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Godel Escher Bach in Discovery
Posted:
Apr 11, 2000 1:33 AM
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It was quite a few months ago that you set up a musical puzzle that
had quite a few mistakes in it. When you set up the musical scale upon
the keyboard you inadvertantly forgot the flats and only used the
sharps also the western uses of the scale are seemingly what you were
asking to create. This leaves out many scales that are arabic,
Japanese, Chinese, Persian etc. Major scales in western music are from
any tone ABCDEFG and all can be flatted and sharped. The pattern is:
tone whole step whole step half step whole step whole step whole step
and a final half step. The minor scales (there are three types:
natural, harmonic and melodic) are created upon the shifted whole and
half steps starting on the sixth degree of the major scale it is then:
tone whole step half step whole step whole step half step whole step
whole step. Thus,the Natural minor scale named a minor is A B C D E F
G A . To get the Harmonic minor, raise the seventh degree to G sharp.
The Melodic minor raises the sixth and seventh degrees ( F sharp and G
sharp) but this is only when going up the scale, when going down you
use the un-raised or natural tones. You also overlooked the ancient
Greek modes and the related scales such as the Locrian mode. One must
not forget that all tones can be flatted and shaped, thus C major CAN
be also thought of as B sharp major, D sharp=E flat E sharp=F etc.
etc. this is the reason JS Bach wrote 24 parts to the Well Tempered
Clavier-- and it was so amazing he wote a complete cycle in the 1740s
So, you may wnat to research this and include as much of the truly
usable and thus used scales but don't forget the pentatonic, whole
tone, Neapolitan, Spanish and even more obscure but still used scales.
Your original quiz was wonderfully thought provoking in a mathematical
way but preposterous in a purely musical way and it ignores the
history of music in a large way. Please look into this there are many
books and many are easy to understand and there are some books of just
scales and chords in musical staff that can clarify. Sorry to nit pick
but minutiae in music is what my life is all about. Ole Bach wouldn't
have it any otherway either! By the way, my e-mail is clavecin and
that is French for HARPSICHORD. Hope all is well and hope to hear from
you soon.
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