Notes with a displeasing blendĪre dissonances. The degree of harmony depends on how the respectiveįundamental frequencies and overtones blend together. Consonance Now consider two strings which are plucked Ratios The theories of Pythagoras and Helmholtzĭepend on the frequency ratios shown in Table 1.įrequency and its overtones, as well as to relationship between Plucking a string thus excites a number of tones. The noteĪlso has overtones at consecutive integer multiples of its fundamentalįrequency. Natural Frequencies of Strings A note played on a string has aįundamental frequency, which is its lowest natural frequency. 'On the Sensations of Tone' to establish the scientific basis of (1821-1894) made further contributions to music theory. When the higher frequency is twice the lower frequency. When he plucked each string, heĭiscovered that the shorter string produced a pitch which was one He thenĭivided one string exactly in half. He subjected two strings to equal tension. Observations in music, mathematics, and astronomy. Pythagoras and his followers believed that all relations could be Philosopher and mathematician, who lived from approximately 560 to 480īC. _ Historical Background Pythagoras of Samos was a Greek Sound Files for Ratios piano_octave_A_A.mp3 piano_twelfth_A_E.mp3 piano_fifth_A_E.mp3 piano_fourth_A_D.mp3 piano_Major_Third_A_C_sharp.mp3 piano_Major_Sixth_A_F_sharp.mp3ĪN INTRODUCTION TO MUSIC THEORY By Tom Irvine tuningfork440.mp3 Kawai Piano (not perfectly tuned) piano_middle_C.mp3 piano_C_sharp.mp3 piano_D.mp3 piano_D_sharp.mp3 piano_E.mp3 piano_F.mp3 piano_F_sharp.mp3 piano_G.mp3 piano_G_sharp.mp3 piano_A.mp3 piano_A_sharp.mp3 piano_B.mp3 SOUND FILES Tuning Fork A4 note at 440 Hz. Integer multiple of the fundamental frequency. The overtones are 'harmonic' if each occurs at an OVERTONES An overtone is a higher natural frequencyįor a given string. The A5 key is thus one octave higher than A4 since it has twice theįrequency. OCTAVES For example, the A4 key has a frequency ofĤ40 Hz.

PIANO KEYBOARD The number beside each key is theįundamental frequency in units of cycles per seconds, or Hertz.

Piano strings theory