In August 2008 I began to cultivate the idea of setting the Psalms of the Old Testament to music. The Book of Psalms consists of 150 psalms, each of which constitutes a religious song. So that’s quite an undertaking – I’ve always been surprised that the master composers have not done so. They concentrate on the latin portions, mass, magnificat, passions etc., but Psalms and Proverbs are really probably the most “popular” books of the Bible even to non-Christians. There’s so much “life” in them – heartache, victory, pain, joy – a roller coaster of emotions. Life.
It was this idea that led me to consider the System of Composition of Joseph Schillinger which I had been introduced to in 1990 in Los Angeles at the Grove School of music where I was enrolled as a student in the Film program. One of the teachers, Joseph Harnell, had brought in the two-volume set as a sort of “show and tell” one day and I was intrigued. When the Internet exploded on the scene I started seeing Schillinger pop up on obscure sites, most of which are now either gone or “dead” (i.e. no longer updated). So by 2008, there was some “new life” on the subject and I began to study the system, as I am still doing now, with complete earnest dedication and seriousness.
A book elsewhere described on this site, the 1921 book, “Keyboard Harmony” came into my possession while I was doing some substitute teaching in the Los Angeles School district in 1993 and I began studying it along with going through the entire Hindemith “Traditional Harmony” in about the beginning of 2009 so I could keep my compositional pencil sharp – since I was also studying the Schillinger system simultaneously, they “accidently” began to blend together. Naturally, I began inserting what I had learned of the Schillinger (Book 1, Theory of Rhythm) into my harmony and modulations exercises. Although I put time and effort into these 4-8 bar exercises, I began wondering if I was doing something worth the effort – what is the good of doing something of value when it is only 4, 5 or six bars? And yet they were important to follow through in order to master the modulations being illustrated in the Carolyn Alden Alchin’s 1921 book.
So then the lightbulb went off: Do the exercises (4,5,6 bars, i.e. whatever the Schillinger resultant I decided to use which would dictate the measure length) and add that exercise to ONE line of one psalm! In this way, I would actually be moving through the entire psalm as I worked on the exercises. The exercises, instead of being isolated pieces of value but unusable fragments, would join forces to complete the whole. “E pluribus unum” as the motto goes as adopted in 1776 on the Seal of the United States. Separately, fragments, but together, a fluid and integrated whole. (I’m writing this blog on the evening of July 4th and hear the fireworks outside my window ;).
I originally began an orchestra/choir version of Psalm 001 which is a full-scale piece and took the normal time to compose. Calculating the time it took to compose the three movement work, times 149 more psalms to complete, I calculated I would complete the series by the age 163.
Sooooooo….instead, I decided I needed something more stream-lined, which is why I began the study of the Schillinger System to begin with: shortcuts – a single voice – or perhaps duets for certain verses, with piano accompaniment – then latter, if desired, the piano part could easily be transcribed for string quartet or small orchestra if necessary (by someone else after me if the value is deemed to be there). I have all Bach Cantatas with piano/vocal lines only and that’s really all you need – from that, anyone could orchestrate them for a larger ensemble.
I also started Psalm 002 as sort of an “in between” effort of the first idea of a large-scale piece like I did in Psalm 001, versus an attempt to simplify so I could move the whole project along in a lifetime, but I was at that time not studying the keyboard modulations or applying the Schillinger ideas so it’s left unfinished (to which I’ll next most likely return with the new format using the Schillinger System and modulations next described) – so I started this new idea of integrating the keyboard modulations (her book gives mostly J.S. Bach chorale examples to illustrate the modulations), and the Schillinger resultants with a fresh Psalm. Psalm 003 shown below.
I’m using a screenshot .avi file saved in Windows Movie Maker to capture the music which was totally composed in Sibelius Notation software. There is nothing I can do (as far as I know) about improving the quality – vocal music just has “Ahs” and “Oohs” and that’s it – so obviously you’re not going to hear a vocalist “sing” the words here – but you will hear the vocal line and follow the text underneath and just have to “imagine” it being sung by a tenor. I’ve used the New Living Translation rather than the traditional King James translation of the text. I’m going for a more contemporary intepretation of the text – although in some settings, the King James with it’s “behold” and “thou” and “verily I say unto you” might be more suitable, in this case I want the most modern interpretation of the text possible so the listener, regardless of religious affiliations, if any, can immediately grasp the meaning of the text rather than being “subjected” to an antiquated format.
There is no attempt to religiously “push” anyone to any particular direction with these renditions – the Book of Psalms are great regardless of any beliefs of the listener and can be enjoyed for what they are: songs of struggle, delight, defeat, and ultimately, victory…. all while believing in a great God as creator of all the Universe and in whose faith and belief and gratitude comes all peace and victory in our own lives.
Daniel Leo Simpson
10:00PM; July 4th, 2009 USA Independence Day (I can hear the fireworks outside my window) San Carlos, California
p.s. one last note: the Roman Numerals were the original 4-6 bar phrases of the exercises. However as I worked to interconnect the phrases, I may have (did) re-work some of the harmonies and now the Roman Numerals do not in every case match up with the chord assigned to it – but I thought rather than remove them I’d leave them in so you can see the idea of the modulations and how the exercises proceeded to move toward an integrated whole.
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:
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.
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:
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:
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:
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:
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:
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:
18. How about no caesura at all?
Now it seems hopelessly confused with no distinction – a jumbled mess:
Play 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):
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
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.
Modulate from Old I to IV of Dominant
From I of the old key to ii of the new - r3÷2 balanced
From Old V to New II - r4÷3 Fractioned
Modulate to Dominant from V of old key to II of new key - r4÷3 Fractioned
Modulate to Dominant by taking iii of old for vi of new - r4÷3, r5÷2, r5÷3
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.
Modulate to Dominant key by I of old to V of new (i.e. same chord repeated) - 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 Part 3 - Hollywood, California USA
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.
For fun, and in spare moments, I am putting the entire Hindemith classic, “Traditional Harmony” in Sibelius – something I’ve long wanted to do. While I’m at it, I’m beginning to incorporate some of the Schillinger technics as well. Here’s a little 4-part harmonization from a Hindemith exercise of Chapter 10 (Secondary 7th Chords) using Schillinger’s non-fractioned resultant from 4:3 (in this case the exercise supplied the Figured Bass – the student then realizes the melody and inner parts).
r4÷3 = (3+1)+(2+2)+(1+3)
And here’s another using the Expansion technic on the 8:5 resultant.
There is great controversary over the last section of J.S. Bach’s great work, “Die Kunst der Fuge” (The Art of the Fugue) as to why it was left unfinished or even if the last section was even meant to be a part of the work since it does not even contain the subject. Those who have studied the Schillinger System are well aware of his rhymic engineering devices, one of which is Permutations (General & Circular) – so I thought it interesting when I found this article in Wikipedia , which if true, shows how J.S. Bach permuted the entrance of his subjects:
The permutation matrix
In 1991 a theory was published by Zoltán Göncz answering the question of how Bach planned the appearance of the fourth subject, the main subject of the cycle:
In the course of the exposition of the first three subjects (first subject: mm. 1–21, second subject: mm. 114–141, third subject: mm. 193–207), Bach applied a serial sequence of voice entries decided in advance, by which he determined the space and time parameters of the subject entries. The superimposition of the three exposition matrices foreshadows, and develops as a negative, the sequence of the voice entries of the fourth subject. The copying of the four subjects onto each other displays a characteristic construction of Bach’s oeuvre occurring mainly in the vocal fugues: that of the permutation fugue.
However paradoxical, it follows from the logic of composing a quadruple fugue that the combinations joining all four subjects (i.e. those combinations which appear last when performing the work) were already completed in the very first stage of composition, because the possibility of overlapping the four subjects (1+2+3+4) is the sine qua non of writing a quadruple fugue. The process of composition does not proceed in a linear way from the beginning, but with all four parts in view.
One of the striking features of Contrapunctus XIV is that in this movement Bach applied the stretto of whole expositions, layering the first two expositions atop each other prior to introducing the third subject. In the exposition of the first three subjects he “programmed” the later permutation stretti, then applied the expositions as “programs”, “algorithms”. The permutation matrix, apart from originating authentically with Bach, can be proved to have been ready at the time of the genesis of the work (that is, earlier than the surviving section).
The discovery of the permutation matrix was one of the most essential requirements for achieving a reconstruction of Contrapunctus XIV which might approach the original form planned by Bach. (Göncz, Z.: Reconstruction of the Final Contrapunctus of The Art of Fugue, in: International Journal of Musicology Vol. 5, pp. 25–93. 1997 ISBN 3-631-49809-8; Vol. 6, pp. 103–119. 1998 ISBN 3-631-33413-3)