Music theory in the context of Minor interval

Eratosthenes of Cyrene (/ɛrəˈtɒsθəniːz/; Ancient Greek: Ἐρατοσθένης [eratostʰénɛːs]; c. 276 BC – c. 195/194 BC) was an Ancient Greek philosopher, polymath and scholar. He was known as a mathematician, geographer, poet, astronomer, and music theorist. Eratosthenes became the chief librarian at the Library of Alexandria. His work was the precursor to the modern discipline of geography, and he introduced some of its terminology, coining the terms geography and geographer.

He is best remembered as the first known person to calculate the Earth's circumference. He was also the first to calculate Earth's axial tilt, which similarly proved to have remarkable accuracy. He created the first global projection of the world incorporating parallels and meridians based on the available geographic knowledge of his era. Eratosthenes was the founder of scientific chronology; he used Egyptian and Persian records to estimate the dates of the main events of the Trojan War, dating the sack of Troy to 1184 BC. In number theory, he introduced the sieve of Eratosthenes, an efficient method of identifying prime numbers and composite numbers.

China has been the source of many innovations, scientific discoveries and inventions. This includes the Four Great Inventions: papermaking, the compass, gunpowder, and early printing (both woodblock and movable type). The list below contains these and other inventions in ancient and modern China attested by archaeological or historical evidence, including prehistoric inventions of Neolithic and early Bronze Age China.

The historical region now known as China experienced a history involving mechanics, hydraulics and mathematics applied to horology, metallurgy, astronomy, agriculture, engineering, music theory, craftsmanship, naval architecture and warfare. Use of the plow during the Neolithic period Longshan culture (c. 3000 – c. 2000 BC) allowed for high agricultural production yields and rise of Chinese civilization during the Shang dynasty (c. 1600 – c. 1050 BC). Later inventions such as the multiple-tube seed drill and the heavy moldboard iron plow enabled China to sustain a much larger population through improvements in agricultural output.

Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, in modern Calabria (Italy) circa 530 BC. Early Pythagorean communities spread throughout Magna Graecia.

Already during Pythagoras's life it is likely that the distinction between the akousmatikoi ("those who listen"), who is conventionally regarded as more concerned with religious, and ritual elements, and associated with the oral tradition, and the mathematikoi ("those who learn") existed. The ancient biographers of Pythagoras, Iamblichus (c. 245 – c. AD 325) and his master Porphyry (c. 234 – c. AD 305) seem to make the distinction of the two as that of 'beginner' and 'advanced'. As the Pythagorean cenobites practiced an esoteric path, like the mystery schools of antiquity, the adherents, akousmatikoi, following initiation became mathematikoi. It is wrong to say that the Pythagoreans were superseded by the Cynics in the 4th century BC, but it seems to be a distinction mark of the Cynics to disregard the hierarchy and protocol, ways of initiatory proceedings significant for the Pythagorean community; subsequently did the Greek philosophical traditions become more diverse. The Platonic Academy was arguably a Pythagorean cenobitic institution, outside the city walls of Athens in the 4th century BC. As a sacred grove dedicated to Athena, and Hecademos (Academos). The academy, the sacred grove of Academos, may have existed, as the contemporaries seem to have believed, since the Bronze Age, even pre-existing the Trojan War. Yet according to Plutarch it was the Athenian strategos (general) Kimon Milkiadou (c. 510 – c. 450 BC) who converted this, "waterless and arid spot into a well watered grove, which he provided with clear running-tracks and shady walks". Plato lived almost a hundred years later, circa 427 to 348 BC. On the other hand, it seems likely that this was a part of the re-building of Athens led by Kimon Milkiadou and Themistocles, following the Achaemenid destruction of Athens in 480–479 BC during the war with Persia. Kimon is at least associated with the building of the southern Wall of Themistocles, the city walls of ancient Athens. It seems likely that the Athenians saw this as a rejuvenation of the sacred grove of Academos.

Porphyry (/ˈpɔːrfɪri/; Koine Greek: Πορφύριος, romanized: Porphýrios; c. 234 – c. AD 305) was a Phoenician Neoplatonic philosopher born in Tyre, Roman Phoenicia during Roman rule. He edited and published the Enneads, the only collection of the work of Plotinus, his teacher.

He wrote original works in the Greek language on a wide variety of topics, ranging from music theory to Homer to vegetarianism. His Isagoge or Introduction, an introduction to logic and philosophy, was the standard textbook on logic throughout the Middle Ages in its Latin and Arabic translations. Porphyry was, and still is, also well known for his anti-Christian polemics. Through works such as Philosophy from Oracles and Against the Christians (which was banned by Constantine the Great), he was involved in a controversy with early Christians.

In music theory, the term period refers to forms of repetition and contrast between adjacent small-scale formal structures such as phrases. In twentieth-century music scholarship, the term is usually used similarly to the definition in the Oxford Companion to Music: "a period consists of two phrases, antecedent and consequent, each of which begins with the same basic motif." Earlier and later usages vary somewhat, but usually refer to notions of symmetry, difference, and an open section followed by a closure. The concept of a musical period originates in comparisons between music structure and rhetoric at least as early as the 16th century.

In Western music theory, a chord is a group of notes played together for their harmonic consonance or dissonance. The most basic type of chord is a triad, so called because it consists of three distinct notes: the root note along with intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz, and other genres.

Chords are the building blocks of harmony and form the harmonic foundation of a piece of music. They provide the harmonic support and coloration that accompany melodies and contribute to the overall sound and mood of a musical composition. The factors, or component notes, of a chord are often sounded simultaneously but can instead be sounded consecutively, as in an arpeggio.

In music theory, counterpoint is the relationship of two or more simultaneous musical lines (also called voices) that are harmonically dependent on each other, yet independent in rhythm and melodic contour. The term originates from the Latin punctus contra punctum meaning "point against point", i.e. "note against note".

John Rahn describes counterpoint as follows:

In music theory, a phrase (Greek: φράση) is a unit of musical meter that has a complete musical sense of its own, built from figures, motifs, and cells, and combining to form melodies, periods and larger sections.

Terms such as sentence and verse have been adopted into the vocabulary of music from linguistic syntax. Though the analogy between the musical and the linguistic phrase is often made, still the term "is one of the most ambiguous in music....there is no consistency in applying these terms nor can there be...only with melodies of a very simple type, especially those of some dances, can the terms be used with some consistency."

In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.

In Western music, intervals are most commonly differencing between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. 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, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.

Noise music (or simply noise) is a subgenre of experimental music that is characterised by its use of unwanted noise as a primary musical element. The genre has roots in early 20th century avant-garde music, but later drew influence from industrial music. It is characterized by a rejection of conventional music theory and traditional song structures, often featuring little or no melody, rhythm, or harmony. This type of music tends to challenge the conventional distinction between musical and non-musical sound.

"Noise as music" originated as an avant-garde music style in the 1910s through the work of Luigi Russolo an Italian Futurist, who published the manifesto The Art of Noises in 1913. Elements of noise music were later explored by artists in the Dada and Fluxus movements, as well as through electroacoustic music, modern classical and musique concrète. Composers such as John Cage, Edgard Varèse and James Tenney would explicitly use the term "noise" to describe some of their experimental practices. During the 1960s and 1970s, compositions such as Robert Ashley's "The Wolfman" (1964) and Pauline Oliveros "A Little Noise In The System" (1967) were among the earliest examples of contemporary noise music. While works by non-academic artists such as Lou Reed's Metal Machine Music were influential for later noise artists.

Musical technique is the ability of instrumental and vocal musicians to exert optimal control of their instruments or vocal cords in order to produce the precise musical effects they desire. Improving one's technique generally entails practicing exercises that improve one's muscular sensitivity and agility. Technique is independent of musicality. Compositional technique is the ability and knowledge composers use to create music, and may be distinguished from instrumental or performance technique, which in classical music is used to realize compositions, but may also be used in musical improvisation. Extended techniques are distinguished from more simple and more common techniques. Musical technique may also be distinguished from music theory, in that performance is a practical matter, but study of music theory is often used to understand better and to improve techniques. Techniques such as intonation or timbre, articulation, and musical phrasing are nearly universal to all instruments.

To improve their technique, musicians often practice ear training. For example, musical intervals, and fundamental patterns and of notes such as the natural, minor, major, and chromatic scales, minor and major triads, dominant and diminished sevenths, formula patterns and arpeggios. For example, triads and sevenths teach how to play chords with accuracy and speed. Scales teach how to move quickly and gracefully from one note to another (usually by step). Arpeggios teach how to play broken chords over larger intervals. Many of these components of music are found in difficult compositions, for example, a large tuple chromatic scale is a very common element to Classical and Romantic era compositions as part of the end of a phrase.

Musica enchiriadis is an anonymous musical treatise authored during the 9th century. It is the first surviving attempt to set up a system of rules for polyphony in western art music. The treatise was once attributed to Hucbald, but this is no longer accepted. Some historians once attributed it to Odo of Cluny (879–942). It has also been attributed to Abbot Hoger (d. 906).

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.

Musicology is the academic, research-based study of music, as opposed to musical composition or performance. Musicology research combines and intersects with many fields, including psychology, sociology, acoustics, neurology, natural sciences, formal sciences and computer science.

Musicology is traditionally divided into three branches: music history, systematic musicology, and ethnomusicology. Historical musicologists study the history of musical traditions, the origins of works, and the biographies of composers. Ethnomusicologists draw from anthropology (particularly field research) to understand how and why people make music. Systematic musicology includes music theory, aesthetics, pedagogy, musical acoustics, the science and technology of musical instruments, and the musical implications of physiology, psychology, sociology, philosophy and computing. Cognitive musicology is the set of phenomena surrounding the cognitive modeling of music. When musicologists carry out research using computers, their research often falls under the field of computational musicology. Music therapy is a specialized form of applied musicology which is sometimes considered more closely affiliated with health fields, and other times regarded as part of musicology proper.

Franchinus Gaffurius (Franchino Gaffurio; 14 January 1451 – 25 June 1522) was an Italian music theorist and composer of the Renaissance.

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed,

The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C.

In music theory, the term mode or modus is used in a number of distinct senses, depending on context.

Its most common use may be described as a type of musical scale coupled with a set of characteristic melodic and harmonic behaviors. It is applied to major and minor keys as well as the seven diatonic modes (including the former as Ionian and Aeolian) which are defined by their starting note or tonic. (Olivier Messiaen's modes of limited transposition are strictly a scale type.) Related to the diatonic modes are the eight church modes or Gregorian modes, in which authentic and plagal forms of scales are distinguished by ambitus and tenor or reciting tone. Although both diatonic and Gregorian modes borrow terminology from ancient Greece, the Greek tonoi do not otherwise resemble their medieval/modern counterparts.