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understanding temperaments
Description
Overview of historical temperaments on keyboard instruments.
The need for temperament arises because it is impossible to have octaves, fifths, thirds, etc., all pure at once, or, in other words, because the ratios of the different pure intervals are incompatible....
temperament, tuning, Pythagore, just intonation, Aaron, Silbermann, Salinas, Kirnberger, Vallotti, Werckmeister, LewareQC
The need for temperament arises because it is impossible to have octaves, fifths, thirds, etc., all pure at once, or, in other words, because the ratios of the different pure intervals are incompatible....
temperament, tuning, Pythagore, just intonation, Aaron, Silbermann, Salinas, Kirnberger, Vallotti, Werckmeister, LewareQC
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May 2, 2005
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8151
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Music translated into Mathematics: Leonhard Euler: english translation;
By the middle of the 1700s, at the time when the music known as classical acquires its letters of nobility with Bach (1685-1750), Handel (1685-1759), Rameau (1683-1764), Haydn (1732-1809), Mozart (1756-1791), etc., two particularly famous mathematicians, Euler and d'Alembert, produce theories of music. This fact is obviously not the result of a "historical chance". It represents on the contrary the prolongation of one tradition.1 By the end of the previous century, several scientists had already become intrigued and put their attention on the same subject: Descartes (Compendium musicae), Galileo (end of the 1st day of Discorsi), Mersenne (the enormous work of the Universal Harmony), Leibniz "as an amateur".2 But in the 1700s, it is the music itself which changes, the traditional harmony dethroning the medieval counterpoint definitively. Thus this change had to be explained, to make the theory of it, and the task could inspire, rightly, any scientist set on music.
Euler (1707-1783) is 24 years old when he writes, in 1731, his Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae (A attempt at a new theory of music, exposed in all clearness according to the most well-founded principles of harmony). It is a work of 263 pages, written in Latin, which will be published only in 1739. It was translated into French one century later with the edition of Brussels of works of the mathematician. I will presently say some words on the quality of this translation.
In 1739 Euler is already known as a mathematician and is in St Petersburg, where he will soon occupy the Chair of mathematics. He is extremely interested by all that touches on music. He published in Basle, in 1727, a "thesis on sound" where he compares the sounds produced by the vibrating cords with those generated by the wind instruments. And about 1726 already, Euler had projected the plan of a considerable work on music. Apart from the fact that the sounds were to be noted there by sequence numbers in the scale, the object of study remained close to musical realities. The last section, for example, was to analyze the various kinds of pieces of music (saraband, courrant, etc) ...
By the middle of the 1700s, at the time when the music known as classical acquires its letters of nobility with Bach (1685-1750), Handel (1685-1759), Rameau (1683-1764), Haydn (1732-1809), Mozart (1756-1791), etc., two particularly famous mathematicians, Euler and d'Alembert, produce theories of music. This fact is obviously not the result of a "historical chance". It represents on the contrary the prolongation of one tradition.1 By the end of the previous century, several scientists had already become intrigued and put their attention on the same subject: Descartes (Compendium musicae), Galileo (end of the 1st day of Discorsi), Mersenne (the enormous work of the Universal Harmony), Leibniz "as an amateur".2 But in the 1700s, it is the music itself which changes, the traditional harmony dethroning the medieval counterpoint definitively. Thus this change had to be explained, to make the theory of it, and the task could inspire, rightly, any scientist set on music.
Euler (1707-1783) is 24 years old when he writes, in 1731, his Tentamen novae theoriae musicae ex certissimis harmoniae principiis dilucide expositae (A attempt at a new theory of music, exposed in all clearness according to the most well-founded principles of harmony). It is a work of 263 pages, written in Latin, which will be published only in 1739. It was translated into French one century later with the edition of Brussels of works of the mathematician. I will presently say some words on the quality of this translation.
In 1739 Euler is already known as a mathematician and is in St Petersburg, where he will soon occupy the Chair of mathematics. He is extremely interested by all that touches on music. He published in Basle, in 1727, a "thesis on sound" where he compares the sounds produced by the vibrating cords with those generated by the wind instruments. And about 1726 already, Euler had projected the plan of a considerable work on music. Apart from the fact that the sounds were to be noted there by sequence numbers in the scale, the object of study remained close to musical realities. The last section, for example, was to analyze the various kinds of pieces of music (saraband, courrant, etc) ...
Category:
2. music theory
Musically theoretical models, musical structures, algorithmic composition.
music theory, harmony, harmonic bindings, G-systems, musical structures, algorithmic composition, algebraic theory
music theory, harmony, harmonic bindings, G-systems, musical structures, algorithmic composition, algebraic theory
Category:
Physics of Music - Notes.
Physics of Music, Musical Scales,
Physics of Musical Instruments, PVC Flute, Equal Temperament,
Musical Scale, Just Temperament, Overtones, Harmonics,
Finger Holes, Wind Chime, Music Composition Paper.
MTU Department of Physics in the College of Sciences and Arts.
Physics, Department of Physics, MTU, Michigan Technological University, academics, research, people, alumni, features, contact, site map
Physics of Music, Musical Scales,
Physics of Musical Instruments, PVC Flute, Equal Temperament,
Musical Scale, Just Temperament, Overtones, Harmonics,
Finger Holes, Wind Chime, Music Composition Paper.
MTU Department of Physics in the College of Sciences and Arts.
Physics, Department of Physics, MTU, Michigan Technological University, academics, research, people, alumni, features, contact, site map
Category:
A musically theoretical model.
The paper submits a musically theoretical model of relations among the tones in the harmonic music stream.
Energy bands (zones) are associated with the tones of a regular musical system. The bands influence each another, the bindings exhausting energy from the bands....
music theory, system, tonality, modality, harmony, harmonic bindings, harmonic functions, physics, continuity, impulse, algorithmic composition
The paper submits a musically theoretical model of relations among the tones in the harmonic music stream.
Energy bands (zones) are associated with the tones of a regular musical system. The bands influence each another, the bindings exhausting energy from the bands....
music theory, system, tonality, modality, harmony, harmonic bindings, harmonic functions, physics, continuity, impulse, algorithmic composition
Category:
Music that is tonal and intensely contrapuntal inspired by New Orleans and classical music traditions.
Category:
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