Page   1   2   3     Chromatic Numbers (page 3)     3. Scales — scale-formula translation tables Tones and intervals are the first building blocks of music. Scales are the next larger constructions. Scales are created by stringing together selected intervals to form distinctly flavored pools of tonal resources. Scales and the intervals they contain are used as guidelines when constructing melody and chords. Any scale must express itself once completely within the boundaries of one octave. e.g. from C to and including the next higher C, or from C# to and including the next higher C#. The number of tones or intervals per scale, meaning the number of divisions of the octave, vary. Most European scales have either seven tones (diatonic), or twelve tones (chromatic), But scales with five tones (pentatonic), and six tones (whole-tone) are also used. There are also many non-western scales to consider. For example, East Indian scales commonly have twenty-four tones/divisions per octave — see quarter-tonal and micro-tonal music. In modern Western music, that is formal and popular music produced since the mid 1600’s, only a small number of seven tone scales provide the basic tonal recourses from which most melody and harmony is derived. Foremost of these is the Major scale, followed by the natural minor scale, plus two variants of minor, the harmonic minor and melodic minor. The natural minor scale itself is considered by some to be a variant or mode of the Major scale. So four seven-tone scales (at most), one Major and three minors, make up the core of modern European music and it’s theory. [Interestingly, the chromatic scale  is often conveniently omitted from such lists of “essential scales”.] It can be argued that Medieval European music was also centered around the Major scale, or more precisely the modes of Major or the modes of the diatonic tetra chord  at least. Modes are scale variations created by taking a single scale (or tetra chord) and repeatedly shifting its starting point so that each of its tones in turn becomes the tonic or “1” tone of the scale. A tetra-chord is series of four tones whose outer two tones span a perfect fourth interval (five half-steps) with it’s inner two tones being variable. A diatonic tetra-chord has four tones exhibiting an overall intervalic pattern of “whole-step - whole-step - half step”  — like the first four tones of any Major scale, e.g. (C, D, E, F). Note, two diatonic tetra-chords joined by one whole-step form a Major scale: 1-1-½ (-1-) 1-1-½. Except for their differences in starting point each mode retains the exact sequence and pattern of intervals exhibited by its parent scale (or tetra-chord). For example, the first mode of a C Major scale begins at tone D (the second tone of C Major) and continues for seven more tones (one octave) of otherwise C Major scale tones, as follows:     Figure 1           Because the Major scale has seven tones, there are seven possible starting points or modes of Major. The idea of modes (incompletely explained here) was central to medieval church music (ecclesiastical music), Gregorian chant, etc. Scale-formula translation tables The three Scale-Formula Translation Tables include formula for the most common scale types. The tables are not exhaustive, but once you know how to use the Cipher System, the Interval Translation Tables in particular, you’ll be able to translate any other standard scale-formula you find elsewhere, yourself. Remember, all digits in any Cipher formula reflect chromatic positions and/or chromatic distances of tones from their tonic (zero). Scale-formula translation tables: Scale formula Table One The Major and three minor scales. Standard scale formula to Cipher (or chromatic) equivalents. Scales are spelled in parallel from a C tonic. [Note, the melodic minor in the descending direction reverts to natural minor.] Scale formula Table Two Modal scales; the modes of Major (ecclesiastic or medieval church modes). Standard scale formula to Cipher (or chromatic) equivalents. Scale formula Table Three Miscellaneous scales. Standard scale formula to Cipher (or chromatic) equivalents.           4. Chords — chord-formula translation tables Scales are the raw material, the laboratory, and the assembly-line factory of chord construction. After applying a technique called chord-construction in thirds to the tones of any seven-tone scale, the resulting take-what-you-get chord-forms reflect (and are limited to) the tones and intervals natural to the given parent scale. Chords so obtained, that is which chord-types and on which scale-degrees, are (in turn) the raw material from which common chord-progressions are derived. So scales, with their predetermined pallets of intervals, dictate the outcome of elementary chord construction. Once obtained, chords are usually analyzed and grouped into families, of which there are three: Major, minor, and dominant. The remaining and not so simply categorized chords, including the quite naturally occurring diminished and augmented chords, are either placed in a separate catch-all category called altered-chords or they’re absorbed into the family having the greatest number of in-common defining features. [Note: A detailed primer on Chord Construction Fundamentals is the subject of Chapter Five of the upcoming book.] Chord-formula translation tables — translating standard diatonic chord-formula to chromatic chord-formula. Two variations of one translation-table are given here. The tables differ only in their organization: Table-One organizes all chords by family — Major, minor, dominant, or altered-chord. Table-Two organizes the same chords by size — all triads, all seventh-chords, all ninth-chords, etc. The following remarks, then, apply to both tables: Both Chord-Formula Translation-Tables include the complete starter-set of chords, triads through thirteenths, of the three families: Major, minor, and dominant. The smaller altered-chords, diminished and augmented triads and seventh-chords, are also included — in the altered-chord column. The larger diminished and augmented chords, meaning ninth, eleventh, and thirteenth constructions, and all other more obscure altered-chords are omitted from these tables. Any chord not shown, however, can easily be created or represented by slightly modifying (altering) one of the chord-formula present in these tables. Further reading and reference: Chapter Five (in the book) — A thirty-five page primer on chord construction fundamentals. A comprehensive set of translation-tables called the Master Charts. The Master Charts are vital to the complete Cipher System, being the master translation reference, but they’re too detailed to introduce here in this chapter meant to introduce you to the Cipher System’s primary components as quickly as possible. The Master Charts catalogue and translate every naturally occurring chord (triad through thirteenth) of every scale-degree of the Major and (all three) minor scales. Also vital to the Cipher System, but too advanced for here, is it’s Speller-Transposer. With it, you can find or transpose the letter spelling of any interval, scale, or chord, on any scale-degree of any mode, in any key.            previous page     Page   1   2   3         Up to Top of page