A mixture is a compound organ stop which has several ranks (usually from 3 to 6) of metal pipes. Sometimes it consisted from as few as 2 ranks or as many as 10 or more ranks (for example, on the Hauptwerk in the 17th century Dutch tradition).
Normally it has ranks with repetitions at the octave and the fifth but some mixtures have also an interval of the major third (especially in the middle German Baroque tradition or England).
This stop can have many versions and may be called Mixtur, Mixtura, Rauschpfeife, Cimbel, Cymbal, Cymbel, Gross-Cymbel, Scharf, Furniture, Fourniture, Plein jeu, Plein jeu harmonique, Progressive, Sesquialtera (in England) or something similar.
I guess the mixtures is the relic of from the older late medieval organ which didn't have separate stops and only relied on large principal chorus (with mixture sound). This was called the Blockweck. It could have as many as 50 or more ranks of pipes for one key and multiple bellows.
Because mixtures tend to be quite high-pitched stops, as they ascend through the keyboard range the pipes begin to be too small to handle (and to listen too) and so usually the highest rank drops down one octave lower (sometimes to the closest fifth).
High-pitched mixtures can based on 1 1/3' or 1'. In the lower range, the mixture can have more ranks but fewer in the upper range because the highest rank in the top can drop out when the pipes are too small and the pitch is too harsh.
In Italian tradition the organ lacked mixtures but had principal stops at octave and fifth pitch level going all the way from 8' or 16' to as high as 1/3'. Drawn together (this is called Ripieno) they resemble the traditional Organo Pleno sound with mixtures.
The low mixtures (based on 2' or 2 2/3') are best used together with the 16' stops on the manual because these lower pitches can interfere with the foundation stops and could make the basic notes difficult to distinguish.
Some mixtures on the pedals can be even lower based on 5 1/3'. By the way, the pedals can even lack mixtures but the low fifth sound of 5 1/3' or 6' as written in some cases (combined with 4') will give the impression of the mixture sound. Here I must also add that even the pedals can have high-pitched mixtures in some traditions such as Baroque in the Netherlands.
The low fifth of 5 1/3' used together with other lower stops can also give the impression of the 32' in the pedals. This is an interesting phenomenon.
Traditionally mixture sound is the crowning glory of the organ. But (and this is a big but) they have to be well-voiced and well-tuned. Otherwise many people (not only listeners with hearing aid) will be angry with you for using them (and some will not like them anyway).
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