tasavälisiin

Tasavälisiin is a Finnish term that translates to "equal intervals" or "even spacing." It is primarily used in music theory and composition to describe the precise division of an octave into a set number of equal parts. The most common and widely recognized system of tasavälisiin is the twelve-tone equal temperament, where the octave is divided into twelve semitones of equal pitch. This system is the foundation of Western music as it allows for modulation to all keys without significant intonational issues.

In tasavälisiin, the ratio between the frequencies of any two adjacent notes is constant. This constant ratio ensures that the perceived distance between notes is consistent across the entire range of an instrument. While twelve-tone equal temperament is dominant, the concept of tasavälisiin can be applied to dividing the octave into other numbers of intervals, leading to microtonal music systems. These alternative tunings, often referred to as just intonation or other temperament systems, explore different sonic possibilities by deviating from the strictly equal divisions.

The mathematical basis for equal temperament involves logarithms. The frequency of each note is found by multiplying the frequency of the reference note by the twelfth root of two, raised to the power of the note's position in the scale. This precise mathematical relationship is what gives equal temperament its name and its practical utility for musicians worldwide. The simplicity and versatility of tasavälisiin have made it the standard tuning system for most instruments today.