1 Hz). This follows from modulation theory. The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval is dissonant. Helmholtz proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35 Hz. Scales The material of a musical composition is usually taken from a collection of pitches known as a scale. Because most people cannot adequately determine absolute frequencies, the identity of a scale lies in the ratios of frequencies between its tones (known as intervals). The diatonic scale appears in writing throughout history, consisting of seven tones in each octave. In just intonation the diatonic scale may be easily constructed using the three simplest intervals within the octave, the perfect fifth (3/2), perfect fourth (4/3), and the major third (5/4). As forms of the fifth and third are naturally present in the overtone series of harmonic resonators, this is a very simple process. The following table shows the ratios between the frequencies of all the notes of the just major scale and the fixed frequency of the first note of the scale. There are other scales available through just intonation, for example the minor scale. Scales that do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are called temperaments, of which equal temperament is the most used. Temperaments, though they obscure the acoustical purity of just intervals, often have desirable properties, such as a closed circle of fifths. See also Acoustic resonance Cymatics Mathematics of musical scales String resonance Vibrating string 3rd bridge (harmonic resonance based on equal string divisions) Basic physics of the violin References External links Music acoustics - sound files, animations and illustrations - University of New South Wales Acoustics collection - descriptions, photos, and video clips of the apparatus for research in musical acoustics by Prof. Dayton Miller The Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA) The Musical Acoustics Research Library (MARL) Acoustics Group/Acoustics and Music Technology courses - University of Edinburgh Acoustics Research Group - Open University The music acoustics group at Speech, Music and Hearing KTH The physics of harpsichord sound Visual music Savart Journal - The open access online journal of science and technology of stringed musical instruments Interference and Consonance from Physclips Curso de Acústica Musical (Spanish) Acoustics Musical terminology