As has been noted, consonance is related to simple frequency ratios such as 2:1. In contrast to these uncomplicated fractions, the frequency ratios of these intervals are actually the irrational numbers: 6 Square root of √ 2:1 and 12 Square root of √ 2:1. In the diatonic, or seven-note scale, for example, which is the basis of Western music and is represented by the white notes on the piano keyboard, there are five steps of one-sixth of an octave and two of one-twelfth. In nearly all musical cultures the octave is subdivided into a number of steps, each a simple fraction of an octave. For this reason, high and low voices naturally sing the same tune an octave apart. The fundamental unit is the octave, which has the unique property that its two notes are felt in some indefinable way to be the same, though in pitch level they are recognizably different. The tendency is either to make the steps in the scale sound equal in size or to place them in simple arithmetic relationship to one another. When instruments are made, it is often necessary to determine precise pitches. Many primitive scales are sung, not played, and are variable in the exact pitches of their notes. So long as music consists of melody without harmony, consonance plays little part in the determination of successive pitches in a scale. When a unison, octave, or fifth is slightly mistuned, the resulting combination is markedly dissonant and is judged “out of tune.” The slight mistunings that occur in systems of tempered tuning are necessary for reasons that will be discussed later in this article. Next in order of consonance comes the octave (2:1), the interval between c and c′ (encompassing eight notes of the piano keyboard) another highly consonant interval is the fifth (3:2, as from c to g). When the two tones are tuned to the same pitch, they are said to be in unison (ratio 1:1) and their consonance is absolute. Consonance results from the absence of beats, which occurs only when the ratio between the frequencies of the two tones is numerically simple. Dissonance is produced by beats (interference between pulsations of sound waves), and it is found that maximum dissonance occurs when the rate of beats between the two tones is about 33 per second. When two tones are sounded together the subjective reaction may be anything from one of perfect consonance to one of extreme dissonance. Various frequency ratios can be reduced to the same basic relationship for example, 440:220 and 30:15 and 750:375 can all be reduced to the ratio 2:1. An interval, or distance between two pitches, can thus be mathematically described as the ratio of the frequency of the first pitch to the frequency of the second. A given musical pitch is determined by the frequency of vibration of the sound wave that produces it, as a′ = 440 cycles per second. Two concepts fundamental to the theory of tuning are those of frequency ratio and of consonance and dissonance. The determination of pitch, the quality of sound that is described as ‘high” or “low,” is based upon the frequency of sound waves. Tuning and temperament, in music, the adjustment of one sound source, such as a voice or string, to produce a desired pitch in relation to a given pitch, and the modification of that tuning to lessen dissonance. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!.Learn about the major environmental problems facing our planet and what can be done about them! Saving Earth Britannica Presents Earth’s To-Do List for the 21st Century.Britannica Beyond We’ve created a new place where questions are at the center of learning.100 Women Britannica celebrates the centennial of the Nineteenth Amendment, highlighting suffragists and history-making politicians.COVID-19 Portal While this global health crisis continues to evolve, it can be useful to look to past pandemics to better understand how to respond today.Student Portal Britannica is the ultimate student resource for key school subjects like history, government, literature, and more.From tech to household and wellness products. Britannica Explains In these videos, Britannica explains a variety of topics and answers frequently asked questions.This Time in History In these videos, find out what happened this month (or any month!) in history.#WTFact Videos In #WTFact Britannica shares some of the most bizarre facts we can find.Demystified Videos In Demystified, Britannica has all the answers to your burning questions.Britannica Classics Check out these retro videos from Encyclopedia Britannica’s archives.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |