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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.

Most, though not all, of Satie’s output was written for the piano. Satie was one of those relentlessly individual turn-of-the-20th-century French artists, musicians and intellectuals who gave us our modern misconceptions of how such people should behave. His training included two mostly unsuccessful enrolments as a student of performance and composition at the Paris Conservatoire, and a brief stint in the army (to escape which he deliberately contracted bronchitis). Thereafter he began to compose, even working for some time as official composer to a breakaway Rosicrucian group led by Sâr Joséphin Péladan (who sported the titles ‘Imperator’ and ‘Super Magician’). However, Satie also enjoyed productive associations with the intellectual and artistic elite of the day, including Maurice Ravel, Jean Cocteau and Pablo Picasso. It was an enduring practice of Satie’s to provide guides to performance in the form of amusing annotations to the scores of his musical compositions. These verbal notes had a degree of popularity independent from the music itself; in the end Satie had expressly to discourage the growing practice among performers of reading them aloud. Upon his death, his mourning friends discovered a number of unknown compositions in Satie’s room in the Arceuil district of Paris. In 27 years of residence there, he had had no previous visitors.

The string section is the largest of a symphony orchestra, with two or three groupings each of violins, violas, celli and basses. It has a central role in generating the expressive power of symphonic music, and the head of the section — the player occupying ‘first chair’ among the first violins — is therefore a figure of importance. Within the strings, the concertmaster is in charge of technical matters such as bowing and fingering. Another important duty is to lead the orchestra in tuning. At a symphony performance, the concertmaster is usually the first musician to appear on stage (and may receive individual applause on doing so), and the conductor the last.

Incalzando is the exceptional word, indicating — in sharp distinction to the others — that the performer’s speed and volume should increase. Although it isn’t always clear from a literal translation (calando means ‘falling’, mancando means ‘missing’, perdendosi means ‘lost’), the other terms are all virtually synonymous.

The correct answer is 36. The octave is the musical interval, or distance, that separates a note from the next higher or next lower note with the same name: from middle C to the next higher C, for example. The relationship between pitch and vibrational frequency is also quite simple: doubling the frequency raises the pitch by one octave exactly. Starting at 20 vibrations (or cycles) per second and doubling repeatedly, we will find that the pitch produced at 40 cycles per second is one octave higher than the original; 80 cycles per second is two octaves higher; and so on. Continuing, we will find that the pitch corresponding to 20,480 cycles per second — inaudibly high to many humans — is exactly 10 octaves higher than our starting pitch at the bottom of the frequency spectrum. If a musical work were (bizarrely) to make full use of that spectrum, and to be written out (impractically) on a single staff, the low pitch would be rendered on the bottom line. Every seven lines counted upwards represents a two-octave elevation in pitch, so 35 additional lines would be required. The grand staff on which piano and harp music is notated is equivalent to a single staff of 11 lines. It covers the pitch range from the second G below middle C to the second G above, corresponding to a frequency range from 98 to 784 cycles per second.

To be fair, Wilhelm Friedrich Ernst Bach (1759-1845), only son of J.S. Bach’s fourth son Johann Christoph Friedrich, is less well known today than some of his uncles and forebears, to say nothing of J.S. himself. Wilhelm Friedrich nevertheless lived a long and productive musical life as a conductor and composer. One of his works, Dreyblatt, is most unusual in being written for three pianists playing at the same instrument (‘six hands’). There is a considerable repertoire of such music for just two players (‘four hands’), but for reasons of physical space that is usually seen as the upper limit. To get around it, Dreyblatt is designed for performance by a tall performer flanked by two much smaller ones. The center player reaches around his companions to address the lowest and highest ranges of the keyboard while they take care of the middle.

Instruments like kazoos have been played in Africa for at least many centuries, and possibly much longer. Because the sound in a mirliton is produced by a membrane, musicologists usually classified it among the membranophones. However, all other membranophones are drums. Only in the mirliton is the vibration of the membrane induced by the player’s vocal mechanism — specifically, by humming. The word ‘kazoo’ was originally a trade-name given by American inventor Warren Herbert Frost to his manufactured toy mirliton in 1883. The paper-and-comb, an instrument even less formal than the kazoo, is another variation on the mirliton pattern.