Here is my method and it work 80% of the time but sometimes it didn't work. What do I do wrong?

I know how to do all the major no problem. so:

  1. C = 0
  2. D = 2#
  3. E = 4#
  4. F = 1b
  5. G = 1#
  6. A = 3#
  7. B = 5#

and if there is a lot of flats i will 7-NUMBER of flat = k and if say k = 3 i will know it is Ab Maj.

The question I am doing right now would give me a signature I will count how many sharp/flat are there. And I will adjust accordingly so:

  1. Ionian NO-CHANGE
  2. Dorain +2#
  3. Phrygian +4#
  4. Lydian +1b
  5. Mixolydian +1#
  6. Aeolian +3#
  7. Locrian +5#

and then I just treat it as a major and go from there. so for example Dorian who have 5 flats. I would 5 flats+2 sharps = 3 flats --> 7-3=4 -->Eb Dorian.

then i econunter the fact that there might be possibility where there is lots of sharps and flat and I learned that you can use 12-NUMBER of SHARPS = equivalent number of flats so 8 flat is same as 4 sharps and 8 sharp is also equivalent to 4 flat....

but then I got this question: which Locrian's signature is 7# so i do 7+5=12 and 12-12=0 so i confidently answer C Locrian.

and it is INCORRECT.

the correct answer is B# locrian and if you work backward it make sense.

what step have I done wrong.

  • 2
    C and B# are pitch-equivalent.
    – Aaron
    Commented Mar 6, 2022 at 21:26
  • @Aaron, but would a musician say that signature(7#) is of a C Locrian or a B# Locrian
    – Math Noob
    Commented Mar 6, 2022 at 22:24
  • 1
    The modes are like the “opposite” of the alterations to make a major scale. So the Lydian mode has a #4, not a b4. Mixolydian has a b7, not a #7. And likewise with the other modes. Commented Mar 6, 2022 at 23:15
  • I see. The Locrian scale corresponding to 7 sharps would be B# Locrian. (C Locrian would have 5 flats).
    – Aaron
    Commented Mar 7, 2022 at 0:09
  • 1
    @ToddWilcox Okay, here's what OP is proposing. I have a certain key signature, and I want to know which Lydian scale shares that key signature. I add one flat, figure out the major key that new key signature corresponds to, and the tonic of that major key is the root of the dorian scale I'm trying to find. Example: Key of 1 flat. What Lydian scale is that? Add a flat, so now two flats. That corresponds to Bb major. So Bb Lydian is the Lydian scale with one flat.
    – Aaron
    Commented Mar 7, 2022 at 1:39

3 Answers 3


Your "12-NUMBER of SHARPS" step to calculate the number of flats intrinsically assumes that enharmonic notes are equivalent. Your "...so i confidently answer C Locrian. and it is INCORRECT. the correct answer is B# locrian" shows that you are in a situation where this is not the case, and enharmonic notes are not treated as the same note.

In order to confidently answer which Locrian scale has a key signature of 7 sharps (assuming you don't subscribe to the alternate theory that the key signature should always reflect the tonic and 3rd scale degree combined), you need to extend your sharps table with this:

F♯ = 6♯

C♯ = 7♯

G♯ = 8♯

D♯ = 9♯

A♯ = 10♯

E♯ = 11♯

B♯ = 12♯

You now go 7 sharps (base) + 5 sharps (Locrian) = 12 sharps and get an answer of B♯ Locrian.

Note how you had to memorize theoretical key signatures in order to calculate that answer. (Truth is, I do not memorize any key signatures with more than 7 accidentals because they virtually never appear in published sheet music: I simply extended the letter name pattern of sharp keys even further in order to finish the sharp table extension.)

  • I did sense the flaw in your system in your question that you didn't have F# = 6# memorized at all, which will bite you in the butt later since 6-sharp key signatures and F sharp major are common enough. This hinted to me that you need to memorize all your key signatures with sharps in them...which I just showed you can lead to needing ridiculous amounts of memorization in order to answer all your scale questions confidently with your current system.
    – Dekkadeci
    Commented Mar 7, 2022 at 13:02
  • Key signatures with seven accidentals virtually never appear in printed sheet music, since standard practice calls for the enharmonically equivalent signature with five of the other accidentals instead. Those with more than seven are probably several orders of magnitude rarer. Can you name a professionally engraved piece of music that employs such a key signature? I can't imagine why anyone would write a piece in (any mode of) G sharp major or F flat major.
    – phoog
    Commented Mar 7, 2022 at 13:18
  • @phoog - Yeah, I personally can't, either (for 8 or more accidentals or at least 1 double accidental in the key signature) - the closest I can think of is the first edition of Chopin's Heroic Polonaise I had to study for music history lessons, which notably notates a section in D sharp major but with a 4-sharp key signature.
    – Dekkadeci
    Commented Mar 7, 2022 at 13:46
  • @phoog - Professionally engraved scores in the public domain that use exactly 7 accidentals in the key signature are actually not that rare, though: I can think of the Well-Tempered Klavier C sharp major entries and the C sharp major portion of Debussy's Toccata of Pour le piano off the top of my head, and a quick search reveals that the 3rd movement, a funeral march, of Beethoven's Piano Sonata No. 12 in A Flat Major is notated in A flat minor and uses a 7-flat key signature.
    – Dekkadeci
    Commented Mar 7, 2022 at 13:52
  • 1
    But memorize? Heyll, I can't tell you the order of sharps and flats past 4 without actually thinking them out "Up a 4th, down a 5th, um..." I feel like the question for the OP is "why"; it seems more like "because I want to know" than "for ease of music making." Commented Mar 7, 2022 at 15:30

Seems like sledgehammers and nuts to me!

There are only 7 modes, and 12 major keys that cover 99% of music in major keys.(Minor modes are more complex).

Learn the 7 modes in order - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Locrian.

Learn the circle of 4s/5s, which gives you the number of sharps/flats.

All the modes of any key will contain those same sharps and flats as its Ionian mode.

So, for example, D Ionian, E Dorian, F♯ Phrygian, etc all have the same sharps as each other.

This way may not be exactly mathematical, but it sure works! And probably is just as easy/difficult to administer!

  • The question's "...so i confidently answer C Locrian. and it is INCORRECT. the correct answer is B# locrian" heavily implies that, for the asker's purposes, there are more than 12 major keys and enharmonic notes are not treated as the same note.
    – Dekkadeci
    Commented Mar 7, 2022 at 12:39
  • @Dekkadeci - true, but pretty impractical, unless we just need a maths formula to tell us something pretty impractical. Can't remember ever playing in B# Locrian. Or any other Locrian, happily!
    – Tim
    Commented Mar 7, 2022 at 14:01

Personally, I think of this in terms of major and minor being modes (because they are), and then modify major or minor into the various major family or minor family modes:

Major (ionian)

  • raise the ^4 degree to get lydian
  • lower the ^7 degree to get mixolydian

Minor (aeolian)

  • raise the ^6 degree to get dorian
  • lower the ^2 degree to get phrygian
  • lower the ^2 and ^5 to get locrian

The practical application of that is some thing like this:

  • start with the given tonic (this is the likely scenario, someone says, for example, play in F# dorian)
  • determine the major/minor key signature, dorian is in the minor "family", so get the F# minor key signature, which is three sharps, F# C# G#
  • determine the ^6 degree relative to tonic F#, that will be some kind of D, specifically by the key signature it is a D natural, raise D natural to D#
  • F# dorian's key signature is four sharps F# C# G# D#

Your examples of...

Dorian who have 5 flats


which Locrian's signature is 7#

...seem more like music theory quiz questions, not practical situations. Who says "play in the dorian mode with five flats?"

Nevertheless, the way to answer those questions is still easiest, IMO, by reference to major key signatures first, then the various rotations of the major scale to the diatonic modes.

For example...

  • five flats is Db major, the dorian mode tonic is the ^2 degree of Db major, which is tone Eb, so Eb dorian has five sharps.
  • seven sharps is C# major, the locian mode tonic is the ^7 degree of C# major, which is tone B#, so B# locrian has seven sharps.

One comment on your method. I may be misuderstanding it but, this part...

C = 0
D = 2#
E = 4#

...will tell you how to get the major key signature on those given tonics. C major is zero sharps/flats, D major is two sharps, E major is four sharps, etc.

But, your mistake seems to be here...

Dorain +2#
Phrygian +4#

...moving to relative terms raising two degrees (adding two sharps as you describe it) does not give us the dorian mode, it gives us the major scale on the second scale degree of the starting scale. So, if we were starting on Eb major, for example, F natural is the second scale degree, raising two tones, the Ab and Eb to A natural and E natural, leaving only the B, gives us F major.

If we look at it as Eb major, called Eb ionian, and we want to the dorian scale/key signature on the second scale degree of Eb ionian, there is no change to the scale/key signature. Eb ionian and F dorian are the same collection of tones, just starting on different points. The key signature is three flats, Bb Eb Ab, and the scales are Eb F G Ab Bb C D Eb and merely its rotation F G Ab Bb C D Eb F.

Your second chart would really be...

Ionian transposed up M2 +2#
Ionian transposed up M3 +4#

...you can use 12-NUMBER of SHARPS...

I don't know why you want a system to handle 12 sharps/flats for key signatures. After seven sharps/flats, key signatures become theoretical key signatures. Those are not normally used, and they wouldn't use up to 12 sharps/flats anyway, they would use double-sharps/double-flats, with only 7 total signs in the key signatures.

Nevertheless, 7 sharps is C# major, 5 sharps is B major, basically adding 7 sharps to a key signature will just add a sharp to the tonic, in other words 5 sharps in B major, add 7 more sharps, it becomes B# major, or add 7 sharps to C# major makes it Cx major.

You sort of 'reset' adding sharps at the F, but make them double-sharps and add 5 of them, so Fx Cx Gx Dx Ax then the rest will be plain sharps until you have 7 total changes to the gamut of letters by fifths FCGDAEB, so E# B#, altogether the key signature of "12 sharps" for B# major is Fx Cx Gx Dx Ax E# B#.

Figuring out a theoretical key signature is the onerous part. But, after determining the theoretical key signature, finding the various theoretical modal key signatures is comparatively easy.

What is the locrian key signature using 12 sharps? 12 sharps minus 7 shaprs is 5 sharps, which is B major, so 12 sharps is B# major. The locrian mode starts on the seventh scale degree of B# major, which is Cx, and so Cx locrian has a key signature of 12 sharps.

There is no practical reason to do that.

The main things to understand for all these aspects of key signatures and modes are:

  • sharps and flats get added to key signatures by ascending or descending perfect fifths
  • the modes of any given major key "rotating" up the scale from the tonic are: ionian, dorian, phrygian, lydian, mixolydian, aeolian, locrian

If you become comfortable with those two sequences, it's relatively easy to "find" key signatures.

  • can you explain what M2 and M3 is and why is it that my original second chart is musically incorrect?
    – Math Noob
    Commented Mar 10, 2022 at 22:00
  • 1
    M2 = major second, M3 is major third. Commented Mar 10, 2022 at 22:27
  • @MathNoob In your second chart, first line "Ionian NO-CHANGE" is that meant to represent a C major scale? Commented Mar 10, 2022 at 22:29
  • yes! i try to change everything so we can treat everything like major scale and from there we can identify the signature.(find the base note? some other people suggest that that this is what i am doing?)
    – Math Noob
    Commented Mar 10, 2022 at 22:39
  • OK, so when going to the next line "Dorain +2#" what is the result you intend in terms of scale and key signature? Commented Mar 10, 2022 at 22:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.