The Derivation of Radially Symmetrical Altered Scales
it covers minor and major pentatonics; aeolian/ionian etc modes; the double harmonic scale; the melodic minor modes; wholetone scales; the diminished scale and the major bebop scale.
these are all obtained by using extremely basic laws of physics and strict logic in only six short steps.
please click below to read this one-page lesson:
https://www.jeff-brent.com/lessons/evolutionofthemajorscale_parttwo.html
There are 11 comments, leave a comment.
2. does it sound good?
yes, but it does nothing to change the way one listen's to music. (not that an article really can)
thanks
it's interesting, but i'm not sure how 'scientific' selectively preserving or neutralising flats and sharps is...
the bottom line is that maths and music are not easy bedfellows. as we know, 12 intervals of a perfect 5th does not quite equal 7 intervals of an octave. the circle of fifths is really a spiral, and not a very regular sort of a spiral at that. there is the pythagorean comma, there is mercator's comma. there is also the harmonic series, which is a direct route to all sorts of unsolved mysteries and points of contention in both music and maths.
my very loose personal theory is that the vibration of a single string and the harmonic series of pitches which it causes, which skew ever more wildly away from the 12 tones pianists use, is directly connected in some as yet undiscovered way to these discrepencies in the circle of fifths, and maybe to a whole lot more.
here's a link you might or might not be interested in:
https://ray.tomes.biz/maths.html
i agree with paul b - raising or lowering notes arbitrarily doesn't strike me as "strict logic"
i've had another quick look and i can see what you are getting at - even if the bb is substituted for the b and the f# for the f, the structure remains symmetrical.
it's interesting to me that the centre of symmetry for 7 perfect 4ths is the note which corresponds to the root of the dorian mode.
also that the centre of symmetry in fig. 8 is the note which corresponds to the root of the lydian dominant scale.
this would give the dorian mode and the lydian dominant mode some special significance and its interesting that they feature a lot in jazz.
anyway the symmetry is very interesting and you have certainly revealed something. the science only becomes a problem when we try and make the 12 tone system work across multiple octaves - because of the compromises involved.
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