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Applying the Cipher to
Isomorphic Chromatic Keyboards






The purpose of the Cipher System is to make the fundamentals of music theory easy to understand (no matter who you are or what your background is) and then apply the elements of music theory to musical instruments. The Cipher System began with music theory itself — by translating the fundamentals to chromatic number equivalents. Then came the application of chromatic numbers to fretted string instruments,  the guitar family (4ths tuned) in particular. The mandolin family (5ths tuned string instruments) followed. Chapman Stick came next, a combination of both 4ths and 5ths tunings. The Cipher and these instruments have one primary thing in common. They are all neutral and chromatic by design,  and they are isomorphic as well.  Isomorphic means being identical or similar in form, shape, or structure. In our context, that means a single pattern on any fretboard is moveable or transportable. One shape or fingering (and one musical number formula) for any interval, scale, or chord, can be used over and over again (nearly anywhere on any fretboard)  to represent any  tonic, root tone, or key.  This is the reason that fretted string  instruments are comparatively easy to learn, and therefore popular.

Traditional piano keyboard, while technically "chromatic", is far from being isomorphic. The piano is designed around the Major scale, and one key of the Major scale, the key of C. Consequently, one must learn 12 different fingerings or shapes for any given musical material (interval, scale, or chord) to able to “get up to speed”. The pain to gain ratio is high. As it happens though, the classical piano keyboard is not the only game in town. There are alternative keyboard designs available. The two best known alternatives have been around since the mid 1800's. Both are isomorphic in design — like all fretboards in standard tunings. Both allow a given fingering to be used for any tonic or in any key. We already have 4ths and 5ths tunings “in the fold” here (from our string instruments). As it happens, the two alternative keyboard maps we'll look at are in 3rds and 2nds tunings. You'll understand what I I’m talking about shortly.

In any event, these instruments and The Cipher were made for each other. I’ve said before that diatonic numbers are not capable of illuminating chromatic things. The original context was regarding fretboards (which are, of course, chromatic things), but the principle is just as true for isomorphic chromatic keyboards as it is for isomorphic chromatic fretboards. It’s another case where you’ll probably ask yourself later how on earth did anyone understand these instruments without using chromatic interval counting numbers?  It beats me.

Remember,  pianos are stringed instruments too. So this really isn’t such a stretch after all. We’re still under the umbrella of “Blumberg’s Music Theory Cipher for String Instruments”.   — whether strummed, picked, bowed, or hammered ;’)

Chromatic Button Accordion (CBA)

Thirds tuned isomorphic keyboard mapping (minor 3rds specifically) was first popularized in the late 1800's on Russian Chromatic button accordions (CBA's, otherwise known as a Bayans). Klezmer bands, for instance, often included a CBA player. Chromatic button accordion has remained popular in Eastern and Western Europe ever since.

Wholetone Keyboard (Janko)

Seconds tuned isomorphic keyboard mapping (that is "whole tone" keyboard), developed by Paul von Janko, also arose in the late 1800's. A few traditional German and English piano manufactures actually made these instruments for a time. "Adaptors", made to fit on top of existing piano keyboards, were also made.

Tradition is hard to buck, but we do it all the time.  That’s the history of the world, if you think about it. So keep at it. Demand fuels the market. Make your desires know. Send letters or e-mail the manufacturers of keyboard instruments (electronic, midi, and acoustic). Ask about these instruments and request they make some. If there’s enough interest, they'll respond. Some already have. For example, chromatic button accordions have already overtaken piano accordion in Europe. Janko Whole Tone keyboards are beginning to appear (again), this time as midi controllers. Here’s one example.



This link is to a Japanese language site, the English version is being prepaired. The keyboard is called the WholeTone Revolution. It’s manufacturer claims that it’s  the number one selling midi controler keyboard in Japan (already).















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© Copyright 2002   Roger Edward Blumberg



All  text, images, system components, devices, key terminology* and logos, on this web site are copyrighted [physically at the U.S. Library of Congress]. Reproduction in any form without written permission from the author and creator is prohibited. Thank you.

Roger E. Blumberg 
















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