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Pythagorean musical definitions The Pythagoreans used to define the musical ratios and the various consonances a jargon traditional greek and thus the ratio 1 : 1 was To Ison, 2 : 1 to diplasion, 3 : 2 emiolion, 4 : 3 epitrito, 9 : 8 epogdoo; then considering as a musical reference the nete composed of 12 units, paramese was 9 units, 8 the mese and the hypate 6 units, for example, that it was the harmony and then the fusion of two sounds that should be pleasing hearing (on the contrary of the dissonance) necessarily derived from mathematical ratios. Everything had to respond to a specific arithmetic ratio, the nete (12) exceeds the mese (8) of the third part of itself (4), and the hypate (6) is exceeded by the mese (8) by a similar part of itself (2). Therefore, the extreme notes exceed the mese and paramese and are exceeded in accordance with the same intervals all in a harmonious balance that had to be correspond in a figurative way also to the universal [eg. planets motion around the Sun]. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Oct 01, 2012 
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 Relaxing Platonic music Damon, a music teacher of Plato, says that children excited by listening to the flutist who sang songs to the Phrygian mode calmed down and relaxed as soon as went to the Doric; also part of the teachings related to singing, dancing and instrumental accompaniment also aimed to a full education, since the child who sings and plays the harp should not only demonstrate wisdom and courage, but also justice. Songs and dances cause a disturbance in the soul and those who are beautiful and are free training for the young as opposed to those that are not, and must also pay attention to new music that may impact negatively not only on individual but in whole society. In addition to relaxing effect (the Pythagorean Cleinias if nervous played the lyre to calm down) the music considered as global harmony for the Platonists had healing effects. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Aug 29, 2012 n: 1987 Pythagorean tuning For the Pythagorean the musical scale corresponded to an octave consists of twelve intervals and the four strings in the lyre were placed in the reports six : eight : nine : twelve, the whole string was plucked in a twelve canon reference, then the half 6/12 was in consonance with its half-octave, the whole string and its 3/4 was the consonance of fourth, full line and its 2/3 consonance of fifth. Pythagoras experimented this relationship with the monochord and identifying with a jumper twelve different intervals, then using different musical instruments checked the various numerical correspondences also about the relations of length and tension of the strings (using calibrated weights). Interval between two notes derived from the ratio of the frequencies and then it followed a scale of twelve intervals in a sequence that had to respect the universal harmony that exceeded the strictly musical sector. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Aug 01, 2012 n: 1963 Pythagorean harmony and balance of the polis For the Pythagoreans the balance of opposites was also harmony and health of body and soul wisdom that were also reflected in the orderly functioning of the polis, with a numeric-type conception of music that came to influence the whole cosmos, in fact for example Philolaus called the eighth (range of four strings of the lyre) "harmony" and the statesman Archytas of Taranto (430-360 BC) friend of Plato tried to apply it to relations between men in order to establish a balance between rich and poor, and then in the administration of justice avoiding the domination of men or caste. Even philosophers like Mersenne and especially Leibniz identified in the music a secret arithmetical exercise and who have enjoyed practicing ignorant handling of numbers, but to the Pythagoreans this exercise led to a better peaceful administration of the polis, according to the adage of not to fight, of do not remove the fire with the sword. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Jun 16, 2012 n: 1923 Musical fractions and Pythagorean Limma In the Pythagorean musical scale were taken into account even small intervals as the Limma (which in greek means "what remains") for example 256/243 that resulted from the difference between the perfect fourth interval 4/3 and the major third 81/64, a diatonic semitone E-F and B-C that is in the piano keyboard represent practically the blacks missing keys and then with intervals lower of the semitone barely perceptible by ear, but indispensable to the Pythagoreans in number sense that was more important than the auditory sensation. These short intervals were derived mathematically with the monochord, and came from the main musical fractions already identified by the Egyptians, considered very experienced in this sector, and probably by the Assyrians-Babylonians which were derived from some knowledge of mathematics and other scientific and of naturalistic type used by Pythagoras to which the tradition attributes (but not all agree) study tours at a young age. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: May 11, 2012 n: 1891 Pythagorean harmony of music and modern physics The concept of quantitative numerical Pythagoreans identified with the cosmic harmony that could be expressed by mathematical relations that music had to be at the root of all reality, such for example with a technique visual and meditative imagining the notes in a diagram according to provision on unitary and universal principles, then with links that could also harmonize discordant elements or opposite nature (number seen as "archè" in which everything can be traced). These theories that suggest an universal harmony could be explained in modern physics, in fact, in quantum mechanics has been demonstrated in 1959 with the so-called Aharonov-Bohm effect that a magnetic field modifies the motion of charged particles even if they not fail in its radius of action, at a distance, thus revealing a structure of matter that was previously unthinkable. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Apr 21, 2012 n: 1876 Rhythm and music criticism When the division of the durations of the notes has a defined order usually speaks of the fundamentals of the science of the rhythms, which deals with the rhythm of the music and ordered the figures associated with them that are shaped own according to their rhythm, and for the powerful action that has the music on the human soul should monitor those involved in these calculations on the rhythms in the same manner in which a controlling influence on other disciplines important for individual growth. Pythagoras based his education in music on the number and Plato fought that type of music too free in which the overall impression was lost for cause of the abuse of alterations and changes, however, the most "critical" of the kind of catchy music made to suit the hearing may be considered S. Augustine (Conf. 10-33) that points out that what we can distract from the true intent of a musical phrase to please the audience. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Feb 28, 2012 n: 1830 The Pythagorean consonance The musical ratios of second, fourth and fifth were consonant for the Pythagoreans, and these considerations on the sounds were first reported by the Egyptians and assets probably of several ancient cultures, but Pythagoras using two monochords side by side noted that the quotient between a fifth and a fourth was a second (3/2 : 4/3 = 9/8) and then there was a music proportion in the same as that found with the calculations of geometric and other mathematical studies carried out by the philosopher. The science of numbers applied to man up and down, inside and outside, and then went to heaven and the world for the study of relationships "across all the strings" (dia-pason) in an octave and also with the principle of identity for which the sound length and speed was required, and the musical harmony was considered of great importance, and if applied to humans can also improve the character (meaning in a figurative sense the relationship between music and the universe). e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Jan 25, 2012 n: 1800 Pythagorean scales of smooth tones Aristoxenus of Taranto (fourth century B.C.) philosopher and musician, also pupil of Aristotle devised in the work "rhythmic elements" a system of thirteen scales of smooth tones, with the thirteenth eighth as a repetition of a scale that perhaps serve as a basis for the fifteen tones or transposition scales of J.S. Bach (Well-Tempered Clavier, forty-eight preludes and fugues), but despite being Aristoxenus a Pythagorean his research relied (opposed by Heraclides Ponticus) more on the ear than on the numbers and then not complying with one of the precepts of the school of Pythagoras to base the perceptions of the senses on the calculation. To note that the Greeks did not use the octave as a base system sounds but the tetrachord, and tuning fork means two tetrachords separated to form an octave; in addition, the Pythagoreans had a different conception of consonance with reports that were probably experienced by Bach (he was expelled from the Oratory). e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Dec 30, 2011 n: 1777 Platonic music valuation A poem or a music composition should be evaluated according to Plato (427-347 BC) from a public that has been carefully educated, because if is proposed to the citizens to give awards on a free subject races more or less complex with the only purpose to provide pleasure is clear that the evaluation would be affected from the age of the viewer, with the youngest perhaps inclined to prize the play, the women and the majority in general to the tragedy, while only the elderly for an accurate recitation of Homer and Hesiod. To decide what are the "ideal laws" suitable for regular assessments on the compositions of a new state should ensure that the verdict is influenced by the noise of the crowd ready to reward unseemly pleasures, not to take the risk that these rules ruin the tastes of all the audience and point instead to promote the noble ways of life and education of the population. e-mail: info@salutary.eu Tel: +39 338 1809310 Date: Dec 03, 2011 n: 1753 Music * The author doesn't assume some kind of responsibility for the bad use of the articles councils (all rights are reserved) |
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