Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Maths and music ppt by Aninda Siddique 3314 views
- Pythagoras and Music by luciano2428 19434 views
- The Connection Between Music and Math by Judah Blumenthal 1858 views
- Math and music by Nurik Ibrahim 3383 views
- Music as Math by Ken James Palacios 3253 views
- From music to math teaching fractio... by Beth Campbell 7827 views

12,679 views

Published on

A powerpoint and podcast presentation on the connection of mathematics and music

Published in:
Education

No Downloads

Total views

12,679

On SlideShare

0

From Embeds

0

Number of Embeds

13

Shares

0

Downloads

306

Comments

0

Likes

4

No embeds

No notes for slide

- 1. Math and Music<br />How are they related?<br />A Think Quest<br />By Ms. Cogley<br />
- 2. Math & Music<br />Math and music have always been considered closely connected in many ways.<br />It is widely believed that students who do well in music also excel in math. <br />Let’s take a look at some of the basic components of music and see what math has to do with them. <br />
- 3. Rhythm is to Music as Numbers are to Math<br />Rhythm measures time<br />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<br />When you play a few different notes together or even repeat the same note on an instrument, you create something called rhythm.<br />
- 4. "Give me an A" = 440hz<br />Music is made up of sound. <br />Sound is made from repeating sound waves. <br />The musical pitch of each note has a corresponding frequency measured physically in hz (hertz) or cycles per second. <br />There are some important mathematical relationships between the notes played in music and the frequency of those notes.<br />
- 5. A table of Frequencies<br />
- 6. Pythagoras<br />The Greek octave had a mere five notes. <br />Pythagoras pointed out that each note was a fraction of a string. <br />Example: Lets say you had a string that played an A. The next note is 4/5 the length (or 5/4 the frequency) which is approximately a C. The rest of the octave has the fractions 3/4 (approximately D), 2/3 (approximately E), and 3/5 (approximately F), before you run into 1/2 which is the octave A<br />
- 7. Ratios<br />Pythagoras was excited by the idea that these ratios were made up of the numbers 1,2,3,4, and 5.<br />Why?<br />Pythagoras imagined a "music of the spheres" that was created by the universe. <br />The 18th century music of J. S. Bach, has mathematical undertones, so does the 20th century music of Philip Glass.<br />
- 8. Golden Ratio and Fibonacci<br />It is believed that some composers wrote their music using the golden ratio and the Fibonacci numbers to assist them<br />Golden Ratio: 1.6180339887<br />Fibonacci Numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21<br />
- 9. From Then to Now<br />So, how did we get the 12 notes scale out of these six notes? <br />Some unknown follower of Pythagoras tried applying these ratios to the other notes on the scale.<br />For example, B is the result of the 2/3 ratio note (E) applied to itself. 2/3 * 2/3 = 4/9 which lies between octave A (1/2) and octave C (4/10). To put B in the same octave we multiply 4/9 by two to arrive at 8/9. G is produced backward from A. As B is a full tone above A at a string ratio of 8/9, we can create a missing tone below A by lengthening the string to a ratio of 9/8. To add G to the same octave we apply 9/8 to 1/2 (octave A) and by multiplication we get 9/16 as the ratio to G. <br />BUT! There was a problem, however, if you performed this transformation a third time. The 12 tone octave created by starting with an A was different than the 12 tone octave created when you started with an A#. <br />Which means that two harps (or pianos, or any other instrument) tuned to different keys would sound out of tune with one another. Also, music written in one scale could not be transposed easily into another because it would sound quite different.<br />The solution was created around the time of Bach. A "well tempered" scale was created by using the 2 to the 1/12th power ratio mentioned above. Using an irrational number to fix music based on ratios, Pythagoras probably rolled over in his grave.<br />
- 10. Your Turn<br />I would like for you to research mathematics and it’s connection to music<br />Conduct a survey of students who played an instrument, for how long, and their grades in mathematics<br />I want to know how you feel about the two and their connection.<br />
- 11. References<br />http://en.wikipedia.org/wiki/Fibonacci_number<br />http://library.thinkquest.org/4116/Music/music.htm<br />http://www.musicmasterworks.com/ConsonanceComplication/TheComplicationWithConsonance.htm<br />http://www.mathhiker.com/archives/496<br />http://www.musicmasterworks.com/WhereMathMeetsMusic.html<br />

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment