Modulation Example – Step By Step Using Schillinger Resultant

It’s interesting how people don’t generally wonder how someone managed to build the house they live in or the car they drive or the clothes they wear or the computer on which they are reading this. But when it comes to music people seem to think there are some “mysterious goings on”. This is not the case. Writing a composition is no different than writing a well-written letter. You have an introduction, “Dear…”, you have a “body”, you have a closing paragraph, you have a salutation – a coda – “sincerely yours….” and it’s done. In a car you have the frame, the body, the engine, the trunk and the rear lights – and it’s done. In a home you have a front door, rooms of living space, a back of the home etc.

Composition is a craft and a system. Composers have all tried to give responses to the “How do you do it” question with everything from flipancy to humor:

J.S. Bach on “How do you play so well?”:

“Play the right note with the right finger at the right time and the piece plays itself.”

Tchaikovsky on “How do you compose”?

“Generally from a seated position”

Now yes, behind every home, every car, every piece of clothing, there is an “idea” and that idea is translated by someone or some team to the finished product. The quality of the home, the really cool car, the elegant piece of clothing, will be related to the degree of expertise of that person or team.

The process is a craft and a system.

The quality is the person/group behind it.

As I work through this Keyboard Harmony book mentioned and scanned in the several previous posts, and study the Schillinger System of Musical Composition, I am naturally doing repetitive exercises in modulations as set forth in the book’s directions. So a “process” begins to unfold. Last night as I sat down to do one, I thought, “You know, it would be fun to do each step, then copy that to the next staff, then add the next step, copy that to the next staff and so on…” until the entire process is completed in its entirety so people could really see the process.

The one below was not chosen for any particular reason. It just happened to the be next one in the book to do. The exercise asks the student to modulate to the dominant key (C to G) by means of V from the old key (a G Chord or “V” in C) to III of the new key (a B chord, or “III” in the key of G)

I have all the Schillinger resultants in front of me which go through the 9 Series and include:

  • Fractioned
  • Unfractioned
  • Balanced
  • Expanded
  • Contracted

I tend to start with the lower series and shorter resultants at this point since the examples I’m working on need only be five or six measures. In this case I randomly chose Unfractioned r6÷5

Let’s see what we can come up with:

The Instruction:1.  The resultant is choosen (r6:5) and the soprano rhythmically entered on the tonic tone:
r6÷5 = (5+1)+(4+2)+(3+3)+(2+4)+(1+5)


2.  The Roman numbers are entered according to the modulation scheme being attempted and 
3.  The rhythm “bracketed” to where the modulation should occur.


Play Example 1:

Schillinger Unfractioned Resultant: r6÷5 = (5+1)+(4+2)+(3+3)+(2+4)+(1+5)

Schillinger Unfractioned Resultant: r6÷5 = (5+1)+(4+2)+(3+3)+(2+4)+(1+5)

4. Bass lines and some harmonies are added

5. The melody begins taking shape

Play Example 2:

Example 2

6. Add the cadence at the end (V-I in new key). Note: I normally would NOT put musica ficta of the new key in the soprano (F# in the case below – i.e. notes F# to G in the soprano). Doing so “forces” the modulation – instead, I want the modulation to come “underneath” a melody that otherwise would not necessarily have to modulate and therefore choose a penultimate soprano tone which is “neutral”

Play Example 3:


7. Begin working “backwards” to the point of the new key (G: iii below)

8. Although I’ve indeed added harmony working backwards now from the final cadence, the penultimate measure which joins to the iii chord of the 2nd half of the 3rd measure and now ready to go back to the beginning and work forward to the new key, I am secretly telling myself that in the penultimate measure, I want to add some kind of dimished chord, and, I want to preceed the Dominant on the last measure with a ii7 chord. This will affect the melody perhaps….

Play Example 4:


9. Begin working forward from the beginning to the point of the new key (G: iii) Although the harmony is there and now “complete” it sounds boring. A student exercise is not necessarily a piece of music. It must now be made at least really “good” if not really “great”.

Play Example 5:


10. Add passing tones and begin working on it as if it were a “composition”

As above, it’s stilted and stagnent – unless that’s the effect you’re going for. For example as a brass quartet, it might be fine as above, but I want it “good for the listening” with the motion afforded by moving parts.

The opening bass line offers some excitment with its motion and the “personality” of the piece begins to assert itself.

As a composer, my interest in the “piece” has now been piqued. The G natural in the tenor bar 2 has been added so as to cancel the feeling of “A minor” as we approach the V of C major on the 1st beat of bar 3. With the density added, the tempo is slowed down a bit.

Play Example 6:


11. Take the motive of the initial bass line and develop this in the voices of the following measure in some sort of meaningful way to establish some sort of coherency.

This is where the “composition” is in its “worse” state. The “rush” of excitment originally generated a step back is now more or less ‘gone’ or at least taken for granted. This is the state where nothing works. Things seem piece-mealed, choppy and “don’t line up” or “don’t go together”. It’s like a construction site where the sidewalks don’t match up or drop off into dirt and a road dug up is half finished on one end – you have no idea that 6 months latter you’lll come back and there will stand a beautiful new city library.

Actually, this isn’t half bad. Other pieces are horrible. You can spend 20 minutes on a couple bars that just “aren’t working”. This one is actually coming pretty easy. Each piece is different.

Play Example 7:


12. Work on the 2nd half.

One thing different about this one is the front half happend to be developed before the 2nd half. Sometimes (I think more so,) it’s the other way around.

The last quarter note of measure 2: I’m in one way likeing the way it “hangs” (holds) up in ‘mid-air’. As if the rhythm for that beat is “suspended” – but in the back of my mind I’m keeping that thought “open” – as the 2nd half is done and there is more motion in the piece, I’m wondering if I’m still going to like that “hanging” effect to where it seems to instead block the flow of the piece.

Note I changed the soprano (beat 4 green note in bar 3) to an “A” to avoid monotony of three “B’s” in a row – however notice now following note “A” (in red) becomes perhaps an unwanted “rocker” – that is, you now have B,A,B,A which is a rocking back and forth between notes which is something I try and avoid. So I’m “suspicious” of the red A and have made a mental note to perhaps change that as I move forward.

Play Example 8:

Example 8

Example 8

13. Work on the penultimate measure to “bring it home”.

Now, I’m coming back to my thought about wanting the dim.7 chord in there if possible. This means I’m now open to the thought of changing the red “A” half note on beat 3 soprano to accommodate a dim.7 chord somehow since I was “suspicious” of that anyway.

Ooops – playing it I noticed the two “D’s” in soprano of last measure. Not so good. Now I can totally understand that you may want the penultimate note to be the same as the last note – an “anticipation” in the old theory books – but here? Why? It’s not an anticipation because the harmony of the that penultimate note is different – an anticipation is really a note moving out of the previous harmony (chord) to a note in the final chord. We don’t have that here. So in this case, leaving the penultimate note the same as the last note simply weakens the last note. The last note being the last, has significance – it should say, “I’m different because I’m the note ending your piece for crying out loud” – so let’s look to an alternate – how about simply raising D to Eb? A nice minor 9th sound?

(p.s. do you see the parallel octaves between the red notes in my eagerness to change the “suspicious” A? They will go!)

Play Example 9:

Example 9

Example 9

14. Work on the penultimate measure to “bring it home”, AND, we now have the musica ficta “Eb” in the last bar as a “beacon” to “aim” for.

Ok, we’re getting there – but something it seems to sound “wrong” in the penultimate measure. Looking closer, I see the Eb/D natural in the Alto/Ten. Then the tenor takes the Eb (in green) previously in the alto two beats before. It does sound kind of cool but I’ve learned that ‘cool’ sometimes means ‘lazy’ – there’s usually a better improved way that I’ll like even more if I take the time to dig a little deeper for some alternatives.

Play Example 10:

Example 10

Example 10

15. So the change is therefore made in the alto at that point – by continuing up from Eb-F-G the tenor coming in on the same Eb seems quite logical since there is motion.

I am concerned about three voices moving in similar motion so I check carefully the intervals. My ear tells me it’s very parallel but not 4ths or 5ths which I want to avoid for these pieces. But we can see the alto/ten. move in 3rds – the bass and tenor moves in 3rds – this is a warning that the bass/alto will indeed move in some kind of 5ths and we see that indeed they do – BUT – not parallel perfect 5ths. The first two, A/Eb to B/F,  are parallel diminished 5ths – then the 2nd set, B/F to C/G is a dim. 5th to a perfect 5th – close, but still not parallel 5ths.  And I do think they sound kind of cool so we’re okay there.

Also, notice I got my dim.7th chord in the penultimate measure but not the way I had expected! This is an example of a sub-conscious level of composing. Not all will follow, understand or believe this, but for those who do, here is the explaination:

Upfront I had put in my “mind” that I wanted a dim.7th chord before the ii before the V7-I at the end. Many times I would simply work that chord right there into that beat – not this time – this time when the thought went into my sub-conscious and it came time for the penultimate measure to be worked on, it had me put the Eb in the last measure which then triggered the opportunity for the dim.7th (A-C-Eb) right where I wanted it. In turn, the dim.7th set up the soprano Eb nicely so that note did note obtrusively “come out of nowhere”. Instead we had heard it 3 beats before in the alto so the ear was prepared.

Play Example 11:

Example 11

Example 11

16. Now just add the missing roman numerals:

In doing so I notice bar 2 beat 3 really isn’t a chord – there’s no sin in that but again, “no sin” can also mean “to lazy to find a better alternative”. But the problem is that there is a C in the soprano and that rhythm can’t be changed because it is the fixed Schillinger resultant. And the bass moving against it with a B natural causes a bit of a problem. So let’s change that (the bass): By holding the “A” in the bass 1/16 longer then moving to the beat in 16th notes, you can see we then have a nice am7 on beat three which we label as such: Remove the redundant E-E Alto, bar 1 beats 5-6 which led to a slight change to avoid again the redundency of E in Alto bar 2 which gives a nice harmony with the tenor and lets the also lilt right back up to the “F”. Bass, Bar 3, add 16ths to give more momentum on that upward lift and to fill in what was a really an obvious major triad (G-B-D)

With that, the only thing left is the initial concern about the “hang” at bar 2 beat 5. Are we okay with it? Well it doesn’t line up with the two rhythmic sections which divides the Schillinger resultant in two. It’s nice like it is but what else can we do?

Play Example 12:

Example 12

Example 12

17. Now it’s lined up with the resultant in the sense that it cuts it in the middle AND it follows Carolyn Alden Alchin’s precept that a modulation invariable begins with a new rhythm. So in that sense this is “better”.

Play Example 13:

Example 13

Example 13

18. How about no caesura at all?

Now it seems hopelessly confused with no distinction – a jumbled mess:

Play Example 14:

Example 14

Example 14

17. And the winner is?

Number 15 for sure; where the caesura is placed directly in the center of the Schillinger unfractioned r6÷5 resultant dividing the two sections so the modulation occurs according to Alchin’s observations.

And what I love about the Schillinger System is that even in 6/8 you have a completely “free” flowing rhythm not tied to the typical 6/8 pattern with those predictable accents on 1 and 4. Here you have something really different which I would have in no way come up with without the Schillinger resultant. Try and count 123 456 and you’ll see what happens: Bar 1 will indeed give you a sense of traditional 6/8 rhythm because of the 6/8 in the bass, but bar 2 because of the soprano is like a 3/4 bar with the half/quarter, and then that is destroyed in the next bar with two dotted quarters thereby completely destroying any hope of 3/4. Bar 4 is the Bar 2 syncopated! In a sense, the last bar is somewhat a return to 6/8. So there is real continuity here.

Lastly, the resultant in the soprano is re-notated for standard 6/8 notation.

Play Example 15 (The Final):

Example 15

Example 15

Thank you for accompanying me on this little journey.

So was it worth it?

An entire evening for 5 good measures?

The Schillinger System of Musical Composition - Vol. I

The Schillinger System of Musical Composition – Vol. I


Published in: on June 8, 2009 at 6:31 pm  Leave a Comment  

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