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Pure tuning
In a pure tuned scale the fundamental frequencies relate to each other as whole numbers  pure tuned intervals are defined by the relationships between the pitches. In an octave interval for example, the octave has twice as high frequency as the fundamental, while the fifth interval is described by the ratio 2:3. Pure tuning is to be considered as an objective term. In our diatonic system (a combination of whole and halftone steps), intervals are calculated by adding and subtracting these ratios. If one achieves pure intervals in one key, the consequence is that harmonies in other keys are "impure." Because of the need to play all keys without having to retune, on a piano, for example, different solutions to this problem have been attempted such as making compromises in tuning by evening out the intervals. Pythagorean tuning is one approach, and equal temperament is another. During the 20th century, equal temperament displaced all other types of tuning, but what one gained through equal temperament was lost in clarity in most intervals. The Norwegian musicologist Eivind Groven (19011977) experienced early on that fiddlers and folk tone singers employed nontempered intervals, and felt that the equal tempered compromise reduced the musical quality. He wished to combine the possibility of playing with pure tuning in all keys with the use of a normal keyboard, and calculated that one could achieve a good pure tuning system by using three pitches per note, in all 36 pitches per octave. He built an automat that chose the right pitches according to a specified key, and the automat also adjusted when the keys changed. Several instruments were connected to the automat, making it possible to play with pure tuning in all keys. In addition, Groven's pure tuned organ could reproduce scales that employed intervals outside of whole and halfnotes, a characteristic of folk music. Musicologist David Code has made a digital version of this automat, and NOTAM has developed a portable pure tuning system that uses a sampler or softsynth in the computer as sound source. The system can be downloaded freely from these web pages, and runs on Max OSXmachines. The next step is tweaking the system to allow it to run on the Windows platform.
