1.
Bach-Werke-Verzeichnis
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The Bach-Werke-Verzeichnis is a catalogue of compositions by Johann Sebastian Bach. It was first published in 1950, edited by Wolfgang Schmieder, the catalogues second edition appeared in 1990. An abbreviated version of second edition, known as BWV2a, was published in 1998. 1126 compositions were assigned a BWV number in the 20th century, more compositions were added to the catalogue in the 21st century. The Anhang of the BWV lists over 200 lost, doubtful, the first edition of the Bach-Werke-Verzeichnis was published in 1950. It allocated a number to every known composition by Bach. Schmieder published the BWVs second edition in 1990, with some modifications regarding authenticity discriminations, and more added to the main catalogue. Several compositions were repositioned in the structure of chapters organised by genre. In 1998 Alfred Dürr and Yoshitake Kobayashi published an edition of the catalogue. This edition, known as BWV2a, contained a few further updates, new additions to BWV2/BWV2a included, BWV 1081–1126 BWV Anh. 190–213 An upper case R was used as an addition to a BWV number to indicate a reconstructed version, numbers above BWV1126 were added in the 21st century. The numbers assigned to compositions by Johann Sebastian Bach and by others in the Bach-Werke-Verzeichnis are widely used for the identification of these compositions. BWV numbers 1 to 1126 appear in the 1998 edition of the Bach-Werke-Verzeichnis, BWV numbers 1127 and 1128 were assigned in the 21st century. Ich sehe, itzt, da ich zur Hochzeit gehe BWV163 – Nur jedem das Seine BWV164 – Ihr, BWV167 – Ihr Menschen, rühmet Gottes Liebe BWV168 – Tue Rechnung. k. a. Mourning Ode BWV199 – Mein Herze schwimmt im Blut BWV200 – Bekennen will ich seinen Namen BWV201 – Geschwinde, ihr wirbelnden Winde a. k. a. The Dispute between Phoebus and Pan BWV202 – Weichet nur, betrübte Schatten BWV203 – Amore traditore BWV204 – Ich bin in mir vergnügt a. k. a. On Contentedness BWV205 – Zerreißet, zersprenget, zertrümmert die Gruft a. k. a. k. a. k. a, coffee Cantata BWV212 – Mer hahn en neue Oberkeet a. k. a. Peasant Cantata BWV213 – Laßt uns sorgen, laßt uns wachen a. k. a, hercules at the Crossroads BWV214 – Tönet, ihr Pauken
2.
Johann Sebastian Bach
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Johann Sebastian Bach was a German composer and musician of the Baroque period. Bachs compositions include the Brandenburg Concertos, the Goldberg Variations, the Mass in B minor and his music is revered for its technical command, artistic beauty, and intellectual depth. He is now regarded as one of the greatest composers of all time. Bach was born in Eisenach, in the duchy of Saxe-Eisenach and his father Johann Ambrosius Bach was the director of the town musicians, and all of his uncles were professional musicians. His father probably taught him to play the violin and harpsichord, apparently at his own initiative, Bach attended St. Michaels School in Lüneburg for two years. He received the title of Royal Court Composer from Augustus III in 1736, Bachs health and vision declined in 1749, and he died on 28 July 1750. Johann Sebastian Bach was born in Eisenach, the capital of the duchy of Saxe-Eisenach, in present-day Germany and he was the son of Johann Ambrosius Bach, the director of the town musicians, and Maria Elisabeth Lämmerhirt. He was the eighth and youngest child of Johann Ambrosius, who taught him violin. His uncles were all musicians, whose posts included church organists, court chamber musicians. One uncle, Johann Christoph Bach, introduced him to the organ, Bachs mother died in 1694, and his father died eight months later. The 10-year-old Bach moved in with his eldest brother, Johann Christoph Bach, there he studied, performed, and copied music, including his own brothers, despite being forbidden to do so because scores were so valuable and private and blank ledger paper of that type was costly. He received valuable teaching from his brother, who instructed him on the clavichord, also during this time he was taught theology, Latin, Greek, French and Italian at the local gymnasium. By 3 April 1700 Bach and his schoolfriend Georg Erdmann–who was two years Bachs elder–were enrolled in the prestigious St. Michaels School in Lüneburg, some two weeks travel north of Ohrdruf and their journey was probably undertaken mostly on foot. His two years there were critical in exposing Bach to a range of European culture. In addition to singing in the choir, he played the Schools three-manual organ and he came into contact with sons of aristocrats from northern Germany, sent to the highly selective school to prepare for careers in other disciplines. While in Lüneburg, Bach had access to St. Johns Church and possibly used the famous organ from 1553. His role there is unclear, but it probably included menial, non-musical duties, despite strong family connections and a musically enthusiastic employer, tension built up between Bach and the authorities after several years in the post. Bach was dissatisfied with the standard of singers in the choir and he called one of them a Zippel Fagottist
3.
Musical keyboard
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A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument. Depressing a key on the causes the instrument to produce sounds, either by mechanically striking a string or tine, plucking a string, causing air to flow through a pipe. On electric and electronic keyboards, depressing a key connects a circuit, since the most commonly encountered keyboard instrument is the piano, the keyboard layout is often referred to as the piano keyboard. The twelve notes of the Western musical scale are laid out with the lowest note on the left, because these keys were traditionally covered in ivory they are often called the white notes or white keys. The keys for the remaining five notes—which are not part of the C major scale— are raised, because these keys receive less wear, they are often made of black colored wood and called the black notes or black keys. The pattern repeats at the interval of an octave, the arrangement of longer keys for C major with intervening, shorter keys for the intermediate semitones dates to the 15th century. The break was between middle C and C-sharp, or outside of Iberia between B and C, broken keyboards reappeared in 1842 with the harmonium, the split occurring at E4/F4. The reverse-colored keys on Hammond organs such as the B3, C3, the chromatic compass of keyboard instruments has tended to increase. Harpsichords often extended over five octaves in the 18th century, while most pianos manufactured since about 1870 have 88 keys, some modern pianos have even more notes. While modern synthesizer keyboards commonly have either 61,76 or 88 keys, organs normally have 61 keys per manual, though some spinet models have 44 or 49. An organ pedalboard is a keyboard with long pedals that are played by the organists feet, pedalboards vary in size from 12 to 32 notes. In a typical layout, black note keys have uniform width. In the larger gaps between the keys, the width of the natural notes C, D and E differ slightly from the width of keys F, G, A and B. This allows close to uniform spacing of 12 keys per octave while maintaining uniformity of seven natural keys per octave, over the last three hundred years, the octave span distance found on historical keyboard instruments has ranged from as little as 125 mm to as much as 170 mm. Several reduced-size standards have been proposed and marketed, a 15/16 size and the 7/8 DS Standard keyboard developed by Christopher Donison in the 1970s and developed and marketed by Steinbuhler & Company. There have been variations in the design of the keyboard to address technical and musical issues, thus, an octave would have eight white keys and only four black keys. During the sixteenth century, when instruments were tuned in meantone temperament, some harpsichords were constructed with the G♯. The broken octave, a variation of the short octave
4.
Keyboard instrument
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A keyboard instrument is a musical instrument played using a keyboard. The most common of these are the piano, organ, and various keyboards, including synthesizers. Other keyboard instruments include celestas, which are struck idiophones operated by a keyboard, and carillons, today, the term keyboard often refers to keyboard-style synthesizers. Another important use of the keyboard is in historical musicology. Particularly in the 18th century, the harpsichord, the clavichord, and the piano were in competition. Hence in a phrase like Mozart excelled as a player the word keyboard is usefully noncommittal. The earliest known keyboard instrument was the Ancient Greek hydraulis, a type of pipe organ, the keys were likely balanced and could be played with a light touch, as is clear from the reference in a Latin poem by Claudian, who says magna levi detrudens murmura tactu. Intent, that is “let him thunder forth as he presses out mighty roarings with a light touch”, from its invention until the fourteenth century, the organ remained the only keyboard instrument. Often, the organ did not feature a keyboard at all, almost every keyboard until the fifteenth century had seven naturals to each octave. The clavichord and the harpsichord appeared during the 14th century—the clavichord probably being earlier, the harpsichord and clavichord were both common until widespread adoption of the piano in the 18th century, after which their popularity decreased. The piano was revolutionary, because a pianist could vary the volume of the sound by varying the vigor with which each key was struck. The pianos full name is gravicèmbalo con piano e forte meaning harpsichord with soft and loud but can be shortened to piano-forte, which means soft-loud in Italian. In its current form, the piano is a product of the late 19th century, in fact, the modern piano is significantly different from even the 19th-century pianos used by Liszt, Chopin, and Brahms. See Piano history and musical performance, keyboard instruments were further developed in the early twentieth century. Early electromechanical instruments, such as the Ondes Martenot, appeared early in the century and this was a very important contribution to the keyboards history. Much effort has gone into creating an instrument that sounds like the piano but lacks its size, the electric piano and electronic piano were early efforts that, while useful instruments in their own right, did not convincingly reproduce the timbre of the piano. Electric and electronic organs were developed during the same period, more recent electronic keyboard designs strive to emulate the sound of specific make and model pianos using digital samples and computer models. Concerns celebrated keyboard players and the various instruments used over the centuries
5.
Harpsichord
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A harpsichord is a musical instrument played by means of a keyboard. It produces sound by plucking a string when a key is pressed, Harpsichord designates the whole family of similar plucked keyboard instruments, including the smaller virginals, muselar, and spinet. The harpsichord was used in Renaissance and Baroque music. During the late 18th century, it disappeared from the musical scene with the rise of the piano. In the 20th century, it made a resurgence, being used in historically informed performances of music, in compositions. Harpsichords vary in size and shape, but all have the basic functional arrangement. The player depresses a key that rocks over a pivot in the middle of its length, the other end of the key lifts a jack that holds a small plectrum, which plucks the string. When the player releases the key, the far end returns to its rest position, the plectrum, mounted on a tongue that can swivel backwards away from the string, passes the string without plucking it again. As the key reaches its rest position, a felt damper atop the jack stops the strings vibrations and these basic principles are explained in detail below. The keylever is a pivot, which rocks on a balance pin that passes through a hole drilled through the keylever. The jack is a thin, rectangular piece of wood that sits upright on the end of the keylever, the jacks are held in place by the registers. These are two strips of wood, which run in the gap between pinblock and bellyrail. The registers have rectangular mortises through which the pass as they can move up. The registers hold the jacks in the location needed to pluck the string. In the jack, a plectrum juts out almost horizontally and passes just under the string, historically, plectra were made of bird quill or leather, many modern harpsichords have plastic plectra. When the front of the key is pressed, the back of the key rises, the jack is lifted, the vertical motion of the jack is then stopped by the jackrail, which is covered with soft felt to muffle the impact. When the key is released, the falls back down under its own weight. This is made possible by having the plectrum held in a tongue attached with a pivot and a spring to the body of the jack
6.
Clavichord
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The clavichord is a European stringed keyboard instrument known from the late Medieval, through the Renaissance, Baroque and Classical eras. Historically, it was used as a practice instrument and as an aid to composition. The clavichord produces sound by striking brass or iron strings with metal blades called tangents. Vibrations are transmitted through the bridge to the soundboard, the name is derived from the Latin word clavis, meaning key and chorda meaning string, especially of a musical instrument. An analogous name is used in other European languages, many languages also have another name derived from Latin manus, meaning hand. Other names refer to the nature of a fully fretted clavichord. Italian also used sordino, a reference to its quiet sound, the clavichord was invented in the early fourteenth century. In 1504, the German poem Der Minne Regeln mentions the terms clavicimbalum and clavichordium, One of the earliest references to the clavichord in England occurs in the privy-purse expenses of Elizabeth of York, queen of Henry VII, in an entry dated August 1502, Item. The same day, Hugh Denys for money by him delivered to a stranger that gave the queen a payre of clavycordes, in crowns form his reward iiii libres. The clavichord was very popular from the 16th century to the 18th century, but mainly flourished in German-speaking lands, Scandinavia, and it had fallen out of use by 1850. In the late 1890s, Arnold Dolmetsch revived clavichord construction and Violet Gordon-Woodhouse, among others, although most of the instruments built before the 1730s were small, the latest instruments were built up to seven feet long with a six octave range. Today clavichords are played primarily by Renaissance, Baroque, and Classical music enthusiasts and they attract many interested buyers, and are manufactured worldwide. There are now numerous clavichord societies around the world, and some 400 recordings of the instrument have made in the past 70 years. Leading modern exponents of the instrument have included Derek Adlam, Christopher Hogwood, Richard Troeger, Thurston Dart, Wim Winters, stevie Wonder uses a Clavinet in many of his songs, such as Superstition and Higher Ground. A Clavinet played through an instrument amplifier with guitar effect pedals is often associated with funky, guy Sigsworth has played clavichord in a modern setting with Björk, notably on the studio recording of All Is Full of Love. Björk also made use of and even played the instrument herself on the song My Juvenile of her 2007 album Volta. Tori Amos uses the instrument on Little Amsterdam from the album Boys for Pele, Amos also featured her use of the Clavinet on her 2004 recording Not David Bowie, released as part of her 2006 box set, A Piano, The Collection. In 1976 Oscar Peterson played songs from Porgy And Bess on the clavichord, keith Jarrett also recorded an album entitled Book of Ways in which he plays a series of clavichord improvisations
7.
Organ (music)
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In music, the organ is a keyboard instrument of one or more pipe divisions, each played with its own keyboard, played either with the hands on a keyboard or with the feet using pedals. The organ is an old musical instrument, dating from the time of Ctesibius of Alexandria. It was played throughout the Ancient Greek and Ancient Roman world, subsequently it re-emerged as a secular and recital instrument in the Classical music tradition. Pipe organs use air moving through pipes to produce sounds, since the 16th century, pipe organs have used various materials for pipes, which can vary widely in timbre and volume. The pipes are divided into ranks and controlled by the use of hand stops, although the keyboard is not expressive as on a piano and does not affect dynamics, some divisions may be enclosed in a swell box, allowing the dynamics to be controlled by shutters. Some organs are enclosed, meaning that all the divisions can be controlled by one set of shutters. Some special registers with free reed pipes are expressive and these instruments vary greatly in size, ranging from a cubic yard to a height reaching five floors, and are built in churches, synagogues, concert halls, and homes. Small organs are called positive or portative, increasingly hybrid organs are appearing in which pipes are augmented with electronic additions. Great economies of space and cost are possible especially when the lowest of the pipes can be replaced, non-piped organs include the reed organ or harmonium, which like the accordion and harmonica use air to excite free reeds. Electronic organs or digital organs, notably the Hammond organ, generate electronically produced sound through one or more loudspeakers, mechanical organs include the barrel organ, water organ, and Orchestrion. These are controlled by means such as pinned barrels or book music. Little barrel organs dispense with the hands of an organist and bigger organs are powered in most cases by a grinder or today by other means such as an electric motor. The pipe organ is the grandest musical instrument in size and scope, along with the clock, it was considered one of the most complex human-made mechanical creations before the Industrial Revolution. Pipe organs range in size from a short keyboard to huge instruments with over 10,000 pipes. A large modern organ typically has three or four keyboards with five each, and a two-and-a-half octave pedal board. Wolfgang Amadeus Mozart called the organ the King of instruments, some of the biggest instruments have 64-foot pipes, and it sounds to an 8 Hz frequency fundamental tone. For instance, the Wanamaker organ, located in Philadelphia, USA, has sonic resources comparable with three simultaneous symphony orchestras, most organs in Europe, the Americas, and Australasia can be found in Christian churches. The introduction of organs is traditionally attributed to Pope Vitalian in the 7th century
8.
Classical music
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Classical music is art music produced or rooted in the traditions of Western music, including both liturgical and secular music. The central norms of this tradition became codified between 1550 and 1900, which is known as the common-practice period, Western staff notation is used by composers to indicate to the performer the pitches, tempo, meter and rhythms for a piece of music. This can leave less room for such as improvisation and ad libitum ornamentation. The term classical music did not appear until the early 19th century, the earliest reference to classical music recorded by the Oxford English Dictionary is from about 1836. This score typically determines details of rhythm, pitch, and, the written quality of the music has enabled a high level of complexity within them, J. S. The use of written notation also preserves a record of the works, Musical notation enables 2000s-era performers to sing a choral work from the 1300s Renaissance era or a 1700s Baroque concerto with many of the features of the music being reproduced. That said, the score does not provide complete and exact instructions on how to perform a historical work, even if the tempo is written with an Italian instruction, we do not know exactly how fast the piece should be played. Bach was particularly noted for his complex improvisations, during the Classical era, the composer-performer Mozart was noted for his ability to improvise melodies in different styles. During the Classical era, some virtuoso soloists would improvise the cadenza sections of a concerto, during the Romantic era, Beethoven would improvise at the piano. The instruments currently used in most classical music were largely invented before the mid-19th century and they consist of the instruments found in an orchestra or in a concert band, together with several other solo instruments. The symphony orchestra is the most widely known medium for music and includes members of the string, woodwind, brass. The concert band consists of members of the woodwind, brass and it generally has a larger variety and number of woodwind and brass instruments than the orchestra but does not have a string section. However, many bands use a double bass. Many of the used to perform medieval music still exist. Medieval instruments included the flute, the recorder and plucked string instruments like the lute. As well, early versions of the organ, fiddle, Medieval instruments in Europe had most commonly been used singly, often self accompanied with a drone note, or occasionally in parts. From at least as early as the 13th century through the 15th century there was a division of instruments into haut, during the earlier medieval period, the vocal music from the liturgical genre, predominantly Gregorian chant, was monophonic, using a single, unaccompanied vocal melody line. Polyphonic vocal genres, which used multiple independent vocal melodies, began to develop during the medieval era, becoming prevalent by the later 13th
9.
C major
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C major is a major scale based on C, with the pitches C, D, E, F, G, A, and B. Its key signature has no flats and no sharps, C majors relative minor is A minor and its parallel minor is C minor. C major is one of the most common key signatures used in western music, most transposing instruments playing in their home key are notated in C major, for example, a clarinet in B♭ sounding a B-flat major scale is notated as playing a C major scale. The white keys of the piano correspond to the C major scale, among brass instruments, the contra-bass tuba is in C. A pedal harp tuned to C major has all of its pedals in the middle position, there are no black keys in the C major scale, thus it doesnt fit the natural positions of the fingers well. Twenty of Joseph Haydns 104 symphonies are in C major, making it his second most often used key, of the 134 symphonies mistakenly attributed to Haydn that H. C. Robbins Landon lists in his catalog,33 are in C major, more than any other key. Before the invention of the trumpet, Haydn did not write trumpet and timpani parts in his symphonies. H. C. Robbins Landon writes that it wasnt until 1774 that Haydn uses trumpets, most of Haydns symphonies in C major are labelled festive and are of a primarily celebratory mood. Many Masses and settings of Te Deum in the Classical era were in C major, mozart wrote most of his Masses in C major and so did Haydn. Of Franz Schuberts two symphonies in the key, the first is nicknamed the Little C major and the second the Great C major, many musicians have pointed out that every musical key conjures up specific feelings. This idea is explored in a radio program called The Signature Series. American popular songwriter Bob Dylan claimed the key of C major to be the key of strength, french composers such as Marc-Antoine Charpentier and Rameau generally thought of C major as a key for happy music, but Hector Berlioz in 1856 described it as serious but deaf and dull. Ralph Vaughan Williams was impressed by Sibeliuss Symphony No.7 in C major, however, C major was a key of great importance in Sibeliuss previous symphonies. Claude Debussy, noted for composing music that avoided a particular key center, once said, in musical catalogs that sort the musical pieces by key, whether they go by semitones or along the circle of fifths, they almost always begin with those pieces in C major. A notable modern use of the key is Terry Rileys In C, johann Sebastian Bach Toccata, Adagio and Fugue in C major, BWV564 Cello Suite No. 3, BWV1009 Ludwig van Beethoven Symphony No,1, Op.21 Piano Sonata No. 21, K.467 Piano Concerto No,25, K.503 Piano Sonata No. 16, K.545 String Quartet No,41, K.551 Sergei Prokofiev Piano Concerto No.3 Maurice Ravel Boléro Franz Schubert Wanderer Fantasy, Op.15 D.760 Symphony No
10.
C minor
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C minor is a minor scale based on C, consisting of the pitches C, D, E♭, F, G, A♭, and B♭. The harmonic minor raises the B♭ to B♮, changes needed for the melodic and harmonic versions of the scale are written in with naturals and accidentals as necessary. Its key signature consists of three flats and its relative major is E-flat major, and its parallel major is C major. In the Baroque period, music in C minor was written with a two-flat key signature. Of the two concertos that Mozart wrote in a minor key, one of them is in C minor. C minor has been associated with heroic struggle since Beethovens time, Beethoven wrote some of his most characteristic works in the key of C minor, including the Symphony No.5 and no fewer than three piano sonatas. Brahmss first symphony and first string quartet were composed in C minor, three of Anton Bruckners ten numbered symphonies are in C minor, as are two of Dmitri Shostakovichs symphonies. Passacaglia and Fugue in C minor, BWV582 – Bach Cello Suite No. 5, BWV1011 – Bach The Musical Offering, BWV1079 – Bach Great Mass in C minor – Mozart Piano Concerto No.24 – Mozart Piano Sonata No.8 – Beethoven Piano Concerto No.3 – Beethoven Symphony No
11.
C-sharp major
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C♯ major is a major scale based on C♯, consisting of the pitches C♯, D♯, E♯, F♯, G♯, A♯, and B♯. Its key signature has seven sharps and its relative minor is A♯ minor and its parallel minor is C♯ minor. The direct enharmonic equivalent equivalent of C♯ major is D♭ major, a harp tuned to C-sharp major has all its pedals in the bottom position. Because all the strings are then pinched and shortened, this is the least resonant key for the instrument,3 in both books of the Well-Tempered Clavier. 6, Franz Liszt takes the step of changing key from D-flat major to C-sharp major near the beginning of the piece. Maurice Ravel selected C-sharp major as the key of Ondine from his piano suite Gaspard de la nuit. Erich Wolfgang Korngold composed his Piano Concerto for the Left Hand, Op.17, in a few scores, 7-sharp key signatures in the bass clef are written with the sharp either for the A or for the A and the B on the top line. Louis Vierne used C-sharp major for the Dona Nobis Pacem of the Agnus Dei of his Messe Solennelle in C sharp minor, overview of compositions with 7 accidentals
12.
C-sharp minor
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C-sharp minor or C♯ minor is a minor scale based on C♯, with the pitches C♯, D♯, E, F♯, G♯, A, and B. For the C-sharp harmonic minor, the B is raised to B♯ and its key signature consists of four sharps. Its relative major is E major and its parallel major, C♯ major, is usually replaced by D♭ major, since C♯ major, which would contain seven sharps, is not normally used. D♭ minor, having eight flats, including the B, has a similar problem, changes needed for the melodic and harmonic versions of the scale are written in with accidentals as necessary. There are only two symphonies in the 18th century written in this key. One of them is by Joseph Martin Kraus, but he appears to have found the key difficult since he later rewrote it in C minor, even in the following two centuries, C-sharp minor symphonies remained rare. Two notable examples are the first movement of Mahlers Symphony No. 5) and this key occurs more often in piano literature from the 18th century onwards. Domenico Scarlatti wrote just two keyboard sonatas in C-sharp minor, K.246 and K.247, but after Beethovens Piano Sonata No. 14, the key became more frequent in the piano repertoire, beethoven himself used this key again in the outer movements of his String Quartet No.14. Even so, Johannes Brahms still felt the need to rewrite his C-sharp minor Piano Quartet in C minor, frédéric Chopin often wrote in this key, examples include the Fantaisie-Impromptu, Scherzo No. 2, and nocturnes No.7 and No.20, another very famous example of a work in C-sharp minor is Rachmaninoffs Prelude in C-sharp minor. Dmitri Shostakovichs Violin Concerto No.2 is in C-sharp minor, jules Van Nuffel wrote his psalm setting In convertendo Dominus for choir and organ in C-sharp minor. Mr. Mister – the chorus in Broken Wings Nicki Minaj – Anaconda The Police – Message in a Bottle Smile. dk – Butterfly Britney Spears – Oops. I Did It Again Britney Spears – Womanizer Train – Drive By Kanye West – Love Lockdown Ed Sheeran – Shape of You Media related to C-sharp minor at Wikimedia Commons
13.
Chromatic scale
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The chromatic scale is a musical scale with twelve pitches, each a semitone above or below another. On a modern piano or other equal-tempered instrument, all the semitones have the same size, in other words, the notes of an equal-tempered chromatic scale are equally spaced. An equal-tempered chromatic scale is a nondiatonic scale having no tonic because of the symmetry of its equally spaced notes, the most common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale. Due to a different tuning technique, the twelve semitones in this scale have two different sizes. Thus, the scale is not perfectly symmetric, many other tuning systems, developed in the ensuing centuries, share a similar asymmetry. Equally spaced pitches are provided only by equal temperament tuning systems, the term chromatic derives from the Greek word chroma, meaning color. Chromatic notes are understood as harmonically inessential embellishments, shadings. The chromatic scale may be notated in a variety of ways, ascending and descending, The chromatic scale has no set spelling agreed upon by all. Its spelling is, however, often dependent upon major or minor key signatures, the images above, therefore, are only examples of chromatic scale notations. As an abstract entity, the chromatic scale is usually notated such that no scale degree is used more than twice in succession. The ancient Chinese chromatic scale is called Shí-èr-lǜ, however, it should not be imagined that this gamut ever functioned as a scale, and it is erroneous to refer to the Chinese chromatic scale, as some Western writers have done. The series of twelve known as the twelve lü were simply a series of fundamental notes from which scales could be constructed. The Indian solfège, i. e. sargam, makes up the notes of the chromatic scale with respective sharps. The total chromatic is the set of all pitch classes. An array is a succession of aggregates and these are 19-EDO just intonation approximations. In Pythagorean tuning the chromatic scale is tuned as follows, with higher than their enharmonic flats. The 12 golden notes of music Hewitt, Michael
14.
B minor
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B minor is a minor scale consisting of the pitches B, C♯, D, E, F♯, G, and A. Its key signature consists of two sharps, the harmonic minor raises the note A to A♯. Changes needed for the melodic and harmonic versions of the scale are written with accidentals as necessary and its relative major is D major, and its parallel major is B major. By the end of the Baroque era, however, conventional academic views of B minor had shifted, beethoven labelled a B minor melodic idea in one of his sketchbooks as a black key. Brahms, Dvořák, Schubert, Liszt, Chopin, Borodin,1, Op.20 Chopin – Étude in B minor, Op.25, No.10 Chopin – Piano Sonata No. 3, Op.58 Chopin – Waltz in B minor, Op.69,3, Op.89 Liszt – Piano Sonata in B minor Felix Mendelssohn – The Hebrides Overture Mozart – Adagio from Flute Quartet No. 1, K.285 Mozart – Adagio in B minor,8, D.759 Alexander Scriabin – Fantaisie in B minor, Op.28 Tchaikovsky – Symphony No. 6, Op.74 Vivaldi – Concerto for 4 Violins and Cello, RV580 Wagner – Ride of the Valkyries from Die Walküre Key Major and minor Chord Chord names and symbols Notes Sources Galeazzi, Francesco. Elementi teorico-pratici di musica con un saggio sopra larte di suonare il violino analizzata, beethovens C-Minor Mood, Some Thoughts on the Structural Implications of Key Choice. Media related to B minor at Wikimedia Commons
15.
Leipzig
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Leipzig is the largest city in the federal state of Saxony, Germany. With a population of 570,087 inhabitants it is Germanys tenth most populous city, Leipzig is located about 160 kilometres southwest of Berlin at the confluence of the White Elster, Pleisse, and Parthe rivers at the southern end of the North German Plain. Leipzig has been a city since at least the time of the Holy Roman Empire. The city sits at the intersection of the Via Regia and Via Imperii, Leipzig was once one of the major European centers of learning and culture in fields such as music and publishing. Leipzig became an urban center within the German Democratic Republic after the Second World War. Leipzig later played a significant role in instigating the fall of communism in Eastern Europe, through events which took place in, Leipzig today is an economic center and the most livable city in Germany, according to the GfK marketing research institution. Since the opening of the Leipzig City Tunnel in 2013, Leipzig forms the centerpiece of the S-Bahn Mitteldeutschland public transit system, Leipzig is currently listed as Gamma World City and Germanys Boomtown. Outside of Leipzig the Neuseenland district forms a lake area of approximately 300 square kilometres. Leipzig is derived from the Slavic word Lipsk, which means settlement where the linden trees stand, an older spelling of the name in English is Leipsic. The Latin name Lipsia was also used, the name is cognate with Lipetsk in Russia and Liepāja in Latvia. In 1937 the Nazi government officially renamed the city Reichsmessestadt Leipzig, the common usage of this nickname for Leipzig up until the present is reflected, for example, in the name of a popular blog for local arts and culture, Heldenstadt. de. Leipzig was first documented in 1015 in the chronicles of Bishop Thietmar of Merseburg as urbs Libzi and endowed with city, Leipzig Trade Fair, started in the Middle Ages, became an event of international importance and is the oldest remaining trade fair in the world. During the Thirty Years War, two battles took place in Breitenfeld, about 8 kilometres outside Leipzig city walls, the first Battle of Breitenfeld took place in 1631 and the second in 1642. Both battles resulted in victories for the Swedish-led side, on 24 December 1701, an oil-fueled street lighting system was introduced. The city employed light guards who had to follow a schedule to ensure the punctual lighting of the 700 lanterns. The Leipzig region was the arena of the 1813 Battle of Leipzig between Napoleonic France and a coalition of Prussia, Russia, Austria and Sweden. It was the largest battle in Europe prior to the First World War, in 1913 the Monument to the Battle of the Nations celebrating the centenary of this event was completed. The railway station has two entrance halls, the eastern one for the Royal Saxon State Railways and the western one for the Prussian state railways
16.
Key signature
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In musical notation, a key signature is a set of sharp, flat, and rarely, natural symbols placed together on the staff. Key signatures are written immediately after the clef at the beginning of a line of musical notation, although they can appear in other parts of a score. A key signature designates notes that are to be played higher or lower than the natural notes and applies through to the end of the piece or up to the next key signature. A sharp symbol on a line or space in the key raises the notes on that line or space one semitone above the natural. An accidental is an exception to the key signature, applying only in the measure in which it appears. Although a key signature may be using any combination of sharp and flat symbols, fifteen diatonic key signatures are by far the most common. A piece scored using a diatonic key signature and no accidentals contains notes of at most seven of the twelve pitch classes. Each major and minor key has a key signature that sharpens or flattens the notes which are used in its scale. However, it is not uncommon for a piece to be written with a key signature that does not match its key, for example, in some Baroque pieces, for example, in his Sonata No.31 in A♭ major, Op. In principle, any piece can be written with any key signature, using accidentals to correct the pattern of whole, the purpose of the key signature is to minimize the number of such accidentals required to notate the music. The sequence of sharps or flats in key signatures is generally rigid in modern music notation and this allows musicians to identify the key simply by the number of sharps or flats, rather than their position on the staff. For example, if a key signature has one sharp, it must be an F sharp. However, in 20th-century music, there are exceptions to this, where a piece uses an unorthodox or synthetic scale. This may consist of a number of sharps or flats that are not the normal ones, key signatures of this kind can be found in the music of Béla Bartók, for example. The effect of a key signature continues throughout a piece or movement, for example, if a five-sharp key signature is placed at the beginning of a piece, every A in the piece in any octave will be played as A sharp, unless preceded by an accidental. In a score containing more than one instrument, all the instruments are usually written with the key signature. Exceptions include, If an instrument is a transposing instrument, If an instrument is a percussion instrument with indeterminate pitch. Composers usually omit the key signature for timpani parts. g, timpani in D–A, if they were tuned A and D
17.
Sharp (music)
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In music, sharp, dièse, or diesis means higher in pitch. More specifically, in musical notation, sharp means higher in pitch by a semitone, and has a sharp symbol, ♯. Sharp is contrasted with flat, which refers to a lowering of pitch, intonation may be flat, sharp, or both, successively or simultaneously. Under twelve-tone equal temperament, B♯, for instance, sounds the same as, or is equivalent to, C natural. In other tuning systems, such enharmonic equivalences in general do not exist, to allow extended just intonation, composer Ben Johnston uses a sharp to indicate a note is raised 70.6 cents, or a flat to indicate a note is lowered 70.6 cents. In tuning, sharp can also slightly higher in pitch. If two simultaneous notes are out of tune, the higher-pitched one is said to be sharp with respect to the other. Furthermore, the verb sharpen means raise the frequency of a note, double sharps also exist, these are denoted by the symbol and raise a note by two semitones, or one whole tone. They should not be confused with a ghost note, less often one will encounter other sharps. A half sharp raises a note by a quarter tone =50 cents, a sharp and a half raises a note by three quarter tones =150 cents and may be denoted. Although very uncommon, a triple sharp can sometimes be found and it raises a note by three semitones. The sharp symbol may be confused with the number sign, both signs have two sets of parallel double-lines. However, a correctly drawn sharp sign must have two slanted parallel lines which rise from left to right, to avoid being obscured by the staff lines, the number sign, in contrast, has two compulsory horizontal strokes in this place. In addition, while the sharp also always has two vertical lines, the number sign may or may not contain perfectly vertical lines. The order of sharps in key signature notation is F♯, C♯, G♯, D♯, A♯, E♯, B♯, each extra sharp being added successively in the sequence of major keys. Similarly the order of flats is based on the natural notes in reverse order, B♭, E♭, A♭, D♭, G♭, C♭, F♭, encountered in the following series of major keys. In the above progression, key C♯ may be conveniently written as the harmonically equivalent key D♭
18.
Accidental (music)
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In music, an accidental is a note of a pitch that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp, flat, and natural symbols, among others, in the measure where it appears, an accidental sign raises or lowers the immediately following note from its normal pitch, overriding sharps or flats in the key signature. A note is raised or lowered by a semitone, although microtonal music may use fractional accidental signs. One occasionally sees double sharps or flats, which raise or lower the note by a whole tone. Accidentals apply within the measure and octave in which appear, unless canceled by another accidental sign. If a note has an accidental and the note is repeated in a different octave within the same measure, the accidental does not apply to the same note of the different octave. The modern accidental signs derive from the two forms of the letter b used in Gregorian chant manuscripts to signify the two pitches of B, the only note that could be altered. The round b became the sign, while the square b diverged into the sharp. Sometimes the black keys on a keyboard are called accidentals or sharps. In most cases, a sharp raises the pitch of a note one semitone while a flat lowers it a semitone, a natural is used to cancel the effect of a flat or sharp. This system of accidentals operates in conjunction with the key signature, whose effect continues throughout an entire piece, an accidental can also be used to cancel a previous accidental or reinstate the flats or sharps of the key signature. Accidentals apply to subsequent notes on the staff position for the remainder of the measure where they occur, unless explicitly changed by another accidental. Once a barline is passed, the effect of the accidental ends, subsequent notes at the same staff position in the second or later bars are not affected by the accidental carried through with the tied note. Though this convention is still in use particularly in music, it may be cumbersome in music that features frequent accidentals. As a result, a system of note-for-note accidentals has been adopted. Accidentals are not repeated for repeated notes unless one or more different pitches intervene, if a sharp or flat pitch is followed directly by its natural form, a natural is used. Cautionary accidentals or naturals may be used to clarify ambiguities, because seven of the twelve notes of the chromatic equal-tempered scale are naturals this system can significantly reduce the number of naturals required in a notated passage. Thus, the effect of the accidental must be understood in relation to the meaning of the notes staff position
19.
Alto recorder
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The alto recorder in F, also known as a treble is a member of the recorder family. Up until the 17th century the instrument was normally in G4 instead of F4. The alto is between the soprano and tenor in size, and is intermediate in pitch. It has the general shape as a soprano, but is approximately 50% larger in all dimensions. A 50% increase in length causes a 50% increase in the wavelength for a given fingering and this lowers the pitch by a perfect fifth, that is from C to F. The F alto is an instrument, though its basic scale is in F, that is, a fifth lower than the soprano recorder. So-called F fingerings are therefore used, as with the bassoon or the low register of the clarinet and its notation is usually at sounding pitch, but sometimes is written an octave lower than it sounds. For adult hands, the recorder is easy to play. Maintenance is the same as for the soprano recorder, recorders are known to have been made in different sizes since at least the 15th century, but a consistent terminology did not exist until the 20th-century revival of the instrument. Appropriate to the highest instrument of the set, it is given a name used for the highest vocal part in music from time, discant. At this time, recorders were made in a single piece and this type of instrument continued to be produced through the 17th century and into the early 18th, though around 1650 it began to be made in three separate parts. It was sometimes called the flauto italiano, particularly after about 1670 when a new type of recorder appeared in France, called flûte douce, what today would be called an alto in F. In contrast to the bright-toned flauto italiano, which was easy to play in the register, the flüte douce was full and resonant in the low register. This new version of recorder was first made in Paris and, shortly later and under French influence, the redesign is traditionally attributed to the Hotteterres, particularly to Jean Hotteterre, though the evidence is rather tenuous. In 1696, Johann Christoph Denner and Johann Schell applied for permission to make the French type of instrument in Nuremberg, in most languages, this was the instrument meant by the word for flute alone, German Flöte, Dutch fluyt, Italian flauto, Spanish flauta. In England, it was usually simply flute, but when necessary to differentiate from the flute or other sizes of recorder. Woodwind Instruments and Their History, third edition, with a foreword by Sir Adrian Boult and this edition reissued, Mineola, New York, Dover Publications, Inc. 1991, and reprinted again in 2012, facsimile reprint, Collezione di trattati e musiche antiche edite in fac-simile
20.
Figured bass
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Basso continuo parts, almost universal in the Baroque era, provided the harmonic structure of the music. The phrase is shortened to continuo, and the instrumentalists playing the continuo part are called the continuo group. The titles of many Baroque works make mention of the section, such as J. S. Bachs Concerto for Two Violins, Strings. The makeup of the group is often left to the discretion of the performers. At least one instrument capable of playing chords must be included, such as a harpsichord, organ, lute, theorbo, guitar, regal, or harp. In addition, any number of instruments play in the bass register may be included, such as cello, double bass, bass viol. The most common combination, at least in modern performances, is harpsichord and cello for instrumental works and secular works, such as operas. Harps, lutes, and other instruments are more typical of early 17th-century music. The keyboard player realizes a continuo part by playing, in addition to the bass line, notes above it to complete chords. The figured bass notation, described below, is a guide, but performers are expected to use their musical judgment. Experienced players sometimes incorporate motives found in the instrumental parts into their improvised chordal accompaniment. Modern editions of music usually supply a realized keyboard part, fully written out in staff notation for a player. With the rise in historically informed performance, however, the number of performers who are able to improvise their parts from the figures, as Baroque players would have done, has increased. Basso continuo, though a structural and identifying element of the Baroque period, continued to be used in many works, mostly sacred choral works. An example is C. P. E. Bachs Concerto in D minor for flute, strings and basso continuo. Examples of its use in the 19th century are rarer, but they do exist, masses by Anton Bruckner, Beethoven, the phrase tasto solo indicates that only the bass line is to be played for a short period, usually until the next figure is encountered. This instructs the chord-playing instrumentalist not to play any improvised chords for a period, composers were inconsistent in the usages described below. Especially in the 17th century, the numbers were omitted whenever the composer thought the chord was obvious, early composers such as Claudio Monteverdi often specified the octave by the use of compound intervals such as 10,11, and 15
21.
Mode (music)
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In the theory of Western music, mode generally refers to a type of scale, coupled with a set of characteristic melodic behaviours. This use, still the most common in recent years, reflects a tradition dating to the Middle Ages, regarding the concept of mode as applied to pitch relationships generally, Harold S. being in the domain of mode. This synthesis between tonus as a tone and the older meaning associated with an octave species was done by medieval theorists for the Western monodic plainchant tradition. Since the end of the century, the term mode has also applied to pitch structures in non-European musical cultures, sometimes with doubtful compatibility. The word encompasses several additional meanings, however, authors from the ninth century until the early eighteenth century sometimes employed the Latin modus for interval. A scale is a series of pitches that, with the key or tonic as a reference point, defines that scales intervals. The concept of mode in Western music theory has three stages, in Gregorian chant theory, in Renaissance polyphonic theory, and in tonal harmonic music of the common practice period. In all three contexts, mode incorporates the idea of the scale, but differs from it by also involving an element of melody type. By the early 19th century, the mode had taken on an additional meaning. At the same time, composers were beginning to conceive of modality as something outside of the system that could be used to evoke religious feelings or to suggest folk-music idioms. Early Greek treatises describe three interrelated concepts that are related to the later, medieval idea of mode, scales, tonoi—, and harmonia —pl. harmoniai—this third term subsuming the corresponding tonoi but not necessarily the converse. The association of ethnic names with the octave species appears to precede Aristoxenus. Depending on the positioning of the tones in the tetrachords. The diatonic genus, the genus, and the enharmonic genus. The framing interval of the fourth is fixed, while the two internal pitches are movable. Within the basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two shades, respectively, the term tonos was used in four senses, as note, interval, region of the voice, and pitch. We use it of the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, in Ptolemys system, therefore there are only seven tonoi. Pythagoras also construed the intervals arithmetically, in their diatonic genus, these tonoi and corresponding harmoniai correspond with the intervals of the familiar modern major and minor scales
22.
Johann Pachelbel
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Johann Pachelbel was a German composer, organist, and teacher who brought the south German organ tradition to its peak. Pachelbels music enjoyed enormous popularity during his lifetime, he had many pupils and his became an model for the composers of south. Today, Pachelbel is best known for the Canon in D, as well as the Chaconne in F minor, the Toccata in E minor for organ, and the Hexachordum Apollinis and he preferred a lucid, uncomplicated contrapuntal style that emphasized melodic and harmonic clarity. Pachelbel explored many variation forms and associated techniques, which manifest themselves in various diverse pieces, Johann Pachelbel was born in 1653 in Nuremberg into a middle-class family, son of Johann Pachelbel, a wine dealer, and his second wife Anna Maria Mair. The exact date of Johanns birth is unknown, but since he was baptized on September 1, during his early youth, Pachelbel received musical training from Heinrich Schwemmer, a musician and music teacher who later became the cantor of St. Sebaldus Church. Some sources indicate that Pachelbel also studied with Georg Caspar Wecker, organist of the church and an important composer of the Nuremberg school. In any case, both Wecker and Schwemmer were trained by Johann Erasmus Kindermann, one of the founders of the Nuremberg musical tradition, financial difficulties forced Pachelbel to leave the university after less than a year. In order to complete his studies he became a student, in 1670. The school authorities were so impressed by Pachelbels academic qualifications that he was admitted above the normal quota. Pachelbel was also permitted to study music outside the Gymnasium and his teacher was Kaspar Prentz, once a student of Johann Caspar Kerll. Prentz left for Eichstätt in 1672, at the time, Vienna was the center of the vast Habsburg empire and had much cultural importance, its tastes in music were predominantly Italian. Several renowned cosmopolitan composers worked there, many of them contributing to the exchange of musical traditions in Europe, in particular, Johann Jakob Froberger served as court organist in Vienna until 1657 and was succeeded by Alessandro Poglietti. Georg Muffat lived in the city for some time, and, most importantly, while there, he may have known or even taught Pachelbel, whose music shows traces of Kerlls style. Pachelbel spent five years in Vienna, absorbing the music of Catholic composers from southern Germany and Italy. In some respects, Pachelbel is similar to Haydn, who too served as a musician of the Stephansdom in his youth. In 1677, Pachelbel moved to Eisenach, where he found employment as court organist under Kapellmeister Daniel Eberlin, in the employ of Johann Georg I and he met members of the Bach family in Eisenach, and became a close friend of Johann Ambrosius and tutor to his children. However, Pachelbel spent only one year in Eisenach, in 1678, Bernhard II, Duke of Saxe-Jena, Johann Georgs brother, died and during the period of mourning court musicians were greatly curtailed. He requested a testimonial from Eberlin, who wrote one for him, describing Pachelbel as a perfect, with this document, Pachelbel left Eisenach on May 18,1678
23.
Georg Muffat
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Georg Muffat was a Baroque composer. Georg Muffat was born in Megève, Duchy of Savoy, of André Muffat and he studied in Paris between 1663 and 1669, where his teacher is often assumed to have been Jean Baptiste Lully. This assumption is based on the statement For six years. I avidly pursued this style which was flowering in Paris at the time under the most famous Jean Baptiste Lully and this is ambiguous as to whether the style was flourishing under Lully, or that Muffat studied under Lully. In any case, the style which the young Muffat learned was unequivocally Lullian, after leaving Paris, he became an organist in Molsheim and Sélestat. Later, he studied law in Ingolstadt, afterwards settling in Vienna and he could not get an official appointment, so he travelled to Prague in 1677, then to Salzburg, where he worked for the archbishop for some ten years. From 1690 to his death, he was Kapellmeister to the bishop of Passau, georg Muffat should not be confused with his son Gottlieb Muffat, also a successful composer. Muffat was, as Johann Jakob Froberger before him, and Handel after him, the information contained within the Florilegium Primum and Secundum is nearly unique. These texts remain extremely valuable for modern historically-interested musicians
24.
Johann Speth
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Johann Speth was a German organist and composer. He was born in Speinshart, some 150 km from Nuremberg, but spent most of his life in Augsburg and his only surviving music is a 1693 collection, Ars Magna Consoni et Dissoni, which includes toccatas, Magnificat versets and variations in south German style. Speth was born in Speinshart, Bavaria, to teacher Heinrich Speth, nothing is known about his life before 1692, when he applied for the position of organist of Augsburg Cathedral. The application, which contained Speths compositions, was accepted, the music he supplied with the application was published the next year in Augsburg as Ars magna Consoni et Dissoni. In the files of the administration there is a note from 1705 showing that Speth had also to work in the office of the cathedral chapter. The exact date of Speths death is unknown, but there is a document that shows that in 1719, he lived with his wife. The composers only surviving work is the published in 1693 in Augsburg. The title may be a reference to Athanasius Kirchers famous book, Musurgia universalis, an early description of the work was included by Johann Gottfried Walther in his Musikalisches Lexicon, Walther claimed Speth only compiled the pieces but did not compose. This hypothesis is now considered false. Ars Magna contains music intended for organ or clavichord,10 toccatas,8 Magnificat settings, the influence of contemporary southern organists is also apparent, particularly that of Georg Muffat and Johann Caspar Ferdinand Fischer. The toccatas are unusually short for the genre, most consist of three sections, there are some interesting features such as dynamic indications in Toccata quarta. The Magnificat settings are, like similar pieces by Johann Kaspar Kerll and others, Ars magna Consoni et Dissoni in vireto hoc Organico-Instrumentali Musico, vere et practice ab Oculos posita. Gwilym Beechey, Speth, Johannes, Grove Music Online ed. L. Macy, http, //www. grovemusic. com/ Gwilym Beechey, A 17th-Century German Organ Tutor, in Musical Times CXIII Lukas, scores of Speths Toccata settima and Toccata octava at Kantoreiarchiv
25.
Equal temperament
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An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In equal temperament tunings, the interval is often found by dividing some larger desired interval, often the octave. That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step, the standard pitch has not always been 440 but has varied and generally risen over the past few hundred years. For example, some music has been written in 19-TET and 31-TET, in Western countries, when people use the term equal temperament without qualification, they usually mean 12-TET. To avoid ambiguity between equal temperaments that divide the octave and ones that divide some other interval, the equal division of the octave. According to this system, 12-TET is called 12-EDO, 31-TET is called 31-EDO. Other instruments, such as wind, keyboard, and fretted instruments, often only approximate equal temperament. Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles, the two figures frequently credited with the achievement of exact calculation of equal temperament are Zhu Zaiyu in 1584 and Simon Stevin in 1585. Kenneth Robinson attributes the invention of equal temperament to Zhu Zaiyu, Zhu Zaiyu is quoted as saying that, in a text dating from 1584, I have founded a new system. I establish one foot as the number from which the others are to be extracted, altogether one has to find the exact figures for the pitch-pipers in twelve operations. Kuttner disagrees and remarks that his claim cannot be considered correct without major qualifications, kuttner proposes that neither Zhu Zaiyu or Simon Stevin achieved equal temperament, and that neither of the two should be treated as inventors. The origin of the Chinese pentatonic scale is traditionally ascribed to the mythical Ling Lun, allegedly his writings discussed the equal division of the scale in the 27th century BC. However, evidence of the origins of writing in this period in China is limited to rudimentary inscriptions on oracle bones, an approximation for equal temperament was described by He Chengtian, a mathematician of Southern and Northern Dynasties around 400 AD. He came out with the earliest recorded approximate numerical sequence in relation to equal temperament in history,900849802758715677638601570536509.5479450, historically, there was a seven-equal temperament or hepta-equal temperament practice in Chinese tradition. Zhu Zaiyu, a prince of the Ming court, spent thirty years on research based on the equal temperament idea originally postulated by his father and he described his new pitch theory in his Fusion of Music and Calendar 乐律融通 published in 1580. An extended account is given by Joseph Needham. Similarly, after 84 divisions the length was divided by a factor of 128,84 =27 =128, according to Gene Cho, Zhu Zaiyu was the first person to solve the equal temperament problem mathematically. Matteo Ricci, a Jesuit in China recorded this work in his personal journal, in 1620, Zhus work was referenced by a European mathematician
26.
Lute
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The European lute and the modern Near-Eastern oud descend from a common ancestor via diverging evolutionary paths. The lute is used in a variety of instrumental music from the Medieval to the late Baroque eras and was the most important instrument for secular music in the Renaissance. It is also an instrument, especially in vocal works. The player of a lute is called a lutenist, lutanist or lutist, the words lute and oud possibly derive from Arabic al-ʿud. Recent research by Eckhard Neubauer suggests ʿud may in turn be an Arabized version of the Persian name rud and it has equally been suggested the wood in the name may have distinguished the instrument by its wooden soundboard from skin-faced predecessors. Gianfranco Lotti suggests the wood appellation originally carried derogatory connotations because of proscriptions of all music in early Islam. Lutes are made almost entirely of wood, the soundboard is a teardrop-shaped thin flat plate of resonant wood. In all lutes the soundboard has a single decorated sound hole under the strings called the rose. The sound hole is not open, but rather covered with a grille in the form of a vine or a decorative knot. Robert Lundberg, in his book Historical Lute Construction, suggests ancient builders placed bars according to ratios of the scale length. He further suggests the inward bend of the soundboard is an adaptation by ancient builders to afford the lutenists right hand more space between the strings and soundboard. Soundboard thickness varies, but generally hovers between 1.5 and 2 mm, some luthiers tune the belly as they build, removing mass and adapting bracing to produce desirable sonic results. The lute belly is almost never finished, but in cases the luthier may size the top with a very thin coat of shellac or glair to help keep it clean. After joining the top to the sides, a half-binding is usually installed around the edge of the soundboard, the half-binding is approximately half the thickness of the soundboard and is usually made of a contrasting color wood. The rebate for the half-binding must be precise to avoid compromising structural integrity. The back or the shell is assembled from strips of hardwood called ribs. There are braces inside on the soundboard to give it strength, the neck is made of light wood, with a veneer of hardwood to provide durability for the fretboard beneath the strings. Unlike most modern stringed instruments, the fretboard is mounted flush with the top
27.
Theorbo
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For his 1607 opera LOrfeo, Claudio Monteverdi lists duoi chitaroni among the instruments required for performing the work. The round-backed chitarra was still in use, often referred to as chitarra Italiana to distinguish it from chitarra alla spagnola in its new flat-backed Spanish incarnation. The etymology of tiorba is still obscure, it is hypothesized the origin may be in Slavic or Turkish torba, according to Athanasius Kircher, tiorba was a nickname in Neapolitan dialect for a grinding board used by perfumers for grinding essences and herbs. It is possible the appearance of new large instrument resulted in jokes. Robert Spencer has noted the confusion the two names were leading to in 1600, Chitarone, ò Tiorba che si dica. In the performance of basso continuo, theorboes were often paired with a pipe organ. The most prominent early composers and players in Italy were Giovanni Girolamo Kapsberger, little solo music survives from England, but William Lawes and others used theorbos in chamber ensembles and opera orchestras. In France, theorbos were appreciated and used in orchestral or chamber music until the half of the 18th century. Court orchestras at Vienna, Bayreuth and Berlin still employed theorbo players after 1750, the tuning of large theorboes is characterized by the octave displacement, or re-entrant tuning, of the two uppermost strings. Piccinini and Michael Praetorius mention the use of metal strings. The Lang Romanische Theorba, Chitarron also appears to have strings attached to the bridge. The string courses, unlike those of a Renaissance lute or archlute, were often single, typically, theorboes have 14 courses, though some used 15 or even 19 courses. This is theorbo tuning in A, modern theorbo players usually play 14-course instruments. Some players have used a theorbo tuned a step lower in G. Most of the repertoire is in the A tuning. The Italians Kapsberger, Castaldi, Piccinini, Viviani, Melli, Pittoni and Bartolotti, in the French treatises, chords in which a lower note sounds after the bass were also used when the bass goes high. The English theorbo had just the first string at the lower octave, diego Cantalupi, La tiorba ed il suo uso in Italia come strumento per il basso continuo, pre-press version of the dissertation discussed in 1996 at the Faculty of Musicology, University of Pavia. Davide Rebuffa, Il liuto, LEpos, Pelermo 2012, ekkehard Schulze-Kurz, Die Laute und ihre Stimmungen in der ersten Hälfte des 17
28.
Saltarello
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The saltarello is a musical dance form originally from Italy. The first mention of it is in Add MS29987, a manuscript probably of Tuscan origin. It was played in a fast triple meter and is named for its peculiar leaping step and this characteristic is also the basis of the German name Hoppertanz or Hupfertanz, other names include the French pas de Brabant and the Spanish alta or alta danza. The saltarello enjoyed great popularity in the courts of medieval Europe, during the 15th century, the word saltarello became the name of a particular dance step, and the name of a meter of music, both of which appear in many choreographed dances. Entire dances consisting of only the step and meter are described as being improvised dances in 15th-century Italian dance manuals. A clearer, detailed description of this step and meter appears in a 16th-century manuscript in the Academia de la Historia in Madrid, during this era, the saltarello was danced by bands of courtesans dressed as men at masquerades. The saltarello gave birth to the quadernaria in Germany, which was fused into the saltarello tedesco in Italy. This German saltarello, in contrast to the Italian variety, was in time and began on the downbeat. In 1540, Hans Newsidler published an Italian dance under the name Hupff auff, after witnessing the Roman Carnival of 1831, the German composer Felix Mendelssohn incorporated the dance into the finale of one of his masterpieces, the Italian Symphony. The only example of a saltarello in the North is saltarello romagnolo of Romagna, the saltarello is still a popular folk dance played in the regions of Southern-Central Italy, such as Abruzzo, Molise, Lazio and Marche. The dance is performed on the zampogna bagpipe or on the organetto, a type of diatonic button accordion. The principal source for the medieval Italian saltarello is the Tuscan manuscript Add MS29987, dating from the late 14th or early 15th century, the musical form of these four early saltarelli is the same as the estampie. Tielman Susato included a saltarello in Het derde musikboexken, Danserye, a guitar piece entitled Saltarello is attributed to Vincenzo Galilei, written in the 16th century. Odoardo Barri, Six morceaux de salon, for alto-viola and piano Felix Mendelssohn-Bartholdy used the Saltarello for the movement of his Symphony No.4 Italian. Berlioz used a saltarello in the Carnival scene of Benvenuto Cellini which was reprised in the Roman Carnival Overture. Op.54 Max Mayer, Fünf Klavierstücke, Op.6 F. Laurent-Rollandez, Saltarello for piano, Op.18 Franz Ries, Nocturne et Saltarello, for violin and piano S. B
29.
Vincenzo Galilei
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This article refers to the father of Galileo Galilei. For Galileo’s son of the name, see Vincenzo Gamba. He was a figure in the musical life of the late Renaissance. Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a phenomenon known to history. It was an extension of a Pythagorean tradition but went beyond it and he was born around 1520 in Santa Maria a Monte, and began studying the lute at an early age. Sometime before 1562 he moved to Pisa, where he married into a noble family, in 1564 Galileo was born, the first of his either six or seven children, another son, Michelagnolo, born in 1575, who also became an accomplished lutenist and composer. Vincenzo was a player of the lute, and early in life attracted the attention of powerful. In 1563 he met Gioseffo Zarlino, the most important music theorist of the century, in Venice. Sometime in the 1570s his interests in music theory, as well as his composition and this describes Baroque practice, especially as he defines rules for resolution of suspensions by a preliminary leap away from, followed by a return to, the expected note of resolution. The use of recitative in opera is widely attributed to Galilei, since he was one of the inventors of monody, Vincenzo Galilei was one of the pioneers in the systematic study of acoustics, mainly in his research in the mathematical formula of stretched strings. Vincenzo made some substantial discoveries in acoustics, particularly involving the physics of vibrating strings and he discovered that while the ratio of an interval is proportional to string lengths it varied with the square root of the tension applied. In the case of strings tuned in a fifth, weights suspended from them needed to be in a ratio of 9,4 to produce the 3,2 perfect fifth. This work was taken further by Marin Mersenne who formulated the current law of vibrating strings, Mersenne was a regular correspondent to many scientists and, after the death of Vincenzo he maintained a regular link to Galileo, and treated him as a prized member of his scientific network. He communicated Galileos ideas for a clock to Christiaan Huygens. Despite being a priest, Mersenne defended Galileo when he came under attack by the church in 1633 and he conducted his own duplicate experiments which improved on their accuracy. Claude Palisca, Vincenzo Galilei, Grove Music Online, ed. L. Macy, Article Vincenzo Galilei, in The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Gustave Reese, Music in the Renaissance. ISBN 0-393-09530-4 The Concise Edition of Bakers Biographical Dictionary of Musicians, della musica antica, et della moderna Fronimo Dialogo
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Ariadne musica
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Ariadne musica is a collection of organ music by Johann Caspar Ferdinand Fischer, first published in 1702. The title refers to the Greek myth in which Theseus finds his way out of Minotaurs labyrinth using a ball of thread that Ariadne, daughter of King Minos of Crete, similarly, the music in the collection can be said to guide the listener through a labyrinth of keys. Fischer also used Greek mythology to name the pieces in large scale music collection of his. The first edition of Ariadne musica was made in 1702 in Schlackenwerth, the work was reprinted several times during Fischers life. The original print mentioned by Johann Gottfried Walther in Musicalisches Lexicon is now lost, most are in common time, with a few exceptions. Some are loosely connected thematically to the accompanying preludes, the ricercars all feature themes written in whole and half notes, the C major Ricercar pro Festis Natalitys being one notable exception with the theme composed mostly of quarter and eighth notes. Three are marked alla breve, Ricercar pro Festis Natalitys is in common time, Ricercar pro Festis Paschalibus was previously attributed to Johann Sebastian Bach and listed in the BWV catalogue as BWV746, chorale prelude Christ ist erstanden. The same six-note subject is found in two 17th century keyboard compositions by the famous Johann Jakob Froberger, Fantasia No.2, the latters opening bars can be seen below, Fischer might have learned the theme from Froberger. Both Bachs and Fischers C major fugues are heavily based on stretto, Ariadne musica is rarely performed or recorded, although individual preludes and fugues frequently appear on miscellaneous compilations of Baroque organ music. Heres a partial list of recordings that feature at least one part of Ariadne musica in full, Johann Caspar Ferdinand Fischer, Ariadne musica, Wolfgang Baumgratz, Johann Caspar Ferdinand Fischer, Blumen-Strauss, Complete Organ Works, Serge Schoonbroodt,2002. A Joy Forever, Opus 41 at Goshen College, Bradley Lehman,2006, Fischer, Ariadne Musica, works of Caldara, Bach, Beethoven, & Sorge, Franz Haselböck
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Phrygian mode
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The Phrygian tonos or harmonia is named after the ancient kingdom of Phrygia in Anatolia. The octave species underlying the ancient-Greek Phrygian tonos corresponds to the medieval, an octave species was then built upon two of these tetrachords separated by a whole tone. This ethnic name was also applied by theorists such as Cleonides to one of thirteen chromatic transposition levels. The early Catholic church developed a system of eight musical modes that medieval music scholars gave names drawn from the used to describe the ancient Greek harmoniai. Alternatively written as a pattern of, Semitone, Tone, Tone, Tone, Semitone, Tone, Tone. Flamenco music uses the Phrygian scale, together with a modified scale resembling the Arab maqām Ḥijāzī, in contemporary jazz, the Phrygian mode is used over chords and sonorities built on the mode, such as the sus4 chord, which is sometimes called a Phrygian suspended chord. For example, a soloist might play an E Phrygian over an Esus4 chord, the First Delphic Hymn, written in 128 BC by the Athenian composer Limenius, is in the Phrygian and Hyperphrygian tonoi, with much variation. The Seikilos epitaph is in the Phrygian species, in the Iastian transposition, gregorian chant, Tristes Erant Apostoli, version in the Vesperale Romanum, originally Ambrosian chant. The Roman chant variant of the Requiem introit Rogamus te is in the Phrygian mode, the following compositions of Josquin are written in the Phrygian mode, 4-part setting of Mille Regretz Missa Pange lingua 6-part motet Praeter Rerum Seriem Orlando di Lassos motet In me transierunt. Giovanni Pierluigi da Palestrinas motet Congratulamini mihi, heinrich Schützs St John Passion is in the Phrygian mode Dieterich Buxtehudes Prelude in A minor, BuxWV152, Anton Bruckner, Ave Regina caelorum, WAB8. 3, passages in the third and fourth movements,6, first, third, and fourth movements. Ralph Vaughan Williams Fantasia on a Theme of Thomas Tallis, based on Thomas Talliss 1567 setting of Psalm 2, Why fumth in sight
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Chorale
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A chorale is a melody to which a hymn is sung by a congregation in a German Protestant Church service. The typical four-part setting of a chorale, in which the sopranos sing the melody along with three voices, is known as a chorale harmonization. Starting in 1523, Martin Luther began translating texts into German from the Latin. This created an immediate need for a repertoire of new chorales. He composed some chorales himself, such as A Mighty Fortress, for other chorales he adapted Gregorian chant melodies used in Roman Catholic worship to fit new German texts, sometimes using the same melody more than once. For example, he fitted the melody of the hymn Veni redemptor gentium to three different texts, Verleih uns Frieden gnädiglich, Erhalt uns, Herr, bei deinem Wort, and Nun komm, der Heiden Heiland. As early as 1524, Johann Walter published Eyn geystlich Gesangk Buchleyn, Johann Sebastian Bach harmonised hundreds of chorales, typically used at the end of his cantatas and concluding scenes in his Passions. In his St Matthew Passion, he set five stanzas of O Haupt voll Blut und Wunden in four different ways and he also used hymns as the base for his cycle of chorale cantatas and chorale preludes. Bach concentrated on the chorales especially in the Chorale cantatas of his second annual cycle, today, many of the Lutheran chorales are familiar as hymns used in Protestant churches, sometimes sung in four-voice harmony. Chorales also appear in chorale preludes, pieces generally for organ designed to be played immediately before the singing of the hymn. A chorale prelude includes the melody of the chorale, and adds contrapuntal lines, one of the first composers to write chorale preludes was Samuel Scheidt. Bachs many chorale preludes are the examples of the form. Anton Bruckner make frequent use of the chorale as a device in Two Aequali, based on his understanding of musical settings of the liturgy. Chorale composition Hymn tune Carragan, William, marshall, Robert L. and Robin A. Leaver. The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie, anton Bruckner 1824–1896, Leven en werken. The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie, the New Harvard Dictionary of Music, third edition. The Harvard Dictionary of Music, fourth edition, cambridge, Belknap Press, for Harvard University Press. Chorale discussion by Bernard Greenberg in the J. S. Matthew Passion
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Ricercar
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A ricercar is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many serve a preludial function to search out the key or mode of a following piece. A ricercar may explore the permutations of a motif. For example, Ricercar sopra Benedictus might develop motifs from a motet titled Benedictus, the term is also used to designate an etude or study that explores a technical device in playing an instrument, or singing. In its most common usage, it refers to an early kind of fugue. However the term has a more varied historical usage. In the sixteenth century, the word ricercar could refer to types of compositions. The second type of ricercar, the imitative, contrapuntal type, was to prove the more important historically, marco DallAquila was known for polyphonic ricercars. Examples of both types of ricercars can be found in the works of Girolamo Frescobaldi, e. g. in his Fiori musicali, gödel, Escher, Bach, An Eternal Golden Braid by Douglas Hofstadter, which includes a section entitled Six-part Ricercar. Ricercar, Fugue, Counterpoint in The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Gustave Reese, Music in the Renaissance. ISBN 0-393-09530-4 Manfred Bukofzer, Music in the Baroque Era, ISBN 0-393-09745-5 Ursula Kirkendale, The Source for Bachs Musical Offering, Journal of the American Musicological Society 33, 99-141. The New Harvard Dictionary of Music, ed, cambridge, Massachusetts, Harvard University Press,1986. ISBN 0-674-61525-5 Arthur J. Ness, Ricercar, Harvard Dictionary of Music, fourth edition, edited by Don Michael Randel, cambridge, Belknap Press for Harvard University Press,2003. The dictionary definition of ricercar at Wiktionary Petrucci Music Library Ricercar Collection
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Johann Mattheson
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Johann Mattheson was a German composer, singer, writer, lexicographer, diplomat and music theorist. Mattheson was born and died in Hamburg and he was a close friend of George Frideric Handel, although he nearly killed him in a sudden quarrel, during a performance of Matthesons opera Cleopatra in 1704. Handel was saved only by a button which turned aside Matthesons sword. The son of a tax collector, Mattheson received a broad liberal education and, aside from general musical training, took lessons in keyboard instruments, violin, composition. By age nine he was singing and playing organ in church and was a member of the chorus of the Hamburg opera. He made his debut with the Hamburg opera in 1696 in female roles and, after his voice changed, sang tenor at the opera, conducted rehearsals. He was cantor at St. Marys Cathedral from 1718 until increasing deafness led to his retirement from that post in 1728, Matthesons chief occupation from 1706 was as a professional diplomat. He had studied English in school and spoke it fluently and he became tutor to the son of the English ambassador Sir John Wich and then secretary to the ambassador. He went on missions abroad representing the ambassador. In 1709 he married an English woman, after his death in 1764, Johann Mattheson was buried in the vault of Hamburgs St. Michaelis Church where his grave can be visited. Mattheson is mainly famous as a music theorist and he was the most abundant writer on performance practice, theatrical style, and harmony of the German Baroque. However his books raise more and more attention and suspicion because Mattheson was a brilliant polemist and his theories on music are often full of pedantry, the bulk of his compositional output was vocal, including eight operas, and numerous oratorios and cantatas. He also wrote a few sonatas and some music, including pieces meant for keyboard instruction. All of his music, except for one opera, one oratorio, and a few collections of music, went missing after World War II. This includes four operas and most of the oratorios, the manuscripts are now located at the Staats- und Universitätsbibliothek Hamburg, the former Hamburg Stadtbibliothek. Letters and writings of George Frideric Handel Notes Bibliography Johann Mattheson, Rhetoric and music from The New Grove Dictionary of Music and Musicians, ISBN 1-56159-174-2 Manfred Bukofzer, Music in the Baroque Era. ISBN 0-393-09745-5 Free scores by Johann Mattheson at the International Music Score Library Project
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Christoph Graupner
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Christoph Graupner was a German harpsichordist and composer of high Baroque music who was a contemporary of Johann Sebastian Bach, Georg Philipp Telemann and George Frideric Handel. Born in Hartmannsdorf near Kirchberg in Saxony, Graupner received his first musical instruction from his uncle, Graupner went to the University of Leipzig where he studied law and then completed his musical studies with Johann Kuhnau, the cantor of the Thomasschule. In 1705 Graupner left Leipzig to play the harpsichord in the orchestra of the Hamburg Opera under the direction of Reinhard Keiser, alongside George Frideric Handel, then a young violinist. In addition to playing the harpsichord, Graupner composed six operas in Hamburg, some of them in collaboration with Keiser, in 1709 Graupner accepted a post at the court of Hesse-Darmstadt and in 1711 became the court orchestra’s Hofkapellmeister. Graupner spent the rest of his career at the court in Hesse-Darmstadt and he wrote music for nearly half a century, from 1709 to 1754, when he became blind. Graupner inadvertently played a key role in the history of music, precarious finances in Darmstadt during the 1710s forced a reduction of musical life. The opera house was closed, and many court musicians salaries were in arrears, after many attempts to have his salary paid, and having several children and a wife to support, in 1723 Graupner applied for the Cantorate in Leipzig. Telemann had been the first choice for this position, but withdrew after securing an increase in Hamburg. Graupners audition Magnificat, set in the style of his teacher, mentor and predecessor, Kuhnau, however, Graupners patron would not release him from his contract. Graupners past due salary was paid in full, his salary was increased, with such favorable terms, Graupner remained in Darmstadt, thus clearing the way for Bach to become the kantor in Leipzig. There are about 2,000 surviving works in his catalog, nearly all of Graupners manuscripts are housed in the ULB in Darmstadt, Germany. Graupner wrote for exotic combinations of instruments, including the oboe damore, flute damore, and viola damore. Over half of his sinfonias require brass and timpani, with about 25 sinfonias requiring 3 to 4 timpani, one 5 timpani, after he died, Graupners works fell into obscurity for a number of reasons. His manuscripts became the object of a legal battle between his heirs and the rulers of Hesse-Darmstadt. A final court decision denied the Graupner estate ownership of the music manuscripts, the heirs were unable to obtain permission to sell or publish his works and they remained inaccessible to the public. Dramatic changes in music styles had reduced the interest in Graupners music, on the positive side however, the Landgraves seizure of Graupners musical estate ensured its survival in toto. Fate was not so kind to J. S. Bachs musical legacy, another factor that contributed to Graupners posthumous obscurity was that, unlike Bach, Graupner had very few pupils other than Johann Friedrich Fasch to carry on his musical legacy. Graupners music is enjoying a revival, due in part to the research efforts of many musicologists, performers
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Enharmonic keyboard
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An enharmonic keyboard is a musical keyboard, where enharmonically equivalent notes do not have identical pitches. A conventional keyboard has, for instance, only one key and pitch for C♯ and D♭, traditionally, such keyboards use black split keys to express both notes, but diatonic white keys may also be split. Enharmonic keyboard is a used by scholars in their studies of enharmonic keyboard instruments with reference to a keyboard with more than 12 keys per octave. Scholarly consensus about the precise definition currently has not been established. In the New Grove Dictionary Nicolas Meeùs defines an enharmonic keyboard as a keyboard with more than 12 keys and he however does not specify the origin of the term in his article. Rudolph Rasch suggested to apply the term enharmonic keyboard more closely to keyboards with 29–31 keys per octave, Patrizio Barbieri, in his turn, raised objection that this usage is not supported by early theoretical works. As for historical evidence, confusion has often reigned over the terminology of split-keyed instruments, the builders of such keyboard instruments often gave them names without any reference to genus, like archicembalo, cembalo pentarmonico, Clavicymbalum universale or even simply Clauocembalo. Some modern scholars describe instruments with such keyboards as split-keyed instruments, one of the first instruments with an enharmonic keyboard was the archicembalo built by Nicola Vicentino, an Italian Renaissance composer and music theorist. The archicembalo had 36 keys per octave and was well suited for meantone temperament. Vicentino also had made one arciorgano in Rome and one arciorgano in Milan, both pipe organs were equipped with enharmonic keyboards, like those of the archicembalo. Many instruments with enharmonic keyboards were built during the Renaissance and Baroque eras, most composers and performers who used these instruments are virtually unknown today. With the advent of music in the 20th century, instruments with enharmonic keyboards became more fashionable, as did early. Isomorphic note-layouts are a class of enharmonic keyboard, opened in 1721 by Ivo Salzingers Tastatura nova perfecta, one isomorphic note-layout, the Wicki, when mapped to a hexagonal array of buttons, is particularly well-suited to the control of enharmonic scales. Hence, the skills gained in learning to play music on a chromatic Wicki keyboard can be applied, without modification. Isomorphic keyboards were not discovered until the half of the 19th century. Equal temperament Fokker organ Meantone temperament Musical tuning Jankó keyboard Barbieri, morelli, Arnaldo, ed. Pietro della Valle, the Esthèr oratorio and other experiments in the stylus metabolicus. With new documents on triharmonic instruments, rivista per lo studio e la pratica della musica antica. Latina, Italy, Il Levante Libreria Editrice, burundukovskaya, E. Zagidullina, M. V. ed
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Interval (music)
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In music theory, an interval is the difference between two pitches. In Western music, intervals are most commonly differences between notes of a diatonic scale, the smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones and they can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic frequencies, for example, any two notes an octave apart have a frequency ratio of 2,1. This means that successive increments of pitch by the same result in an exponential increase of frequency. For this reason, intervals are often measured in cents, a derived from the logarithm of the frequency ratio. In Western music theory, the most common naming scheme for intervals describes two properties of the interval, the quality and number, examples include the minor third or perfect fifth. These names describe not only the difference in semitones between the upper and lower notes, but also how the interval is spelled, the importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G♯ and G–A♭. The size of an interval can be represented using two alternative and equivalently valid methods, each appropriate to a different context, frequency ratios or cents, the size of an interval between two notes may be measured by the ratio of their frequencies. When a musical instrument is tuned using a just intonation tuning system, Intervals with small-integer ratios are often called just intervals, or pure intervals. Most commonly, however, musical instruments are tuned using a different tuning system. As a consequence, the size of most equal-tempered intervals cannot be expressed by small-integer ratios, for instance, an equal-tempered fifth has a frequency ratio of 2 7⁄12,1, approximately equal to 1.498,1, or 2.997,2. For a comparison between the size of intervals in different tuning systems, see section Size in different tuning systems, the standard system for comparing interval sizes is with cents. The cent is a unit of measurement. If frequency is expressed in a scale, and along that scale the distance between a given frequency and its double is divided into 1200 equal parts, each of these parts is one cent. In twelve-tone equal temperament, a system in which all semitones have the same size. Hence, in 12-TET the cent can be defined as one hundredth of a semitone
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Musical temperament
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In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system, tempering is the process of altering the size of an interval by making it narrower or wider than pure. The development of well temperament allowed fixed-pitch instruments to play well in all of the keys. The famous Well-Tempered Clavier by Johann Sebastian Bach takes full advantage of this breakthrough, however, while unpleasant intervals were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own character. In just intonation, every interval between two pitches corresponds to a whole number ratio between their frequencies, allowing intervals varying from the highest consonance to highly dissonant, for instance,660 Hz /440 Hz constitutes a fifth, and 880 Hz /440 Hz an octave. Such intervals have a stability, or purity to their sound, if, for example, two sound signals with frequencies that vary just by 0. When a musical instrument with harmonic overtones is played, the ear hears a composite waveform that includes a fundamental frequency, the waveform of such a tone is characterized by a shape that is complex compared to a simple waveform, but remains periodic. When two tones depart from exact integer ratios, the shape waveform becomes erratic—a phenomenon that may be described as destabilization, as the composite waveform becomes more erratic, the consonance of the interval also changes. Tempering an interval involves the use of such minor adjustments to enable musical possibilities that are impractical using just intonation. Before Meantone temperament became widely used in the Renaissance, the most commonly used tuning system was Pythagorean tuning, Pythagorean tuning was a system of just intonation that tuned every note in a scale from a progression of pure perfect fifths. This was quite suitable for much of the practice until then. The major third of Pythagorean tuning differed from a just major third by an amount known as syntonic comma, with the correct amount of tempering, the syntonic comma is removed from its major thirds, making them just. This compromise, however, leaves all fifths in this system with a slight beating. Pythagorean tuning also had a problem, which meantone temperament does not solve, which is the problem of modulation. A series of 12 just fifths as in Pythagorean tuning does not return to the pitch, but rather differs by a Pythagorean comma. In meantone temperament, this effect is more pronounced. The use of 53 equal temperament provides a solution for the Pythagorean tuning, when building an instrument, this can be very impractical. Well temperament is the given to a variety of different systems of temperament that were employed to solve this problem, in which some keys are more in tune than others
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Musical tuning
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In music, there are two common meanings for tuning, Tuning practice, the act of tuning an instrument or voice. Tuning systems, the systems of pitches used to tune an instrument. Tuning is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones, Tuning is usually based on a fixed reference, such as A =440 Hz. Out of tune refers to a pitch/tone that is too high or too low in relation to a given reference pitch. While an instrument might be in relative to its own range of notes. Some instruments become out of tune with damage or time and must be readjusted or repaired, different methods of sound production require different methods of adjustment, Tuning to a pitch with ones voice is called matching pitch and is the most basic skill learned in ear training. Turning pegs to increase or decrease the tension on strings so as to control the pitch, instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the violin can be tuned manually. Modifying the length or width of the tube of an instrument, brass instrument, pipe, bell. The sounds of instruments such as cymbals are inharmonic—they have irregular overtones not conforming to the harmonic series. Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other, a tuning fork or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a piano is used. Symphony orchestras and concert bands tend to tune to an A or a B♭, respectively, interference beats are used to objectively measure the accuracy of tuning. As the two approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected, for other intervals, this is dependent on the tuning system being used. Harmonics may be used to facilitate tuning of strings that are not themselves tuned to the unison, for example, lightly touching the highest string of a cello at the middle while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the fifth between the fundamentals of the two strings. In music, the open string refers to the fundamental note of the unstopped. The strings of a guitar are tuned to fourths, as are the strings of the bass guitar. Violin, viola, and cello strings are tuned to fifths, however, non-standard tunings exist to change the sound of the instrument or create other playing options
