Thought for the Day - Mar 31

Subject: Thought for the Day - Mar 31
From: Peter T.
Date: 31 Mar 00 - 08:48 AM

Yet One More Amusing, if Desperate, Attempt To Get People Interested in Mathematics (from a Mathematics Newsletter):

"Of all the academic subjects, math is most closely connected with music. Music is all based on fractions and patterns," says Michele Adams, a middle grades mathematics teacher, music teacher, and piano player from The Woodlands, Tex. "Where fractions are concerned, music focuses on divisions of time for the rhythm and space for dealing with intervals such as octaves or fifths." Adams points to the Gregorian chants. "They are based on strict rules of mathematics," she notes. Adams points out some mathematical concepts underpinning music:

Counting: It's fundamental to playing music. One must count beats per measure and count how long to hold notes.
Patterns: Music is full of patterns--patterns of notes, chords, and key changes. Musicians learn to recognize these quickly. Patterns, and being able to invert them (known as counterpoint), help musicians form harmonies.

Geometry: Music students use geometric shapes to help them remember the correct finger positions for notes or chords (more than one note played simultaneously)--for instance, guitar players' fingers often form triangular shapes on the neck of the guitar.
Ratios and proportions/ equivalent fractions: Reading music requires an understanding of ratios and proportions. For instance, a whole note needs to be played for twice as long as a half note, four times as long as a quarter note, and so forth. In addition, since the amount of time allotted to one beat in a given time signature is a mathematical constant, the durations of all the notes in that piece are all relative to one another and are played on the basis of that constant. Finally, different frameworks of time with which musicians work are based on an understanding of fractions and multiples--for example, understanding the rhythmic difference between 3/4 and 4/4 time signatures.

Sequences: Music and mathematics are also related through sequences, particularly intervals. Teacher Eli Maor expounded on this relationship further in the September 1979 Mathematics Teacher: "Although a mathematical interval corresponds to the difference between two numbers, a musical interval corresponds to the ratio of the frequencies of the tones." He goes on to say, "Here, then, is a single principle that underlines all musicomathematical relations: Arithmetic progressions in music correspond to geometric progressions in mathematics; that is, the relation between the two is logarithmic."

Subject: RE: Thought for the Day - Mar 31
From: GUEST,Neil Lowe
Date: 31 Mar 00 - 08:59 AM

Was it in another thread a few months back that a comment was made about Einstein's interest in music? Seems E was a so-so violinist. He had a chance to meet a premiere violinist and play music with him, except Einstein's rhythm was choppy.

"The problem with you, Albert," the eminent violinist told him, "is, you can't count."

Neil

Subject: RE: Thought for the Day - Mar 31
From: MMario
Date: 31 Mar 00 - 09:06 AM

And the beauty of it all is that you don't have to KNOW mathematics in order to perform or appreciate music. However, there is an underlying beauty in the mathematics that can lend a whole new sense and appreciation of the music.

Subject: RE: Thought for the Day - Mar 31
From: Crowhugger
Date: 31 Mar 00 - 09:15 AM

Bach knew.

Subject: RE: Thought for the Day - Mar 31
From: Mbo
Date: 31 Mar 00 - 10:22 AM

I'm lousy at math but can ace music theory. Go figure!

--Mbo

Subject: RE: Thought for the Day - Mar 31
From: GUEST,Jack
Date: 31 Mar 00 - 11:06 AM

There's a difference between arithmetic and mathematics. I know lots of people who are great arithmeticians, who calculate sums and differences and proportions in their head without effort, who don't understand real mathematics and its use as an elegant descriptive (and even poetic) language.

Subject: RE: Thought for the Day - Mar 31
From: Mbo
Date: 31 Mar 00 - 11:09 AM

True. The Greek composer Xenaxis used probabilatic calculus as inspiration for his music.

--Mbo

Subject: RE: Thought for the Day - Mar 31
From: Rick Fielding
Date: 31 Mar 00 - 11:16 AM

It's still a good point though. How can someone with an absolute FEAR of mathmatics as a kid, relish them when applied to music. My other dilemma has always been trying to find out why my rhythm's so good, yet I practically fall over when trying to dance. Enquiring minds want to know.

Rick

Subject: RE: Thought for the Day - Mar 31
From: GUEST,Neil Lowe
Date: 31 Mar 00 - 11:36 AM

I read in an article a long time ago that some of guitarist Mason Williams' tunes were derived mathematically.

Subject: RE: Thought for the Day - Mar 31
From: Little Neophyte
Date: 31 Mar 00 - 11:41 AM

It would be nice if my calculator could help me figure out the music theory faster.

Little Neo

Subject: RE: Thought for the Day - Mar 31
From: katlaughing
Date: 31 Mar 00 - 12:40 PM

When my brother would go into schools to teach about music, the kids loved it when he would tell them to give him a telephone number and he would show them how to turn it into a full blown musical composition, tonal, with orchestration.

In his First Symphony, he introduces all seven themse in the first few measures in an amazing, very mathematical weaving, with melodies turned upside down, backwards, forwards, etc.

He never did that well beyond basic math, but all of his music has a mathematical precision to it which demands the performer pay close attantion, much as Mozart's does.

Subject: RE: Thought for the Day - Mar 31
From: GUEST,Jack
Date: 31 Mar 00 - 02:01 PM

Ofthen the key to understanding mathematics (or geometry, or physics for that matter) is intuition--some kind of internal mental construction whos manipulation we understand. Perhaps learning music and how to play it (particularly on the guitar or piano where intervals are spatially coded on the fretboard and keyboards) provides an intuition that makes the leap to understanding the theory of chord construction, inversions, and progressions in their numerical representations a lot easier to understand. I imagine if one tried to learn the theory cold, without ever having played a scale or learned the finger patterns for different chords, or couldn't read music, it would be as difficult as some people find math.

Subject: RE: Thought for the Day - Mar 31
From: BlueJay
Date: 01 Apr 00 - 03:50 AM

It's been proven that five out of four people have difficulty with fractions!

Subject: RE: Thought for the Day - Mar 31
From: wysiwyg
Date: 01 Apr 00 - 09:50 AM

For a long time I have wondered what would be the song, if the notes were the musical translation of the movement of a flock of birds in flight-- the mathematical expression of their position, velocity, direction, relation to one another.... veering, rising, turning... can you see it?

Can you hear it?

Can you write it?

~S~

Subject: RE: Thought for the Day - Mar 31
From: katlaughing
Date: 01 Apr 00 - 09:52 AM

I think MC Escher must've come close to it in his artwork, Praise.

Subject: RE: Thought for the Day - Mar 31
From: Jeri
Date: 01 Apr 00 - 10:41 AM

The problem with mathematics is being taught it scares the heck out of people and confuses them. I hated math because I had some teachers who said "do this, then this...and you get the correct answer." If they had explained why doing something worked, I think I might have been good at math and even enjoyed it if my teachers had focused on reasons instead of memorization.

Rick, if your hands can dance on a guitar, your feet can dance too. You probably just haven't put as much effort into it. Think of the floor as having strings, and your feet are picking them.

Subject: RE: Thought for the Day - Mar 31
From: Dave (the ancient mariner)
Date: 01 Apr 00 - 10:48 AM

"In art, and in the higher ranges of science, there is a feeling of harmony which underlies all endeavour. There is no greatness in art or science without that harmony". Albert Einstein (on the connection between music and science)

Albert Einstein played the violin with some enthusiasm. He once played for Gregor Piatigorsky, the distinguished cellist, and he asked him: "How well did I play?" Piatigorsky replied: " You played relatively well."

When asked if the phenomenom of mathematicians often being good musicians worked in the reverse, replied. " Definately not, but I wish it did. Why, I can hardly add two and two." Yours, Aye. Dave

Subject: RE: Thought for the Day - Mar 31
From: Dave (the ancient mariner)
Date: 01 Apr 00 - 10:50 AM

Last quote was by the composer Ralph Vaughan Williams...