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emusic theory
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eMusicTheory.com provides online tools for teachers and students of basic music theory, everywhere.
music, theory, teacher, learn, online, scale, chord, staff, triad, seventh
music, theory, teacher, learn, online, scale, chord, staff, triad, seventh
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Apr 30, 2005
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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:
Few musicians know that keyboard instruments are not tuned today as in Bach’s day and before. Even fewer people understand the differences and are able to tune a piano or harpsichord as did Bach and other composers before him. Such music was composed to be played on specific tunings such as meantone or well temperament, not equal temperament, which is almost exclusively used today....
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The musical temperament of Bach comprises within its circle 5 well tempered fifths and 7 perfect fifths.
Bach,
Das wohltemperierte Clavier,
Das wohltemperirte Clavier,
wohltemperiert,
wohltemperirt,
well-tempered,
welltempered,
well tempered,
Forty-Eight,
Musical temperament,
tuning,
organ,
organs,
harpsichord,
Orgeln,
Cembali,
Werckmeister,
Kirnberger,
Herbert Anton Kellner
Bach,
Das wohltemperierte Clavier,
Das wohltemperirte Clavier,
wohltemperiert,
wohltemperirt,
well-tempered,
welltempered,
well tempered,
Forty-Eight,
Musical temperament,
tuning,
organ,
organs,
harpsichord,
Orgeln,
Cembali,
Werckmeister,
Kirnberger,
Herbert Anton Kellner
Category:
4. mark sherman
Mark Sherman: Music Instructor:
Mark Sherman teaches improvisational music:
Juilliard graduate, Lincoln Center soloist, well-known artist and resident of Riverdale, New York. Mark Sherman will take your music skills to a new level. Using unique teaching methods, Mark offers a variety of programs that fit any budget or intensity level.
Teaching:
Drums, percussion, including mallets (vibes, marimba), improvisational skills (soloing), classical, repetoire, piano, harmony, music concepts.
All ages.
Mark Sherman teaches improvisational music:
Juilliard graduate, Lincoln Center soloist, well-known artist and resident of Riverdale, New York. Mark Sherman will take your music skills to a new level. Using unique teaching methods, Mark offers a variety of programs that fit any budget or intensity level.
Teaching:
Drums, percussion, including mallets (vibes, marimba), improvisational skills (soloing), classical, repetoire, piano, harmony, music concepts.
All ages.
Category:
Beethoven in the temperaments-historical tunings on the modern concert grand.
"Temperament" is both the process and result of making slight changes to the pitches of a pure musical scale, so that the octave may be conveniently divided into a usable number of notes and intervals. In the history of Western music's 12-note octave tradition, there have been several, fundamentally different forms of temperament applied to the developing keyboard. Music suffers when performed in a tuning that is different than that which the composer used in its creation...
tuning, pianos, pianos beethoven, temperaments
"Temperament" is both the process and result of making slight changes to the pitches of a pure musical scale, so that the octave may be conveniently divided into a usable number of notes and intervals. In the history of Western music's 12-note octave tradition, there have been several, fundamentally different forms of temperament applied to the developing keyboard. Music suffers when performed in a tuning that is different than that which the composer used in its creation...
tuning, pianos, pianos beethoven, temperaments
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