. Bringing it down an octave gives us a 600Hz tone, which is the “perfect fifth” in our diatonic scales. Continuing this process with other overtones fills out the rest of our scale... notes more dissonant than major 7ths and minor 2nds are not used because the extra dissonance vs those intervals is not generally musically useful, but theoretically we could add as many notes as we like to our scales using this method.
“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.”
It’s all about those harmonic overtones.
Ancient Greek Music - The Lyre of Classical Antiquity
So did Democracy.
Damn those old "_________" dudes.
You know that the Patriarchy was bound to follow.
Apollo's lyre: Greek music and music theory in antiquity and the Middle Ages
I think Wagner figured this out a while back. Dream Theater, Rush & Kamelot may have improved on it. Depending on your own tastes, of course.
THank you. You do need to start me at Page 1, but with a little application I can get it :o)
All is energy.
All is vibrating.
Ooh, I know the answer to this one.
Ok, as some others on the thread have noted, we get all the notes in our musical scale from something called harmonic overtones, which are these extra notes that are also playing whenever you hit a note on a stringed instrument like a guitar or piano. So if you play a guitar string open (not pressing down on any of the frets on the neck), you get the loudest note, which is the sound of the whole length of the string vibrating, but you also get a quieter note that is the same as if only half the string was vibrating. You’ll also get an even quieter note that is the same as 1/3 of the string vibrating, then 1/4, etc, on to infinity.
So our 12 musical notes are made up of those “overtones” and take advantage of the natural harmonies that occur between them. The funny thing is, though, some overtones in the sequence do not occur exactly on one note or the other of our musical scale, but are actually between two of the notes. This is because when we made our musical scale we didn’t put our notes EXACTLY where the overtones were, but just roughly where they were, because if you put them exactly on the overtones, then that instrument only sounds good playing in a single key of music. So arrange a keyboard to play exactly in the key of C and it will be off key if you try to play it in the key of F. So we “tempered” the tunings by changing them to be slightly out of tune in every key, but not dramatically so in any particular key.
Now the consequence of this tempered tuning is what you are noticing with blues music, jazz, etc. There are a couple overtones that are kind of important that quite match up with the musical scale anymore, because we of how we tuned the instruments. However, you can still play them if you just use some tricks. So for a guitar player to play those overtones, they bend the string a little while playing, which makes it very slightly out of tune and allows them to reach that missing overtone. A singer can just slide their voice off the normal scale and find it. For a keyboard player, we can’t do either of those things, but we can play the key above the missing tone and the key below the missing tone at the same time, or slide from one to the other, and get some approximation of that “blue note” as they are called.
4 later
FMCDH(BITS)
octaves and other arrangements [are] a foregone conclusion, not an arbitrary invention by humans.
Like a human voice, too. :)
I’m with you. My favorite band is The Who...their singer, Roger Daltry, was quoted as saying “give me a bum note and a bead of sweat.”
Bump for later
Hi.
I wonder how Mick Jagger Is doing?
5.56mm
The ancient Greek mathematician Pythagoras found that music followed mathematical principals. It only took us 2500 years to rediscover that connection. It is amazing how much knowledge the ancient Greeks and Egyptians and others knew that are lost to antiquity that we do not know today.
You can thank the Muslims for burning down the Library at Alexandria. It would have held a bounty of ancient knowledge lost to us today.
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