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The distinctions between D-sharp and E-flat only make sense in the context of a key. For instance, you construct a major key in E-flat and not D-sharp for the

The distinctions between D-sharp and E-flat only make sense in the context of a key. For instance, you construct a major key in E-flat and not D-sharp for the practical need to represent the scale nicely on the staff - so each tone in the scale should have a unique place in the staff. You can construct the E-flat major scale with just three flat tones (Eb F G Ab Bb C D), whereas you would need four sharp and two double-sharp(!) tones if you started with D# (D# E# F## G# A# B# C##). And having to use F## and C## to refer to G and D tones is just ugly. (I had made a mistake in the earlier version of this comment.)

tuukkah 4y ago
> Also, having to call the G tone F# is just ugly. I presume you mean having to call the F tone E#.
- alex_smart 4y ago
  Sorry, I had made a mistake. Wanting to create a major key starting with D# would end up looking like D# E# F## G# A# B# C##. The ugliness is even more stark. - two double sharp keys - F## to refer to G, C## to refer to D, B# to refer to C Yikes.
  - klodolph 4y ago
    D# would be extremely rare. I’ve only ever seen G#, and that was a temporary modulation within something larger. Most people write “x” for double-sharp, instead of ##, in order to match how it looks on a score.
klodolph 4y ago
Sometimes you call a G as F double-sharp. I don’t think of it as ugly. It’s just what happens sometimes. Like if you start in G# minor and then use the leading tone. It’s way better to see F-double sharp than to see two different Gs fighting each other on the page. And it’s even worse to have to decipher those awful chromatic systems that are all painful to read.
- alex_smart 4y ago
  That came out different than I had intended. Of course people use double-sharp keys. And like you said, it is usually done in cases where it is the simpler notation to describe what is happening musically. Simplicity is beautiful and construction of the major key in E-flat is decidedly simpler than in D-sharp.
- josteink 4y ago
  > Like if you start in G# minor Technically speaking that’s a Ab minor. New minor scales are constructed by modifying the A-minor scale (which contains the same flat notes as C-major) by adding Bs, not adding #’s. Adding #’s are used for deriving new major scales. At least that’s how I understand it. You can see this on the Wikipedia article on various minor[1] and major scales[2]. [1] https://en.wikipedia.org/wiki/F_minor https://en.wikipedia.org/wiki/F_minor [2] https://en.wikipedia.org/wiki/D_major https://en.wikipedia.org/wiki/D_major
  - moefh 4y ago
    > New minor scales are constructed by modifying the A-minor scale (which contains the same flat notes as C-major) by adding Bs, not adding #’s. I think you're confusing two different ways of constructing the minor scales. One way is to start with the A minor scale (which has no sharps or flats) and to go around the circle of fifths[1] adding sharps or flats. Whether you add sharps or flats depends on whether you're going clockwise or counter-clockwise: for example, D minor[2] (one step from A minor going counter-clockwise) has one flat, and E minor[3] (one step from A minor going clockwise) has one sharp. Another way to construct a minor scale is to start with its parallel major[4] and add a flat to the 3rd, 6th, and 7th. But note that the result can still have sharps (like in the E example above, where E major has 4 sharps). In any case, G# minor is definitely a key that is used[5]. [1] https://en.wikipedia.org/wiki/Circle_of_fifths https://en.wikipedia.org/wiki/Circle_of_fifths [2] https://en.wikipedia.org/wiki/D_minor https://en.wikipedia.org/wiki/D_minor [3] https://en.wikipedia.org/wiki/E_minor https://en.wikipedia.org/wiki/E_minor [4] https://en.wikipedia.org/wiki/Parallel_key https://en.wikipedia.org/wiki/Parallel_key [5] https://en.wikipedia.org/wiki/G-sharp_minor https://en.wikipedia.org/wiki/G-sharp_minor
  - 4y ago
d23 4y ago
I get the inclination to make comments like this without reading, but the article goes into far more depth than this.
wumpus 4y ago
About 80% of the article is devoted to explaining why your comment is missing the point.
OscarCunningham 4y ago
If you go outside of the diatonic scales it can get even worse. For example E, F♭, G♭♭, A♭♭♭, B♭♭♭♭, C♭♭♭♭, D♭♭♭♭♭.
InCityDreams 4y ago
Rule of thirds...for chord construction. 1 3 5 7 9 11 13 C e g b d f a - Cmaj13 Easy to explain to a beginner. C e g b db f a - Cmaj13b9 C db g b d f a - confusion (for beginners) as that would not have a third....'d' is the 2nd letter alphabetically. Any key sig can be represented... Ie 'E' has to be followed by a g 'of some kind', so even e# can be followed by a gb g or g# to construct a chord. Easy to see on a guitar, especialky with multiple positions to sound the same note. e g b d f a c e g b d f a c e....rotates forever, whatever the starting note.
tzs 4y ago
If we keep the constraint that each letter has to be used exactly once when naming the notes of a major scale, but drop the constraint that the tonic has to be named using the same letter as the scale name (e.g., we can write G major starting at F##) then that pattern of sharps and flats generalizes nicely. Number the 12 tones of 12-TET starting with C=0, C#/Db=1, ..., B=11. Then if you write a major scale starting at note N, the sum of all the accidentals counting sharps as +1 and flats as -1 will be equal to 7N mod 12. For example G is note 7. G major then should have an accidental sum of 7 x 7 = 1 mod 12. We get that writing it G A B C D E F#. But it could also be written with a sum of 13, as F## G## A## B# C## D## E##, or with a sum of -11 as Abb Bbb Cb Dbb Ebb Fb Gb. Note that because 7 x 7 = 1 mod 12, if we have to answer the question what scale N would have an accidental sum of K mod 12, we can solve 7N = K mod 12 by multiplying both sides by 7, giving N = 7K mod 12. E.g., what major scale as 3 flats? 7 x -3 = -21 = 3 mod 12, which gives us the major scale starting at Eb. Personally I find this approach a lot easier than memorizing the circle of 5ths to find key signatures given the key or to find the key given the signature. A couple of questions naturally arise at this point. Why 7N? Why mod 12. The 12 part is easy to guess--it is because we are picking our major scale out of an underlying 12 tone scale. The major scale has 7 notes out of those underlying 12 notes, so a reasonable guess is that is where the 7 comes from. But if you think about starting with C major (all white keys) and going up half a step, because the white keys are 0 2 4 5 7 9 11 12 (I've included the octave at 12 to make things clearer), and two of those (4 and 11) are white keys that do not have a black key immediately to the right, it might seem that how many accidentals get added or removed each time you go up in key half a step is going to vary a lot. Going from C to C#, every position goes black except those two. Those two will go black when you go C# to D, and all the ones on black will go to white. The way the white and black keys are distributed gives you some different regions of the keyboard, each of which has a distinct pattern of adding and removing accidentals as you step through, and the overall pattern of accidentals is a result of those different patterns interacting. So maybe the 7 depends on those regions, and would be different if you had a 7 tone major scale chosen from 12 underlying tones but did not have the same pattern of white/black that we have. I spent a while trying to show that the patterns would interact in such a way as to make 7N mod 12 work, but utterly failed. To check that out we can try imagining alien music. Maybe some aliens who also use a 12-TET underlying scale and also have a 7 tone major scale have picked 0 2 3 4 7 9 10 as their major scale. Quite a different pattern. However, it turns out that 7N mod 12 works for that too. It also works even with alien music whose major scale is 0 1 2 3 4 5 6. You can have to use a crazy number of sharps or flats in that system! What the pattern of white/black keys affects is which notes get accidentals when, not the total number of accidentals. By having the white and black keys spread out about as evenly as you can for a 7 white/5 black system we can write every key using the "right" starting note without needing any note to have more than one sharp or flat. Less even distributions of the black keys make it so you need multiple sharps and flats on some notes, but don't change the total number of accidentals mod 12. Once you realize it really doesn't have anything to do with the pattern of black/white but only on the number of white keys, it is then not too hard to prove that it does indeed only depend on the number. This can be further generalized. If aliens used a 5 note major scale, then the accidental sum of key N would be 5N mod 12. Since 5x5 = 1 mod 12, they could also go the other way and find the key from the accidental count K via 5K mod 12. In general for a M note major scale from a T tone underlying scale, transposing that scale to note N uses NM mod T accidentals.

tuukkah 4y ago

> Also, having to call the G tone F# is just ugly. I presume you mean having to call the F tone E#.

alex_smart 4y ago
Sorry, I had made a mistake. Wanting to create a major key starting with D# would end up looking like D# E# F## G# A# B# C##. The ugliness is even more stark. - two double sharp keys - F## to refer to G, C## to refer to D, B# to refer to C Yikes.
- klodolph 4y ago
  D# would be extremely rare. I’ve only ever seen G#, and that was a temporary modulation within something larger. Most people write “x” for double-sharp, instead of ##, in order to match how it looks on a score.

klodolph 4y ago

Sometimes you call a G as F double-sharp. I don’t think of it as ugly. It’s just what happens sometimes. Like if you start in G# minor and then use the leading tone. It’s way better to see F-double sharp than to see two different Gs fighting each other on the page. And it’s even worse to have to decipher those awful chromatic systems that are all painful to read.

alex_smart 4y ago
That came out different than I had intended. Of course people use double-sharp keys. And like you said, it is usually done in cases where it is the simpler notation to describe what is happening musically. Simplicity is beautiful and construction of the major key in E-flat is decidedly simpler than in D-sharp.
josteink 4y ago
> Like if you start in G# minor Technically speaking that’s a Ab minor. New minor scales are constructed by modifying the A-minor scale (which contains the same flat notes as C-major) by adding Bs, not adding #’s. Adding #’s are used for deriving new major scales. At least that’s how I understand it. You can see this on the Wikipedia article on various minor[1] and major scales[2]. [1] https://en.wikipedia.org/wiki/F_minor https://en.wikipedia.org/wiki/F_minor [2] https://en.wikipedia.org/wiki/D_major https://en.wikipedia.org/wiki/D_major
- moefh 4y ago
  > New minor scales are constructed by modifying the A-minor scale (which contains the same flat notes as C-major) by adding Bs, not adding #’s. I think you're confusing two different ways of constructing the minor scales. One way is to start with the A minor scale (which has no sharps or flats) and to go around the circle of fifths[1] adding sharps or flats. Whether you add sharps or flats depends on whether you're going clockwise or counter-clockwise: for example, D minor[2] (one step from A minor going counter-clockwise) has one flat, and E minor[3] (one step from A minor going clockwise) has one sharp. Another way to construct a minor scale is to start with its parallel major[4] and add a flat to the 3rd, 6th, and 7th. But note that the result can still have sharps (like in the E example above, where E major has 4 sharps). In any case, G# minor is definitely a key that is used[5]. [1] https://en.wikipedia.org/wiki/Circle_of_fifths https://en.wikipedia.org/wiki/Circle_of_fifths [2] https://en.wikipedia.org/wiki/D_minor https://en.wikipedia.org/wiki/D_minor [3] https://en.wikipedia.org/wiki/E_minor https://en.wikipedia.org/wiki/E_minor [4] https://en.wikipedia.org/wiki/Parallel_key https://en.wikipedia.org/wiki/Parallel_key [5] https://en.wikipedia.org/wiki/G-sharp_minor https://en.wikipedia.org/wiki/G-sharp_minor
- 4y ago

d23 4y ago

I get the inclination to make comments like this without reading, but the article goes into far more depth than this.

wumpus 4y ago

About 80% of the article is devoted to explaining why your comment is missing the point.

OscarCunningham 4y ago

If you go outside of the diatonic scales it can get even worse. For example E, F♭, G♭♭, A♭♭♭, B♭♭♭♭, C♭♭♭♭, D♭♭♭♭♭.

InCityDreams 4y ago

Rule of thirds...for chord construction. 1 3 5 7 9 11 13 C e g b d f a - Cmaj13 Easy to explain to a beginner. C e g b db f a - Cmaj13b9 C db g b d f a - confusion (for beginners) as that would not have a third....'d' is the 2nd letter alphabetically. Any key sig can be represented... Ie 'E' has to be followed by a g 'of some kind', so even e# can be followed by a gb g or g# to construct a chord. Easy to see on a guitar, especialky with multiple positions to sound the same note. e g b d f a c e g b d f a c e....rotates forever, whatever the starting note.

tzs 4y ago

If we keep the constraint that each letter has to be used exactly once when naming the notes of a major scale, but drop the constraint that the tonic has to be named using the same letter as the scale name (e.g., we can write G major starting at F##) then that pattern of sharps and flats generalizes nicely. Number the 12 tones of 12-TET starting with C=0, C#/Db=1, ..., B=11. Then if you write a major scale starting at note N, the sum of all the accidentals counting sharps as +1 and flats as -1 will be equal to 7N mod 12. For example G is note 7. G major then should have an accidental sum of 7 x 7 = 1 mod 12. We get that writing it G A B C D E F#. But it could also be written with a sum of 13, as F## G## A## B# C## D## E##, or with a sum of -11 as Abb Bbb Cb Dbb Ebb Fb Gb. Note that because 7 x 7 = 1 mod 12, if we have to answer the question what scale N would have an accidental sum of K mod 12, we can solve 7N = K mod 12 by multiplying both sides by 7, giving N = 7K mod 12. E.g., what major scale as 3 flats? 7 x -3 = -21 = 3 mod 12, which gives us the major scale starting at Eb. Personally I find this approach a lot easier than memorizing the circle of 5ths to find key signatures given the key or to find the key given the signature. A couple of questions naturally arise at this point. Why 7N? Why mod 12. The 12 part is easy to guess--it is because we are picking our major scale out of an underlying 12 tone scale. The major scale has 7 notes out of those underlying 12 notes, so a reasonable guess is that is where the 7 comes from. But if you think about starting with C major (all white keys) and going up half a step, because the white keys are 0 2 4 5 7 9 11 12 (I've included the octave at 12 to make things clearer), and two of those (4 and 11) are white keys that do not have a black key immediately to the right, it might seem that how many accidentals get added or removed each time you go up in key half a step is going to vary a lot. Going from C to C#, every position goes black except those two. Those two will go black when you go C# to D, and all the ones on black will go to white. The way the white and black keys are distributed gives you some different regions of the keyboard, each of which has a distinct pattern of adding and removing accidentals as you step through, and the overall pattern of accidentals is a result of those different patterns interacting. So maybe the 7 depends on those regions, and would be different if you had a 7 tone major scale chosen from 12 underlying tones but did not have the same pattern of white/black that we have. I spent a while trying to show that the patterns would interact in such a way as to make 7N mod 12 work, but utterly failed. To check that out we can try imagining alien music. Maybe some aliens who also use a 12-TET underlying scale and also have a 7 tone major scale have picked 0 2 3 4 7 9 10 as their major scale. Quite a different pattern. However, it turns out that 7N mod 12 works for that too. It also works even with alien music whose major scale is 0 1 2 3 4 5 6. You can have to use a crazy number of sharps or flats in that system! What the pattern of white/black keys affects is which notes get accidentals when, not the total number of accidentals. By having the white and black keys spread out about as evenly as you can for a 7 white/5 black system we can write every key using the "right" starting note without needing any note to have more than one sharp or flat. Less even distributions of the black keys make it so you need multiple sharps and flats on some notes, but don't change the total number of accidentals mod 12. Once you realize it really doesn't have anything to do with the pattern of black/white but only on the number of white keys, it is then not too hard to prove that it does indeed only depend on the number. This can be further generalized. If aliens used a 5 note major scale, then the accidental sum of key N would be 5N mod 12. Since 5x5 = 1 mod 12, they could also go the other way and find the key from the accidental count K via 5K mod 12. In general for a M note major scale from a T tone underlying scale, transposing that scale to note N uses NM mod T accidentals.