Kromatiokerroin

Kromatiokerroin, also known as the chromatic ratio, is a mathematical concept used in music theory and acoustics to describe the relationship between the frequencies of two adjacent notes in a chromatic scale. It is defined as the ratio of the frequency of a higher note to the frequency of a lower note, where the interval between the two notes is a semitone. The chromatic ratio is approximately 2^(1/12), which is roughly equal to 1.05946. This value is derived from the equal temperament tuning system, which divides the octave into 12 equal parts.

The chromatic ratio is significant in music because it determines the pitch of each note in a chromatic scale. By multiplying the frequency of a given note by the chromatic ratio, one can find the frequency of the next higher note in the scale. For example, if the frequency of a middle C (C4) is 261.63 Hz, then the frequency of the next higher note, C#4, would be approximately 261.63 * 1.05946 = 277.18 Hz.

The chromatic ratio is also used in acoustics to describe the relationship between the frequencies of harmonics in a musical sound. Harmonics are integer multiples of the fundamental frequency of a sound, and the chromatic ratio determines the pitch of each harmonic. For example, the second harmonic of a sound with a fundamental frequency of 261.63 Hz would have a frequency of 261.63 * 2 = 523.26 Hz, which is the pitch of an E above middle C.

In summary, the chromatic ratio is a fundamental concept in music theory and acoustics that describes the relationship between the frequencies of adjacent notes in a chromatic scale. It is used to determine the pitch of each note in the scale and to describe the relationship between the frequencies of harmonics in a musical sound.