| | Category | MA | P21 | Harmony and Discord |
| | Abstract | Harmony and Discord |
| | Pelham C. Barron |
| | Huron High School, Ann Arbor, Michigan |
| | |
| | This project compared irrational ratios of sound wave frequencies with |
| | rational ratios of sound wave frequencies. These were generated by |
| | plucking taut strings of specific lengths and subjectively rating them as |
| | harmonious or discordant. Drawings of the frequency ratios were |
| | produced by a harmonograph and a computer model. The closer the |
| | irrational ratio was to a rational ratio, the more organized and less chaotic |
| | the drawing was. Ratios very close to rational ratios almost sounded |
| | pretty good while those that were way off sounded very dissonant or out |
| | of tune. Frequencies in rational number ratios align themselves periodically |
| | caused the rational sounds and drawings to look neat. The irrational ratio |
| | drawing and sounds never completely aligned making the drawing and |
| | sound very chaotic. |
| | |
| | Bibliography | Harmonograph, A visual Guide to the Mathematics of Music |
| | by Anthony Ashton 2003 |
| | |
| | The World of Mathematics– chapter ‘The Mathematics of Music’ |
| | by James Roy Newman 2000 |
| | |
| | Temperament: The Idea That Solved Music's Greatest Riddle |
| | by Isacoff, Stuart M. 2001 |
| | |
| | Paper: |
| | On Regulation and Hidden Harmony William S. Huff 2008 |