I think it’s interesting that music is another aspect of the mathematical nature of empirical reality.

We know from physics that the nature of empirical reality is mathematics: what physicists discover about empirical reality are mathematical relations (E=mc²; F=ma; F=k(q₁q₂)/d²; the law of conservation of energy--which is a mathematical law, proved by theorem; Schrodinger’s equation, etc., etc.). Music is another aspect of the mathematical nature of empirical reality (but didn’t I already say that?).

For instance, there is obviously no non-mathematical reason why perfect intervals are ratios of frequency.

There are no non-mathematical reasons why (1) the fundamental frequency of a string is inversely proportional to its length; (2) the fundamental frequency of a string is directly proportional to the square root of the tension (the elastic restoring force); and (3) the fundamental frequency of a string is inversely proportional to the cross-sectional mass of the string, as given by the mathematical relation:

f = √(TL/m)/2L

where f is the frequency in Hertz; T is the string tension in Newtons; L is the length of the string in meters; and m is the cross sectional mass of the string in kilograms.

The fundamental frequency (first harmonic) is the lowest frequency that will produce a standing wave in a one-dimensional medium.

From (1) above, the Pythagoreans deduced the numeric proportions of intervals, and eventually the three means of music: the arithmetic mean, the geometric mean and the harmonic mean.

The harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency.

As Cris Forster points out in Musical Mathematics (Chronicle Books, 2010):     

Marin Mersenne (1588–1648) was the first European to accurately describe and mathematically define the first six harmonics — 1/1, 2/1, 3/1, 4/1, 5/1, 6/1 — of vibrating strings. These discoveries forever changed Western music theory. Suddenly, scientists and musicians realized that the rational ratios of just intonation not only constitute a convention of man, but also reflect a phenomenon of nature. Consequently, integer number ratios, which comprised the core of tuning and music theory since the time of the ancient Greeks, had a physical reality in nature, and could, therefore, not be dismissed as antiquated entities of long-forgotten civilizations.

May 26, 2012 -- 3:16PM, Stardove wrote:

I grew up in a musical family mainly playing and singing country music.  Although one of my uncles had a big swing band with 16 musicians when I was a child.  

My husband and I had several bands in the past.  Today we have circled back to mainly playing music and singing with the family. 

We have a son-in-law who teaches music at the studio in their home.  I met our son-in-law who was playing in a band before our daughter met him.  First time he saw my daughter we were dancing together and he thought she and I were a couple. They have been married six years this month.

Cool. What instrument(s) do you play?

I think it must be nice to be able to say that one grew up in a musical family. The non-musicians in my family greatly outnumber the musicians.  

I banged around on our piano from the time I was old enough to sit and bang on something. I took piano lessons for about three years when I was a child, from about 7-10 years old. I enjoyed it, and, unlike with many things I’ve tried to grasp, I seemed to have caught on quickly--at my first-year recital, which the teacher sponsored yearly for all of her students, I recall that I played a piece that other of her students had played at their third-year recitals. But then we moved to another state, and I had kind of lost interest in piano playing--I wasn’t practicing much at that point. I had just become more interested football. (That’s a joke, by the way. And it’s a very funny joke for those who understand it--unfortunately neither of whom are reading this.) Around the age of 15 I became interested in playing music again, and at that point I could have pointed out where middle C was on the piano, but that was the extent of my musical knowledge. I could no longer read music. But I had the urge to bang around on the piano again, so I did. Also, this was around the time that primitive little synthesizers, such as Casio, came on the market, and I got one of these and did primitive little synthesizer things on it. I also bought a guitar--a couple of my friends played guitar. But that instrument was a mystery to me. I began to think that my fingers were not constructed right in order to make an A chord.

I did kind of re-learn to read music at the most elementary level. I haven’t progressed beyond that elementary level in the many years since. I have taught myself three chords on the guitar, so I am well on my way to becoming a rock star. Actually, my son is the musician in the family, and is studying music. Whatever career he may make of that no one knows.

Anyway, the OP article reminds me of something not mentioned and that no one here has mentioned: Apparently an important part of Gabrielle Giffords rehabilitation has entailed using music to help her remember and/or articulate things. It was found that she could more easily remember and repeat a sentence or fact if it was part of a song that she sung. This was noted during the big interview that Giffords gave back in January, I think.

I think the issue mentioned in the article concerning other animals’ “appreciation” or recognition of music is interesting. I am not at all convinced that humans are the only animals who recognize when a beat is rhythmic. The article doesn’t mention any research that establishes that “monkeys can’t . . . recognize beats.” Nevertheless, humans are obviously one of the very few animals whose consciousness is adequately evolved to recognize such fundamentals of music as when a beat is rhythmic. Humans are also able distinguish when a string is out of tune, and when a voice of off-key. We are able to make these distinctions because these are mathematically objective distinctions.

Regarding the subject:  I am convinced that music education is a big part of my daughter's success.

We read somewhere that early childhood music education causes synapses to form in the brain that would otherwise remain unformed.  These synapses are important later in life when attempting to gain understanding of mathmatical concepts and principles.  My daughter started piano lessons at age four, and she picked up the alto sax in 6th grade. That was followed by the bassoon and bass clarinet in high school.  She can play classical, jazz, and just about anything else.

Her mother and I had no music training whatsoever in our childhoods, and we both struggle to balance a checkbook, and forget about working algebraic, geometric, or trigonomic equations.  My daughter, on the other hand, scored a 750 on the math section of the SAT and she just graduated with a degree in actuarial science.  All through her college years, she worked as a math tutor.  Soon she will be an actuary, and her future is looking very bright.

I know this is anecdotal, but I'm a believer in early music education.  

Music definatly changes my mood/s. Mostly music amps me up where I feel much better. Music is my self therapy.

May 27, 2012 -- 1:30PM, Stardove wrote:

May 27, 2012 -- 10:32AM, drawout wrote:

birds can dance  www.upi.com/Odd_News/2009/05/01/Research... 

My cockatiel lives for music.He loves jazz, classical and pop music. I Love hanging out with a fellow music lover. He has been spoiled by my collection of vinyl LPs. He just sits there quietly when I play a CD or MP3 and suddenly tweets exitedly when I put on a record. He contributes to the music,especially Jazz.

Sweet Drawout! My thousands of LPs sit flat on the shelves and don't get much play.

Here is a video of Snowball, the cockatiel in action. There are plenty more videos on You Tube of Snowball dancing to different songs.  I went for a shorter clip.  Snowball also like to "sing" with the music too.

That's a bad bird, Stardove. He's got his moves and his groove going.

Jun 8, 2012 -- 7:59PM, Ed_3 wrote:

However though, I think that what you described in your quote is more of a thing where every generation prefers to 'own' the current music of their generation. And that's regardless of how harsh or ugly or unappealing it may sound to the older generation. Plus, a lot of the Rap and Hip Hop that we've had(and I actually think that some of it is changing and becoming less harsh and more melodic) reflected the harsher realities that younger generations lived through and experienced. Realities that our generation/s never had to experience. 

Urban music of course reflects the life many young people in those environments live in.

Yet my kids and their friends live in an upper middle class suburb, and their lives are not in the slightest harsh.  Yet many of them also like this sort of music.  Go figure.