page_title: Kirnberger temperament
section_title: Kirnberger III
hierarchical_section_title: Kirnberger temperament / Kirnberger III
caption_attribution_description: Français&#160;: Tempérament de Kirnberger III Gerard
context_page_description: Kirnberger temperament is an irregular temperament developed in the second half of the 18th century by Johann Kirnberger. Kirnberger was a student of Johann Sebastian Bach, held great admiration for his teacher and was one of his principal proponents.
  The first Kirnberger temperament, "Kirnberger I", had similarities to Pythagorean temperament, which stressed the importance of perfect fifths all throughout the circle of fifths. 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 one tunes C-G, G-D, D-A, A-E, E-B, B-F♯, F♯-C♯, C♯-G♯, A♭-E♭, E♭-B♭, B♭-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, which would be unacceptable. This difference between the initial "c" and final "c" that is derived from performing a series of perfect tunings is generally referred to as the Pythagorean comma. In Kirnberger I, the D-A fifth is reduced by a syntonic comma, making the major thirds F-A, C-E, G-B, and D-F pure, though the fifth based on D is a ratio of 40/27 instead of 3/2.
context_section_description: After some disappointment with his sour, narrow fifths, Kirnberger experimented further and developed another possibility, later named the Kirnberger III. 
  This temperament splits the Syntonic comma between four fifths instead of two. 1/4-comma tempered fifths are used extensively in meantone and are much easier to tune and to listen to. This also eliminates two of the three pure thirds found in Kirnberger II. Therefore, only one third remains pure (between C and E), and there are fewer Pythagorean thirds. A greater middle ground is thus reached in this improvement, and each key is closer to being equal to the next. The drawback is an aesthetic one: fewer chords have pure thirds and fifths. But every temperament system has a give-and-take compromise; each has to find a way of dealing with the comma.
caption: Kirnberger III temperament
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