BEYOND THE SINGLE NOTE Whenever two or more pitches are sounded simultaneously "harmony" is created. This word may me a misnomer in that it does imply a subjective evaluation of how "pleasing" two or more pitches may sound, when in fact harmony is created whether or not the sound is pleasant. Another term used to describe harmony is "chord." The meaning is the same, and there may even be a hold-over from previous ages of the same kind of implication. In discussion of tonal music, we will refer to chords and harmony which have been accepted as being more or less pleasing, but keep in mind that just as individual pitches may have varying degrees of "agitation" in relation to other pitches, and thus may be more or less "pleasant," so chords may attain the same conditions depending upon context. The preeminent chord in tonal music consists of three pitches, and thus is known as a triad. Any three-note chord is a triad, but the tonal triad is made of intervals of a third and is thus known as a tertian triad. We have previously encountered this sound as the 4th, 5th, and 6th frequencies of the harmonic series: Stacking three notes with intervals other than thirds will also create triads, but not tertian triads. Having successive 4ths, for instance, will yield "quartal" triads, while successive 5ths make "quintal" triads: These are legitimate sounds which may form the basis for entire compositions. Such sounds were not fully explored until the 20th century, however. Since it is the tertian triad which underlies the harmonic organization of tonal music, and since tonality has been the predominant organizing principle in Western music for the past 300-400 years, when the word triad is referred to without further qualification, we can assume that one is speaking of the tertian triad. THE TERTIAN TRIAD There are, as we know, two primary forms of the interval of a third, major and minor. Varying combinations of these two intervals produce 4 different kind of triads. These are commonly derived by stacking up thirds above each of the notes in either a major or minor scale: TRIADS IN MAJOR Examination of the intervallic patterns of the triads in the major key above reveals three different chords. 1. Major 3rd, Minor 3rd (MAJOR TRIAD, found on 1,4,5) 2. Minor 3rd, Major 3rd (MINOR TRIAD, found on 2,3,6) 3. Minor 3rd, Minor 3rd (DIMINISHED TRIAD, found on 7) The conventional labelling of these triads, within the given key, is a Roman numeral, with upper-case representing major, lower-case stand- ing for minor, and lower-case with a for dimininished. Let's look more closely at each one of these: TRIADS IN MINOR The same configurations occur in minor keys, but shifting to different places within the scale. Furthermore, since the 7th scale degree in minor is usually raised a half step (thus Harmonic Minor), the chord on the 5th (the Dominant) is nearly always major rather than minor, the chord on the 7th is usually diminished rather than major, and the chord on the 3rd is sometimes augmented. The latter situation is a new configuration, M3+M3 (making an A5) = Augmented Triad. Since this is a new triad, and because the raised 7th is most common, we'll focus our attention on the application of harmonic minor to triad structure: EXERCISE 1 Triads built upon the scale tones in C Major and A Harmonic minor will be played at random when you hit "H". First identify the quality of the triad, (MAJ for MAJOR, MIN for MINOR, DIM for DIMINISHED, and AUG for AUGMENTED). Then spell the triad from the given root (e.g. CEG, G#BD, etc). HARMONIC RELATIONSHIPS Just as one pitch may have a greater or lesser tendency to move toward another when set in a melodic shape, depending upon the pitch set con- text, one triad may have a greater or lesser tendency to move toward another in a series of chords. Both the tonic pitch and the triad built upon that pitch form the center of gravity in the tonal system. The model chordal relationship in this system is that of tonic to dominant (the triad built upon the 5th scale degree). Let's examine this relationship more closely: From tonic, we could go to any triad built upon any other scale degree. But upon reaching the dominant triad, there is a strong tendency to resolve to the tonic. This is so because the dominant triad contains the leading tone, (which most readily resolves to the tonic note), the 5th (which also tends to resolve to the tonic note, either by movement of a 5th downward or a 4th upward), and the 2nd, which may either move to the tonic note or the 3rd of the tonic triad. As tonal harmony evolved, this movement of a triad's root (generating tone) by a 5th downward or 4th upward, together with the other two notes in the triad moving to their nearest neighbors, became the preferred chord "progression" sound. If this principle is extended in successive similar instances, we progress around the circle of 5ths, with the specific case of the diminished 5th root movement from the triad built upon the 7th scale degree (the leading tone triad) to that on the 4th (the subdominant triad) keeping the series within the original key. Model: V - I same pattern: ii - V vi - ii iii - vi vii - iii IV - vii In this series, I moves to IV and then follows the pattern all the way through successive root movements by an interval of a 5th until reaching I again. The example is on the next page. While this pattern of chord relationships is common, there are two chords which usually function differently. The vii chord more often moves to I than to iii, and the IV chord usually goes to V rather than to vii. With these changes, we can devise a hierarchy of chords, conceiving of I as the center of gravity, with successive "levels" of chords above I having a "most likely" path back down: Level 5: iii Level 4: vi Level 3: ii, IV Level 2: V, vii Level 1: I (center of gravity) Examination of the vii chord reveals two strong tendency tones, the leading tone and the subdominant. In fact, the vii chord is very similar to the V chord. If we superimpose a vii and a V the result is a 4-note chord consisting of a triad plus an interval of a 7th. This is called a 7th chord. Given V as the root, this chord would be labelled a dominant 7th. Adding the 7th strengthens the tendency to move to I. In some ways, we could consider the vii chord to be a V7 without the root! The IV chord bears the same relationship to ii as vii does to V. A very common cadential "formula" is ii7-V-I. In this instance, a 7th has been added to the supertonic chord, strengthening its tendency to progress to V. The subdominant chord could be viewed as a ii7 chord without the root. IV is thus a substitute for ii, and in fact is used more often then ii in much folk and pop music. Basic Principles of Harmonization Within the system of traditional tonality there is an obvious link between melody and harmony. Melody tones in strong rhythmic positions are likely to outline chords. As a first principle of harmonization, we may thus look to the first beat of each measure to provide a clue as to the most likely chord for that measure. Such folk tunes as "Oh, Susannah" provide perfect illustrations. (Next page) Note the preponderance of notes that are members of the tonic triad. The tune is firmly grounded in tonic. Observe also the movement to V as a counterbalance to I, and the brief contrast on the subdominant. The essential harmonic "message" here is a movement from I to V to I. Most simple tunes can be harmonized with one chord per measure. The one instance where this is not possible in "Oh, Susannah" is clear. The sense of conclusiveness on tonic requires the momentary tension created by dominant. The rate of change of one harmony to another is called harmonic rhythm. Harmonic changes are most likely to occur on the first beat of a measure, since this reinforces emphasis. In a four-beat measure, harmonic change is also likely on beat 3. Changing harmony on a weak beat may cause rhythmic confusion. The Vertical Aspect There are three chief factors in the vertical deployment of notes that affect the resultant sound of a chord: 1. Spacing 2. Doubling 3. Inversion Spacing refers to the intervallic distance between adjacent tones. Common practice follows the example of the harmonic series: notes are farther apart when low, closer together when high. The most obvious reason for this is that if notes are close together in the lower registers, the resultant sound will be "muddy." The rule-of-thumb in the spacing of notes (referred to as "voices," though not having to be vocal!) is never to have more than an octave between the upper voices. Since most of the "rules" of harmony were derived from analysis of Bach's 4-part chorale settings, we often say that an interval greater than an octave is allowable between the bass and tenor voices, but that the upper three (tenor, alto,soprano) should not be greater than an octave. This principle is applicable to instrumental as well as vocal music, and to music having more than 4 simultaneous sounds. Deploying the notes of a triad for four or more voices clearly necessi- tates doubling one or more of those notes. Which of the notes is thus doubled will affect the "weight" of the sound. In general, doubling the root of the chord will make it sound more centered, while doubling the third will reinforce its "majorish-ness" versus "minorish-ness". Doubling the fifth will tend to tug the ear in the direction of that chord's dominant, making it sound unstable. Our ears are most responsive to the notes in the outer voices of a chord. In the previous example, the fact that the root note is in the lowest voice contributes to its stability, while the 5th in the highest voice create a slight instability. The most stable distribution of notes in a chord would double the root in the outer voices. While the highest note in a chord is important in shaping the relative stability of the chordal sound, since it is usually being tracked as the melodic tone, it affects the chord less than the lowest note. A chord which has its root in the lowest voice is in ROOT POSITION. If any other chord tone is in the lowest voice, the chord is in one of several possible INVERSIONS. Triads have 3 positions, 7th chords have 4: The Horizontal Aspect Simultaneously-sounding notes create chords. Successive adjacent tones create melodies. The emphasis here is on the word "adjacent." The ear follows the movement of one pitch to another if those pitches are more or less conjunct (technically no more than an interval of a 2nd). In relating one chord to another, then, the most common sense approach is to move each chord tone to its nearest neighbor in the following chord. This is possible with the upper notes of chord, less so with the bass note if it is sounding the root of chords. If the previous example sounds vaguely familiar, it's because it is the chord structure of the first four measures of Bach's Prelude #1 in C Major. We'll examine the whole piece in more detail later. For now, notice that it consists of 5 voices and that Bach was able, via chord inversion, to keep all 5 voices moving to their successors without any disjunct motion (intervals greater than a 2nd). Notice also which tones are doubled. Figured Bass Jazz musicians are used to reading off "lead sheets." These contain the melody together with symbols for the appropriate harmonization. Figured bass functioned in the same way a couple centuries ago. It is a system that identifies chords, given a bass line and sometimes a melody line. The system is not in current use for performance, but is still used as an analytical tool. The premise of the figured bass system is to identify what notes should be sounding to produce a chord, and which inversion the chord is in. A Roman numeral identifes the root of the chord in relation to the tonal center of the music (the key of the piece). Arabic numbers are then used to identify the chords inversion. These numbers label the intervals above the lowest sounding voice, reduced to within an octave - although they reveal nothing about the possible doubling or spacing of the chord. The Arabic number identifiers are as follows: Triad: 7th Chord: Root Position --------- none Root Position -------- 1st Inversion --------- 1st Inversion -------- (3rd in lowest voice) 2nd Inversion --------- 2nd Inversion -------- (5th in lowest voice) 3rd Inversion -------- (7th in lowest voice) The following page presents the harmonic structure of Bach's first Pre- lude from the first book of the Well Tempered Clavier. An analysis of the first 13 measures is given; the remainder is left unanalysed, for you to attempt and for class discussion. Bach's actual music arpeggiates the chord tones in a constant 16th-note pattern with each arpeggiation repeated twice in every measure, up to the last 2 measures. You can play the piece by repeatedly tapping the "P" key to hear each note in turn. You can go to any measure by hitting "M" and entering the measure number. This piece offers a wealth of information about tonal harmonic relationships - its sense of forward momentum is entirely dependent upon these relationships - but a detailed discussion is beyond the scope of this text. Non-Chord Tones One final issue regarding harmony needs to be touched upon briefly. If all melody tones were members of the underlying harmony, melodic structures would be limited to intervals larger than a 2nd. This would be akin to restricting melodies to the format of bugle calls, which essentially only sound the 3rd through 6th harmonics above a given fundamental (thus outlining a tertian triad). For variety and to add tension, judicious inclusion of tones which are not members of the underlying chord is welcome. We've already seen instances of the two most common "non-chord" tones in "Oh, Susannah": The measures in question are harmonized by the tonic chord (C major in this case). The D's and A are not members of this chord. The D's are passing tones, and the A is a neighbor tone. Non-chord tones are defined by how they are approached and left: 1. Passing Tone Approached by step, left by step in same direction (if in strong rhythmic position, known as Accented Passing Tone) 2. Neighbor Tone Approached by step, left by step in opposite direction (if above main note, known as Upper Neighbor) (if below main note, known as Lower Neighbor) 3. Suspension Approached by repetition or tie, left by step (consists of 3 parts: Preparation, Suspension, Resolution) (usually resolved downwards - upward resolution, known as Retardation) 4. Appogiatura Approached by leap, left by step (usually left in opposite direction from approach) (usually on strong beat, sometimes sounded without preparation) 5. Escape Tone Approached by step, left by leap (usually left in opposite direction from approach) 6. Free Tone None of the above (least common - lease effective) Discussion of the suspension, appogiatura, escape tone, and free tone will be left for the classroom. Our main compositional concern for now is with the capacity to inject variety through the use of passing and neighboring tones. Remember that in your own efforts to compose melodies, occasional use of these tones will add "color" and contribute of the balance among factors of unity and variety.