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66-452: This music theory treatise, along with its companion text, Scolica enchiriadis , was widely circulated in medieval manuscripts , often in association with Boethius ' De institutione musica . It consists of nineteen chapters; the first nine are devoted to notation , modes , and monophonic plainchant . Chapters 10-18 deal with polyphonic music . The author here shows how consonant intervals should be used to compose or improvise

132-448: A connotation of engaging with or discussing a subject in depth, which aligns with the modern understanding of a treatise as a formal and systematic written discourse on a specific topic. The works presented here have been identified as influential by scholars on the development of human civilization. Euclid's Elements has appeared in more editions than any other books except the Bible and

198-604: A distance from actual musical practice. But this medieval discipline became the basis for tuning systems in later centuries and is generally included in modern scholarship on the history of music theory. Music theory as a practical discipline encompasses the methods and concepts that composers and other musicians use in creating and performing music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments , and other artifacts . For example, ancient instruments from prehistoric sites around

264-501: A given meter. Syncopated rhythms contradict those conventions by accenting unexpected parts of the beat. Playing simultaneous rhythms in more than one time signature is called polyrhythm . In recent years, rhythm and meter have become an important area of research among music scholars. The most highly cited of these recent scholars are Maury Yeston , Fred Lerdahl and Ray Jackendoff , Jonathan Kramer , and Justin London. A melody

330-646: A greater or lesser degree. Context and many other aspects can affect apparent dissonance and consonance. For example, in a Debussy prelude, a major second may sound stable and consonant, while the same interval may sound dissonant in a Bach fugue. In the Common practice era , the perfect fourth is considered dissonant when not supported by a lower third or fifth. Since the early 20th century, Arnold Schoenberg 's concept of "emancipated" dissonance, in which traditionally dissonant intervals can be treated as "higher," more remote consonances, has become more widely accepted. Rhythm

396-718: A particular composition. During the Baroque period, emotional associations with specific keys, known as the doctrine of the affections , were an important topic in music theory, but the unique tonal colorings of keys that gave rise to that doctrine were largely erased with the adoption of equal temperament. However, many musicians continue to feel that certain keys are more appropriate to certain emotions than others. Indian classical music theory continues to strongly associate keys with emotional states, times of day, and other extra-musical concepts and notably, does not employ equal temperament. Consonance and dissonance are subjective qualities of

462-488: A pipe, he found its sound agreeable and named it huangzhong , the "Yellow Bell." He then heard phoenixes singing. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes to match the pitches of the phoenixes, producing twelve pitch pipes in two sets: six from the male phoenix and six from the female: these were called the lülü or later the shierlü . Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as

528-512: A science of sounds". One must deduce that music theory exists in all musical cultures of the world. Music theory is often concerned with abstract musical aspects such as tuning and tonal systems, scales , consonance and dissonance , and rhythmic relationships. There is also a body of theory concerning practical aspects, such as the creation or the performance of music, orchestration , ornamentation , improvisation, and electronic sound production. A person who researches or teaches music theory

594-779: A surging or "pushed" attack, or fortepiano ( fp ) for a loud attack with a sudden decrease to a soft level. The full span of these markings usually range from a nearly inaudible pianissississimo ( pppp ) to a loud-as-possible fortissississimo ( ffff ). Greater extremes of pppppp and fffff and nuances such as p+ or più piano are sometimes found. Other systems of indicating volume are also used in both notation and analysis: dB (decibels), numerical scales, colored or different sized notes, words in languages other than Italian, and symbols such as those for progressively increasing volume ( crescendo ) or decreasing volume ( diminuendo or decrescendo ), often called " hairpins " when indicated with diverging or converging lines as shown in

660-463: A theoretical nature, mainly lists of intervals and tunings . The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts [about music] are united by the use of a terminology for music that, according to the approximate dating of

726-457: A tone comprises. Timbre is principally determined by two things: (1) the relative balance of overtones produced by a given instrument due its construction (e.g. shape, material), and (2) the envelope of the sound (including changes in the overtone structure over time). Timbre varies widely between different instruments, voices, and to lesser degree, between instruments of the same type due to variations in their construction, and significantly,

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792-678: A tradition of other treatises, which are cited regularly just as scholarly writing cites earlier research. In modern academia, music theory is a subfield of musicology , the wider study of musical cultures and history. Guido Adler , however, in one of the texts that founded musicology in the late 19th century, wrote that "the science of music originated at the same time as the art of sounds". , where "the science of music" ( Musikwissenschaft ) obviously meant "music theory". Adler added that music only could exist when one began measuring pitches and comparing them to each other. He concluded that "all people for which one can speak of an art of sounds also have

858-399: Is a balance between "tense" and "relaxed" moments. Timbre, sometimes called "color", or "tone color," is the principal phenomenon that allows us to distinguish one instrument from another when both play at the same pitch and volume, a quality of a voice or instrument often described in terms like bright, dull, shrill, etc. It is of considerable interest in music theory, especially because it

924-410: Is a group of musical sounds in agreeable succession or arrangement. Because melody is such a prominent aspect in so much music, its construction and other qualities are a primary interest of music theory. The basic elements of melody are pitch, duration, rhythm, and tempo. The tones of a melody are usually drawn from pitch systems such as scales or modes . Melody may consist, to increasing degree, of

990-789: Is a music theorist. University study, typically to the MA or PhD level, is required to teach as a tenure-track music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by western music notation. Comparative, descriptive, statistical, and other methods are also used. Music theory textbooks , especially in the United States of America, often include elements of musical acoustics , considerations of musical notation , and techniques of tonal composition ( harmony and counterpoint ), among other topics. Several surviving Sumerian and Akkadian clay tablets include musical information of

1056-453: Is an additional chord member that creates a relatively dissonant interval in relation to the bass. It is part of a chord, but is not one of the chord tones (1 3 5 7). Typically, in the classical common practice period a dissonant chord (chord with tension) "resolves" to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there

1122-402: Is called an interval . The most basic interval is the unison , which is simply two notes of the same pitch. The octave interval is two pitches that are either double or half the frequency of one another. The unique characteristics of octaves gave rise to the concept of pitch class : pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring

1188-464: Is common in folk music and blues . Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classical Ottoman , Persian , Indian and Arabic musical systems often make use of multiples of quarter tones (half the size of a semitone, as the name indicates), for instance in 'neutral' seconds (three quarter tones) or 'neutral' thirds (seven quarter tones)—they do not normally use

1254-587: Is derived from the Greek music scale, and that Arabic music is connected to certain features of Arabic culture, such as astrology. Music is composed of aural phenomena; "music theory" considers how those phenomena apply in music. Music theory considers melody, rhythm, counterpoint, harmony, form, tonal systems, scales, tuning, intervals, consonance, dissonance, durational proportions, the acoustics of pitch systems, composition, performance, orchestration, ornamentation, improvisation, electronic sound production, etc. Pitch

1320-419: Is often referred to as "separated" or "detached" rather than having a defined or numbered amount by which to reduce the notated duration. Violin players use a variety of techniques to perform different qualities of staccato. The manner in which a performer decides to execute a given articulation is usually based on the context of the piece or phrase, but many articulation symbols and verbal instructions depend on

1386-427: Is one component of music that has as yet, no standardized nomenclature. It has been called "... the psychoacoustician's multidimensional waste-basket category for everything that cannot be labeled pitch or loudness," but can be accurately described and analyzed by Fourier analysis and other methods because it results from the combination of all sound frequencies , attack and release envelopes, and other qualities that

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1452-635: Is one of the most important mathematical treatises ever. It has been translated to numerous languages and remains continuously in print since the beginning of printing. Before the invention of the printing press, it was manually copied and widely circulated. When scholars recognized its excellence, they removed inferior works from circulation in its favor. Many subsequent authors, such as Theon of Alexandria , made their own editions, with alterations, comments, and new theorems or lemmas. Many mathematicians were influenced and inspired by Euclid's masterpiece. For example, Archimedes of Syracuse and Apollonius of Perga ,

1518-521: Is produced by the sequential arrangement of sounds and silences in time. Meter measures music in regular pulse groupings, called measures or bars . The time signature or meter signature specifies how many beats are in a measure, and which value of written note is counted or felt as a single beat. Through increased stress, or variations in duration or articulation, particular tones may be accented. There are conventions in most musical traditions for regular and hierarchical accentuation of beats to reinforce

1584-554: Is the lowness or highness of a tone , for example the difference between middle C and a higher C. The frequency of the sound waves producing a pitch can be measured precisely, but the perception of pitch is more complex because single notes from natural sources are usually a complex mix of many frequencies. Accordingly, theorists often describe pitch as a subjective sensation rather than an objective measurement of sound. Specific frequencies are often assigned letter names. Today most orchestras assign concert A (the A above middle C on

1650-407: Is the study of theoretical frameworks for understanding the practices and possibilities of music . The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the " rudiments ", that are needed to understand music notation ( key signatures , time signatures , and rhythmic notation ); the second is learning scholars' views on music from antiquity to

1716-572: The "horizontal" aspect. Counterpoint , which refers to the interweaving of melodic lines, and polyphony , which refers to the relationship of separate independent voices, is thus sometimes distinguished from harmony. In popular and jazz harmony , chords are named by their root plus various terms and characters indicating their qualities. For example, a lead sheet may indicate chords such as C major, D minor, and G dominant seventh. In many types of music, notably Baroque, Romantic, modern, and jazz, chords are often augmented with "tensions". A tension

1782-597: The Anglo-French term tretiz , which itself comes from the Old French traitis , meaning "treatise" or "account." This Old French term is rooted in the verb traitier , which means "to deal with" or "to set forth in speech or writing". The etymological lineage can be traced further back to the Latin word tractatus , which is a form of the verb tractare , meaning "to handle," "to manage," or "to deal with". The Latin roots suggest

1848-700: The Western tradition. During the thirteenth century, a new rhythm system called mensural notation grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatise Ars cantus mensurabilis ("The art of measured chant") by Franco of Cologne (c. 1280). Mensural notation used different note shapes to specify different durations, allowing scribes to capture rhythms which varied instead of repeating

1914-470: The chord C major may be described as a triad of major quality built on the note C . Chords may also be classified by inversion , the order in which the notes are stacked. A series of chords is called a chord progression . Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing key in common-practice harmony . To describe this, chords are numbered, using Roman numerals (upward from

1980-402: The difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's. Musical tuning systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. In Western culture , there have long been several competing tuning systems, all with different qualities. Internationally,

2046-451: The ever-expanding conception of what constitutes music , a more inclusive definition could be the consideration of any sonic phenomena, including silence. This is not an absolute guideline, however; for example, the study of "music" in the Quadrivium liberal arts university curriculum, that was common in medieval Europe , was an abstract system of proportions that was carefully studied at

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2112-657: The figure, motive, semi-phrase, antecedent and consequent phrase, and period or sentence. The period may be considered the complete melody, however some examples combine two periods, or use other combinations of constituents to create larger form melodies. A chord, in music, is any harmonic set of three or more notes that is heard as if sounding simultaneously . These need not actually be played together: arpeggios and broken chords may, for many practical and theoretical purposes, constitute chords. Chords and sequences of chords are frequently used in modern Western, West African, and Oceanian music, whereas they are absent from

2178-514: The first type (technical manuals) include More philosophical treatises of the second type include The pipa instrument carried with it a theory of musical modes that subsequently led to the Sui and Tang theory of 84 musical modes. Medieval Arabic music theorists include: The Latin treatise De institutione musica by the Roman philosopher Boethius (written c. 500, translated as Fundamentals of Music )

2244-513: The geometry of three-dimensional objects such as polyhedra), number theory, and the theory of proportions. It was essentially a compilation of all mathematics known to the Greeks up until Euclid's time. Drawing on the work of his predecessors, especially the experimental research of Michael Faraday , the analogy with heat flow by William Thomson (later Lord Kelvin) and the mathematical analysis of George Green , James Clerk Maxwell synthesized all that

2310-406: The graphic above. Articulation is the way the performer sounds notes. For example, staccato is the shortening of duration compared to the written note value, legato performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation. For example, staccato

2376-427: The greatest mathematicians of their time, received their training from Euclid's students and his Elements and were able to solve many open problems at the time of Euclid. It is a prime example of how to write a text in pure mathematics, featuring simple and logical axioms, precise definitions, clearly stated theorems, and logical deductive proofs. The Elements consists of thirteen books dealing with geometry (including

2442-1002: The greatest music had no sounds. [...] Even the music of the qin zither , a genre closely affiliated with Confucian scholar-officials, includes many works with Daoist references, such as Tianfeng huanpei ("Heavenly Breeze and Sounds of Jade Pendants"). The Samaveda and Yajurveda (c. 1200 – 1000 BCE) are among the earliest testimonies of Indian music, but properly speaking, they contain no theory. The Natya Shastra , written between 200 BCE to 200 CE, discusses intervals ( Śrutis ), scales ( Grāmas ), consonances and dissonances, classes of melodic structure ( Mūrchanās , modes?), melodic types ( Jātis ), instruments, etc. Early preserved Greek writings on music theory include two types of works: Several names of theorists are known before these works, including Pythagoras ( c.  570 ~ c.  495  BCE ), Philolaus ( c.  470 ~ ( c.  385  BCE ), Archytas (428–347  BCE ), and others. Works of

2508-400: The instrument and musical period (e.g. viol, wind; classical, baroque; etc.). Treatise A treatise is a formal and systematic written discourse on some subject concerned with investigating or exposing the principles of the subject and its conclusions. A monograph is a treatise on a specialized topic. The word "treatise" has its origins in the early 14th century, derived from

2574-426: The interval between adjacent tones is called a semitone , or half step. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales. The most commonly encountered scales are the seven-toned major , the harmonic minor , the melodic minor , and the natural minor . Other examples of scales are the octatonic scale and the pentatonic or five-tone scale, which

2640-476: The key-note), per their diatonic function . Common ways of notating or representing chords in western music other than conventional staff notation include Roman numerals , figured bass (much used in the Baroque era ), chord letters (sometimes used in modern musicology ), and various systems of chord charts typically found in the lead sheets used in popular music to lay out the sequence of chords so that

2706-438: The moral character of particular modes. Several centuries later, treatises began to appear which dealt with the actual composition of pieces of music in the plainchant tradition. At the end of the ninth century, Hucbald worked towards more precise pitch notation for the neumes used to record plainchant. Guido d'Arezzo wrote a letter to Michael of Pomposa in 1028, entitled Epistola de ignoto cantu , in which he introduced

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2772-572: The music of many other parts of the world. The most frequently encountered chords are triads , so called because they consist of three distinct notes: further notes may be added to give seventh chords , extended chords , or added tone chords . The most common chords are the major and minor triads and then the augmented and diminished triads . The descriptions major , minor , augmented , and diminished are sometimes referred to collectively as chordal quality . Chords are also commonly classed by their root note—so, for instance,

2838-399: The musician may play accompaniment chords or improvise a solo. In music, harmony is the use of simultaneous pitches ( tones , notes ), or chords . The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line , or

2904-497: The nature and functions of music. The Yueji ("Record of music", c1st and 2nd centuries BCE), for example, manifests Confucian moral theories of understanding music in its social context. Studied and implemented by Confucian scholar-officials [...], these theories helped form a musical Confucianism that overshadowed but did not erase rival approaches. These include the assertion of Mozi (c. 468 – c. 376 BCE) that music wasted human and material resources, and Laozi 's claim that

2970-444: The performance or perception of intensity, such as timbre, vibrato, and articulation. The conventional indications of dynamics are abbreviations for Italian words like forte ( f ) for loud and piano ( p ) for soft. These two basic notations are modified by indications including mezzo piano ( mp ) for moderately soft (literally "half soft") and mezzo forte ( mf ) for moderately loud, sforzando or sforzato ( sfz ) for

3036-598: The performer's technique. The timbre of most instruments can be changed by employing different techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, the player changes their embouchure, or volume. A voice can change its timbre by the way the performer manipulates their vocal apparatus, (e.g. the shape of the vocal cavity or mouth). Musical notation frequently specifies alteration in timbre by changes in sounding technique, volume, accent, and other means. These are indicated variously by symbolic and verbal instruction. For example,

3102-461: The phenomenon of light dispersion where other models failed. John William Strutt (Lord Rayleigh) and Josiah Willard Gibbs then proved that the optical equations derived from Maxwell's theory are the only self-consistent description of the reflection, refraction, and dispersion of light consistent with experimental results. Optics thus found a new foundation in electromagnetism . Hertz's experimental work in electromagnetism stimulated interest in

3168-584: The piano) to the frequency of 440 Hz. This assignment is somewhat arbitrary; for example, in 1859 France, the same A was tuned to 435 Hz. Such differences can have a noticeable effect on the timbre of instruments and other phenomena. Thus, in historically informed performance of older music, tuning is often set to match the tuning used in the period when it was written. Additionally, many cultures do not attempt to standardize pitch, often considering that it should be allowed to vary depending on genre, style, mood, etc. The difference in pitch between two notes

3234-513: The possibility of wireless communication, which did not require long and expensive cables and was faster than even the telegraph. Guglielmo Marconi adapted Hertz's equipment for this purpose in the 1890s. He achieved the first international wireless transmission between England and France in 1900 and by the following year, he succeeded in sending messages in Morse code across the Atlantic. Seeing its value,

3300-471: The practice of using syllables to describe notes and intervals. This was the source of the hexachordal solmization that was to be used until the end of the Middle Ages. Guido also wrote about emotional qualities of the modes, the phrase structure of plainchant, the temporal meaning of the neumes, etc.; his chapters on polyphony "come closer to describing and illustrating real music than any previous account" in

3366-496: The present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of

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3432-404: The quarter tone itself as a direct interval. In traditional Western notation, the scale used for a composition is usually indicated by a key signature at the beginning to designate the pitches that make up that scale. As the music progresses, the pitches used may change and introduce a different scale. Music can be transposed from one scale to another for various purposes, often to accommodate

3498-457: The range of a vocalist. Such transposition raises or lowers the overall pitch range, but preserves the intervallic relationships of the original scale. For example, transposition from the key of C major to D major raises all pitches of the scale of C major equally by a whole tone . Since the interval relationships remain unchanged, transposition may be unnoticed by a listener, however other qualities may change noticeably because transposition changes

3564-408: The relationship of the overall pitch range compared to the range of the instruments or voices that perform the music. This often affects the music's overall sound, as well as having technical implications for the performers. The interrelationship of the keys most commonly used in Western tonal music is conveniently shown by the circle of fifths . Unique key signatures are also sometimes devised for

3630-556: The same fixed pattern; it is a proportional notation, in the sense that each note value is equal to two or three times the shorter value, or half or a third of the longer value. This same notation, transformed through various extensions and improvements during the Renaissance, forms the basis for rhythmic notation in European classical music today. D'Erlanger divulges that the Arabic music scale

3696-473: The shipping industry adopted this technology at once. Radio broadcasting became extremely popular in the twentieth century and remains in common use in the early twenty-first. But it was Oliver Heaviside , an enthusiastic supporter of Maxwell's electromagnetic theory, who deserves most of the credit for shaping how people understood and applied Maxwell's work for decades to come; he was responsible for considerable progress in electrical telegraphy, telephony, and

3762-538: The sonority of intervals that vary widely in different cultures and over the ages. Consonance (or concord) is the quality of an interval or chord that seems stable and complete in itself. Dissonance (or discord) is the opposite in that it feels incomplete and "wants to" resolve to a consonant interval. Dissonant intervals seem to clash. Consonant intervals seem to sound comfortable together. Commonly, perfect fourths, fifths, and octaves and all major and minor thirds and sixths are considered consonant. All others are dissonant to

3828-409: The system known as equal temperament is most commonly used today because it is considered the most satisfactory compromise that allows instruments of fixed tuning (e.g. the piano) to sound acceptably in tune in all keys. Notes can be arranged in a variety of scales and modes . Western music theory generally divides the octave into a series of twelve pitches, called a chromatic scale , within which

3894-545: The texts, was in use for over 1,000 years." Much of Chinese music history and theory remains unclear. Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed. The Lüshi chunqiu from about 238 BCE recalls the legend of Ling Lun . On order of the Yellow Emperor , Ling Lun collected twelve bamboo lengths with thick and even nodes. Blowing on one of these like

3960-403: The type of early-medieval polyphonic music called organum , an early style of note-against-note polyphony; several examples of which are included in the treatise. ( Scolica enchiriadis also observes that some melodies should be sung "more quickly" ( celerius ), others "more slowly" ( morosius ).) The nineteenth chapter of Musica enchiriadis relates the legend of Orpheus . The scale used in

4026-745: The word dolce (sweetly) indicates a non-specific, but commonly understood soft and "sweet" timbre. Sul tasto instructs a string player to bow near or over the fingerboard to produce a less brilliant sound. Cuivre instructs a brass player to produce a forced and stridently brassy sound. Accent symbols like marcato (^) and dynamic indications ( pp ) can also indicate changes in timbre. In music, " dynamics " normally refers to variations of intensity or volume, as may be measured by physicists and audio engineers in decibels or phons . In music notation, however, dynamics are not treated as absolute values, but as relative ones. Because they are usually measured subjectively, there are factors besides amplitude that affect

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4092-512: The work, which is based on a system of tetrachords , appears to have been created solely for use in the work itself, rather than taken from actual musical practice. The treatise also uses a very rare system of notation, known as Daseian notation. This notation has a number of figures which are rotated ninety degrees to represent different pitches. A critical edition of the treatises was published in 1981, and an English translation by Raymond Erickson in 1995. Music theory Music theory

4158-531: The world reveal details about the music they produced and potentially something of the musical theory that might have been used by their makers. In ancient and living cultures around the world, the deep and long roots of music theory are visible in instruments, oral traditions, and current music-making. Many cultures have also considered music theory in more formal ways such as written treatises and music notation . Practical and scholarly traditions overlap, as many practical treatises about music place themselves within

4224-419: Was a touchstone for other writings on music in medieval Europe. Boethius represented Classical authority on music during the Middle Ages, as the Greek writings on which he based his work were not read or translated by later Europeans until the 15th century. This treatise carefully maintains distance from the actual practice of music, focusing mostly on the mathematical proportions involved in tuning systems and on

4290-423: Was confirmed by Heinrich Hertz . In the process, Hertz generated and detected what are now called radio waves and built crude radio antennas and the predecessors of satellite dishes. Hendrik Lorentz derived, using suitable boundary conditions, Fresnel's equations for the reflection and transmission of light in different media from Maxwell's equations. He also showed that Maxwell's theory succeeded in illuminating

4356-553: Was known about electricity and magnetism into a single mathematical framework, Maxwell's equations . Originally, there were 20 equations in total. In his Treatise on Electricity and Magnetism (1873), Maxwell reduced them to eight. Maxwell used his equations to predict the existence of electromagnetic waves, which travel at the speed of light. In other words, light is but one kind of electromagnetic wave. Maxwell's theory predicted there ought to be other types, with different frequencies. After some ingenious experiments, Maxwell's prediction

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