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johann sebastian bach's tuning
Description
Johann Sebastian Bach's tuning:
I believe that Johann Sebastian Bach notated a specific method of keyboard tuning. He did not express it in our normally-expected formats of theory, or numbers, but rather drew a diagram for a practical hands-on sequence. The resulting temperament has been absent from our history books: lost under layers of assumptions and habits that have led away from it.
I believe its particular sound, as an integrated part of musical practice, has profound implications for all of Bach's instrumental and vocal music that uses keyboards: either with written-out parts or in the basso continuo.
My main scholarly article proposing this reading of the evidence is published in the February and May 2005 issues of Early Music. That article describes the historical context and provides musical and mathematical analysis ...
I believe that Johann Sebastian Bach notated a specific method of keyboard tuning. He did not express it in our normally-expected formats of theory, or numbers, but rather drew a diagram for a practical hands-on sequence. The resulting temperament has been absent from our history books: lost under layers of assumptions and habits that have led away from it.
I believe its particular sound, as an integrated part of musical practice, has profound implications for all of Bach's instrumental and vocal music that uses keyboards: either with written-out parts or in the basso continuo.
My main scholarly article proposing this reading of the evidence is published in the February and May 2005 issues of Early Music. That article describes the historical context and provides musical and mathematical analysis ...
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Dec 11, 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:
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:
Music that is tonal and intensely contrapuntal inspired by New Orleans and classical music traditions.
Category:
Tuning and Maintenance of English-made Concertinas.
The information is generally applicable to Anglo Concertinas which have been manufactured in England, or according to the construction practices common in England. Some of the information is also applicable to the tuning and maintenance of Accordions, Melodeons, and Anglo concertinas manufactured in other locations, such as Germany, Italy, etc. You will have to use some imagination to determine how best to apply the applicable parts, and even to determine which parts are applicable....
The information is generally applicable to Anglo Concertinas which have been manufactured in England, or according to the construction practices common in England. Some of the information is also applicable to the tuning and maintenance of Accordions, Melodeons, and Anglo concertinas manufactured in other locations, such as Germany, Italy, etc. You will have to use some imagination to determine how best to apply the applicable parts, and even to determine which parts are applicable....
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The first time that I visited Ivor Darreg (in 1981) he was living in Glendale, California. I was impressed by his amazing array of experimental instruments, but what grabbed me most was his re-fretted guitars. He had a large collection of them, guitars that he had carefully altered over the years. There were so many that it was a veritable feast to me! I had never played re-fretted guitars before, and it was almost overwhelming. Many of his guitars were pretty trashy - Ivor was not a wealthy man, but his dedication to the exploration of alternative tunings was quite impressive. A handful of them were pretty good - I think that I played all of them for a few minutes that unforgettable day....
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