Just intonation or pure intonation is based on the intervals of the natural overtones, the natural overtone series. Pure intonation is therefore the only natural tuning. All other tunings, such as equal temperament or Pythagorean tuning, are deviations from pure tuning.

Our hearing is always oriented towards these pure intervals. A violinist practicing intonation will always find his way to these intervals without any problems.

Pure intonation emerged in Europe with the advent of polyphony in the second half of the 15th century. Tuning is the determination of pitches (frequencies) of sound sources, especially of musical instruments.

The distances between pitches are called intervals.
Tone systems in pure tuning consist exclusively of intervals whose frequency ratios are the quotients of small whole numbers, e.g. 3/2 for a fifth.
Pure tuning is based on tuning an instrument using an overtone series. The overtone series is therefore subdivided in order to have 12 semitones per octave. A fifth, for example, has 1.5 times the frequency of the fundamental tone and a third has 1.25 times the frequency of the fundamental tone.

The side effect of this pure tuning: as the frequencies of the individual overtones are dependent on the fundamental, the „same“ note f has a slightly different frequency in an instrument tuned to C than in an instrument tuned to G.
An instrument tuned to C in pure tuning can therefore only be played in C.

Pure tuning is also known as diatonic tuning.

on for the English Bb, B is the German designation for the English Bb.