Music: Factors of beauty in nature, art, and especially in musical intervals مقالة

ملخص الجهاز:

This Gamme is known as the "Aristoxe?ne" or "Zarlin" scale, which contains the most melodious musical intervals, and because of these characteristics, it is recognized as a system that possesses sounds with very precise quality (Just intonation); however, since there are two types of whole-Tone intervals in this system, the value of the "Chromatic semitones" distance between some neighboring Degrees is different. This means that the interval between "Fa" (Fa) and "Fa sharp" (Fa die?se), which are located between the fourth and fifth "Degrees" of the scale, as well as "La" (La) and "La sharp" (La die?se), which are between the sixth and seventh degrees of the scale, is the same 123/23 "Savart", whereas the interval between "Sol" (Sol) and "Sol sharp" (sol die?se) between the fifth and sixth degrees of the scale is equivalent to 728/17 Savart. For example, in the "Zarlin system," the interval between the first and fifth degrees (Do-Sol), third and seventh (Mi-Si), fourth and eighth (Fa-Do), fifth and ninth (Sol-Re), and sixth and tenth (La-Mi) has a frequency ratio of 3/2, equivalent to 176 "Savart" (Savart), which is a "Perfect Consonant" (Perfect Consonant) interval; whereas the frequency (Frequency) ratio between the second and sixth degrees (Re-La) is 27/40, equivalent to 171 "Savart," and is not considered a consonant interval. Also, they divide the logarithm of the 4/5 ratio, which is the major third of the Zarlin scale, into two parts to create a tempered whole-step interval; as a result, a relatively tempered scale (Tempered) is obtained, where the intervals of its steps are all equal to 48/45 Savart, its perfect fifths are somewhat less than the actual perfect fifth interval by an amount of 174.