a sequence of numbers increases or decreases exponentially when you reach each number in the sequence of the above by multiplying it by a number. For example, the sequence 1, 2, 4, 8, 16 is generated by multiplying by 2. This number is multiplied by obviously changes in different sequences.
some people claim that the mathematicians are good musicians, although if ever heard me play the piano, I could not accept! Use music to introduce exponential growth follows a valuable topic: there is a pattern mathematician in something we recognize our around. Most of us can hear an octave in music, or a dominant chord or Subdominant, although we are not able to put a name to any of them. Therefore, something that surrounds us fit a pattern; that pattern is about to be revealed.
when a symphony orchestra tunes up, an instrument, usually of an oboe, plays a note and tune other instruments in relation to it. That note is the A-above-middle-C that sounds when air vibrates 440 beats per second. A note of an octave (8 notes or 13 semitones) below is listening when the air vibrates at 220 beats per second (220 is half of 440). It will vibrate an octave above A 880 beats per second. The twelve spaces between thirteen scale Halftones are equally divided these days. This division is called “temperament” equal and j. S. Bach meant when he used the title “The well-tempered harpsichord” of one of its main works.
the technical term for “beats per second” is “Hertz;” To have 440 Hertz (Hz).
as each note is raised in pitch by a semitone, the number of beats per second increases 1,0595 times. If you want to check the figures in the following list, which you would like to take this increase as 1.0594631.
here is a list of hits per second for each of the notes (semitones) on a scale starting at the. Figures to the nearest whole number. Note that the sequence of numbers is an exponential sequence with a common ratio of 1.0594631. Who would have guessed?
a is 220 Hz to # 233, B is 247, C is 262, C# is 277, D is 294, D # is 311, E is 330, F is 349, F # is 370, G is 392, G # is 415, it is 440.
the pot of musical riot between you, keep in mind that I had to put D # instead of E flat because there is a symbol for “sharp” – sign the hash – on a keyboard, but not for “flat”.
when playing music in the key of A, the other key that is most likely from time to time drift is E, or the dominant key of which is what is called. If you wants to make a great bar end or two to the following piece of the music, you probably will end with the chord of E (or E7) followed by the chord end of to.
another point interesting here is that the armor of the 3 sustained, while the tonality of E is 4 sustained. About that more later.
there is a beautiful word in English: “sesquipedalian”. “Sesqui” is a prefix Latin that means “one and half,” while “pedalian” us gives “feet.” Note here the “pedal” of Word. So the word means “one and half feet” (in length) and is used sarcastically of the people that used words long when words more short. However, other side here is that the word sesquipedaliophobia means a fear to words long. Sesquipedaliophobics do not know, of course!
now again to the music: sesqui or the ratio of 2:3 us takes of them beats by second of a key, the hertz of the key key. To have 220 Hz. increase in the proportion 2:3 and get 330 Hz of E, the key dominant of to.
the fun continues! Search it in Hertz of the note D in the list above-294- and “sesqui”, the increase in the proportion 2:3. You will get 294 + 147 = 441 (must be 440, but we are approaching). Like this? To is the dominant hue of re, and tonality of D has 2 sharps to S 3.
to summarize: here are the key in order “sharp”, starting from C that not has sustained in his armor and the increase of one acute simultaneously (G has a sustained).
C, G, D, A, E, B, F #, C#. Is going to do. Notice that climb by the interval music of a 5. To go “towards down” of C, you removed an acute, or in other words, add a floor.
I have no space to show you how to tune a guitar, but is related to this work and it is much clearer because you can see the relationships of the buttons on the fret Board. Perhaps another article later?