F8 in Kirnberger III
In Kirnberger III, F8 is tuned to 5632.012 Hz (+13.69 cents from equal temperament). The surrounding chromatic notes at octave 8 are tuned according to a circulating temperament concentrating comma adjustments on one highly narrowed fifth (D-A) and one slightly adjusted fifth, keeping most other fifths pure.
This system was used for Classical-era German keyboard music and Fortepiano performance.
Chromatic Scale at Octave 8 in Kirnberger III
The table below shows all 12 chromatic notes at octave 8 in Kirnberger III. Frequencies use A=440 Hz as the concert pitch reference.
| Note | Equal Temp (Hz) | Kirnberger III (Hz) | Deviation (cents) |
|---|---|---|---|
| C8 | 4186.009 | 4210.891 | +10.26 |
| Db8 | 4434.922 | 4436.178 | +0.49 |
| D8 | 4698.636 | 4707.927 | +3.42 |
| Eb8 | 4978.032 | 5017.552 | +13.69 |
| E8 | 5274.041 | 5263.632 | -3.42 |
| F8 | 5587.652 | 5632.012 | +13.69 |
| Gb8 | 5919.911 | 5923.263 | +0.98 |
| G8 | 6271.927 | 6296.792 | +6.85 |
| Ab8 | 6644.875 | 6659.900 | +3.91 |
| A8 | 7040.000 | 7040.000 | 0.00 |
| Bb8 | 7458.620 | 7502.954 | +10.26 |
| B8 | 7902.133 | 7886.538 | -3.42 |
Positive cents = sharper than equal temperament. Negative = flatter. 100 cents = 1 semitone.
Kirnberger III: Mathematical Formula
Kirnberger III concentrates its comma adjustments on just two fifths: D-A is narrowed by a full syntonic comma (21.51 cents), making it substantially narrow at 680.45 cents, while E-B is narrowed by one Pythagorean comma minus one syntonic comma. The other ten fifths are pure 3:2 intervals. This creates a system where C, G, F, and Bb major are extremely well-tuned (with nearly pure major thirds close to 5:4), while D, A, and E major still function but have less pure thirds. Kirnberger III is unusual in concentrating the full comma distortion on a single fifth (D-A), making it a least-equal circulating temperament.
Formula type: Cent offsets from equal temperament
How Kirnberger III Sounds
Kirnberger III has a distinctive warmth in the keys of C, F, G, and Bb major, which feature beautifully pure major thirds almost indistinguishable from just intonation. These keys have a lush, singing quality that rewards slow harmonic progressions. The D-A fifth — the most compressed in the system — creates a notably narrow interval that gives the D major and related keys a slightly tense, metallic quality when this fifth appears melodically. Key contrast in Kirnberger III is concentrated around this single narrow fifth, creating an asymmetric pattern of key colors. Johann Philipp Kirnberger promoted this temperament as the one most consistent with the natural harmonic series.
Historical Context
Johann Philipp Kirnberger, a student of Johann Sebastian Bach, introduced this temperament in his 1779 treatise Die Kunst des reinen Satzes (The Art of Strict Musical Composition). Kirnberger argued that his system was the most consonant circulating temperament and claimed it was consistent with Bach's own tuning preferences. This claim has been disputed by scholars, particularly those who favor the Bach-Lehman reconstruction. Kirnberger III found adoption among German keyboard players in the late 18th century and into the early 19th century, particularly for fortepianos. The system is valued today for its unusually pure near-key major thirds.
Other Tuning Systems for F8
For a full deep dive into Kirnberger III, see the Tunable guide to Kirnberger III.
Tune in Kirnberger III with precision — Get Tunable.
Tunable supports 15+ historical tuning systems. Switch between equal temperament, Pythagorean, just intonation, and well temperaments in real time as you play.
