The New Language And Rules Of Music

A Formal System That Improves Musical Representation And Computation

Title: A Formal System Improves Musical Representation And Computation

Author: Kelvin Sholar (Composer, Performer, Theorist)

1. Background: because language and staff notation are problematic, musicians need an alternative symbolic language and rules of computation.

2. Purpose: this document describes a systematic method to represent and compute music; despite staff and language.

3. Method: musicians should perfectly map acoustic expressions of tones and beats in states of rest and non rest, as well as logical theory about them and bitwise processes on them, to a formal language of colored circles with a typographical calculus.

4. Result: by this method music is represented both perfectly and universally, while music is computed consistently.

5. Conclusion: in relation to staff and language, digital binary systems: 1. solve problems that staff and language have, 2. are more convenient, 3. have a higher fidelity, 4. improve musical analysis, synthesis, composition, performance and theory, and 5. provides the lacking rules of musical computation.

6. Keywords: music theory, staff notation, symbolic language, digital binary system, perfect language, universal language, consistency, musical analysis, synthesis, composition, performance, rules of computation


1. Introduction

This essay is essentially about music and music theory. What I call “music” is collections of tones and beats in states of rest or non rest; while “music theory” is the study of such collections, and statements about them.

All musicians need some form of representation and computation of sets of states of tones and beats, and statements about them, in order to think about, compose, arrange, perform, listen and form theories about music. Otherwise, music making would be impossible.

For an example in visual arts, imagine being a painter and you try to paint a meaningful picture without knowing what colors (like red, yellow or blue), and values (like black or gray) are, without having paints as expressions of those colors, and without knowledge of how paints are arranged on the space of a canvas over time. After this painting experiment, try to talk about the painting with others; but, without any words to describe colors and values. Now try to manipulate your painting by adding, subtracting, changing the size of or otherwise transforming colors without any sense of rule of form.

In this example, it is clear that painting and talking about painting is impossible without some form of representation and computation of sets of color and values, as well as, techniques of applying paints to canvas and rules for transforming a painting from one form into another. Likewise, music is impossible without knowledge of what tones and beats in states of rest and non rest are, without being able to make statements about them, without rules of transformation, and without techniques of expressing music and theory by linguistic scripts and performance.

Everyone knows that beginners need to learn about music and its theory to make music at all; but it should also be clear that even untrained but successful musicians still depend on intuitive knowledge of how music and theory is represented and computed in order to make music.

2. Method

Despite staff and language, musicians should perfectly map acoustic expressions of tones and beats in states of rest and non rest, as well as logical theory about them and bitwise processes on them, to a formal language of colored circles with a typographical calculus.

The formal language consists of an alphabet and grammar rules on it:

1. darkis a symbol

2. brightis a symbol

3. if A is a symbol, then AA is a string of symbols

4. if A and B are symbols, then AB and BA are strings of symbols

5. symbols can be combined any number of times, one at a time with repetitions, to make a string of symbols of any length

Acoustic expressions of tones and beats in states of rest and non rest, and logical statements about them, are analyzed into typographs: the symbol * represents a syntagm that is false or invalid, as well as a tone or beat in a state of rest. * is a syntagm that is true or valid, or a tone or beat in state of note or non rest. A series of tones or beats is analyzed into a string of digital binary symbols in the formal language. For example, a major scale (i.e. a unique series of seven tones) within the equal tempered tuning system is represented symbolically as


The symbolic strings in M can be interpreted in two dimensions, so that when symbols are numbered as non negative integers, including zero, then even numbered symbols define spaces and odd numbered exponents define lines. Then a graph like the staff is generated with six lines and spaces.


Syntax Rules:

1. if A is a theorem, then AA is a theorem

2. if A and B are theorems, then AB and BA are also theorems

3. If A and B are theorems, then AAA, AAB, BAA, BAB, ABA, ABB, BBA, BBB are also theorems

Syntax rules define how the permutation of symbols forms postulates o theorems with a positional syntax similar to that of exponents or logarithms.

Theorems are generated by the system according to rules.

Theorem 1: Mary Had A Little Lamb (Traditional)


Theorem 2. A Major Scale majorscale

symbolic proof

Another way to give symbolic proofs is to use circular strings instead of linear strings. For example, a circular proof of theorem 2 is diagrammed as:

proo of major scale

In the logical diagram above, the ends of symbolic strings are joined to form geometrical symbols which are placed at the positions of corresponding parts of symbolic proof or logical argument.

Shosys M symbology of “Mary Had A Little Lamb” is translated into eight sub diagrams that represents the rhythmic structure of each measure of the composition (the first four measures at the top, and the last four measures at the bottom):


3. Result

As a result of mapping musical elements and processes to corresponding parts of a digital binary formal system (i.e. Shosys M), musicians perfectly represent music, in all languages (universally), and consistently transform music.

4. Discussion

There are four implications of implementing Shosys M relative to staff and language; it: 1. solves problems that staff and language have, 2. is more convenient, 3. has a higher fidelity, 4. improves composition, performance and theory, and 5. provides lacking rules of musical computation.

5. Bibliography

Eco, Umberto. The Search for the Perfect Language (The Making of Europe). London, Wiley-Blackwell, 1997.

Forte, Allen. The Structure Of Atonal Music. London: Yale University Press, 1973.

Hofstaedter, Douglas R. Godel, Escher, Bach: An Eternal Golden Braid. New York: Vintage, 1979.




Sholar has been awarded: Best of Music (#8 of 10)/ Artforum International (2009), IAJE Outstanding Service To Jazz Education (2005), Winner of Scholarships from James Tatum Foundation For The Arts (1989 and 1990), Winner of the Michigan Bach Festival Competition (1990), IAJE Outstanding musician in Montreaux/Detroit Jazz Festival (1991), Outstanding musician in Aquinas Jazz Festival- (1992), Best Soloist, and Best Band in WEMU/Heritage Jazz Festival (1993), Outstanding pianist at The Clark Terry Jazz Camp (1994), Outstanding musicianship/ Elmhurst Jazz Festival (1995 and 1996), Outstanding musicianship/ Wichita Jazz Festival (1995 and 1996).

Sholar is also an author and educator that has given master classes on music in many important international schools- including: the Phillipos Nakas Conservatory (Athens, Greece), Cite de la Musique (Marseilles, France), North Carolina Central University (Durham, NC, USA), Kyo Rei Hall (Tokyo, Japan), Escola International (Sao Paulo, Brazil), Porto Jazz school (Porto, Portugal), and Columbia University (New York, USA). Recently Sholar has lectured on Civil Rights and Black American Music at Alfred Nobel School and OZ TIEM in Berlin and Amerika Haus in Munich- supported by the U.S. Embassy Berlin and the U.S. Consulate General Munich and the B.A.A.A.

All of these things confirm why Kelvin Sholar is a unique musical artist, often defined as „genre-defying“. He sees where music is going and he brings this future to the present, beyond the boundaries of style, cliché and tradition.


This Blog is dedicated to essays about a formal system that I have created, called Shosys M. Shosys M was created to be applied to isomorphic parts of music theory in order to solve problems of perfect representation and consistent confirmation of sets of states of tones and beats, and logical statements about them. Shosys M is composed of an artificial language of geometrical symbols (dark and bright circles) with a computational apparatus of rules that consistently change symbols from one form into another. When Shosys M is applied to music, the musician’s ability to represent and compute music improves, thus effecting abilities to externalize music in composition, arrange, internalize music while listening, perform from written music and form theories about music; including the improvement of previous levels of effectiveness, convenience and fidelity; despite staff notation and language.

After you read these free blogs and download the free Ebook, buy the much more detailed Ebook “SHOSYS M: The New Language And Calculus Of Music And Music Theory” for 5.99 euro via Pay Pal, or buy other products, or personal ssistance via Skype- at


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