If you thought the music was not a mathematical language, then think again. In fact, music and mathematics are very intertwined, so I guess you could say that you can not live without the other. Here we investigate a report that clearly shows the strength of this bond. Let the music play.
For those with a rudimentary knowledge of music, the diatonic scale is something very familiar. To understand why some pairs of notes sound good together andothers do not, you must consider the sine wave pattern and the physical frequency. The sine wave is one of the more basic models in mathematics and is represented by a smooth transition ridge-trough regularly. Many physical phenomena and the real world can be explained by this basic wave patterns, including many of the basic tonic properties of music. Some notes sound well together (musically that is called harmony or consonance), because its sine waveModels reinforce each other at selected intervals.
If you play the piano, then as each of the different notes, sounds, depending on how your instrument is tuned. There are several ways to adjust these instruments and methods rely on mathematical principles. These scales are used for multiple frequencies, based on a particular note, and as such determination of these multiple groups if the notes sound good together, in this case, we say, like notes in harmony, orill-formed, in this case, we say, as notes of harmony or dissonance.
Where these are dependent on multiple criteria set by the manufacturer of the instrument, and today there are some rules to follow these processors. But despite the many criteria of a mathematical nature. For example, in more advanced math, students study the series of numbers. A series of numbers is simply a model that determined by a rule. A famous series is the harmonicSeries. This includes the reciprocals of the integers is 1 / 1, 1 / 2, 1 / 3, the harmonic series 1/4...The serves as a set of criteria for certain moods, called a Pythagorean tuning.
In Pythagorean tuning, the notes are tuned to the "rule of the perfect fifth." A perfect fifth includes the musical "distance" between two notes, such as C and G to try again without this product in a treatise on musical theory, in turn, the notes between C and GC #, D, D #, E, F, F #, and G. The "distance" between these notes will be a half step. So a perfect fifth is seven semitones, CC #, C #, D, DD #, D #-E, EF, and FF # F #-G. If we take the number of musical notes in a harmonic series, the number is attributed to note that the C and attributed to the note G to be always in a 2:3 ratio. Therefore, the frequencies of these notes will be adjusted so that their reports match 2:3. This is the C-note frequency 2 / 3, G-Note frequencyor vice versa, the tone frequency G 3 / 2 is the frequency note C, as measured by frequency in Hertz or cycles per second.
Now, the fifths tuning, is the fifth above G D. The application of the perfect fifth report, the note D, at a frequency that is 3-2 on the G-frequency can be set, or looking at it from below the note G is remarkable 2 / 3 the frequency of D. We can continue in the same way until you complete the so-called circle of fifths,brings us back to a note C from subsequent reports 3 / 2, the previous note in circulation. This requires twelve steps and after completion, if the frequency of the second C, the eighth note C or higher, you'll see exactly twice the frequency of the low C. This is a prerequisite for all octaves. However, this does not happen by applying this ratio to 3 / 2.
Musicians have corrected this problem by using nothing other than irrational numbers. Recall that these numbersare not as fractions, ie, their decimal representations, such as pi or the square root of two can be expressed, not at the end and do not repeat. So, as a result of the failure of the method of development of Pythagoras to produce perfect eighth, methods of development have been developed to remedy this situation. One is called "equal temperament" tuning, and this is the standard method for most practical applications. Believe it or not, contains the tuning method of rationalPowers of two. That's right: the fractional powers of two. So, if you think you've learned rational exponents used for any other class of algebra, here is an example in which this issue is in real life.
The way the mood of the work is as follows: each note in its eighth through twelfth roots, its frequency must be multiplied by two in a row to enter the higher grade. That is, if you start to vibrate with the notice of default to 440Hertz, for example, # to get to A, multiply 440 2 ^ (1 / 12). Since the twelfth root of two is equal to 1.05946 to five decimal places, # 440 * A would be granted or 1.05946 464.18 Hertz. And so the mood to the next grade of B, giving them 2 ^ (12.02) * 440 Note that we have the power 2 1 twelfth increases each time received a power of 2 that are 1 / 12, 2 / 12, 3 / 12, etc.
The beauty of this method, its accuracy, in contrast to the imprecision of PythagorasTuning method discussed above. So, if you note in the octave to the next A on the standard A to reach that vibrate at twice the frequency of 440 Hz at the original received, we have an eighth = 440 * 2 ^ (12/12), 440 * 2 = 880 Hz, as it should be exact ---. As we mentioned earlier, when the method of Pythagorean tuning, does not mean the repeated use of the relation 3 / 2 done, and must therefore be accommodation in order to reconcile the inaccuracy of this method.These accommodations tangible result in dissonance between some notes, and in particular key.
This atmosphere makes it clear that mathematics and music are intertwined with each other well, and indeed one might say that these two disciplines are inextricably linked. Music is mathematics and mathematics is really, well, musical. Since many people think of musical talent from the "creative" forms and mathematical skills such as "nerd" or non-creative, this article in somePart to help people get rid of them this term. But the question remains: when two seemingly disparate fields such as music and mathematics are happily married, are, as in many other areas that we have to do, at first glance to do with mathematics, linked to the complexity of this fascinating subject . Meditate for a while '.
