The Melody Book is about some great song subsets arranged for piano in the simplest possible way without losing the beauty of the composition. So for example nothing is simplified to just a minor or major chord. The full code is used for example on this verse extract, if you look and hear closely the code is C, B6, G7, A7. And it can be clearly seen that in this great song by Savage Garden, this is how J. S. Bach would have written it too. So no C E G, B D F, G B D, A C E. But exactly as it can be seen on Back's manual on composition for his students: Bach General Bass Rules pdf:
https://normanschmidt.net/scores/bachjs-general_bass_rules.pdf
Bach and his great Italian contemporaries for example were really advanced at that time.
They did not even need to write whether a chord is minor or major since this was automatically derived from the scale used by choosing the right note 3 or 5 or 7 or 9 or 11 or 13 or 15 steps above bass. Om music everything we reference everything to the white keys of the piano keyboard.
So in our Moon and Back Example:
The key is C minor, meaning that all B, E, A are flat ie bB, bE, bA.
So the figured bass code C, B6, G7, A7 is really:
C with bE with G
bB with D with G (not F)
G with bB with D with F
bA with C with bE with G
which is "modern" notation is
Cm
bB6
Gm7
Amaj7
The problem with the modern notation is that chords appear to come out of thin air, with nobody really knowing how they came from.
Where as on Bach's great teaching all you need to know is that you step bass down the scale, avoid parallel 5ths ie C and G, B and F, and using the principle of least change in music, which may come from the fact that we prepare 7ths, 9ths, for the listener's brain.
So instead of
C bE G
bB D F (wrong as it sounds really bad)
G bB D
bA C bE
we have
C bE G
bB D G (note how G is kept)
G bB D F
G A C bE (which is really bA C bE G in a different order).
So to recap, we can only write or play
C
B6
G7
A7
and have a masterpiece created or recreated.
You are welcome to try the correct version on the above score on any keyboard and hear the magic of just 3 or 4 part harmony correctly or rather beautifully implemented.
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