Keyboard Harmony – Schillinger Resultants – Bach Chorales

Principles and exercises taken from Keyboard Harmony Part III -
1923 by Carolyn Alden Alchin (see scans at bottom of this post)

It’s an amazing book (impossible to find, and I mean Amazon, eBay, Abe Books, et al) on modulation with exercises for the intention of learning to improvise at the keyboard. She uses Bach chorales as her examples to illustrate the particular modulation being considered. Well I have no interest in improvising on the piano whatsoever, but as a composer, I have an incredible interest in Bach and his chorales since they are just gems of instruction on modulations. So when she illustrates a modulation, (say, “move to the new key through the III chord;” or “modulate to the dominant key” etc.) I am using Schillinger resultants for a rhythm pattern. She does from time to suggest patterns in the book as well saying:

21. “The student should now improvise, applying the principles of the foregoing discussions. It will no doubt be easier if the rhythmic groups are planned first. The same pattern may be used for the after-phrase, or it may be varied. The choice of keys is optional. That is, the after-phrase may be all in D, or, the first section in A.
At this time, make the changes from I to I, not because it is necessarily the best way, but to acquire skill by doing a definite thing, and not simply letting the hands wander over the keyboard in a haphazard way.”

Since the Bach chorales have accompanying text, I have borrowed his Cantata text settings for my chorales since often times the prosody between the text and chord choices are part of the effect; since the original German text rhymes and the English translations don’t, I simply change what I like of the text to suit my purpose if I so decide.

Note: The Schillinger resultant is only rendered in the Soprano since that is the melody in the chorale and the other three voices are accompaniment with respective passing tones to generate rhythms of their own which compliment the resultant.

Play Example:


r3÷2 Balanced

r3÷2 Balanced

Play Example:


r3÷2 Balanced - modulating from I to V back to I

r3÷2 Balanced - modulating from I to V back to I

Play Example:


r3÷2 Balanced - Modulating I to V to I

r3÷2 Balanced - Modulating I to V to I

Play Example:


Modulate from I to V by means of vii7

Modulate from I to V by means of vii7

Play Example:



Old I to New I of Dominant

Old I to New I of Dominant

Play Example:



Old I to New V of Dominant

Old I to New V of Dominant

Play Example: r3÷2 Expanded [E = ra ÷ b + ra + b]


Old I to New IV of Dominant Key - r3÷2 Expanded

Old I to New IV of Dominant Key - r3÷2 Expanded

Play Example: r3÷2 Expanded [E = ra ÷ b + ra + b]


Old I to New vi of Dominant Key - r3÷2 Expanded

Old I to New vi of Dominant Key - r3÷2 Expanded

Play Example: r3÷2 Expanded [E = ra ÷ b + ra + b]


Old I to New III of Dominant Key - r3÷2 Expanded

Old I to New III of Dominant Key - r3÷2 Expanded

Play Example: r3÷2 Expanded [E = ra ÷ b + ra + b]


Old I to New vii7 of Dominant Key

Old I to New vii7 of Dominant Key

Play Example: r4÷3 Balanced [B = r4 ÷ 3 + r4 ÷ 3 + [4(4-3)=4]


Modulate from Old I to IV of Dominant

Modulate from Old I to IV of Dominant

Keyboard Harmony - Carolyn Alden Alchin - 1923 Hollywood, California

Keyboard Harmony - Carolyn Alden Alchin - 1923 Hollywood, California

Keyboard Harmony - Carolyn Alden Alchin Part 3 - Hollywood, California USA

Keyboard Harmony - Carolyn Alden Alchin Part 3 - Hollywood, California USA

Keyboard Harmony - Part III Pg. 9

Keyboard Harmony - Part III Pg. 9

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Published in: on May 13, 2009 at 7:45 pm  Leave a Comment  
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