Origin

Kirnberger temperament is an irregular temperament which was developed in the second half of the eighteenth century by Johann Kirnberger. Kirnberger was a student of Johann Sebastian Bach, and it is rumored that they had many disagreements concerning tuning systems at the time. Eventually, they went their separate ways, and each developed his own temperaments as time passed. In psychology, temperament is the general nature of an individuals personality, such as introversion or extraversion, it derives from the theory of the humours. ... Johann Philipp Kirnberger (1721-1783) was a musician, composer (primarily of fugues), and music theorist. ... Johann Sebastian Bach (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together almost all of the strands of the baroque style and brought it to its ultimate maturity. ...

The first Kirnberger temperament, "Kirnberger I" had similarities to just intonation, which stressed the importance of perfect fifths all throughout the circle of fifths. Unfortunately, a complete circle of perfect fifths is not possible, because when the circle comes to an end at the tone it began, it will have overshot its original pitch. Thus, if we tune C-G, G-D, D-A, A-E, E-B, B-F#, F#-C#, C#-G# (Ab), Ab-Eb, Eb-Bb, Bb-F, F-C... the new "C" will not be the same frequency as the first. The two "C"s will have a discrepancy of about 23 cents (a comma), which would be unacceptable. In music, Just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ... In music theory, the circle of fifths is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... The term comma has various uses; comma is the name used for one of the punctuation symbols: , The term comma is also used in music theory for various small intervals that arise as differences between approximately equal intervals. ...

Practical Temperaments: Kirnberger II

Kirnberger's first method of compensating for and closing the circle of fifths was to split the "wolf" interval known to those who have used meantone temperaments in half between to different fifths. That is, to compensate for the one extra comma, he removed 1/2 a comma from two of the formarly perfect fifths in order to complete the circle. In so doing, he allowed the remaining fifths to stay pure. At the time, however, pure thirds were more valuable than pure fifths (meantone temperament had 8 pure thirds and sacrificed four entire chords in order to achieve this end.) So, Kirnberger allowed for 3 pure thirds, the rest being slightly wide and the worst being three Pythagorean thirds (22 cents wider than pure) on the opposite end of the circle from the pure thirds. To put it graphically: Meantone temperament is a system of musical tuning. ... The Pythagoreans were an Hellenic organization of astronomers, musicians, mathematicians, and philosophers; who believed that all things are, essentially, numeric. ...

 C-----G-----D------A-----E-----B-----F#-----C#-----Ab(G#)-----Eb-----Bb-----F-----C p p -1/2 -1/2 p p p p p p p p |__________pure 3rd______| |__________pure 3rd______| |_______pure 3rd________| |__________Pythag. 3rd_________| |_________Pythag. 3rd___________| |________Pythag. 3rd___________| 

The above table represents Kirnberger II temperament. The first row under the intervals shows either a "p" for pure, or "-1/2" for those which were narrowed to close the circle of fifths (D-A), (A-E). Below these are shown the pure 3rds (between C-E, G-B, D-F#), and Pythagorean (very wide) 3rds (between B-D#, F#-A#(Bb), Db-F.)

Temperament, however, is a give-and-take situation: none is a perfect solution. It must also be remembered that temperament applies only to instruments with fixed pitch: any keyboard instrument, lutes, viols, and so forth. Wind musicians, singers and string players all have a certain degree of flexibility concerning the exact pitch and intonation of what they play and may therefore be free of such restrictive systems. When the two classes of players come together, it's important when evaluating a temperament to look at the tendencies of the instruments vs. those of the temperment. Kirnberger II would only have been applicable to keyboard instruments such as the harpsichord and organ. The perks of this system are its three perfect thirds: certainly pleasing to especially singers and winds at the time and lovely to hear. In fact, after hearing perfect thirds, one is shocked by the wide thirds of modern equal temperament used on all pianos. Also, the temperament uses 10 perfect fifths, which is good news to string players whose strings are tuned in fifths. The drawbacks are, of course, the two narrow "half-wolf" fifths and the three Pythagorean, super-wide thirds. The chords are not unusable but certainly must not be used frequently or in close succession within the course of a piece. The lute is a plucked string instrument with a fretted neck and a deep round back. ... Various Viola da gamba The viol or viola da gamba family of musical instruments is related to the vihuela, rebec, etc. ... Harpsichord in Flemish style; for more info, click the image. ... An organ is the following: In anatomy, an organ is a group of tissues which perform some function. ... Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...

Kirnberger III

After some disappointment with his sour, narrow fifths, Kirnberger experimented further and developed another possibility, Kirnberger III. Remember, of course, that these names were not used at the time and are of modern invention.