Conventions for Spelling Diminished Scales


The symmetrical diminished scale(s) (and diminished 7th chords) is/are regarded as "non-tonal" or "atonal" structures.

One spelling convention for the diminished scales is the "Fraternal Neighbors" system.

Here the neighboring chromatic pairs are each assigned different letter names:


"Fraternal Neighbors"

C hW-diminished scale

| C Db | D# E | F# G | A Bb |
2# / 2b

C# hW-diminished scale

| C# D | E F | G Ab | A# B |
2# / 1b

D hW-diminished scale

| D Eb | F Gb | G# A | B C |
1# / 2b

(NB. the total number of sharps in this system is equal to the total number of flats)


* * *

Another spelling convention for the diminished scale is to regard it as two stacked diminished tetrachords separated by a whole-step (same as the hW-diminished scale: h-W-h-W-h-W-h-W)

Not coincidentally, this results in the EXACT same spellings as the "Fraternal Neighbors" convention above.

As regards guitar fingerings, this system results in one diminished tetrachord per string. They are perfectly regular patterns that are easy to visualize, easy to remember, and easy to finger.

example:

6th string: F Gb G# A (frets 1 2 4 5)
5th string: B C D Eb (frets 2 3 5 6)
4th string: F Gb G# A (frets 3 4 6 7)
3rd string: B C D Eb (frets 4 5 7 8)
2nd string: F Gb G# A (frets 6 7 9 10)
1st string: B C D Eb (frets 7 8 10 11)

Of course there are other fingerings for the diminished scale on guitar, but that is beyond the focus of this article on diminished scale spellings.

Note in the
[diminished tetrachord] W [diminished tetrachord] system illustrated below that the total number of sharps is, once again, equal to the total number of flats.

(NB. All splits occur at either the primary or secondary axes of symmetry)

C hW-diminished scale

[C diminished tetrachord] W [F# diminished tetrachord]
| C Db D# E | F# G A Bb |
2# / 2b

F# hW-diminished scale

[F# diminished tetrachord] W [C diminished tetrachord]
| F# G A Bb | C Db D# E |
2# / 2b

D# hW-diminished scale

[D# diminished tetrachord] W [A diminished tetrachord]
| D# E F# G | A Bb C Db |
2# / 2b

A hW-diminished scale

[A diminished tetrachord] W [D# diminished tetrachord]
| A Bb C Db | D# E F# G |
2# / 2b



C# hW-diminished scale

[C# diminished tetrachord] W [G diminished tetrachord]
| C# D E F | G Ab A# B |
2# / 1b

G hW-diminished scale

[G diminished tetrachord] W [C# diminished tetrachord]
| G Ab A# B | C# D E F |
2# / 1b

E hW-diminished scale

[E diminished tetrachord] W [A# diminished tetrachord]
| E F G Ab | A# B C# D |
2# / 1b

A# hW-diminished scale

[A# diminished tetrachord] W [D diminished tetrachord]
| A# B C# D | E F G Ab |
2# / 1b



D hW-diminished scale

[D diminished tetrachord] W [G# diminished tetrachord]
| D Eb F Gb | G# A B C |
1# / 2b

G# hW-diminished scale

[G# diminished tetrachord] W [D diminished tetrachord]
| G# A B C | D Eb F Gb |
1# / 2b

B hW-diminished scale

[B diminished tetrachord] W [F diminished tetrachord]
| B C D Eb | F Gb G# A |
1# / 2b

F hW-diminished scale

[F diminished tetrachord] W [B diminished tetrachord]
| F Gb G# A | B C D Eb |
1# / 2b


* * *

For pianists, it proves extremely uncomfortable to finger the diminished scale as two stacked diminished tetrachords.

However, a common convention used both for piano fingerings (for those who are fans of Liszt's advanced "Thumb Over" technique) AND for spellings, is to visualize the diminished scale as two stacked minor tetrachords separated by a half-step (this is inconvenient to finger on guitar, although not impossible).

This arrangement of notes is the same as the Wh-diminished scale (W-h-W-h-W-h-W-h).

Both the spelling decisions and the piano fingerings in this system are based on function, so consequently the spelling of accidentals is not as regular as in the more common "Fraternal Neighbors / Stacked Diminished Tetrachords" systems illustrated above.

C Wh-diminished scale
[C minor tetrachord] h [F# minor tetrachord]
| C D Eb F | F# G# A B |
2# / 1b

F# Wh-diminished scale

[F# minor tetrachord] h [C minor tetrachord]
| F# G# A B | C D Eb F |
2# / 1b

Eb Wh-diminished scale

[Eb minor tetrachord] h [A minor tetrachord]
| Eb F Gb Ab | A B C D |
0# / 3b

A Wh-diminished scale

[A minor tetrachord] h [Eb minor tetrachord]
| A B C D | Eb F Gb Ab |
0# / 3b



C# Wh-diminished scale

[C# minor tetrachord] h [G minor tetrachord]
| C# D# E F# | G A Bb C |
3# / 1b

G Wh-diminished scale

[G minor tetrachord] h [C# minor tetrachord]
| G A Bb C | C# D# E F# |
3# / 1b

E Wh-diminished scale

[E minor tetrachord] h [Bb minor tetrachord]
| E F# G A | Bb C Db Eb |
1# / 3b

Bb Wh-diminished scale

[Bb minor tetrachord] h [E minor tetrachord]
| Bb C Db Eb | E F# G A |
1# / 3b


D Wh-diminished scale

[D minor tetrachord] h [G# minor tetrachord]
| D E F G | G# A# B C# |
3# / 0b

G# Wh-diminished scale

[G# minor tetrachord] h [D minor tetrachord]
| G# A# B C# | D E F G |
3# / 0b

F Wh-diminished scale

[F minor tetrachord] h [B minor tetrachord]
| F G Ab Bb | B C# DE |
1# / 2b

B Wh-diminished scale

[B minor tetrachord] h [F minor tetrachord]
| B C# D E | F G Ab Bb |
1# / 2b

Note in the above [minor tetrachord] h [minor tetrachord] system that the total number of sharps is, once again, equal to the total number of flats.




Another possible system for spelling diminished scales is "Identical Neighbors". This contrasts with the "Fraternal Neighbors" system as its chromatic neighbor pairs share the same letter name (except in the cases of B/C and E/F).


"Identical Neighbors"

C hW-diminished scale

| C C# | Eb E | Gb G | A A# |
2# / 2b

Db hW-diminished scale

| Db D | E F | G G# | Bb B |
1# / 2b

D hW-diminished scale

| D D# | F F# | Ab A | B C |
2# / 1b

 

But that's just silly.

However, note in the "Identical Neighbors" system illustrated above that the total number of sharps is, once again, equal to the total number of flats.



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