# Key signature calculation



## conclass (Jan 12, 2013)

I was wondering if anyone has used this site on musical theory before?
http://www.musictheory.net/lessons/25

Has anyone tried to use this calculation method?

I'm trying to find out, through this calculation method only, how many flats or sharps does a D flat Minor has.
Can anyone share some light on this for me?

Thank you!


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## Petwhac (Jun 9, 2010)

Db-Eb-Fb-Gb-Ab-Bbb(double flat)-Cb
Thats 7 flats or 8 if you count the double flat as two.


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## millionrainbows (Jun 23, 2012)

conclass said:


> I was wondering if anyone has used this site on musical theory before?
> http://www.musictheory.net/lessons/25
> 
> Has anyone tried to use this calculation method?
> ...


*There is no key of "D flat minor."* If you tried to spell it, you'd get Db-Eb-Fb-Gb-Ab-*A (or Bbb)*-Db. See the glitch? A diatonic scale must have 7 different letter names, and no double-flats or sharps.

See my blogs, page 3, "Key Signatures."

Here's a relevant excerpt:
-------------------------------------------
A scale must consist of seven different letter-names.

If one starts building fifths from a starting point of C, then going "forward" or clockwise around the "circle of fifths" would yield C-G-D-A-E-B-F#(C#-no need for D#).

If, on the other hand, you go in reverse (counter-clockwise), you travel the "circle of fourths", which yields C-F-Bb-Eb-Ab-Db-Gb (Cb).

As you can see, there are three keys which "overlap" under two different names: B (Cb), F# (Gb), and C# (Db). The reason it goes no further has to do with the physical layout of the keyboard itself (there are two semitone steps in the letter sequence), and the subsequent "letter-naming" of notes which results. *To be a diatonic scale, you must have seven different letter names. *

For example, there is no key of "Fb" because this is E, a sharp key; but if we named it anyway, we would get Fb-Gb-Ab-Bbb (you can't repeat A - there must be seven different letter names with no repeats), Cb-Db-Eb-Fb. This "repeating letter or double-flat" dilemma does not arise on the three "repeat" keys of B (Cb), F# (Gb), and C# (Db), because this is the "seven-letter limit".


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## conclass (Jan 12, 2013)

Thanks, but what calculation do i use to find out that D flat minor has 7 (8) flats? According to that website there's a calculation method that you can use but for some reason it does not work for all key signature.

Thanks anyways!


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## OboeKnight (Jan 25, 2013)

Hm...this is a very interesting method. I'd never thought if it this way (probably because I'm not a math person). To find relative majors from a minor key I just go three notes up the scale in the key I'm in. I like this method though. Thanks for sharing.


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## millionrainbows (Jun 23, 2012)

conclass said:


> Thanks, but what calculation do i use to find out that D flat minor has 7 (8) flats? According to that website there's a calculation method that you can use but for some reason it does not work for all key signature.


The question is flawed. You should call it C# minor, not Db minor.

Db minor does not exist.

If you go up 4 semitones from Db, but correctly call it C#, you get C#-D#-E-F#-G#-A-B-C#. See? Now it works.

E is a sharp key, and its relative minor is C# minor.

There is no key of "Fb major" with a relative minor of "Db minor.":lol:


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## KenOC (Mar 7, 2011)

I confess to being confused about all this. Bach's WTC has preludes and fugues in A-flat major and G-sharp minor (both books) and in E-flat major and D-sharp minor (book 2). What's this all about? Just Bach having some notational jollies?


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## Mahlerian (Nov 27, 2012)

You can notate a piece in D-flat minor temporarily, and you could theoretically write one in that key, but the key signature would require double flats and would elicit a headache from any performer who attempts it. Regardless, there are brief passages in certain works notated "in" D-flat minor (part of the development of Mahler's 4th comes to mind), double flats and all.

It's easy to get the theoretical key signature of some unused (unusable) key. You just add or subtract the correct number of sharps/flats. A# minor has 7 sharps. The major key based in A# would have 10, counting double sharps as 2. C-flat major has 7 flats, so the hypothetical minor key based on C-flat would have 10, with the same rules as before.

Obviously, none of this matters with equal tuning and enharmonic equivalence, but it's kind of an interesting theoretical question.



KenOC said:


> I confess to being confused about all this. Bach's WTC has preludes and fugues in A-flat major and G-sharp minor (both books) and in E-flat major and D-sharp minor (book 2). What's this all about? Just Bach having some notational jollies?


Whichever one is easier for the performer to read is the one that should be used. In this case, G-sharp minor is a bit easier to read than A-flat minor with its 7 flats. D-sharp and E-flat minor have six either way, so it's a bit of a toss-up there.

Edit: I looked up the passage in Mahler's 4th in question, and found it's only partly notated in D-flat. The trumpet is playing a (transposed) D-flat, but when the line moves up an augmented third, it flips around to being notated in sharps instead, and some of the other parts are notated enharmonically as well.


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## violadude (May 2, 2011)

KenOC said:


> I confess to being confused about all this. Bach's WTC has preludes and fugues in A-flat major and G-sharp minor (both books) and in E-flat major and D-sharp minor (book 2). What's this all about? Just Bach having some notational jollies?


In some cases, both enharmonic equivalent key signatures are possible.


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## conclass (Jan 12, 2013)

millionrainbows said:


> A scale must consist of seven different letter-names.
> 
> If one starts building fifths from a starting point of C, then going "forward" or clockwise around the "circle of fifths" would yield C-G-D-A-E-B-F#(C#-no need for D#).
> 
> ...


Thanks for your input, but i'm just starting to learn music theory, and your explanation, to a certain extent, makes sense to me, but then i wonder about how you got those flats and sharps.


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## Mahlerian (Nov 27, 2012)

conclass said:


> Thanks for your input, but i'm just starting to learn music theory, and your explanation, to a certain extent, makes sense to me, but then i wonder about how you got those flats and sharps.


Do you know the circle of fifths? The whole system of keys we use is based on it.

Starting from C, it goes: C, G, D, A, E, B (Cf), F# (Gf), C# (Df), Af (G#), Ef (D#), Bf (A#), F, C

Each one of those, you add one sharp as you move to the right, until you reach C# major, which has 7. Then you could potentially keep going, but the way our tuning works, you can flip around to the flat side, and go to Af major, which has 4 flats, and subtract one flat as you keep moving to the right.

Naturally, the same system goes for minor keys as well.

Edit: I realize now that this is really already covered in Millionrainbows' post, but I think it's best to think of the circle of fifths as one continuous line, rather than backtracking with a circle of fourths as well.


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## Hausmusik (May 13, 2012)

millionrainbows said:


> Db minor does not exist.


millions, I believe I grasped everything in your post, other than this statement. What do you mean by the statement that the key of D-flat minor _does not exist_? (As opposed to, D-flat minor is C# minor in a clumsy and impossibly awkward guise.)


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## millionrainbows (Jun 23, 2012)

Hausmusik said:


> millions, I believe I grasped everything in your post, other than this statement. What do you mean by the statement that the key of D-flat minor _does not exist_? (As opposed to, D-flat minor is C# minor in a clumsy and impossibly awkward guise.)


Perhaps it should be "D-flat minor has been rejected, snubbed, thrown in the trash-heap, because it's a loser, it didn't conform to the system."

Db minor does not exist (has been snubbed), and neither does its dysfunctional "parent" scale Fb, because these have workable counterparts of E major and C# minor, which can be notated within our limits, which are:

A diatonic scale must have 7 different letter names, and no double-sharps or double-flats.

Other keys which don't exist:

D# major, and its relative, B# minor. Try spelling them, and the system fails:

D#-E#-*F##*-G#-A#-B#-*C##*-D#. This one is really Eb major, easily spelled as Eb-F-G-Ab-Bb-C-D-Eb.

Or its relative minor, B# minor: B#-*C##*-D#-E#-*F##*-G#-A#-B#. This has a flat counterpart of C minor, spelled C-D-Eb-F-G-Ab-Bb-C.

To answer KenOC's question:



KenOC said:


> I confess to being confused about all this. Bach's WTC has preludes and fugues in A-flat major and G-sharp minor (both books) and in E-flat major and D-sharp minor (book 2). What's this all about? Just Bach having some notational jollies?


Although Ab and G# are the same physical note on the keyboard, Ab Major and G# minor are related to their own separate major/minor relatives:

Ab Major has F minor (a flat key) as its relative, spelled with the same letters a minor third lower;

...while G# minor is the relative of B major (a sharp key), spelled with the same letters a minor third higher.

Apply this same logic to E-flat major (with C minor) and D-sharp minor (with F# Major).

What may be confusing is that F is physically a white note on the piano, but is a flat key signature, while B is also physically a white note on the piano, but is spelled with sharps.

This has to do with how the keyboard is configured. The key signature system is a product of the keyboard, and that's where this all derives from, as confusing to non-keyboardists as it may be.


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## PetrB (Feb 28, 2012)

KenOC said:


> I confess to being confused about all this. Bach's WTC has preludes and fugues in A-flat major and G-sharp minor (both books) and in E-flat major and D-sharp minor (book 2). What's this all about? Just Bach having some notational jollies?


Those minor keys have 'neat' signatures, their relative majors: G# minor; B major / D# minor; F# major. Those do not require any double accidental within the signature itself.

Later, especially in the mid-late romantic era, temporary modulations do happen, going to a number of those keys with double sharps and flats (Chopin, really all one needs to say there

_There are, as per those keys with double sharps and double flats, no 'theoretical' keys. They exist and are written in._ There are, only because they are cumbersome as the head signature, theoretic key signatures....

So and Buuuut --for the sake of legibility and polite musical grammar, for example -- setting up a piano piece in D# would require double sharps in the signature, the "polite" grammar would be to write it in Eb.

As per the OP: the best way to know how to spell any scale is to know its pattern of whole and half steps, and be certain always to use all seven letters in sequence (no repeats, no jumps). Learn how to build them, you will never forget them. You will then always know which requires an accidental (or a double accidental) and where, and you won't go wrong, ever.


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## KenOC (Mar 7, 2011)

Are the double flats and sharps what people mean when they talk about (for instance) Beethoven occasionally writing in enharmonic keys?


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## millionrainbows (Jun 23, 2012)

Hausmusik said:


> millions, I believe I grasped everything in your post, other than this statement. What do you mean by the statement that the key of D-flat minor _does not exist_? (As opposed to, D-flat minor is C# minor in a clumsy and impossibly awkward guise.)


The key of D-flat minor "does not exist" in the conventional sense. My answer was basic information about key signatures, offered in response to what I thought were basic questions from people who appeared to be novices genuinely asking for answers. It's interesting that your question uncovered some unorthodox exceptions to the norm, and that experts then arrived as if on cue. Anyway, my explanation was intended to clarify things for novices on the subject, and I didn't expect it to be scrutinized for unorthodox exceptions in such critical detail.

There are special cases, such as when modulating from a sharp key at the end of the cycle, such as (C#), into (G#) the next fifth away, and it's logical to add a double-sharp rather than change the key signature to A-flat.

This example can be seen in the WTC Book I, the fugue III in C# Major. On the second page it modulates further into G#, but Bach just writes F-double sharp rather than changing the key signature.

I'd be interested in seeing an example of one of these "theoretical" keys written-out in a key signature. Chopin was mentioned.

:devil::lol::tiphat:


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## PetrB (Feb 28, 2012)

KenOC said:


> Are the double flats and sharps what people mean when they talk about (for instance) Beethoven occasionally writing in enharmonic keys?


Enharmonic is, the different spelling of (theoretically) the same pitch.

"enharmonic
adj. Music
Of, relating to, or involving tones that are identical in pitch but are written differently according to the key in which they occur, as C sharp and D flat, for example."

Yep, that's what composers sometimes do. A piece can be chugging along, and 'that sustained Ab' can be turned into a G# by modulation and harmonic context.

Technically on stringed instruments or in singing, that C# is a titch lower than that Db. On keyboards, there is no control of this slight differential.


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## KenOC (Mar 7, 2011)

Thanks PetrB!


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## conclass (Jan 12, 2013)

PetrB said:


> As per the OP: the best way to know how to spell any scale is to know its pattern of whole and half steps, and be certain always to use all seven letters in sequence (no repeats, no jumps). Learn how to build them, you will never forget them. You will then always know which requires an accidental (or a double accidental) and where, and you won't go wrong, ever.


The pattern being the "formulas"? Major: wwhwwwh , Minor: whwwhww, Harminoc: raise 7 half step, melodic raise 6-7 half step?

the sequence being c d e f g a b?

Thanks!


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## millionrainbows (Jun 23, 2012)

I guess everybody has had their questions answered to their satisfaction. Let me know if you can use me again.


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## Mahlerian (Nov 27, 2012)

millionrainbows said:


> I'd be interested in seeing an example of one of these "theoretical" keys written-out in a key signature. Chopin was mentioned.
> 
> :devil::lol::tiphat:



View attachment 12557


There. Well, you asked...


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## millionrainbows (Jun 23, 2012)

Mahlerian said:


> View attachment 12557
> 
> 
> There. Well, you asked...


No further explanation? I'll step up, old friend.

This looks like it would be F-flat, arrived at by being at the "end of the cycle" (F-Bb-Eb-Ab-Db-Gb-Cb) in the key of Cb.

If in the key of Cb the necessity to modulate to the next key a fourth away should arise, then the composer can use the "theoretical" key of Fb, spelled Fb-Gb-Ab-B-double flat-Cb-Db-Eb-Fb, rather than E, which uses the same pitches spelled in sharps.

This thread has turned out to live up to its starter's name, a real "con-class.":lol:


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## Petwhac (Jun 9, 2010)

millionrainbows said:


> No further explanation? I'll step up, old friend.
> 
> This looks like it would be F-flat, arrived at by being at the "end of the cycle" (F-Bb-Eb-Ab-Db-Gb-Cb) in the key of Cb.
> 
> ...


Fb as the relative major to Db minor which is what I posted a earlier.:tiphat:


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## Petwhac (Jun 9, 2010)

millionrainbows said:


> No further explanation? I'll step up, old friend.
> 
> This looks like it would be F-flat, arrived at by being at the "end of the cycle" (F-Bb-Eb-Ab-Db-Gb-Cb) in the key of Cb.
> 
> ...


Fb as the relative major to Db minor which is what I posted earlier.:tiphat:


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## millionrainbows (Jun 23, 2012)

Petwhac said:


> Fb as the relative major to Db minor which is what I posted earlier.:tiphat:


Gotcha, Petwhac; you were certainly there first. If you see my last post as redundant, I offer it as perhaps clarifying previous information which was not as detailed.

:tiphat:


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## millionrainbows (Jun 23, 2012)

I guess I should have gone to that "key signature calculation site" first, and I would have seen mention of the theoretical keys of G# and Fb. I already have this memorized, and I see this "calculation" method as being rather cumbersome. The only time I'm going to be adding and subtracting is if I'm using set theory to normalize wide intervals.


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