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C# major versus Db major


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I am learning the major scales. To help me I thought I would write out every note in every major scale as a reference. Then I hit a bit of confusion. Why for example are C# and Db defined as different scales when they contain exactly the same notes? Further why are these same notes named differently?

C# major contains the notes;

C# - D# - E# - F# - G# - A# - B#

Db major contains the notes;

Db - Eb - F - Gb - Ab - Bb - C

 

I am guessing it is a convention to only name sharps in a sharp scale and flats in a flat scale.

 

Using Wikipedia again I thought it would follow that the same situation would exist when comparing A# major and Bb major. However Wikipedia has no listing for A# major, it says "see Bb major". This seems to be at odds with the C# major versus Db major situation where the two enharmonic scales are detailed as separate entities and represented differently graphically.

 

So in summary it seems to me at the moment that A# major and Bb major are exactly the same both in terms of the notes played and the way they are presented graphically while C# major and Db major consist of the same notes BUT are presented differently graphically. In fact maybe the A# major scale does not even exist in music theory??

 

The major scales starting on the natural notes seem straight forward, every note in these scales that is not a natural note is denoted as a sharp. However the scales starting on sharp or flat notes are confusing me.

 

This goes pretty deep into music theory, which I am trying to teach myself after 25 years of playing. I have seen hints at the reason but another explanation would help if you have time. I have probably made many mistakes in my little spiel, please correct me where appropriate. Thanks.

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Read through the Beginners to Advance Series at my site: http://lessons.mikedodge.com It'll help you catch up on your theory in an organized fashion. It's free too! It'll help you grasp some of the following info too.

 

Now, in regards to your post.

 

You're talking about Keys, not so much scales. Sounds conflicting, the whole # and b thing relates to Key. Keys have either all #'s or all b's...but each Key contain ONLY ONE occurance of each note name, IOW it only contains each note name ONCE.

 

There's a simple way to know the note names are how the sharps and flats are laid out. It's simple but let me see if I can explain it simply ;)

 

First realize that you will only have one note name in each scale, IOW...you won't find a Bb and a B in a Key/scale. It would either be A# and B, or Bb and Cb.

 

Here's how YOU should decipher it...

 

always start by writing down the notes, starting from your root, IN ORDER through the first octave. Say we want to learn the notes of the A Major scale. First write the Cycle of Notes starting on A trough the first octave...

 

A B C D E F G A

 

Now use the WWHWWWH Interval formula for the Major scale..

 

A is A,

a whole step from A is B...so B is B,

a whole step from B is...C#

a half step from C# is D

a whole step from D is E

a whole step from E is F#

a whole step from F# is G#

a half step from G# is A

 

So, you have A B C# D E F# G# A

 

So by starting with the note names/cycle written out, you just add the sharps (of flats if needed) and you end up with one of every note and the correct enharmonic name for it...so you don't mix sharps and flats, and you don't double the letters.

 

Look at F Major...

 

1. F G A B C D E F cycle using each note in one octave

2. WWHWWWH Interval formula

 

F is F

a whole step from F is G

a whole step from G is A

a half step from A is Bb

a whole step from Bb is C

a whole step from C is D

a whole step from D is E

a half step from E is F

 

You would use Bb not A#. Because you DON'T want A AND A# in your scale.

 

So write the notes out, let them determine the closest note name, then fill in the sharps and flats as you go through the cycle of notes.

 

This will also keep you in line with your Key Signatures stated in the Cycles of Fifths.

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I have done a little more research and my confusion deepens. I found this. Under the heading "The twelve major scales", it lists 15 major scales contained in three groups??? It says;

 

by convention the major scales are divided into three groups:

 

the 'sharp' keys G major, D major, A major, E major, B major, F sharp major, C sharp major

 

the 'natural' key C major - which uses only the white keys

 

the 'flat' keys F major, B flat major, E flat major, A flat major, D flat major, G flat major, C flat major

 

So Cb major and B major are discrete keys (but they are enharmonic, aren't they?) F# major and Gb major are discrete keys but the keys of A# major and G# major don't exist. To the total noob it seems like there are a few inconsistencies here. Further the key of Cb major exists but neither the keys E# major nor Fb major exist. There must be a consistent underlying logical rule set to this that I am not yet privvy to. I can't see a logical pattern at the moment.

 

NOTE - This was posted before I read you reply gennation. Thanks, I am studying it now.

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Thanks, I think I can work out the notes in the major keys now. However the rules that govern whether or nor a particluar key actually exists and how to name the keys elude me.

 

The Cycle of 5th is the end all list of Keys and what makes them the Key.

 

co5.gif

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Thanks, I think I can work out the notes in the major keys now. However the rules that govern whether or nor a particluar key actually exists and how to name the keys elude me.

 

 

You are going to drive yourself nuts if you let yourself believe you need the basics to make logical sense before you'll let yourself commit to learning them. The best approach is to just follow the rules for a while - whether they make sense or not. Once you've worked with scales for a week or so (not very long at all) you'll start to see the logic behind the system.

 

Follow Genn's advise:

1) Each note name is used in each major scale once and only once.

2) Apply sharps or flats (but not both) as needed to follow the

W W H W W W H interval formula from note to note.

 

That's it. Those are the only rules - only Two rules. It's pretty easy to follow. Understanding why it's this way is more complicated to explain. And since you haven't yet developed the frame of reference to understand keys, scale degrees, note and chord function - there's no way to explain why the major scales are constructed this way.

 

But it has been this way for hundreds of years - and it does have it's own logic. You will see with time, it makes perfect sense once you understand it's purpose. But you cannot understand it's purpose until you know it. LOL it's a bit of a "catch 22". When the student is ready the teacher appears.

 

cheers,

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If I give it a shot it would go like this !

You are correct in wondering why there are some the same and some the not same :)

If you begin to read more sheet music you might run across a player that notes all of his Staff's with C# while another player does it with Dflat. Mainly it has to do with feel. The key of C# when played for the purpose of C# sounds different then Dflat. Figure that out... hard to do. Use your ears and you will tell a difference.

You can find flaws in ANY human invention specially when it's written like a language.

To answer your question, I can't really. You are right that C# and Dflat exist and you are also right that G# doesnt really exist. Should you try and wrap your head around why. Probably not haha

I find C# is used when a guitar player for example is tuned down a half step and wants to make a lively song. So they play in the key of C, but as far as script is concerned they write it C# and the note that the guitar is de-tuned.

If a player is in standard tuning and wants a dulled key they use Dflat. Same thing, different effects... yup :)

I've never on the other hand seen C flat or anything like that. That seems stupid to me.

What are you trying to learn ?

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I think it just comes to be accepted conventions as to why everyone thinks in terms of Bb instead of A#.

 

 

It's a common convention born of the desire for simplicity.

Bb = Bb C D Eb F G A Bb - 2 flats, the rest are natural notes.

A# = A# B# C## D# E# F## G## - 10 sharps

 

which would you rather deal with - 2 flats or 10 sharps?

 

 

You know...most people think "F", not E#.... or "C" and not B#. Its just less confusing so those note names, and the scales that contain them, are avoided.

 

 

E# is available in only two of the 15 common keys - F# major / D# minor (6 sharps) and C# major / A# minor (7 sharps). On the other hand F natural is diatonic to seven of the 15 major scales and their relative minors - C, F, Bb, Eb, Ab, Df & Gb

 

B# is available in only one of the 15 common keys - C# major / A# minor (7 sharps). On the other hand C is diatonic to seven of the 15 major scales and their relative minors - G, C, F, Bb, Eb, Ab, & Db.

 

There are many reason why people would prefer think in terms of Gb major (6 flats) than F# major (6 sharps), or Db major (5 flats) rather than C# major (7 sharps).

 

In part is has to do with the transposition of woodwind parts (Bb & Eb)

In part is has to do with minimizing the number of sharps of flats for ease of reading and playing. (part of the above)

In part is has to do with the relative minor:

 

On some level to play the minor keys using the Harmonic and Melodic Minors, we may want to think of the minor key relative to it's parallel major. In the case of F# major the relative minor is D# - it's parallel - D# major has 9 sharps! While for Gb major the relative minor is Eb minor - it's parallel Eb major has only 3 flats.

 

There are lots more examples, . but you get the idea.

 

cheers,

 

Jed

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Thanks for all the help. I don't expect to learn this in a day. However every response I get adds a piece to the puzzle. At the moment I don't really know what I want to learn. I just know that I want to expand my playing style and that I have a lot to learn. I am finding it very interesting and exciting, not frustrating at all. I am just throwing questions out as they come to mind. Sorry if this is becoming tedious, I will give you all a break from me for a while as I now have enough to contemplate for a while. I was the kid who asked a thousand questions in school. Some teachers loved it and others thought I was a serial pest. I firmly believe that there is no such thing as a silly question. Even when you are told your question makes no sense you learn something. I really appreciate ALL the input. I'll be back.

 

How do you eat an elephant? One bite at a time. I have chomped wildly for a few days in order to get some bearings. I am now just starting to settle into a rhythm (no pun intended).

 

I first started learning guitar with my brother when I was about 6 years old. The teacher was a pro musician and we soon drove him nuts. "Ma'am those boys of yours are too much for me!". Our second attempt at learning was when I was about 12 years old. We got a groovin' young teacher that let us run free. We were too busy belting out AC/DC and Led Zep riffs on our guitar teacher's various hot guitars and amps to contemplate his attempts to teach us music theory. Now I realize I should have listened to the guy! However he let us feral boys off the leash and as a result we kept playing and loved every minute of it, which was the main thing. Now that I am an old fogey I want more!

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Ok. Here's more. All these enharmonics are only redundant in contexts like keyboards and theory text books. To a choir in Vienna, C# major would be sung brighter or sharper than Db major which would be sung flatter or darker. This of course relative to each other.

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Ok. Here's more. All these enharmonics are only redundant in contexts like keyboards and theory text books. To a choir in Vienna, C# major would be sung brighter or sharper than Db major which would be sung flatter or darker. This of course relative to each other.

 

 

Is this true? I always thought it was two ways to describe the exact same thing. You know...6 or a half dozen. Why would the notes sound differently? Would they not be the same frequency?

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Is this true? I always thought it was two ways to describe the exact same thing. You know...6 or a half dozen. Why would the notes sound differently? Would they not be the same frequency?

 

 

Not necessarily. Our various temperaments just 'funnel' notes into identical frequencies as others.

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Is this true? I always thought it was two ways to describe the exact same thing. You know...6 or a half dozen. Why would the notes sound differently? Would they not be the same frequency?

 

 

Yes true. A rough example with arbitrary numbers:

A - 440 hz

Bbb - 435 hz

G## - 444 hz

======================

 

Today's fixed chromatic scale is called Equal Temperament. The actual overtone series doesn't even line up from octave to octave. The frequencies are mathematically perfect but the ear thinks everything gets flatter as the pitches get higher. Even within a single major key it's not uncommon to hear a chamber group play notes as much as a quarter tone off anything you'd consider 'in tune'.

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Is this true? I always thought it was two ways to describe the exact same thing. You know...6 or a half dozen. Why would the notes sound differently? Would they not be the same frequency?

 

 

It has to do with what degree of the scale they are, but even then, there are inconsistencies with that idea (one some chords, you won't flatten/sharpen a note, but on others, in the same key, you will). The basic reasoning is that the equal temperament system we use today makes all 12 notes in music slightly out of tune (since you can't evenly divide an octave into 12 parts otherwise). Some notes suffer more than others. For example, the interval of a major third is very sharp, and is often contracted to sound better. In the key of C# major, the E# forms a major third above C#, and in the context of a C# major chord, that note is often lowered by instruments that can lower the note. The same would apply between F# and A#, and between G# and B# in the scale. However, in the key of C major, F natural (enharmonically E#) is a perfect fourth above C, so the intonation problem isn't an issue (fourths and fifths are both very in-tune intervals in the equal temperament system).

 

However, our ears have become quite accustomed to the out-of-tune sound of these intervals in equal temperament, especially since two of the most commonly used instruments, guitar and piano, are both fixed and can't make these adjustments. For practical purposes, you can consider this tunning issue to be a minor bit of trivia info, and not an essential piece of knowledge when you're first learning your major scales. This is why I dislike it when people mention this in the topic of enharmonics, because it can be a confusing subject as it is, and to throw in such an obtuse topic as temperament compensation seems like a bit of needless complication.

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It makes me realize how massive this field is. Being from a scientific background I kind of wish everything was expressed in Hertz!

 

EDIT - gennation, the fretboard warrior is addictive and useful! Does the full version cover up to the 22/24th fret? Does the full version have scales in it?

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Yes true. A rough example with arbitrary numbers:

A - 440 hz

Bbb - 335 hz

G## - 444 hz

======================


Today's fixed chromatic scale is called Equal Temperament. The actual overtone series doesn't even line up from octave to octave. The frequencies are mathematically perfect but the ear thinks everything gets flatter as the pitches get higher. Even within a single major key it's not uncommon to hear a chamber group play notes as much as a quarter tone off anything you'd consider 'in tune'.

 

 

I heard a theory from one of my teachers many years ago, that in renaissance times some intruments (harpsichord? harp?) had different keys/strings for "equivalent" flats & sharps. So one string to play F# and one string to play Gb, with a minor pitch difference.

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Yes true. A rough example with arbitrary numbers:

A - 440 hz

Bbb - 335 hz

G## - 444 hz

======================


Today's fixed chromatic scale is called Equal Temperament. The actual overtone series doesn't even line up from octave to octave. The frequencies are mathematically perfect but the ear thinks everything gets flatter as the pitches get higher. Even within a single major key it's not uncommon to hear a chamber group play notes as much as a quarter tone off anything you'd consider 'in tune'.

 

 

I'm assuming you meant 435 for Bbb and not 335. ;)

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It has to do with what degree of the scale they are, but even then, there are inconsistencies with that idea (one some chords, you won't flatten/sharpen a note, but on others, in the same key, you will). The basic reasoning is that the equal temperament system we use today makes all 12 notes in music slightly out of tune (since you can't evenly divide an octave into 12 parts otherwise). Some notes suffer more than others. For example, the interval of a major third is very sharp, and is often contracted to sound better. In the key of C# major, the E# forms a major third above C#, and in the context of a C# major chord, that note is often lowered by instruments that can lower the note. The same would apply between F# and A#, and between G# and B# in the scale. However, in the key of C major, F natural (enharmonically E#) is a perfect fourth above C, so the intonation problem isn't an issue (fourths and fifths are both very in-tune intervals in the equal temperament system).


However, our ears have become quite accustomed to the out-of-tune sound of these intervals in equal temperament, especially since two of the most commonly used instruments, guitar and piano, are both fixed and can't make these adjustments. For practical purposes, you can consider this tunning issue to be a minor bit of trivia info, and not an essential piece of knowledge when you're first learning your major scales. This is why I dislike it when people mention this in the topic of enharmonics, because it can be a confusing subject as it is, and to throw in such an obtuse topic as temperament compensation seems like a bit of needless complication.

 

 

Great post.

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Being from a scientific background I kind of wish everything was expressed in Hertz!

 

 

Sweet, how about Logarithmic Pitch Notation? Pitches are expressed as the binary logarithm of their fundamental frequency, with C's represented as powers of two, middle-C being 8 (256 Hz). An octave below that is 7 (128 Hz) and an octave above it is 9 (512 Hz).

 

Duodecimal numeration allows us to easily express equally-tempered semitones as fractions of an octave...

 

 

8'0 C (2^8'0 Hz) "middle-C"

8'1 (2^8'1 Hz)

8'2 D (2^8'2 Hz)

8'3

8'4 E

8'5 F

8'6

8'7 G

8'8

8'9 A

8'X

8'E B

9'0 C

9'1

9'2 D

9'3

9'4 E

...

 

As you can see, all notes of the same letter name would end in the same number.

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Great idea Leo. Viva la revolution! In all seriousness do you think this system would have advantages over the one currently used? Its academic of course. Here I am, a total music theory noob trying to change western music notation. The gall! I am at the beginning of a long journey and my questions are based on issues I only vaguely sense through gut instinct. I don't yet have my head completely around the equal temperament issues but I feel they are the key to many of these doors I am blundering into. Back to the major scales and the Fretboard Warrior! This is better than Tetris.

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In all seriousness do you think this system would have advantages over the one currently used?

 

Personally, yes. I think standard diatonic notation is overly complex for the amount of information it conveys, and feel the system I've hinted at represents an improvement over it. However, not everyone to which I've pitched the idea have been so enthusiastic, with "too many numbers" being the usual criticism.

 

I don't have a problem with the numbers, though it can be worked into a chromatic staff version. :thu:

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