Bach & Schillinger resultants

This post continues Keyboard Harmony modulation from the book “Keyboard Harmony” by Carolyn Alden Alchin (1923) described in detail on an earlier post. (see scans at bottom of this post)

The 1923 Keyboard Harmony book by Carolyn Alden Alchin uses three or four measures of J.S. Bach chorales to illustrate examples of modulation such as I of the old key (C) to V7 of the new key (D). So that would be a C chord to an A chord. Then she includes an excerpt from a Bach chorale illustrating that modulation. I’ll put up a scan of a page so you can see her format.

We are then to do our own modulations. Now I personally love to practice “writing” my own “Bach chorales” – of course they are my melodies, but I enjoy using the harmonies he used. I am constantly struck (not suprisingly) at the use of systems. Bach’s music is a system. If you have mastered the Hindemith Traditional harmony book1 (I mean really mastered it) then you can almost do these in your sleep. There are simply rules you follow and the music is “there.” Same with Schillinger. Now if you’re going for something more interesting then just being “there” then you need to be a composer. There is certainly no shame in not being so….have fun with it and let the math and rules make the music for you. I love that. But whether you use Schillinger to spin out the music using pitch scales set to underlying resultants, or whether you join 4-part harmony using established rules of voice leading, you are not “composing” unless you have included an “original thought”. There must be something in your “Bach chorale” or your pitch scale that is not only original but worthwhile listening to. As the law of the arts states:

“And if it be novel without being great, how shall we be the better off?”

I love doing these modulation examples to keep my pencil sharp. When I constantly practice how to modulate between the ii chord of Dmaj. for example through the vi chord of Gmaj. I can’t help but have that fluency show up in my music somewhere along the way. When I study to master the resultants of Schillinger then somewhere while composing I’m naturally going to think, “Oh r5÷4 as a phrase would be great here, let’s try it…” – after all, as composers, we are constantly looking for ways to be able to express ourselves so Schillinger is a sea of opportunities of techniques and strategies which can be applied to our “craft”. I for one, insist on myself having a “firm foundation” of traditional harmony and even species counterpoint. So the Schillinger system is a natural progression for me as a composer and I intend to learn as much as possible. My goal is Mastery.

Ok, back to the post. These pieces therefore use Schillinger resultants in fractioned, unfractioned, balanced, contracted and expanded forms. I’m introducing them in no particular order other then typically starting with the least complex first (unfractioned) beginning in the lower part of the Power series working up to the move involved (expanded in the upper portions of the Power series).

You can see I’ve left r3÷2 and now am moving into the 4 and 5 section of the Power series. BTW, isn’t it interesting how Schillinger uses the term “Power Series”? The word “Power” at least in the U.S. became totally way over-used in the 1990’s – there was “Power” everything: personal power, power bars, power drinks, power this and power that. Schillingers use of the word seems to naturally and seemlessly flow in today’s general conversational manner.

So, below are my modulation examples. One specific modulation is indicated.

Example: modulate to the dominant key from V of the old key to V7 of the new key – so modulation from C to G, you would start the piece in C and then a bar or two latter, go from a G7 chord in C to a D7 chord and eventually cadence in the key of G.

Play Example:

Modulate from Old I to IV of Dominant - r4÷3 Balanced

Modulate from Old I to IV of Dominant

Play Example:

From I of the old key to ii of the new - r3÷2 balanced

From I of the old key to ii of the new - r3÷2 balanced

Play Example:

From Old V to New II - r4÷3 Fractioned

From Old V to New II - r4÷3 Fractioned

Play Example:

Modulate to Dominant from V of old key to II of new key - r4÷3 Fractioned

Modulate to Dominant from V of old key to II of new key - r4÷3 Fractioned

Play Example:

Modulate to Dominant by taking iii of old for vi of new - r4÷3, r5÷2, r5÷3

Modulate to Dominant by taking iii of old for vi of new - r4÷3, r5÷2, r5÷3

Play Example:

 Modulate from I to iii of the new key - r5÷3 unfractioned

Modulate from I to iii of the new key - r5÷3 unfractioned

Notice how the r5÷4 resultants brings in a beautiful and flowing 5/4 time signature yet doesn’t fall into the predictable 1-2-3-1-2, 1-2-3-1-2 that we’re so accustomed to hearing in 5/4. Here Schillinger’s resultant really keeps the rhythm fresh and we are not “held hostage” to the over-used 4/4 or 3/4 time signature – it really flows.

Play Example:

Modulate to Dominant key by I of old to V of new (i.e. same chord repeated) - r5÷4 resultant

Modulate to Dominant key by I of old to V of new (i.e. same chord repeated) - r5÷4 resultant

Play Example:

Modulate to Dominant key from V of old key to V7 of new key - r5÷4 resultant

Modulate to Dominant key from V of old key to V7 of new key - r5÷4 resultant

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 June 1, 2009 at 8:07 pm  Leave a Comment  

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