On Mathematics and Music - On Mathematics and Music Both...

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On Mathematics and Music Both music and math have concepts, and special symbols. What is a musical key? What is a number? The definitions of things in both disciplines are somewhat circular and vague, unless you understand what they are. You cannot define a number, but you know what they are much of the time and you can use them. It's no different with a musical notion like a minor key. Once you know what it means you can spot one, though you cannot really define it rigorously. There are many things in music that are obviously math-related, and many musical notions can be explained in numbers. But it is important to note that numbers are not some way to describe music-- instead think of music as a way to listen to numbers, to bring them into the real world of our senses. The ancient Greeks figured out that the integers correspond to musical notes. Any vibrating object makes overtones or harmonics, which are a series of notes that emerge from a single vibrating object. These notes form the harmonic series: 1/2, 1/3, 1/4, 1/5 etc. The fundamental musical concept is probably that of the octave . A musical note is a vibration of something, and if you double the number of vibrations, you get a note an octave higher; likewise if you halve the number of vibrations, it is an octave lower. Two notes are called an interval ; three or more notes is a chord . The octave is an interval common to all music in the world. Many people cannot even distinguish between notes an octave apart, and hear them as the same. In western music, they are given the same letter names. If you blow across a coke bottle and it produces the note F, and you drink enough so that the air remaining in the bottle is twice as much, the note will be also an F, but an octave lower. If you shorten a string exactly in half, it makes a note an octave higher; if you double its length, it makes a note an octave lower. You can think of the concept of octave and the number 2 as being very closely associated; in essence, the octave is a way to listen to the number 2. If you shorten a string to 1/3 its length, a new note is produced, and the second most fundamental musical concept, that of a musical 5th emerges. We call it a 5th, because it is the 5th scale note of the Western do-re-mi scale, but it represents the integer 3. (Incidentally, the 5th is the only interval other than the octave that is common to all musics in the world.) Strings of a violin are tuned a 5th apart. Men and women often sing a 5th apart, and most primitive harmony singing involves octaves and fifths. In fact, they say that when you are learning to tune a stringed instrument, you can only trust your ear to hear octaves and fifths, and you should not rely on your ability to compare other musical intervals properly. The next note in the harmonic series corresponding to the number 4 is 2 times 2 and thus a second octave. The number 5 produces a new note, called the musical 3rd. The 3rd is the other note in the fundamental chord, called the
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This note was uploaded on 10/10/2011 for the course HRM 400 taught by Professor Mrs.redman during the Spring '11 term at University of Maryland Baltimore.

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On Mathematics and Music - On Mathematics and Music Both...

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