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Math, Music, and Pentatonic Scales

No one knows how long humans have been creating music, but the earliest attempts at understanding the theory seem have been made by that strange society called the Pythagoreans. Its founder, Pythagoras, lived on the Greek island of Ionia, sometime between 600 and 500 B.C.E. He is famous mostly for the statement of the Pythagorean Theorem — a fact known to the Babyloneans for at least a millenium before him. There are lots of interesting legends — some of which may actually be facts — about the Pythagoreans, but I don’t have time to go into them now. As Casey Stengel used to say “You could look it up.”

Anyway, the Pythagoreans seemed to have experimented with the sounds produced by strings and hollow flute-like tubes of differing lengths. They noticed that (all other things being equal, like tension for strings or diameter for tubes) that the most pleasant intervals between notes are produced when the lengths were in simple ratios. For example, if the length of one string is double the length of another, then the shorter one produces a tone that, in our current terminology, is called one octave higher than the longer one. This is the interval between, say, a C on the piano, and the next C above it. It’s the interval from Do to Do in the scale Do Re Mi Fa Sol La Ti Do.

The next most interesting ratio is 3 to 2. If one string is 3 units long, and the other 2 units, the shorter string will be a perfect fifth above the lower one. This is the distance from C to G on the piano, or from Do to Sol, as in Do Re Mi Fa Sol. Other ratios are: 4 to 3: a perfect fourth (C to F or Do to Fa) and 81 to 64: a major third (C to E or Do to Mi). The third was considered a dissonance in early music.

We now know that sound is simply a vibration of the air; the faster the vibration, the “higher” the pitch. A modern “middle C” is 256 cycles or vibrations per second. The vibrations per unit time — say second — is called the frequency. If two similar strings or tubes have lengths in a certain ratio, then the frequencies they produce will be in the opposite ratio. In other words, the shorter the length, the higher the frequency. If C has a frequency of 256, then G should have a frequency of 256 times 3/2 or 384.

It turns out that the fifth, or 3:2 ratio, can be used to get all the other “named” notes in the scale that we use. Starting with C, say, we keep going up by fifths. This gives C – G – D – A – E – B – F# – C# etc. You eventually get back to C, so this is called the “circle (or cycle) of fifths.” If you take the first five of these, C, G, D, A, E and arrange them in order: C, D, E, G, A, you get what’s sometimes called the “major pentatonic scale”. Pentatonic means, simply, “five-toned.” There are other forms of pentatonic scales, but this is what is usually meant by the term. Play these on the piano or whatever instrument you can find, or go to

The Pentatonic Scale.

to hear them on your computer.

It turns out that there are serious flaws in trying to create all of the notes of the modern “12 tone” scale using the circle of fifths: you don’t exactly get back to where you started, and some of the intermediate notes which should be, say, a fifth apart themselves, aren’t! This created problems for centuries in playing music in various keys and on different instruments. It wasn’t solved until about the (early) 18 century with the development of the “well-tempered” musical tuning. The idea in well-tempering, basically, is to divide the ratio 2 to 1 (the octave) into 12 equal parts or ratios; 12 because there are 12 “half tones” in an octave: C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C. The frequency ratios between successive notes in the “chromatic” scale (all 12 tones) are set equal. This means that the product of all 12 of these ratios must equal the ratio 2:1 ( = 2 numerically) of the octave. Thus, each ratio is the twelfth root of 2. Now the twelfth root of 2 (written 21/12) is about 1.059463094 (by my calculator). Thus, to get from C to G, a space of seven of these half tones, requires multiplying the frequency of C by 21/12 seven times. Mathematically this is 27/12 which is approximately 1.4983: very close to 3/2 ( = 1.5), but not exactly. By making this ever so slight mathematical adjustment, we can build and tune instruments which sound beautiful together in all keys and in all combinations.

Thus we use math in our daily musical lives.

May 18, 2010 Posted by | Off Topig, Pentatonic Scales | , , , | Leave a comment

An Easy Way to Download Free Music

Everybody around the world is so much interested about free music but nobody likes to be sued. However, there are many websites are offering this free music for those people who are seeking free music online. And now a question raised in your mind that how to download music with legal sources. At this point, the internet will help you to find legal sources; you can include the words like legal free mp3 songs and legal music downloads and more, when doing an online search.

Free music offered legally is usually done so because the copyrights have run out, the artists have provided the free music themselves or for other reasons. Be sure to read the terms and conditions provided by each site and verify that the free music is legally available.

Most of the people are having much knowledge about these pod-casts. Pod-casting is online audio content that is delivered via an RSS feed. Many people liken pod-casting to radio on demand. However, in reality, pod-casting gives far more options in terms of content and programming than radio does. In addition, with Pod-casting, listeners can determine the time and the place, meaning they decide what programming they want to receive and when they want to listen to it.

Rock music has been a volatile, unpredictable creature that has constantly redefined and reinvented itself since its emergence in the late nineteenth century. Not surprisingly, then, it can be extremely difficult to apply a straightforward definition to such a restless musical format. As rock music enters the 21st century, the most successful acts possess the same spirit as their early predecessors, even if they sound quite different.

If you are a music enthusiast and you want to permanently striving to take your passion for music to the next level by regularly updating your music collection and looking for music news about your favorite numbers, artists and bands. However, there are some well established and experienced websites offers this music news and rock music to their valuable customers.

May 16, 2010 Posted by | Arts & Entertainment, Music | , , , , | Leave a comment