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Scala is a freeware software application with versions supporting Windows, macOS, and Linux.It allows users to create and archive musical scales, analyze and transform them with built-in theoretical tools, play them with an on-screen keyboard or from an external MIDI keyboard, and export them to hardware and software synthesizers.
For the ordinary diatonic scales described here, the T-s are tones and the s-s are semitones which are half, or approximately half the size of the tone.But in the more general regular diatonic tunings, the two steps can be of any relation within the range between T = 171.43 ¢ (for s = T at the high extreme) and T = 240 ¢ (for s = 0 at the low extreme) in musical cents (fifth, p5, between 685 ...
The name "meantone temperament" derives from the fact that in all such temperaments the size of the whole tone, within the diatonic scale, is somewhere between the major and minor tones (9:8 and 10:9 respectively) of just intonation, which differ from each other by a syntonic comma.
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Well temperament means a mathematical-acoustic and musical-practical organisation of the tone system within the twelve steps of an octave, with the goal of impeccable performance in all tonalities, based on the natural-harmonic tone system [i.e., extended just intonation], while striving to keep the diatonic intervals as pure as possible.
Richter tuning is a system of choosing the reeds for a diatonic wind instrument (such as a harmonica or accordion).It is named after Joseph Richter, a Bohemian instrument maker who adopted the tuning for his harmonicas in the early 19th century and is credited with inventing the blow/draw mechanism that allows the harmonica to play different notes when the air is drawn instead of blown.
In any meantone or Pythagorean tuning, where a whole tone is composed of one semitone of each kind, a major third is two whole tones and therefore consists of two semitones of each kind, a perfect fifth of meantone contains four diatonic and three chromatic semitones, and an octave seven diatonic and five chromatic semitones, it follows that:
Diatonic scale on C, equal tempered Play ⓘ and Ptolemy's intense or just Play ⓘ.. Ptolemy's intense diatonic scale, also known as the Ptolemaic sequence, [1] justly tuned major scale, [2] [3] [4] Ptolemy's tense diatonic scale, or the syntonous (or syntonic) diatonic scale, is a tuning for the diatonic scale proposed by Ptolemy, [5] and corresponding with modern 5-limit just intonation. [6]