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Enter. . . The Cipher
As I said earlier, ultimately, all of music theory is discussed by way of numbers. So it’s extremely important that our numbers make sense. This is what the Cipher System is all about. The Cipher System adds a second set of numbers, a set of real countable numbers (half-step or semitone value numbers) along side every instance of the would-be numbers used in music theory.
The Cipher System begins by renumbering (translating) all musical materials and formula, including single tones, intervals, scale-formula, and chord-formula, and compiling the results in a series of
Number Formula Translation Tables. The numbering reference used to renumber those materials is the chromatic scale — our full twelve-tone pallet of tones, rather than the seven tones and seven numbers of the Major scale. Numbers assigned to all tones and all formula-digits reflect chromatic positions and chromatic distances on a chromatic (twelve parted) number-line. Said simply; our new additional set of numbers will be counting numbers. The Cipher System allows us to think of music and the guitar fretboard chromatically, that is; in half-steps or frets-worth of pitch. So the Cipher System's numbers are simply half-step numbers, and half-step numbers are counting numbers.
The numbers used in the Cipher System are in fact a real, true, and natural part of music theory. They’ve always been here and we even use them (already) on occasion. For example, students are always given either the whole-step or half-step number value of any interval. Where, for example, a Perfect-fifth interval equals 3½ whole-steps or 7 half-steps. In The Cipher System, we use the later value, half-steps, to number, describe, and identify all tones. So the main difference in The Cipher System is that we’ll be using half-step numbers (directly chromatic numbers) rather than whole-step values. We’ll be exploiting chromatic numbers to their fullest potential, and depending upon them as our primary communication tool as we explore the numbers, formula, and patterns of standard (common practice) Western music theory and the fretboards of all popular string instruments. We can’t and shouldn’t avoid using music theory’s common (diatonic) number-names, but we can use a different approach to gain access to their meaning and content. We will sidestep as much of music’s notational nonsense as possible and translate the essentials of music theory into language and symbols that we can understand — counting numbers.
The name Cipher System was not chosen by accident. The word Cipher has two meanings, both of which relate directly to the system/method documented on this web site. Ciphers are most often associated with code-breaking (cryptography), where a cipher is a decoding key — a set of translation characters and procedures used to decipher encrypted information. But the word cipher has another meaning, less known outside of Great Britain. Cipher, from the Arabic sifr, means zero — the most important but least appreciated digit of the ten Arabic numerals (0-9). And zero is very much a part of the Cipher System. I said earlier that the Cipher System converts music theory's diatonic numbers using a chromatic number-line as its tone-numbering referent. But more than that, the chromatic number-line must start at zero, not one. And that detail is very important. I could say, matter-of-factly; The Cipher System begins with a zero-based chromatic number-line (0-12) marking the twelve lettered tones of any chromatic scale — which it does — and move on. But that sentence is saying and assuming a few things that should probably be explained a little further.
First, be assured, there's nothing radical or new about using zero in the system-mechanics of music. Music theory's whole-step and half-step numbers, being units of measurement, have always been zero-based numbers — like all units of measure in all other fields. But attention is rarely drawn to that fact. Also, but not the least of our concerns, zero in natural to all fretted string instruments. The nut of any stringed instrument is it’s zero-point. This is explained a little more thoroughly on the page titled Why Zero. The main thing to understand now about the Cipher System's use of zero-based numbers is that we will never, at any time, use one-based chromatic numbers on this web site or in the book. To do so, to mix two kinds of chromatic numbers, one-based and zero-based, within the same system, would most certainly cause unnecessary confusion. And that's the main thing in creating the Cipher System that I mean not only to avoid, but to solve in the first place. So zero, while important to understand, should not alarm you in any way. Zero has always been a natural part of music theory, but an obscure or hidden part. In the Cipher System, however, zero is a dominant and key element. You'll soon understand that there are many reasons why this is so. So again, zero is not new. We'll simply be using it consciously, and exploiting it to our greatest advantage.
While zero is not new to music theory; using the chromatic scale as a primary tone-numbering referent is. And that’s the part about the previous definition statement (The Cipher System begins with a zero-based chromatic number-line (0-12) marking the twelve lettered tones of any chromatic scale) that many would find strange and unusual — the part that should draw your attention. You may not know it yet, but thinking chromatically — talking about the chromatic scale, numbering its tones (with zero or not), and using those numbers to convey the stuff of tonal (or Classical) music theory is itself the radical act. Such things are normally not done and not encouraged in music theory nor music education. You can prove this yourself by examining the first ten pages of any dozen music theory textbooks. You'll be lucky to find even one reference to the chromatic scale there, in those pages where the elemental building blocks of music, the indispensable prerequisites, are (presumably) gathered and introduced. If you do see the chromatic scale it will only be in passing, an obligatory nod, but no real use or discussion of it would follow.
So thinking chromatically, and regarding the chromatic scale as a primary referent and center of the musical universe in a world that behaves as if it doesn't and need not exist, is far from normal. It's definitely not typical, matter-of-fact, operating procedure. Understand, it is normal, particularly for guitarists, to try to think of music and the guitar fretboard chromatically and to try to use counting numbers. It's the well ordered logical approach, the natural thing to do. But acknowledging that fact, and helping students succeed, by providing them with the tools necessary to do it, has simply never been done. And that’s the strangest thing of all.
There is one other place in the greater halls of Western music theory where you’ll find numbers that at least initially resemble those used in The Cipher System. In Twentieth Century atonal music theory there’s a method of musical analysis called Pitch-Class Set Theory. Pitch-Class Set Theory begins by numbering the twelve tones of the chromatic scale with the integer numbers 0 though 11, just like The Cipher System does. And (if you look hard enough) you’ll even find
translation tables for intervals, scales, and chords — similar to those used in The Cipher.
As an aside, I developed The Cipher System, including it’s number formula translation tables, independently and many years before I ever heard of Set Theory.
But that’s about the end of the correlation or connection between the two. In Set Theory, after starting with that simple line of numbers, it’s practitioners almost immediately head for left field, adding layers of transformations and reductions, looking for patterns. This is all fine and well yet seems to me to loose sight of the simple beauty and potential utility of that initial set of numbers if only they were employed to conveying the stuff of Classical harmony, meaning tonal music rather than atonal music.
At any rate, the use of chromatic numbers (including zero) in Set Theory is further precedence, another place in music theory (albeit an obscure, advanced, and atonal form of Western music theory) where such (initial) numbers are recognized as being “natural” and are used every day.
This is a topic I needed to bring up at some point anyway. Someone is bound to say “there’s nothing new about the numbers used in The Cipher System” so therefore (by extension) nothing new about The Cipher System itself. What is new about The Cipher System is that it uses those numbers to communicate the fundamentals, the elements of tonal music theory, to the average person, and further it introduces a way to apply those numbers to a musical instrument (a first), one capable of generating chords, the guitar. This is the key, the thing that makes a new system, a way to apply chromatic counting numbers to the guitar fretboard — The Cipher System’s fretboard component called the Five Degree Calculation Line.
The Cipher System is both a discovery and creation. Its major parts, its chromatic numbers and the fretboard’s Five Degree Calculation Line and Pattern of Unisons and Octaves, already existed in music theory and on the guitar fretboard — or at least their seeds already existed. Being unable to read staff notation, I needed some new and better tools to help me understand the mechanics of both music theory and the guitar. So I went looking for The Cipher System, found its parts, and assembled them. So while the Cipher System is newly acquired, it’s not new in an absolute sense. Its parts have always been here, lying just below the surface, waiting to be found. Once the stuff of The Cipher System is uncovered, like an internal organ usually hidden from sight, it can hardly be thought of as being alien-to or incompatible-with the previously known parts of the body — in this case, the numbers and systems commonly used in music theory and on the guitar fretboard. They’re all natural, necessary, and valid parts of the same thing. The Cipher System simply makes a few existing but under-used system parts of music theory and the fretboard visible and available to us for the first time. The Cipher System is truly the other half, the missing half of our tool set.
In the beginning, it will be necessary for me to make distinctions between The Cipher System’s numbers and music’s more traditional notations and vocabulary. For want of a name, I have little choice but to use the term “standard procedure” when referring to staff notation and its related letter-names and number-names. But the term is unfortunate because it implies that The Cipher System is non-standard, hence problematic, which isn’t the case. The only real difference between the new and the old (if you will) is their respective points of focus. The natural focus and number-language of The Cipher System is chromatic or twelve-thing oriented, while the historically natural or preferred number-language and focus of Western music is diatonic or seven-thing (Major scale) oriented. But both number-languages, chromatic and diatonic, are natural parts and equal halves of traditional European music theory. It’s taken for granted (at this point in history) that what we normally call “standard procedure”, though diatonically biased, includes the resources of the chromatic scale. You only have to look at the piano keyboard or guitar fretboard to know that. The diatonic world is now essentially dependent upon the chromatic scale, meaning the 12 tone (half-step or semitone) octave, (the stuff of the Cipher System) and The Cipher System (the chromatic translator) and we music students are dependent upon standard procedure’s catalogue of diatonic number-formula. That’s the language that the historical record of European music is written in. So the Cipher System needs something to translate, and we (who don’t read notation) need the translated diatonic information that The Cipher System provides. In other words, there is only one system. Both halves, diatonic and chromatic, are dependent upon and include the other, and only when both halves are combined do we have a complete system — whether we call the chromatic half The Cipher System or something else.
While you’re gathering your first impressions of The Cipher System I want to make one thing absolutely clear.
The Cipher system is not a new music theory. It’s a way of learning and teaching the elements of Classical and popular Western tonal music and harmony, i.e. standard Western music theory. Also understand that I’m not suggesting for one minute that you or any student should use chromatic numbers instead of diatonic numbers. This is not an either/or thing, it’s both/and.
The point is to use both sets of numbers, to integrate them, as needed and for as long as they’re needed, to help you understand the elements of Classical Western music theory and the necks of string instruments (from guitar to violin).
By right, the chromatic half of our musical materials should never have been excluded from our understanding of what “standard procedure” is. But the Western world, having relied on the seven-tone scale as its foundation and framework for two thousand years, has never fully accepted and acknowledged its relatively new dependence on the chromatic scale. Over time we’ve managed to loose sight of just how important the chromatic scale was to the full development of our beloved diatonic pallet. How many of us remember, for example, that without the chromatic scale the Major scale would have been doomed to a single key! The point here is that The Cipher System is no more “non-standard” than the chromatic scale is. If we grant that the chromatic scale is a natural and necessary part of music theory — and of course it is — then it follows that the chromatic scale is standard procedure, a full-fledged part of it, even though it’s not a diatonic thing.
So the Cipher System’s provenance, its validity, propriety, and belonging to music theory, the guitar fretboard, and music education in general, is by right a given. Standard procedure, by way of the chromatic scale, the piano keyboard, and the guitar fretboard, agrees and ordains that the stuff of The Cipher System should be (and was already) wedded to standard procedure as standard procedure. So while I must distinguish The Cipher System’s chromatic numbers from the diatonic numbers normally used to teach music theory that does not mean that the Cipher system is truly something “other than” or separate from music’s traditional systems and materials. Now that we have a practical and illustratable way to use and include chromatic numbers, that chromatic half of our tool-set should at last become synonymous with the phrase “standard procedure”. When we think of one, we will automatically and consciously think of the other — or guitarists and other string instrument players will, at least.
Half-steps, counting numbers, and the chromatic environment generally constitute a full and missing half of music’s technical and teaching lexicon. The Cipher is the best representative and champion that the chromatic realm has ever had, and ironically, it’s also the best helping-hand and other-half that the diatonic world could ever have hoped for. What one set of numbers can’t tell you about diatonic music theory and the structure of fretboard patterns the other can. Used together, the two halves of our musical sphere, the diatonic and chromatic halves, form a single grand suite of tools, the completed set of tools we should have had in the first place. I believe that The Cipher System is the most important academic advance of music education since Guido’s Do, re, mi. It too was developed to help communicate simple patterns of music to untrained musicians (singers) who couldn’t read numes (notation). The Cipher System is the great equalizer. It makes the technical information about music (hence music education itself) accessible to people who can’t (and probably never will) read music.
So The Cipher System serves the other half of us — that majority of guitarists and would-be music students who can’t read music but still want to learn. If the goal of education is to make knowledge accessible to all people, then it doesn’t get much better than The Cipher. You’ll soon see just how much can be learned and taught without reading or writing music. Remember, children learn to speak, to understand and communicate using a small set of elemental words, and to count, before they learn how to read and write. So reading and writing music needn’t come first either. Understanding, and being able to communicate simple ideas verbally comes first. Once it’s freed from it’s encryption musical information is not only easy to understand but music theory's true mysteries can be appreciated with unimpeded wonder. Having successfully gotten once around the track, at a good pace and with little pain, will inspire students to do more and to learn more. By removing the frustration typically associated with “formal” music education, learning regains its rightful qualities of adventure, reward, and joy.
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