Музыкалық аспапты келтіру әдісі

Method of tuning a musical instrument
[[Image:Rank 2 temperaments with the generator close to a fifth and period an octave. jpg|right|250px|thumb|The syntonic tuning continuum, showing Pythagorean tuning at 702 cents. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2 (i. e., the untempered perfect fifth), which is ≈ 702 cents wide. The system dates to Ancient Mesopotamia; see The system is named, and has been widely misattributed, to Ancient Greeks, notably Pythagoras (sixth century BC) by modern authors of music theory, while Ptolemy, and later Boethius, ascribed the division of the tetrachord by only two intervals, called "semitonium", "tonus", "tonus" in Latin (256:243 × 9:8 × 9:8), to Eratosthenes. The so called "Pythagorean tuning" was used by musicians up to the beginning of the 16th century. "The Pythagorean system would appear to be ideal because of the purity of the fifths, but some consider other intervals, particularly the major third, to be so badly out of tune that major chords [may be considered] a dissonance." In Greek music it was used to tune tetrachords, which were composed into scales spanning an octave. A distinction can be made between extended Pythagorean tuning and a 12 tone Pythagorean temperament. Extended Pythagorean tuning corresponds 1 on 1 with western music notation and there is no limit to the number of fifths. In 12 tone Pythagorean temperament however one is limited by 12 tones per octave and one cannot play most music according to the Pythagorean system corresponding to the enharmonic notation, instead one finds that for instance the diminished sixth becomes a "wolf fifth".

The system dates to Ancient Mesopotamia, and consisted of alternating ascending fifths and descending fourths; see Within Ancient Greek music, the system had been mainly attributed to Pythagoras (who lived around 500 BCE) by modern authors of music theory; Ancient Greeks borrowed much of their music theory from Mesopotamia, including the diatonic scale, Pythagorean tuning, and modes. The Chinese Shí èr lǜ scale uses the same intervals as the Pythagorean scale and was invented between 600 BCE and 240 CE. Because of the wolf interval when using a 12 tone Pythagorean temperament, this tuning is rarely used today, although it is thought to have been widespread. In music which does not change key very often, or which is not very harmonically adventurous, the wolf interval is unlikely to be a problem, as not all the possible fifths will be heard in such pieces. In extended Pythagorean tuning there is no wolf interval, all perfect fifths are exactly 3:2. Because most fifths in 12 tone Pythagorean temperament are in the simple ratio of 3:2, they sound very "smooth" and consonant. The thirds, by contrast, most of which are in the relatively complex ratios of 81:64 (for major thirds) and 32:27 (for minor thirds), sound less smooth depending on the instrument. From about 1510 onward, as thirds came to be treated as consonances, meantone temperament, and particularly quarter comma meantone, which tunes thirds to the relatively simple ratio of 5:4, became the most popular system for tuning keyboards. At the same time, syntonic diatonic just intonation was posited first by Ramos and then by Zarlino as the normal tuning for singers. However, meantone presented its own harmonic challenges. Its wolf intervals proved to be even worse than those of the Pythagorean tuning (so much so that it often required 19 keys to the octave as opposed to the 12 in Pythagorean tuning). As a consequence, meantone was not suitable for all music. From around the 18th century, as the desire grew for instruments to change key, and therefore to avoid a wolf interval, this led to the widespread use of well temperaments and eventually equal temperament. Pythagorean temperament can still be heard in some parts of modern classical music from singers and from instruments with no fixed tuning such as the violin family. Where a performer has an unaccompanied passage based on scales, they will tend towards using Pythagorean intonation as that will make the scale sound best in tune, then reverting to other temperaments for other passages (just intonation for chordal or arpeggiated figures, and equal temperament when accompanied with piano or orchestra). Such changes are never explicitly notated and are scarcely noticeable to the audience, just sounding 'in tune'.