Traditional Key Scheme Patterns for Works in All 24 Major and Minor Keys

For all formulae, "x" is the order number in the set, and "n" is the pitch-class integer of the tonic.

J.S. Bach: The Well-Tempered Clavier. 48 Preludes and Fugues in 2 Volumes

(If your WTC Book II is numbered 1 - 24 instead of 25 - 48, revert to the formula given for Book I.)

Key Prelude/Fugue No. BWV No.
Book I
C major I 846
C minor II 847
C# major III 848
C# minor IV 849
D major V 850
D minor VI 851
Eb major VII 852
Eb minor VIII 853
E major IX 854
E minor X 855
F major XI 856
F minor XII 857
F# major XIII 858
F# minor XIV 859
G major XV 860
G minor XVI 861
Ab major XVII 862
Ab minor XVIII 863
A major XIX 864
A minor XX 865
Bb major XXI 866
Bb minor XXII 867
B major XXIII 868
B minor XXIV 869
Formula for
major keys 		x = 2n + 1
n = (x - 1)/2 		BWV No. = 2n + 846
n = (BWV - 846)/2
Formula for
minor keys 		x = 2n + 2
n = x/2 - 1 		BWV No. = 2n + 847
n = (BWV - 847)/2
Book II
C major XXV (I) 870
C minor XXVI (II) 871
C# major XXVII (III) 872
C# minor XXVIII (IV) 873
D major XXIX (V) 874
D minor XXX (VI) 875
Eb major XXXI (VI) 876
Eb minor XXXII (VIII) 877
E major XXXIII (IX) 878
E minor XXXIV (X) 879
F major XXXV (XI) 880
F minor XXXVI (XII) 881
F# major XXXVII (XIII)882
F# minor XXXVIII (XIV)883
G major XXXIX (XV) 884
G minor XL (XVI) 885
Ab major XLI (XVII) 886
Ab minor XLII (XVIII) 887
A major XLIII (XIX) 888
A minor XLIV (XX) 889
Bb major XLV (XXI) 890
Bb minor XLVI (XXII) 891
B major XLVII (XXIII)892
B minor XLVIII (XXIV)893
Formula for
major keys 		x = 2n + 25
n = (x - 25)/2
BWV No. = 2n + 870
n = (BWV - 870)/2
Formula for
minor keys 		x = 2n + 26
n = x/2 - 13 		BWV No. = 2n + 871
n = (BWV - 871)/2

Frédéric Chopin: Préludes, Op. 28. 24 Preludes in all Major and Minor Keys

Key Prelude No.
C major 1
A minor 2
G major 3
E minor 4
D major 5
B minor 6
A major 7
F# minor 8
E major 9
C# minor 10
B major 11
G# minor 12
F# major 13
Eb minor 14
Db major 15
Bb minor 16
Ab major 17
F minor 18
Eb major 19
C minor 20
Bb major 21
G minor 22
F major 23
D minor 24
Formula for
major keys 		x = 2((7n) mod 12) + 1
n = 7((x-1)/2) mod 12
Formula for
minor keys 		x = 2(7(n+3) mod 12) + 2
n = (7((x-2)/2) mod 12) - 3

Paul Hindemith: Ludus Tonalis

Key Fugue No.
Praeludium
C 1
Interludium
G 2
Interludium
F 3
Interludium
A 4
Interludium
E 5
Interludium
Eb 6
Interludium
Ab 7
Interludium
D 8
Interludium
Bb 9
Interludium
Db 10
Interludium
B 11
Interludium
F# 12
Postludium
There is no formula for the order of these fugues
The order comes from the system of scale formation introduced in Chapter II § 8-10 of The Craft of Musical Composition, Book I
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