Math and Music

[bloodhound]

u will probably go to the wrong side of the car all the time, or almost get run over while trying to cross a road. well thats what happened to me when i went to paris!!!!!

[coquina]

My favorite "mom" story. Her first name was Muriel, she was 21 and very naive. When she got off the ship in NYC, she saw a neon sign flashing in the distance, "MURIEL-MURIEL-MURIEL". She thought, "How nice, they're giving a "Welcome To America Party" in my honor, so she decided to track down the sign. Right off the bat, she stepped off the curb after looking the wrong way, and almost got run down by a cab. The cabbie rolled down the window and yelled at her, "Look out there, sister, are you trying to commit suicide?" She was appalled that a stranger would speak to her in such a manner. Any way, she continued her quest, only to eventually find a cigar store.

 

http://www.altadisusa.com/cigar/muriel.asp

[NavajoEverclear]

this is a really interesting topic. I wish i could say i was more musically acomplished. Guess its just a matter of work, that i intend to get around to someday. It would be really cool to see what kinds of things you could do if you figured the right way to consciously apply more complex mathmatics concepts to music. What these are, i'm not sure. Math is kinda like magic to me, as is anything you dont know much about. Pre-calc is about as far as i've gone. I'd definately be interested in learning more if there was a good program or book to read or something. I had an awesome pre-calc teacher, so i loved that. Then my calculus teacher friggen sucked, and i dropped out at the semester. I'm in Stats now, which is cool, but mostly just about entering in a butload of numbers (far as i can tell, but i've only been in school a couple of weeks

[matt grime]

why is that difficult to grasp?

 

Erm, cos you say there's a link and you'd be stupid to deny it, but the only evidence you put forward of combined mathematical and musical skills is your own, and you say you can't do maths, but can do music. The evidence doesn't remotely support your conclusion. And saying, wow, look at an oscilloscope doesn't help since that is a mathematical model of a sound wave, not a sound wave. (sound waves are longitudinal for pity's sake, not even transverse.) It's like saying there's a link between mathematics and national debt: look at the graph.

[prokaryote]

well, helmholz tried to give physical/physiological reasoning for affinity towards particular tonality in western compositions. and there are more than a few ongoing researches in the area of mathematics applied to music (in both composition and analysis). there definitely exist a connection, even if strictly as a consequence of a construct. but i suppose, this thread is more about abstract and tenuous (anthropic) connections.

[coquina]

As we have discussed, there are various ways that math & music go together - let's address one aspect at the time:

 

The concept of "in tune" vs "sharp" or "flat".

Everyone in the orchestra tunes to "concert pitch" or A440. The wave for the note "a" (above middle c) vibrates 440 times a second.

 

If you are flat, the note you play vibrates slower, if you are sharp, it vibrates faster. If you are out of tune, when you listen to the two notes played together, you will hear "beat waves", defined as:

 

in physics, the pulsation caused by the combination of two waves of slightly different frequencies. The principle of beats for sound waves can be demonstrated on a piano by striking a white key and an adjacent black key at the bass end of the keyboard. The resulting sound is alternately soft and loud—that is, having characteristic pulsations, or throbs, called beats. …

If you look at the waves of the two tones, overlapping one another, every so often the waves will peak at the same time. When they do, you hear the "beat". The farther apart the two notes are, the farther apart the beats, the closer together, the faster the beats, until the two waves overlap exactly, and you don't hear them any longer.

 

Incidentally - this not only works for tuning instruments, but for synchronizing engines as well. If you have a twin engine boat, you want to be sure that both engines are turning at precisely the same RPM to get the most efficiency (and RPM meters aren't that accurate). If you don't have an electronic engine synchronizer, you put one engine at the rpm you want to run, and the other significantly lower. You listen for the "beat waves" and bring the slow one up to speed until you can't hear them any more.

 

When it comes to mathmatical ability - I'm good at geometry and trig, 'cause that's what I use all the time. What about these "musical waves", would someone care to write the mathmatical formula that describes them and explain it?

[matt grime]

The most obvious thing to say to that explanation is that if the frequencies differ by an irrational proportion then the peaks never overlap. seeing as you hear them when they do, surely you don't hear them in this case either, since they don't occur, so how is that different from what you describe you (don't) hear for perfectly attuned instruments/strings/notes? A similar comment applies when one is an integer multiple of the other. Of course when the over lap perfectly there are *some* (ie all) peaks that meet so why do you no longer hear them then? I think what you're trying to describe is constructive interference, which is a slightly different phenomenon.

 

What do you mean by musical wave?

[Martin]

 

If you are flat' date=' the note you play vibrates slower, if you are sharp, it vibrates faster. If you are out of tune, when you listen to the two notes played together, you will hear "beat waves",...

 

[/quote']

 

that is right. it is the main way I use for tuning instruments

(like adjusting the electronic keyboard to agree with the piano)

 

but as you get closer and closer to being in tune the beats come more slowly. until it takes so long for the next beat to come that you dont care and you say the two are in tune.

 

I don't understand the next poster's comment. You dont have to have a rational proportion between the frequencies to hear beats. Beats is a common well-defined technical term---my General Physics teacher used it, my Physics of Music teacher, and also our piano tuner, and also plenty of musicians. It is periodic constructive interference. this seems clearly what Coquina is talking about.

 

 

The most obvious thing to say to that explanation is that if the frequencies differ by an irrational proportion then the peaks never overlap. seeing as you hear them when they do' date=' surely you don't hear them in this case either, since they don't occur, so how is that different from what you describe you (don't) hear for perfectly attuned instruments/strings/notes?

[/quote']

 

I cant make out matt grime's objection, if he has one, but anyway it seems like what Coquina is asking is, if you know how far apart the two frequencies are, can you predict how often the "throbs" come?

Or viceversa.

 

Two notes on piano are 6 percent different

if one is 440 then the other is 466-----that is, 6 percent higher.

 

If you play those two together, what is the "beat frequency"?

 

I guess it would be 26 cycles per second (the difference)

 

Probably you should get two notes closer than that if you really want to hear the beats

 

Like the A that is 2 octaves lower than 440 is 110

and 6 percent higher than that is 116 or so

so if you play those two keys---the A and the A-sharp

then you should hear a beat frequency of about 6 per second

 

when a lady has two outboard motors on the back end of her boat

she deserves special consideration, even if her mother did play the pipe organ, so everybody listen up and see if they can hear the beats

[matt grime]

inorder to have (repeated) overlapping peaks, the frequencies must be some rational multiple of each other. now coquina's logic states that we hear beats when some peaks overlap but that when they perfectly overlap there are none. now that makes no sense since there are STILL over lapping peaks, all of them, it is the fact that coquina has attempted to describe constructive interference but gotten her phenomenology a little wrong as far as i can tell: how can constructive intereference "disappear" when the waves are in perfect sync?

[coquina]

http://www.umanitoba.ca/faculties/arts/linguistics/russell/138/sec4/acoust1.htm

 

I was explaining it the way I was taught - check out the link - I'm not sure I understand how the blue wave was generated from the 2 red ones.

 

Martin

Like the A that is 2 octaves lower than 440 is 110

and 6 percent higher than that is 116 or so

so if you play those two keys---the A and the A-sharp

then you should hear a beat frequency of about 6 per second

 

I don't think you will hear beat waves in this case, if both tones are "in tune" because they are the same note. 440/110=4 so if you start both tones at the same instant, and play them for exactly one second the lower "A" will have one complete wave, and the higher one will have exactly 4 - right?

 

So - what happens when you combine the two sets of waves to make one, as per the above link?

 

I saw some research that was done at NASA Langley Research center where noise was eliminated by generating a wave that was the reciprocal of the noise. I read that the same technology is being used to develop a treatment for tinnitus (ringing in the ears). I hope it comes to market soon, because I have that. (Probably from listening to too much machine shop noise and too many boat engines.) BTW, Martin, a wee correction... - they're not outboards. They're twin 330HP inboards.

[Martin]

[. 440/110=4 .....They're twin 330HP inboards.

 

I did not mean play 440 and 110

those are both A!

 

I meant to play 110 and 116

A and A sharp!

 

I think then the beat frequency is 6 per second

because it is the difference

 

 

the next halftone up is always about 6 percent up

so A to A sharp can be 440 and 466

 

or it can be 110 and 116 (about)

 

 

what are you doing with twin 330HP inboards?

sounds like cruising up and down the inland waterway

or in the rivers of the Eastern Shore

sounds nice

had some summers on chesapeake as a kid