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An Understandable Guide to Music Theory
The Most Useful Aspects of Theory for Rock, Jazz & Blues Musicians
By Chaz Bufe
See Sharp Press Copyright © 1994 Charles Q. Bufe
All rights reserved.
All scales and chords are simply patterns of intervals, and intervals are simply the distances between notes. They are measured in "steps." The distance between adjacent white and black keys on the piano, or adjacent frets on the guitar, is one half-step. The distance between two white keys separated by a black key, or two frets separated by another, is a whole step. All intervals have names corresponding to the distance between the notes in them.
The following musical example shows intervals as distances from middle C to notes above it, and between notes selected at random.
The names for intervals wider than an octave are found by moving the upper note down an octave and adding the resultant interval to the number seven (not eight). For example, the interval from middle C to Db above high C would be a minor 9th (7 plus a minor 2nd).
These are the only intervals normally referred to in the octave-plus range; the other notes above an octave — 10th, 12th, and 14th — duplicate notes already present as the 3rd, 5th, or 7th in most chords with members (notes) more than an octave above their roots. It's also worth noting that there is more than one way to refer to many of these intervals. Beyond the octave, it's probably more common to refer to intervals containing sharped or flatted notes as "sharp" or "flat" rather than "augmented" or "minor." So, for example, a flat 9th (or [??]9, or flatted 9th) is the same as a minor 9th, and a sharp 9th (or #9) is the same as an augmented 9th.
Don't be frightened by all of these intervals; their names are simply a convenient form of musical shorthand which musicians use to make communicating with each other easier. If you spend much time with other musicians, you'll get used to hearing and using these interval names in short order.
The most familiar scale is the major scale, do-re-mi-fa-sol-la-ti-do. The easiest way to the think of the major scale (C major in this case) is as the white keys of the piano, with the scale beginning and ending on C.
The distances between the notes in the C major scale are not equal. The notes E and F (the third and fourth degrees — notes — of the scale) and B and C (seventh and first degrees) are adjacent on the piano, while all of the other notes in the scale have a black key between them. The distance from E to F and from B to C is a half-step, or minor 2nd; the distance between the other notes in the scale is a whole step, or major 2nd.
All other major scales have the same arrangement of whole steps and half-steps as the C major scale. Here are two examples, the D major and E[??] major scales:
At this point you might be wondering how you can figure out where the major scale starts in various key signatures. The easiest way in sharp key signatures is to remember that the major scale starts a half-step above the last sharp (the sharp farthest to the right). So, for example, when the last sharp is C#, the key is D major, and when the last sharp is G#, the key is A major.
The procedure is almost as simple with flat key signatures. When only one flat is present in the key signature, that key signature is F major — in other words, the major scale begins and ends on F. When more than one flat is present, the key signature is that of the next-to-the-last flat to the right. So, for example, when the next-to-the-last flat is E[??], the key is E[??] major, and when the next-to-the-last flat is D[??], the key is D[??] major.
And, of course, when no flats or sharps are present, the key is C major.
After the major scale, the next most common type of scale is the minor scale. There are three common forms of the minor scale. The simplest is the natural minor, which uses the same notes as the major scale, but which begins and ends on a different note — the sixth note of the major scale.
The notes and key signatures of C major and A minor are identical. The only difference is that the minor scale starts on the sixth note of the major scale. Scales sharing the same notes and key signatures are called relatives. A minor is the relative minor of C major, and C major is the relative major of A minor. (Scales beginning on the same note, but sharing neither the same key signature nor all of the same notes, are called parallel; for example, C minor is the parallel minor of C major.)
The two other common forms of the minor scale — both of which, like the natural minor, begin on the sixth note of the relative major scale — are the harmonic and melodic minor. The only difference between the natural and the harmonic minor scales is that the seventh note of the harmonic minor is raised half a step above the seventh note of the natural minor, creating a 1 ½-step (augmented 2nd) gap between the sixth and seventh notes in the scale. So, for example, the notes in the A harmonic minor scale are the same as the notes in the A natural minor except that the seventh note in the harmonic minor scale is a G# rather than a G[??] (G natural); and the distance from F (the sixth note in the scale) to G# is 1 ½ steps (an augmented 2nd).
The only difference between the natural minor and the melodic minor scales is that the sixth and seventh notes of the melodic minor are raised half a step above those of the natural minor when ascending; when descending, the notes of the melodic minor are the same as those of the natural minor. For example, the only difference between A natural minor and A melodic minor are that when ascending the sixth and seventh notes of the melodic minor are F# and G# rather than F and G natural as in the natural minor. (When descending, the two scales are identical.) The following example shows the differences between the G natural, harmonic, and melodic minor scales:
The harmonic and melodic minor scales are variations of the natural minor scale — and they're variations with purpose. The melodic minor is more useful for writing and playing melodies, and the harmonic minor is more useful for harmonizing melodies, than the natural minor. (The harmonic minor can, however, be used to good effect melodically, a good example being "Song for the Pharoah Kings" on Chick Corea's Where Have I Known You Before? album.) But the natural minor remains a useful scale, and will tend to sound fresh in solos because it's heard less frequently than many other scales.
Modal scales are relatives of the major scale — scales like the natural minor which utilize the notes and key signature of a major scale, but which begin and end on different notes, and thus have different sequences of intervals. This is most easily seen with the C major scale and its relative modal scales:
One method of finding the notes in modal scales is to take the whole step/half-step patterns from example 9 and transpose them. For example, to find the notes in the G Dorian scale, begin the scale on G and follow the whole step/half-step pattern for the Dorian mode:
Similarly, to find the notes in A Lydian, you would transpose the Lydian pattern
Another way to find the notes in modal scales is to remember that modal scales always use the notes of the major scale and that they always begin on certain notes (degrees) of the major scale. Those notes are:
Beginning Note in Major Scale Mode
1st Ionian (major) 2nd Dorian 3rd Phrygian 4th Lydian 5th Mixolydian 6th Aeolian (natural minor) 7th Locrian
So, to find the notes in the A Dorian scale, for instance, all you need to do is to find the major scale in which A is the second note (G major).
And to find the notes in a B[??] Phrygian scale, you need to find the major scale in which B[??] is the third note (G[??] major).
All of the modes contain certain notes which give them their particular characters, which distinguish them from the major and minor scales and from each other. Those notes are:
Dorian 6th Phrygian 2nd Lydian 4th Mixolydian 7th Locrian 2nd & 5th
In modal melodies, these characteristic notes should be emphasized in order to retain the modal flavor. We're so used to hearing the major and minor scales that our ears, given half a chance, will hear modal melodies as being major or minor; to avoid this, it's necessary to emphasize the characteristic notes of the modes. Similarly, when harmonizing modal melodies, the most important chords are the chord rooted on the first note of the scale and chords containing the characteristic note(s).
It's worth noting that the Locrian mode is rarely used and can for all practical purposes be ignored. The reason for this is that its first and fifth notes form a tritone, which has a very strong tendency to resolve to the relative major, which would destroy the modal feeling. For instance, the B Locrian mode has a strong tendency to resolve to C major. So, it's very tricky to use the Locrian mode effectively. As well, there's little point in using this mode, as the Phrygian mode, which also has the flatted 2nd as a characteristic note, can often be used in place of the much harder-to-use Locrian.
The theoretical number of synthetic scales — scales other than major, minor, and modal — is astronomical. In practice, only a relative few are of much use, and most of them are scales from which "tertian" harmonies (that is, chords build from intervals of a third — major, minor, 7th, and 9th chords, for example) can be constructed.
Synthetic scales can be classified in several ways. The simplest is to divide them into two types: asymmetric and symmetric. The most common of the useful synthetiic scales are asymmetric. The most familiar of these is the diatonic pentatonic (five-note) scale. (While there are other pentatonic scales, the diatonic pentatonic is by far the most common; references to the "pentatonic scale" almost always refer to the diatonic pentatonic.) This scale is very useful to beginning improvisers, in that it's virtually impossible to make a mistake when using it. There are actually five versions of the pentatonic scale, each utilizing the same notes, but beginning on a different note:
There are other types of pentatonic scale; three of the most common are:
Another very familiar asymmetric scale is the blues scale. It's a wonderful tool, but it's overworked. When you use the blues scale, it's usually a good idea to mix it in with other scales. (Notice the similarity between the C blues scale and the fifth version of the Eb diatonic pentatonic — of which C is the relative minor.)
The Hungarian minor is another useful asymmetric scale. Like the pentatonic scales with flatted third notes, it can be used to produce "oriental"-sounding melodies. The Hungarian minor is, however, especially well suited to producing such melodies because it contains two augmented 2nd (1 ½-step) intervals, which are characteristic of "oriental" melodies.
While the preceding scales are the most commonly encountered asymmetric synthetic scales, there are many other useful asymmetric scales. The following example features several which you might find of use:
Symmetric synthetic scales — scales with regularly repeating patterns of intervals within an octave — are less common, but are very useful. A distinguishing feature of all such scales is that they come in either one, two, three, four, or six versions. (Major, minor, modal, and asymmetric synthetic scales all come in twelve versions — versions starting on C, C#, D, D#, etc.) Because of the regularly repeating patterns within them, versions of the same symmetric scale beginning on different notes will contain both the same notes and the same pattern of intervals. That can easily be shown with the whole tone scale.
There are only two versions of the whole tone scale, as it contains six notes and all intervals between adjacent notes are equal — a major second or whole tone. So, a whole tone scale beginning on C contains exactly the same notes and patterns of intervals as whole tone scales beginning on D, E, F#, G#, and A#. The other version of the whole tone scale begins on D[??] (or E[??], F, G, A, or B).
The whole tone scale is of limited use because there are only two versions of it and because it never resolves harmonic tension — there are no chords which function as dominants (Vs) in progressions derived from it — and few things are more tedious than unresolved tension.
Examples of whole tone scale use can be found in Voiles and Le Tombeau des Naides, by Debussy; in the bridge of "Vital Transformation" on the Mahavishnu Orchestra's Inner Mounting Flame album; and in "Space Junk" on Devo's Are We Not Men? album.
The diminished scale is the most widely used of the common symmetric scales. While there are only three versions of it, it "works" with a large number of chord types and is very versatile. It is used by virtually all jazz and fusion musicians and is also found as early as the late 19th century in the works of Rimsky-Korsakov.
The augmented scale is the least used of the common symmetric scales. There are only four version of it and it "works" with relatively few chords, but even given its limitations this scale is rarely encountered. For an example of its use, see movement IV of Bartok's Concerto for Orchestra.
The other commonly used symmetric scale is the chromatic scale, which is typically employed as a "filler" in runs. Since it contains all 12 notes, there is only one version of the chromatic scale, and it can be used with any type of chord.
There are many other useful synthetic scales — and you can invent your own. An easy way to do that is to alter a note in, and/or add a note to, a common scale, as in the following example which utilizes the whole tone scale.
An outstanding example of what can be done with roll-your-own synthetic scales is the work of the brilliant 20th Century French composer and theoretician Olivier Messiaen, who catalogued and made extensive use of symmetric scales containing six or more notes. Two of Messiaen's scales (he refers to them as "modes") are the familiar whole tone and diminished scales. The others are of his own invention.
Messiaen also did some very interesting things with rhythms, and he set forth his theories in an easily understandable book, The Technique of My Musical Language. Messiaen's "modes" (neglecting the whole tone and diminished scales) are:
Another useful synthetic "scale" is the 12-tone row, which was invented by the Austrian theorist/composer Arnold Schoenberg shortly after World War I. Twelve-tone rows consist of the 12 tones of the chromatic scale arranged in an order determined by the composer. In standard 12-tone practice, none of the notes in a row may be repeated until all of the other notes have sounded.
The number of possible rows is virtually infinite; and there are 48 versions of most rows — that is, there are normally 48 possible versions of the pattern of intervals comprising the row. (Rows can be designed so that there are fewer versions.) Rows can be transposed to start on any note, played backwards (retrograde), upside down (inversion), and backwards and upside down (retrograde inversion).
Despite their almost limitless numbers, the usefulness of 12-tone rows is rather limited in that their ability to convey emotions is severely restricted. The only moods they really convey well are tension, terror, anguish, suspense, and uncertainty.
Interesting variants of the 12-tone row are 9-, 10-, and 11-note rows. These can be used in the same manner as 12-tone rows, but, in addition, can be used as preparation for passages featuring the tone(s) not in the row(s). After a passage featuring a 9-, 10-, or 11-note row, a strong entrance highlighting the note(s) omitted in the row can be extremely effective. Consider the following example which uses a 9-note row derived from the 12-note row in the preceding example:
Note: When writing 12-tone music, or music using any type of row, the conventions of music writing vary somewhat. Normally, when an accidental (sharp, flat, or natural sign) appears in a measure, it holds until it's cancelled by another accidental within the measure or by the next bar line to the right. But in row writing, an accidental only applies to the note it immediately precedes — that is, all notes are played as naturals unless they're immediately preceded by a sharp or a flat. For instance, if you had an A flat appear at the beginning of a measure and had another note appear on the A space two beats later, that second note would be played as an A natural; if the second note was supposed to be an A flat, you would have to write in the flat sign again immediately before it. There is, however, also the matter of "courtesy cancellations" when successive notes appear on the same line or space: for instance, if the A flat at the beginning of the measure immediately preceded the A natural, you would normally — as a courtesy to performers — write a natural sign before the A natural.
Excerpted from An Understandable Guide to Music Theory by Chaz Bufe. Copyright © 1994 Charles Q. Bufe. Excerpted by permission of See Sharp Press.
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