http___livro-ensino-medio.f1cf.com.br_matematica_hr_mathematics-65.html_1.xml
1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 11.1 12.1 13.1 14.1 15.1 16.1 18.1 19.1 20.1 21.1 22.1 23.1 24.1
Mathematics Why linking mathematics and music? A small set of musical notes was known as the harmonic series, with its pleasant and frequencies audible to humans. Pythagoras, who lived in the sixth century BC, stretched a rope and analyzed the sound produced by its vibration. Found that by dividing the rope in half, the vibration of the sound was the same as produced with the whole string, but one octave higher, producing a higher pitch. From this experiment, Pythagoras various relationships established as the fifth interval to be longer in line with the series was the basis for the construction of most musical scales in the world. In 1635, Mersenne proposed a system of mild thinning, known as tempered scale. In this system it is necessary that the relations of the frequency of any adjacent half-tones are constant. But this was only accepted from the compositions of The Well-Tempered Clavier, which was made from 1722 to 1744 by Bach But who was Bach? The German composer Johann Sebastian Bach (1685-1750) is considered the forerunner of modern Musia and one of the leading composers of all time. He realized that the sounds of music notes may be more or less pleasant as the manner in which the notes are grouped. See, for example, the scale of seven sounds known: C, D, E, F, G, A, B. The choice of the separation of sounds in these 7 shares is considered pleasant. The proposal of the tempered scale was to divide the musical scale into 12 parts, twelve sounds that were pleasing to the ear and soul (Nascimento, This scale has all or nearly all intervals slightly inaccurate, but not distorted. How? The tempered sense refers to seasoning the same which divides the interval of an octave into 12 semitones of frequencies associated with relationships are exactly alike. The temper process has not occurred as a sudden developed in different ways over time. The tempered scale was divided this way: Source: adapted from BIRTH (2005) Mathematics, Music and Earthquake, What's In Common?
1.1 2.1 3.1 3.2 3.3 3.4 4.1 4.2 4.3 5.1 7.1 8.1 8.2 8.3 8.4 9.1 11.1 12.1 13.1 13.2 14.1 15.1 16.1
Matematika Zašto se povezuje matematiku i glazbu? Mali skup glazbene note je poznat kao harmonijske serije, s ugodnim i zvučnim frekvencijama za ljude. Pitagora, koji je živio u šestom stoljeću prije Krista, rastegnut konop i analizirao zvuk kojeg proizvodi svoje vibracije. Utvrđeno je da se dijeljenjem uže na pola, vibracije zvuka je isti kao i proizvodi s cijelom nizu, ali jedan oktavu više, proizvodnju veću visinu. Iz ovog eksperimenta, Pitagora različite odnose uspostavljene kao peti intervalu biti više u skladu s nizom bio temelj za izgradnju većine glazbenih mjerila u svijetu. U 1635, Mersenne predložila sustav blagi stanjivanje, poznat kao kaljeno ljestvice. U ovom sustavu, potrebno je da je odnos svih frekventnih Nijanse sive su u susjedstvu konstantna. No, to je samo bio prihvaćen od sastava Dobro uštimani Clavier, koji je napravio 1722-1744 Bacha (Abdounur, 1999) Ali tko je Bach? Njemački skladatelj Johann Sebastian Bach (1685-1750) se smatra pretečom modernog Musia i jedan od vodećih skladatelja svih vremena. Shvatio je da su zvukovi glazbe bilješke mogu biti više ili manje ugodno kao način na koji su bilješke su grupirani. Vidi, primjerice, ljestvica sedam zvuči poznato: C, D, E, F, G, A, B. izbor odvajanje zvukova u ovih sedam dionica smatra se ugodno. Prijedlog kaljeno ljestvice bio da podijeli glazbene ljestvice u 12 dijelova, dvanaest zvukova koji su ugodni za uho i dušu (Nascimento, 2005) Ova ljestvica ima sve ili skoro sve intervale nešto netočne, ali ne i iskrivljene. Kako? Kaljeno razum se odnosi na začina koji dijeli isti interval oktavi u 12 polustepena frekvencija povezane s vezama su upravo na isti način. Temperament proces još nije došlo kao odjednom razvijati na različite načine tijekom vremena. Kaljeno ljestvice bila podijeljena na ovaj način: Izvor: preuzeto iz ROĐENJA (2005) Matematika, Glazba i potresa, Što je zajedničko?