Weierstrass:

(1815 -1897) German mathematician, considered the originator of modern analysis; he formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano–Weierstrass theorem using it to study the properties of continuous functions on closed bounded intervals.  Although he left university without a degree, he studied mathematics and trained as a teacher, eventually teaching mathematics, physics, botany and gymnastics. 

 

tone colour and tone effects:

(aka timbre) sound which is NOT characterized as pitch, rhythm or volume but is that which identifies a specific instrument (e.g. a trumpet sounds different from a violin, even if they play a tone at the same frequency, amplitude, duration); differentiates between instruments of the same type.  It is produced by several factors: the raw material of the instrument (wood versus metal); variations within the material (silver flute versus steel); different performance techniques used by the player.

 

bow instruments:

Cello, Double bass, Hurdy-gurdy, Viol, Viola, Violin

 

space commanding (organ): * see Endnote 15

a musical instrument producing sound by driving pressurized air through organ pipes selected via a keyboard.  Each pipe produces a single pitch, the pipes are provided in sets called ranks, each having a common timbre & volume throughout the keyboard compass.  Most organs have multiple ranks of pipes of differing timbre, pitch & volume that can be employed singly or in combination through the use of controls (stops).  The first organ was built in Winchester Cathedral in the 10th century, with 400 pipes, it could be heard throughout the city.  By the 17th century, most of the sounds available on the modern classical organ had been developed.  From that time, the pipe organ was the most complex man-made device - a distinction it retained until it was displaced by the telephone exchange in the late 19th century.

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Bach JS:

(1685-1750) German composer & musician of the Baroque period, known for instrumental compositions(Brandenburg Concertos, Goldberg Variations) & vocal music (St Matthew Passion, Mass in B minor.).  As a young man he worked as a musician for various Lutheran Churches in Germany, to include courts at Weimar where he developed his repertoire for the organ.  In 1723 he began work as a cantor in Leipzig & composed music for the Lutheran churches of the city & for its university's student ensemble.  In 1726 he began publishing his keyboard & organ music.  In 1736 he was granted the title of court composer by the Elector of Saxony & King of Poland. In his final decades he reworked and extended many of his earlier compositions.

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four human voices:

Soprano (a high female or young boy’s voice)-Alto (a low female or young boy’s voice)-Tenor (a high adult male voice)-Bass (a low adult male voice)

 

modern orchestra: * see Endnote 16

organized according to a logical order of categories (string, woodwind, brass, percussion), then families, high to low (strings from violin to double bass; woodwinds from highest piccolo to bassoon; brass from French horn to tuba; percussion from Timpani to organ)