About the MIDI Files for Bach's Goldberg Variations
© 2011 Ed Kotski
MIDI ( .mid ) files will play music, although the sound a listener hears depends somewhat on the listener's own computer. My files are in MIDI Type 1 format, which means that the individual parts have their own staff. If you have music reading and writing software you should be able to see and manipulate the music in addition to hearing it.
MIDI files are instructions which tell the sound programs on individual computers the proper notes to play. They are the equivalent of electronic sheet music, and are not actual recordings. MIDI files are much smaller than real music files, and so take up less space and download faster. They have an additional property that can be exploited by a mildly skilled user, in that they can be taken apart for viewing and modification. Music writing programs can work with them, and, after conversion, so can word processors.
Two free programs mf2t.exe and t2mf.exe, along with instructions in a text file, are readily available on the web for download. mf2t turns a midi file into a simple text file which lists the notes, the instruments (identified by numbers), tempi, and special effects. t2mf turns the text file back into a MIDI file. These are very powerful programs for someone so inclined.
The Goldberg MIDI files
Bach often inverted his themes, in the sense of turning them upside down and mirroring them about some line or space on the staff. The Goldberg - Agnus Dei is a good example. He apparently used the original Gregorian melody of the Agnus Dei as a starting point to generate the first voice (tenor) of his canon. Once he found a suitable melody for the first he used that melody to generate the second part's line at the seventh.
In the process, he continued to harmonize with the Agnus Dei, although he did not try to harmonize it exactly. The first "re" of miserere is a B natural in the original chant, and it clashes with Bach's B flat. I left the chant in its native form in the first eight measures.
Bach's inverted (and modified) themes in measures 9 - 16 do not harmonize with the original Gregorian Agnus. So, how did he come up with his new themes? He transposed the original chant, from the natural A minor to the natural C minor, and then inverted it, mirroring it about high C. He then found a second voice (soprano) which harmonized with the inverted Agnus, and then worked out the first voice (tenor). There are no clashes.