Veltempered

Veltempered is a term that can refer to several related concepts, primarily in the context of music and temperaments. In music, a temperament describes how the pitches of a musical scale are adjusted or "tempered" to make them sound consonant when played together. Historically, various temperaments have been developed to address the mathematical imperfections of tuning instruments like the keyboard.

One prominent example is meantone temperament, where intervals like perfect fifths are tuned slightly smaller than pure to create pure major thirds. This, however, leads to some intervals becoming very out of tune when moving through keys. Veltempered in this context suggests a system that tries to balance these compromises.

The term "well-tempered" is often used interchangeably with veltempered, particularly in relation to "well-tempered clavichord" or "well-tempered clavier," famous works by Johann Sebastian Bach. These works were composed using a tuning system that allowed music to be played in all keys without sounding excessively out of tune. The precise nature of Bach's temperament is a subject of scholarly debate, with various historical temperaments proposed as possibilities.

Modern understanding of veltempered systems often points to equal temperament, where the octave is divided into twelve precisely equal semitones. This is the standard tuning system used on most modern instruments today, allowing for seamless modulation between any key. While this system is mathematically precise and universally applicable, some argue it sacrifices some of the unique character and color found in historical temperaments. The core idea behind veltempered is achieving a desirable balance of consonance across a range of musical keys.