Johann Sebastian Back was a Scientist

(Random notes for a lecture on music)

Johann Sebastian Bach was the greatest baroque composer. His death in 1750 is used as the ending date of the baroque era.

Contributions

His music, especially the cantatas, are the basis for modern music theory. Chord structure, etc. Some rules ("never double the seventh") are followed simply because that is how Bach did it.

His book "Das Wohltempierte Klavier" (The Well-Tempered Clavier) was written to advocate the equal-temperament method of tuning. It contains compositions in each of the major and minor keys, as proof that the equal tempered tuning system works for all keys. We still use equal tempered tuning today.

Math in Music and tuning problems

Play a note on a stringed instrument. Press down in the center of the string, and play again. The note is an octave higher. Each time you divide the string by 2, the note is raised on octave.

Sound is made of waves. Notes are sound of specific frequencies (waves per second). Middle A is 440 waves for second or 440 hertz. Each time you double the frequency the notes is raised on octave; each time you halve the frequency the note is lowered an octave. (Because of this, note frequencies follow a logarithm scale.)

An interval of a fifth (five notes scale) follows the ratio 3/2. E above middle A is 660 Hz. A fourth is 4/3. Note that fifth+fourth = 3/2 * 4/3 = (cancel 3's) 4/2 = 2/1 = octave. A major third is 5/4, so middle C is 550 Hz. etc. (Pythagorus was among the first to notice these relations.)

One can get all 12 notes of the keyboard but progressing through the circle of fifths, going up 12 fifths (3/2¹² = 129.75), and down an octave when needed (7 octaves = 2⁷ = 128), but you don't end up back exactly the same frequency you started at. And small differences in frequency are very noticable to the ear as dissonance.

Eventually, there were various systems of tuning developed (Just intonation), but an instrument tuned in the key of C would sound bad when played with an instruments tuned in the key of B-flat, for example. Some players of wind instruments, such as recorders, would carry around a number of instruments, each tuned to a different key. But an organist or pianist cannot do that.

Bach advocated a new tuning system call Equal Temperament, in which each of the 12 notes of the chromatic scale are spaced at equal intervals (a ratio equal to the twelfth root of 2). He published "Das Wohltempierte Klavier", a book with 24 original compositions in each of the major and minor keys to show that an instrument tuned in Equal Temperament sounded good in any key. He later published a second volume of 24 more pieces.

Other notable accomplishments

He was famous in his day as a great Organ player, and often called upon to test new organs.

Much of his music is counterpoint (two or more melodies which are played at the same time and complement each other). Counterpoint is considered the most complex form of music and his counterpoint is considered the most complex of any. (e.g. two or three-part invention)

He stated all his music was done for the glory of God.

Another new science

Bach's music was respected by other composers, but nearly forgotten by the public until 1829, when the composer Felix Mendelssohn rediscovered and staged a performance of Bach's "St. Matthew Passion". This started a revival of interest in Bach's music and Mendelssohn become known as the first Musicologist.