Rudolf Schramm

A Comparative Study of Josef Schillinger’s Approach to Musical Composition and of the Traditional Academic Approach


Rudolf Schramm

When a new book on the subject of harmony, counterpoint, fugue, melody writing, musical form or orchestration appears in print, it is proper to make a comparative analysis. If the new book turns out to be an improvement over existing method, it will be worthy of serious consideration as educational material for students of music. So far no one book has succeeded in teaching all of the above mentioned or anything resembling a complete method or system of composition. It is therefore rather difficult to compare the newly arriving book “A SYSTEM OF MUSICAL COMPOSITION BY JOSEPH SCHILLINGER’ published by Carl Fisher, Inc.. with any other system.

A general comparison with other previously published books on all branches of musical theory would bring out the following points of difference.

  1. Schillinger adequately covers all branches of musical theory necessary to the successful composition of music; others do not.
  2. Schillinger actually teaches’ how’ to compose as a rational science to any person who can think intellectually; others do not.
  3. The difference between Schillinger and other theorists lies in Schillinger’s entirely new concept of presenting all his findings and facts in a basic, fundamental order, and in showing the simple, as well as the complex natural patterns music, may adopt.

In the Beginning there was Rhythm

“Begin with the End in Mind”

 Stephen Covey

In music that beginning is Rhythm.

In this series of posts, we will explore the science of rhythm.  We will discover where science and mathematics meet music.

Where is the Science of Traditional Music Theory

It is hard to believe that you can find many articles, YouTube and Ted Talks videos exclaiming the connection between science/math and music. Sound is scientific, it is governed by the law of physics. Sound can be measured in many different ways frequency (pitch), amplitude (loudness), and timbre (tone color/wave shape).  Why is this fact so amazing?

The reason is the notation system that is used was devised in the 16th Century.

Why Traditional  Music Notation has Prevented Further development of Music Styles.

The scientific process must use a systematic form of notation so that theories can be continually tested and proven and expanded. Traditional music notation is not and has never been a scientific process. It was developed over the years by trial and error. Traditional musical notation has been a source of confusion because of its non-scientific process which has lead to stifling music development.

Traditional music notation influences the way music is written. It is biased toward certain rhythm families and virtually non-existent for others. Traditional notation is efficient for rhythms of 2, 4, 8 or 3, 6, and 9, however, limitations arise with rhythms of 5, 7 and 10.
Confusion begins in the early music learning process because of this non-scientific logic, for example, the symbols we use to represent note durations are given qualitative names such as quarter notes, half notes, eighth notes etc.. and they are not a quarter, half or eighth of anything. It would have been easier to name these notes Fred or  Margaret, at least we would think they had any mathematical value.

Let’s Simplify

What do we need to do to measure rhythm?

Reduce it to its lowest common denominator. Instead of giving note values confusing mathematical names like quarter, half, and eighth lets say that the fastest duration is 1.

Here is the terminology:


t = 1      where   1 = 1/8 note  

(1 is the fastest duration it could be 1/4,  1/16 etc..)

T = measure /bar

t = 1          1 equals 1/8 note

   T = 6      1 measure equals 6 (1/8) notes

           2      1      1       2

T = (2 + 1 + 1 + 2)


Next, we will look at how we organize rhythms in Style Families


The Composers Manifold-Rhythm

The Schillinger System presents us with every possible choice of every possible element we use in composing. That can be very overwhelming.

That is why many Systems can be devised from the Schillinger System. Those Systems are determined by the Manifold of choices that are chosen prior to composing.

This Manifold is the pre-composition planning that makes it possible to explore areas and styles of music that have yet to be explored.

Let’s explore what the elements are in a Composition Manifold.

The Determinant is the number of divisions in a measure. This very different than the Traditional  Time Signature. The top number in the Traditional Time signature is similar to the determinant.

 The middle term in the Power Series t/t  is the determinant. The whole numbers on right are the number of bars and the fractions on the left are the note durations within the bars.

Music Without Schillinger

Joe playing theremin

A question was posed during one of our Thursday evening Speaking Schillinger Lectures, that had us all in a buzz. At first what seemed like an innocent remark caused a bit of a controversy. Would the state of music composition and education be any different had Schillinger not been born? You know kind of “It’s a Wonderful Life” but Schillinger playing the George Bailey character.

So the knee-jerk reaction is to say no difference. His teachings and System was just an annotation in the history of music and music education.  Then the layers of the onion get peeled back one argument or Schillinger influence at a time. What if:

Gershwin never met Schillinger?

Glen Miller never wrote Moonlight Serenade?

Schillinger House/Berklee College of Music never opened?

Westlake School of Music Never was opened.

Rudolf Schramm, Bob Bianco, Richard Benda, Charlie Banacos never taught the Schillinger System?

Nathan Van Cleave, Leith Stevens, Franklyn Marks, Robert Emmett Dolan, Vic Mizzy, Lyn Murray etc.. never went to LA and Film Composers were never influenced by Schillinger.

Muhal Richard Abrams never learned the Schillinger System? Would the AACM ever have formed?

Charles Stepney never learned the Schillinger System would Earth Wind and Fire, Minnie Ripperton, the Dells, Ramsey Lewis and all his work ever been produced.

What if I never met Lou Pine and Jerome Walman?

Well There is a start.  We will investigate these questions and more

Thinking Out Loud.



Slonimsky’s Thesaurus and the Schillinger System

Nicolas Slonimsky was a Russian-born American conductor, author, pianist and composer. He wrote the Thesaurus of Musical Scales and Patterns. These scales and patterns were derived from the Schillinger System of Musical Composition and was used by Rudolf Schramm in his teaching of the Schillinger System at NYU in the 1950's. In fact a pamphlet accompanied the first edition that explains the techniques in the Music Scales Thesaurus that coincides with the Schillinger Books. Below you will find this Pamplet along with the Master Scales.



Nicolas Slonimsky was a Russian-born American conductor, author, pianist and composer. He wrote the Thesaurus of Music Scales and Patterns. These music scales and patterns were derived from the Schillinger System of Musical Composition and was used by Rudolf Schramm in his teaching of the Schillinger System at NYU in the 1950’s. Schillinger’s Theory of Symmetric Pitch Scales derives scales by dividing the octave into equal intervals. Those divisions would be in half or 2 Tonics, in thirds or 3 Tonics, 4 Tonics , 6 Tonics and 12 Tonics. The scales are derived by using the same music scale intervals in each tonic. Though Slonimsky’s nomenclature is unique his music scales are derived from this theory. In fact a pamphlet accompanied the first edition that explains the techniques in the Thesaurus that coincides with the Schillinger Books. Below you will find this Pamplet along with the Master Scales.

pamphlet-1  Pamphlet2  pamphlet3  pamphlet4  MasterChordChart1

The Theory of Melody

The thoughts of having a theory of melody brings much skepticism. The thoughts of engineering music has set off ongoing debates that have lasted decades. The truth is, whether we look at music or in this case a melody with tools to analyze them or through trial and error, come up with a melody that our brain has endorsed, the process is the same.

In this Logical Theory of Music, Schillinger reduced music down to terms we can measure. The data he accrued comes mostly from music written by composers who have used their intuition to compose. So the hypothesis that Schillinger sets forth comes from the way composers compose intuitively.

The tools that Schillinger gives us, enhances our own abilities to come up with melodies. Procedures that we can see to write the emotions we want to convey. Almost like when I writer searches for the perfect word or phrase to convey a thought or feeling to his readers.



So takes this journey if you dare.

This has been an ongoing topic on Thursday Evenings at our free Speaking Schillinger talks.

Henry Cowell’s Overture to the Schillinger System


Overture to the Schillinger System
Henry Cowell (~1941)

The Schillinger System makes a positive approach to the theory of musical composition by offering possibilities for choice and development by the student, instead of the rules hedged round with prohibitions, limitations and exceptions, which have characterized conventional studies.

If a creative musician has something of importance to say, his need for studying the materials with which he must say it is acknowledged as a matter of course. No great composer has ever omitted the study of techniques. Musical theory as traditionally taught, however, has always been a profound disappointment to truly creative individuals. Such men have invariably added to the body of musical theory with researches of their own. Invariably, also, they have not followed the “rules” laid down in conventional text-books with any consistency. If these rules had been based on something inevitable in the nature of music, composers would have had no reason to disregard them.

Actually, musical theory has dealt with no more than a small part of the potential musical materials; its assumptions concerning the science of sound have often been based on misapprehension, and the rules it lays down often reflect the personal taste of a certain theorist, or they may be based on the study of a single composer or of some one historical period. The resulting generalizations are far from being objective, but they are nonetheless imposed upon the student in the form of “rules”. Writers on theory have not been scientists, and no scientist has tried to make a complete and co-ordinated system of musical possibilities.

Joseph Schillinger is the single exception: he was superbly competent in the two fields of musical composition and science. His monumental System of Musical Composition represents a lifetime of work in research, co-ordination, and creative discovery. The synthesis he achieved has resulted in an entirely new point of view about the function of theory studies.

In the course of the research which led to the formulation of his system of musical composition, Schillinger took all known facts concerning the nature of musical materials from conventional theory studies, and added to the discoveries and speculations of modern and less conventional theorists such as Schoenberg, Conus and myself. By applying the laws of mathematical logic, he found that he could co-ordinate all of the seemingly diverse factors. He found also that he could open further untried possibilities for the development of new materials. A glance at his Table of Contents will show an extraordinary number of aspects of music here organized for the first time for inclusion in the theoretical approach to the study of composition.

The idea behind the Schillinger System is simple and inevitable: it undertakes the application of mathematical logic to all the materials of music and to their functions, so that the student may know the unifying principles behind these functions, may grasp the method of analyzing and synthesizing any musical materials that he may find anywhere or may discover for himself, and may perceive how to develop new materials as he feels the need for them. Thus the Schillinger System offers possibilities, not limitations; it is a positive, not a negative approach to the choice of musical materials. Because of the universality of the esthetic concepts underlying it, the System applies equally to old and new styles in music and to “popular” and “serious” composition.

Schillinger is sometimes criticized on the basis that his system reduces everything to mathematics and that musical intuition and the subjective side of creativity are neglected. I have never been able to understand this criticism. The currently taught rules of harmony, counterpoint, and orchestration certainly do not suggest to the student materials adapted to his own expressive desires. Instead he is given a small and circumscribed set of materials, already much used, together with a set of prohibitions to apply to them, and then he is asked to express himself only within these limitations. It has been the constant complaint from students of composition that their teachers fail to make clear the distinction between the objective and subjective factors in music. A young composer is constrained, as things are now, to spend several years following rules deduced or assumed from the works of his predecessors, but as soon as his works begin to be heard he is reproached, and rightly so, if they sound like somebody else’s. He has not been shown what possibilities there really are in music in any objective, scientific way, nor has he been trained in the manner best calculated to develop an original talent, by exercising his own taste and judgment in choosing from among those possibilities the materials best suited to his musical intention.

Whether or not one agrees with Schillinger’s great personal interest in the scientific realities of music, it is nevertheless true that no composer is well equipped to express himself subjectively until he has so profound a knowledge of musical materials and their relationships that, consciously or unconsciously, he seizes on just the right ones to use for whatever he wishes to say in music. He can be trained to do this if he will subject himself to the disciplines inherent in musical materials themselves, as they are set before him by the Schillinger System.


Welcome Chromatic Cube

We would like to introduce Chromatic Cube’s Blog here at the Logical Theory of Music.

Slonimsky Variations

a variation of slonimsky’s divisions of the octaves, this one is 3 octaves divided into 16 parts, or 9 half-steps divided into 4 parts. this is my first post, so i’m experimenting to see how graphic jpgs appear. i have a whole bunch of these and was curious to find out if anyone’s been working with stuff like this…

Cube 1

Jymie Merritt and Schillinger

Jymie Merritt has worked in jazz, R&B, and blues. In the early 1950s he toured with rock and roll pioneers Bullmoose Jackson and Chris Powell moving on to work with legendary bluesman BB King from 1955 to 1957. In 1957 Jymie moved to Manhattan, New York, to work with Art Blakey and the Jazz Messengers. The Messenger ensemble Merritt joined featured his friend Benny Golson as well as Bobby Timmons and Lee Morgan. Merritt’s touring and recording with Blakey extended until 1962, when an unknown ailment forced him to stop touring.

By 1964 Merritt was back, working with the trumpeter and vocalist Chet Baker,[1] and is featured prominently in Baker’s unfinished autobiography published under the title As Though I Had Wings: The Lost Memoir.

From 1965 to 1968 Merritt worked with the drummer, composer and activist Max Roach, not only in the rhythm section but as a composer, recording “Nommo” on Roach’s critically acclaimed 1966 Atlantic album The Drum Also Waltzes. “Nommo” would earn Merritt a nomination for Best Jazz Composer in Downbeat Magazine’s Critics Poll.