Good Vibrations: The Physics of Music

6. Down Melody Lane with Chords and Chord Sequences

6 Down Melody Lane with Chords and Chord Sequences What would music be without harmony? Harmony, which comes from the playing or singing of several notes simultaneously, is one of the things that makes music beautiful. And for harmony we need chords. A chord is several notes—two, three, or more—played at once, and as we will see, chords play a major role in any type of music. Many musical instruments, such as trumpets and clarinets, play only a single note at a time, but others, such as the piano and the guitar, use chords extensively. Indeed, even though many instruments play only a single note, when they are in a band or orchestra, they are forming part of a chord. Instruments in an orchestra usually play different notes of a chord. Dyads and Intervals When two notes are played together they form a dyad, or interval. Several of these intervals are of particular importance because they are more harmonic than others (we have, of course, already met them). Because of their importance we refer to them as perfect consonances . They are shown in table 7. There are also several other dyads of importance—the major consonances—and they are shown in table 8. The smaller the ratio of numbers, the more harmonic the sound. In short, 3:2 is considerably more harmonic than 8:5. These intervals are illustrated in musical notation as follows 94 The Building Blocks of Music Table 7. The perfect consonances Perfect consonance Frequency ratio Examples in C major Octave 2:1 C–C⬘ Fifth 3:2 C–G Fourth 4:3 C–F Table 8. The major consonances Major consonance Frequency ratio Examples in C major Major third 5:4 C–E Minor third 6:5 C–E♭ Major sixth 5:3 C–A Minor sixth 8:5 C–A♭ Chords Triads Three notes played together form a triad. We have already met the triad C-E-G and know that the frequency ratio of the three notes is 4:5:6; furthermore, from the previous section we know that the 4:5 ratio forms a major third and the 5:6 ratio forms a minor third. Our triad is therefore made up of a major and a minor third. In the same way, we can form several other important triads; they are listed in table 9. These are, of course, only a few of the triads that can be formed within an octave, but they are the most melodic ones. Table 9. Some triads and their components Triad Components Frequency ratio C-F-A Fourth + major third 3:4:5 E-G-B Minor third + major third 5:6, 4:3 E-G-C⬘ Minor third + fourth 5:6, 3:4 C-E-A Major third + fourth 4:5, 3:4 E-A-C⬘ Fourth + minor third 3:4, 5:6 When we talk about a triad, we refer to the bottom note as the root; in the case of the major triad, the upper two notes are the third and fifth. It’s easy to see that the number of half tones (in the major triad C-E-G) between the root and the third is four. If we form a triad a tone up, such as Chords and Chord Sequences 95 we see that there are only three half tones between the two lower notes, so it can’t be a major. It is, in fact, a minor chord; in this case it is D minor. If we continue up another tone we get the triad and again, if we count the number of half tones between the lower two notes we get three, so this is also a minor chord. It is, in fact, E minor. The triad above it is F major, above that is G major, and above it is A minor. The last chord, which starts on B, is different. As we will see later, it is a “diminished” chord. Earlier, we referred to the notes as we proceeded up the scale by the Roman numerals I, II, III, and so on. From the above we see that it is useful to also refer to the type of chord. If Roman numeral I is the tonic we write I ii iii IV V vi vii° where capital Roman numerals designate major chords, small numerals designate minor chords, and the degree symbol (°) designates a diminished...