Open Guitar
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 Country Blues Guitar In Open Tunings Tab Book 3 Cd Set  US $18.95
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Introduction
When we start to learn music in the 4th or 5th grade, we are taught the names of all the notes: A, B, C, D, E, F and G. And that is the simple natural major scale in the key of C. However, these first seven letters of the alphabet do not even begin to reveal the complexity and mathematical beauty contained within the basis of all western music - the equal temperament chromatic scale.
What is Pitch?
In musical language or "every day" language, we refer to a note's pitch or tone. In technical or scientific terms, just what is pitch?
In the terminology of physics, pitch is the frequency of a note. The unit of measurement of frequency is Hertz (formerly cycles-per-second). So what exactly does this mean? It is simply a measure of how fast something vibrates. So let's take a guitar string as an example.
If you pluck an open guitar string, it will vibrate at a certain rate or frequency. So, for instance, if you pluck the open A string, it will vibrate back and forth at a rate of 110 Hz (Hertz). And as the string swings back and forth 110 times each second, it pushes the air around it 110 times each second. And these disturbances travel through the air 110 times per second and they smack into our head. As they do this, they push our ear drums in and out 110 times per second. That causes signals to be sent to our brain and we "hear" an A note.
The Chromatic Scale
In western music, the scale is divided up into 12 notes. You may know them as the musical alphabet: A, A# or Bb, B, C, C# or Db, D, D# or Eb, E, F, F# or Gb, G and G# or Ab. (Where the symbol '#' stands for 'sharp' and the symbol 'b' designates a flatted note). This is also known as the chromatic scale. Each of these notes has a different pitch or frequency. How were these different tones defined or derived?
Octaves
Let's look at two notes as an example. Our first note is defined as an A4. This means it is the A note in the fourth octave on a piano. An A4 has a frequency of 440 Hz. This means it travels back and forth (or vibrates) 440 times every second. Interestingly enough, if we move up an octave; we, once again encounter an A note (this time A5). A5 vibrates at a frequency of 880 Hz.-twice as fast as an A4.
This is no coincidence. This is by design. The technical definition of an octave is a doubling of frequency. So a low E string (which has the same tone as the second E on a piano: E2) vibrates at 82.407 HZ. If we double this frequency, we get 164.814 Hz-which just happens to be the E note an octave above (E3).
The Equal Tempered Scale
The modern chromatic scale has exactly the same frequency ratio (or multiplier) between each adjacent note or half step. How is this ratio determined?
We now know that octaves are a doubling of frequency. And we know that the chromatic scale is made up of 12 notes or half steps.
These two facts put together tell us that it takes 12 half steps to double the pitch or frequency. Accordingly, the ratio between two adjacent notes is the twelfth root of 2 (about 1.05946309). This is because the twelfth root of 2 is the number which, when multiplied by itself 12 times, will equal two. (Try it.)
So, if we multiply A (440 Hz) by the twelfth root of 2, we get A# (466.16 Hz). If we again multiply this by the twelfth root of 2, we get B (493.88). If we do this 10 more times, we will find ourselves, once again, at A-only this time it will be the A at 880 Hz.
Summary
The modern chromatic scale is technically called the Equal Temperament Scale because of the equal ratios between each note or half step. The ratio between each note was set at the twelfth root of 2 (about 1.05946309) based upon very logical and mathematical reasoning. It is based on two facts: 1) there are 12 notes per octave and 2) an octave is defined as a doubling of frequency.
Robert M. Matthews (better known as Bob Matthews) is currently retired after more than 30 years of engineering and management experience.
As an avid guitar player for more than 35 years, Bob has created a website specifically for guitar players and future guitar players. The site is packed with a wealth of information and articles on guitars, music theory, guitar tips and lessons, as well as many entertaining and instructional videos.
Feel free to visit the site at http://www.Learn-Guitar-Quick.com for great guitar-related information. While there, be sure to claim your FREE GUITAR LESSONS available on the front page.
And... be sure to follow me on Twitter at http://twitter.com/GuitarBobb
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