Messages from

The ‘Neapolitan’, or ‘Neapolitan sixth’, chord can be described technically as the first inversion of the major triad on the flatted supertonic. Major triads are the simplest and most familiar kind of chord. The major triad on the first, or tonic, note of a C major scale contains the notes C, E and G. (When a guitarist plays a ‘C chord’, it is a mixture of these notes.) The supertonic is the second ‘degree’ of the scale. In C major, it is the note D. The flatted supertonic is thus Db, and the major triad with that ‘root’ contains the notes Db, F and Ab. (A guitarist would call this a ‘Db chord’.) The first inversion of the chord is produced by using its second note, not the first, at the bottom of the chord. In C major, the lowest note of the Neapolitan chord is therefore F. The distinctive interval of a minor 6th between the F and the Db — a note foreign to the C major scale — is the ‘Neapolitan sixth’, and that name is often applied to the chord itself. Introduced in the 17th century, when it would have sounded dangerously radical, the chord became a favorite harmonic variation of many composers, including Beethoven.

The jigs of traditional Celtic music are generally in the lilting 6/8 meter, although ‘straight jigs’ in 2/4 and ‘triple jigs’ in 9/8 are also found. The minuet, like the waltz and many another dance form, is always in 3/4. Most piano rags are in a duple meter, either 2/2 or 2/4, with occasional exceptions such as Joplin’s Bethena: A Ragtime Waltz. A march, whether by Sousa or another composer, is essentially always in 4/4 (‘common’ or ‘march’) time.

Until Guido d’Arezzo introduced the earliest version of modern staff notation, the music performed in churches and monasteries throughout medieval Europe was recorded using neumatic notation, in which symbols called neumes played approximately the same role as the notes of written music today. However, the neumatic system was comparatively imprecise and clumsy with regard to specifying the pitch and timing of the music to be performed. Another of Guido’s accomplishments was the assignment of particular syllables to the notes of the scale, which eventually gave rise to the sol-fa system of today. The syllables he used — ut, re, mi, fa, so and la — remain in use today, except that ut is often replaced by do for its rounder sound, and ti (or si) has been added as the seventh degree of the scale. The original set came from the first syllable of each of the first six lines of the medieval hymn to John the Baptist, Ut queant laxis, which was chosen because the corresponding notes of the melody are the first six notes of the major scale, in order. The clarinet was invented near the start of the 18th century by the German instrument-maker Johann Christoph Denner, who adapted it from the earlier chalumeau. The use of voice and instruments together goes back at least as far as classical Greece, and probably to almost the dawn of music itself. The melody of Greensleeves is believed to have originated in England in Elizabethan times; a persistent tradition that it was composed by Henry VIII for the purpose of wooing Anne Boleyn appears alas to be false.

In the harmonic system used in Western classical music, the smallest difference in pitch normally considered is the semitone, or half-step, anything smaller being regarded as a microtone. A semitone is the interval between the third and fourth notes of an ordinary major scale (from mi to fa in the sol-fa system), and between the seventh and eighth notes as well (from si to do). On an equal-tempered instrument like the piano, a semitone is exactly one-twelfth of an octave, and all other intervals are also exact multiples of the semitone. Other musical traditions, such as those of India, have made use for centuries of notes that fall between the stepping-stones of Western scales. Even in the West, musicians have experimented with microtonal concepts for some time outside the mainstream. A famous example is that of the 16th-century Italian composer and theorist Nicola Vicentino, who constructed a keyboard instrument he called the ‘archicembalo’ with 36 keys per octave. Starting in the late 19th century, some composers embraced microtonal concepts as a fresh means of expression. They began to to develop quasi-harmonic systems, and methods of notation, for handling microtones of various kinds. The development of elecronic tone generation, which allows the use of ‘notes’ of arbitrary frequency, has opened limitless possibilities for further experimentation. Nevertheless, it is also true that to date microtonal music has failed to capture a large listening audience in the West.