rlr@pyuxn.UUCP (Rich Rosen) (06/22/84)
[IF YOU WANT THE SEMI-LONG-WINDED EXPLANATION FOR WHAT MARK HAD REQUESTED A LESSON ON, READ THIS ARTICLE. I'D BE GLAD TO ANSWER ANY REQUESTS FOR ELABORATION OF CERTAIN POINTS, PROVIDED IT DOESN'T GET OVERWHELMING. IF YOU WANT THE SHORT AND SWEET EXPLANATION, READ THE LAST PARAGRAPH (AFTER THE ************) FIRST, AND THEN BROWSE THE REST OF THE ARTICLE. WITH ANY LUCK, AND PROBABLY LOTS OF PATIENCE, YOU MAY FIND SOMETHING THAT'S ACTUALLY UNDERSTANDABLE (WELL...) ] As you may or may not know, the notes of the basic musical scale for C major are as follows: C D E F G A B C Lest you think that these are the only notes in existence, or that they are somehow arbitrarily placed in space and time, let's look at the piano keyboard to see ALL the notes used in Western music (pre-Charles Ives :-) : C# D# F# G# A# <== black keys Db Eb Gb Ab Bb (and alternate names) C D E F G A B C <== white keys Every note is (technically) musically equidistant from the next. In other words, the ratio of the frequencies of two adjacent notes is the same as the ratio of frequencies for any other two adjacent notes. Because of the equidistance between adjacent notes, this is known as the equal-tempered scale. Notes that are one note apart (e.g., C and C#) are said to be a half-step apart, while notes like C and D are said to be a whole step apart. Notice that E and F, though they are both white keys like C and D, are only a half-step apart (NOTE: there is no "black key" between them). Since we have shown that the white keys make up the basic C major scale, we can draw the INTERVALS that make up the spacing of notes in a major scale: |whole|whole|half|whole|whole|whole|half| |step |step |step|step |step |step |step| | | | | | | | | C-----D-----E----F-----G-----A-----B----C This particular spacing and ordering of note intervals is what makes a basic major scale. Notice that if you were to start a scale using the above notes on, say, D, the ordering would be different (whole-half-whole-whole-whole- half-whole), "shifted right by one", so to speak. Later we will see how *real* major scales can be established based on notes other than C. Chords. A "chord" is a selection of notes all played at the same time. A "major chord" is a TRIAD (three-note chord) based on a given note such that the INTERVALS between the three notes chosen are two whole steps between the lowest two notes and 1-1/2 steps between the uppermost two notes. The three notes C, E, and G fulfill these requirements. This combination of notes is considered to sound *good* (some would say *happy* as compared to other chords). There is a scientific reason for this. (So they say.) ...which I'll go into only upon request. (It has to do with frequency ratios.) Notice that aside from C-E-G, there are two other major chords available to us in the C major scale: F-A-C and G-B-D. Since these chords are based on the first, fourth, and fifth notes of the C major scale, let's call them "I", "IV", and "V". These notes are referred to in classical music theory as the TONIC, the SUBDOMINANT, and the DOMINANT, respectively. A sequence of chords that includes the DOMINANT followed by the TONIC is called a CADENCE. Let's look at an example of how such a cadence would look if we had four ongoing individual musical instruments/voices playing in harmony (four-part harmony): g a b c d e f g a b c d e f g a b c d e f g a b c ... G D G B | ------/ \ | \ | time C E G C V Note the "linear motion" of the "voices" (D to E, B to C). B is considered the LEADING TONE of the C major scale because it "leads" to the tonic note C (only a half step away). For reasons best ascribed to linear motion and harmonic tradition, this CADENCE is said to be a resolution of musical tension, appropriate to end a piece of music (or a section of a piece). Thus, in the traditions of such tonal music, the DOMINANT chord is thought to be leading up to the TONIC chord (the chord representing the key). Though the G chord is just another simple major chord, in the context of the KEY of C major, it is a "tension" that should be resolved to the TONIC. g a b c d e f g a b c d e f g a b c d e f g a b c ... G F D B (V7) | /-------/ / \-----\ \ | time C E G C (I) V What I've drawn above is an example of a V7 or DOMINANT SEVENTH chord used in a cadence. Note that it is like a V chord with an added note (F) in the chord, leading to the E of the C chord (TONIC). This chord provides more tension than just the simple V chord (G major chord), lending it more to resolution through cadence. OK. Confused? Wait, there's more. This was all for the scale in C major. Yup, there are other keys. (What did you think all those black notes would get used for?) Remember, a major scale is defined to have certain intervallic attributes. (WHOLE STEP-WHOLE STEP-HALF STEP-WHOLE STEP-WHOLE STEP-WHOLE STEP-HALF STEP) If we shifted the TONIC from C to, say, G, we could make a major scale based on G only if we use the F# note instead of the F. w = whole-step, h = half-step w w h w w h? w? w w h w w w h G---A---B---C---D---E---F---G G---A---B---C---D---E---F#--G ^ This would make the prime chords of G major G-B-D, C-E-G, and D-F#-A, with D-F#-A-C as the DOMINANT SEVENTH chord used in G major. This process of using sharps (or flats) for certain notes instead of their "natural" values can adjust the intervals in the different major scales based on different notes. This is how we get different KEYS. A key is (sort of) defined by the base note of the major scale you are using, and the notes in that scale are defined by the necessary note intervals required for a scale based on that note; thus a given key, like E major, would have certain notes sharped (or flatted) to accommodate a major scale (E-F#-G#-A-B-C#-D#-E preserves the intervals). Let's stick to C major and G major. We know that the dominant seventh is sort of a leading chord to the TONIC in a simple cadence. In C major, that chord is G-B-D-F. But what if, in the key of C major, we played a chord D-F#-A-C??? It would *feel* like you were in G major, because that chord is the dominant seventh for G major. So, in C major, you have played a chord that makes you think you're in G major, leading to the G chord, which is in fact the dominant of C major. You have played the dominant of the dominant, or a SECONDARY DOMINANT. Wait, there's more. It can get much more elaborate and contorted than this... And that's what chromaticism is all about. Through obscure linear movement of the voices in a musical harmonic context, one can "move" to chords that are somehow inappropriate to the current sense of key, where chords have "roles" that are outside of the current key, BUT WITHIN THE SCOPE OF SOME OTHER KEY. If the final goal of such movement is to actually *keep* the piece in the other key, that is called a modulation. If it is like in the example above, where a secondary dominant was a leading chord to the dominant (G) which led to a cadence in the original key (C), then it is just a very simple example of chromaticism. But when you get a series of fleeting modulations, or tertiary and quaternary dominants or other obscure uses of a chord outside of its "intended" context, or where the "role" of the chord in a key sense is unclear or ambiguous, and this process continues over a period of time, possibly (but not necessarily) leading to an eventual resolution in a key (not necessarily the original), THEN you've got some really intense chromaticism. ********************************************************* What chromaticism depends upon is the following: 1) that a given "key" has certain notes appropriate to it, and that triadic chords can be built on those notes and given appropriate "roles" in the scope of the key in relation to the dominant and tonic chords, 2) by simply sharping, flatting, or naturalizing certain notes within a scale, you effectively create a major scale for another key, and thus another set of notes (and chords!) that are appropriate and that have particular functions within that key, 3) playing of "inappropriate" harmonies can make the listeners think that they are "in" another key, with the possibility of permanent change of key (modulation), temporary change of key as a deception (simple chromaticism) or fleeting changes of the context in which a series of chords is played such that the feeling of "key" is unclear, ambiguous, or altogether lost (intense chromaticism). -- "So, it was all a dream!" --Mr. Pither "No, dear, this is the dream; you're still in the cell." --his mother Rich Rosen pyuxn!rlr