|There is one thing more painful than learning from mistakes (our own or somebody else's): Not learning from them. - Barbara Johnson|
A musical interval is the ratio or space between two musical notes.
Pythagorous of Samos (c.582 - c.507 B.C.) is credited with the idea of tuning an instrument up and down by fifths to create a complete musical scale that sounded harmonious. By tuning each successive note in turn by the ratio of a fifth in the pattern of the Circle of Fifths, Pythagoras realized that eventually he returned to almost an exact higher octave of the note he started with. There is, however, a slight error between the octave harmonic relationships and the tuning by fifths that occurs when you tune using this method. The error is today still called the Pythagorean comma and represents a ratio of about 74/73.
If you would like hear these sound ratios at length, BioWaves has produced several meditation CD's that use some of the above intervals. The Perfect Fifth is comfortable to listen to, the Tri-Tone Drone is for balancing and increasing consciousness, while the experimental Phi-Tone Drone uses the Golden Mean Ratio.
These note relationships, or intervals, are used in creating a musical scale. But the error from the Pythagorian Comma means that a scale cannot be truly harmonic.
Longitudinal Wavelength Sound Waves Pitch and Frequency Speed of Sound Doppler Effect Sound Intensity and Decibels Sound Wave Interference Beat Frequencies Binaural Beat Frequencies Sound Resonance and Natural Resonant Frequency Natural Resonance Quality (Q) Forced Vibration Frequency Entrainment Vibrational Modes Standing Waves Law of Octaves Psychoacoustics Tacoma Narrows Bridge Schumann Resonance Animal BioAcoustics More on Sound
Law Of Octaves Sound Harmonics Western Musical Chords Musical Scales Musical Intervals Musical Mathematical Terminology Music of the Spheres Fibonacci Sequence Circle of Fifths Pythagorean Comma
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Aristotle Copernicus Einstein Fibonacci Hermann von Helmholtz Kepler Sir Isaac Newton Max Planck Ptolemy Pythagoras Thomas Young
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