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MATH AND MUSIC

MATH AND MUSIC. Ms. Wiltshire’s Math Class Horace Mann Middle School. PYTHAGORAS. I was considered to be a Greek philosopher who was responsible for developments in mathematics, astronomy and the theory of music.  Born: 582? BC in Samos, Ionia {y-ohn'-ee-uh}

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MATH AND MUSIC

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  1. MATH AND MUSIC Ms. Wiltshire’s Math Class Horace Mann Middle School

  2. PYTHAGORAS • I was considered to be a Greek philosopher who was responsible for developments in mathematics, astronomy and the theory of music.  • Born: 582? BC in Samos, Ionia {y-ohn'-ee-uh} • Died: about 500 BC in Metapontum, Lucania

  3. PYTHAGOREANS • The Pythagoreans and I noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers.

  4. BASIC MUSIC TERMS • Rhythm is the basis of music just as numbers are the basis of math

  5. BASIC MUSIC TERMS • "Measure" is the space between two bar lines on the staff that represents the division of time by which air and movement of music are regulated.

  6. BASIC MUSIC TERMS • The pitch of a tone is the listener’s evaluation of the frequency (number of vibrations per second usually shown in Hertz) and is perceived as how high or low a note sounds. The higher the frequency ,the higher the pitch. The lower the frequency, the lower the pitch.

  7. BASIC MUSIC TERMS • Time signature is found at the beginning of the piece next to the key signature. It looks like a fraction without a dividing bar such as 34 or 44 .

  8. PYTHAGORAS & MUSIC • He observed that when the blacksmith struck his anvil, different notes were produced according to the weight of the hammer. • Pythagoras discovered that the frequency (pitch) of a vibrating string is proportional to its length. Doubling the length of a vibrating string lowers the pitch by one octave. If one string is twice as long as the other, the pitch of the shorter string is one octave higher than the longer.  If the length of one string is 2/3 the length of the other, the change in pitch is a fifth.  If the length of one string is 3/4 the length of the other, the change in pitch is a fourth. 

  9. Thanks to Pythagoras, we have a scale that measures pitch and frequency called the dB scale. The scale is based on a logarithm function. As the dB level increases the rate at which one can have hearing loss increases. The softest sound a human can hear is set at 0 decibels. A rock concert can be 10^13 times stronger. We need to understand that loud music can have harmful effects and it is, of course, measured mathematically. Again thanks, Pythagoras.

  10. Are math and music related? • Math and music are related. • Without math: • We could not have timing or beats in our music. • We may have high levels of hearing loss because we would not be able to measure sound. • We would not have different types of instruments. • We would not be able to distinguish between types of music. • And last, we would not make any money at concerts 

  11. Resources “Astronomy.Rocks: Pythagoras of Samos.” Intelligent Child. Intelligent Child. 26 June 2001 http://www.intelligentchild.com/astronomy/pythagoras.html. Eisenkraft, Arthur. “Medicine: Hearing”. Active Physics. 2000. Its About Time. Katz, Nikki. “Mathematicians: Pythagoras”. Math For Kids. 12 March 2001. About.com. 26 June 2001. http://kidsmath.about.com/kids/kidsmath/library/weekly/aa031201a.htm “Online Math Applications: Math and Music”. Online Math Applications. 26 June 2001. Thinkquest. http://tqjunior.thinkquest.org/4116/Music/music.htm

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