My music book lists fifteen Major scales, C through C-flat, and explains that three of those are “enharmonic”, or duplicates of other scales that just denote the same keys using flats instead of sharps or vice-versa. But they don’t list three scales: there isn’t an D-sharp, a G-sharp or an A-sharp, although there are E-flat, A-flat and B-flat, which should amount to the same thing. If they list some duplicates why not all? Is it just a convention, or is there some reason I’m not getting why there can’t be such a thing as an “A-sharp Major” scale?
That’s because that can only be up to 7 sharps or 7 flats in a key signature. G# would have 8 sharps, D# would have 9, A# would have 10. Similarly, scales like Fb are also not listed.
Any book I’m familiar with only lists twelve major scales and three forms of twelve minor scales. Cb and Fb are enharmonics of B and E. Not sure what the third enharmonic would be.
Now, as to your D#, G#, A# scales. Yes, they are enharmonic with Eb, Ab, and Bb respectively. However, they require double-sharps to denote (notated as ‘x’). Therefore, your A# scale is A# B# Cx D# E# Fx Gx A# . The double-sharps are required because you cannot have two notes with the same letter in a scale. You also cannot mix flats and sharps. I cannot imagine why your book wants to get into all that.
By the way, a double-sharp, as its name implies, raises the pitch by one whole step. A double-flat (bb) lowers the pitch one whole step. This notation is often used when writing scale runs in music where the composer wishes to raise the pitch without changing the key.
Are you sure about it having fifteen scales? This really bugs me. These are the scales I know: Bb/A#, B/Cb, C/B#, Db/C#, D, Eb/D#, E/Fb, F/E#, Gb/F#, G, Ab/G#, A. I don’t see how to get fifteen out of that. I can see twelve. I can imagine twenty, if you want to include enharmonic spellings. I don’t get fifteen
From what I understand from the OP, the book includes enharmonic scales that do not require double flats or double sharps:
Bb, B, Cb, C, Db, C#, D, Eb, E, F, Gb, F#, G, Ab, A.
15 scales.
Look up “circle of fifths,” if it’s in your book. Because of the nature of the equal temperment system of notes, enharmonics are created where certain notes can be described with two different names, e.g. D# and Eb.
After C# major (7 sharps) you have to switch to flats otherwise you’d have 8 sharps (G# major). A# major would be 10 sharps, and by that point it’s easier to switch to flats, since Bb major is only two flats. If you’re the musician, you’d much rather read 2 flats than 10 sharps.
So yeah, I guess the easy answer is, it’s a convention created by equal temperment.
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I think there should only be 12, since that’s how many progressions around the circle of fifths you need to go before repeating.
Or another way of looking at it, the book lists the 15 Major scales that have each note of that octave on it’s own line. Skipping ahead to the chapter on Major and minor keys, it explains key signatures, which would be harder to use if you mix natural and sharp notes on the same line. So it’s mainly a way of making the notation convenient and consistent.
Since I’m trying to teach myself out of a book, I wanted to make sure I wasn’t misunderstanding something. I’m still working on intervals though. Right now I’m still having to convert degrees into half-steps and manually count up or down, which I thought using degrees was supposed to eliminate. It doesn’t help that I think my book has typos, so I can’t tell if I’m counting right or wrong.
What instrument are you learning on? There are some GREAT web resources for the more popular ones.
An old harmony book, published in the 1940’s, was one of the first texts I read on music theory. It introduced the concept of the tetrachord and by way of that idea made the concept of keys and scales very intuitively clear for me.
Using the C Major scale as its foundation, and the sequence of half-steps and whole-steps in it, the idea of the interlocking or interweaving of tetrachords made all the sense in the world.
C to D is a whole step (two frets on a guitar), D to E is whole, and E to F is half. So the first tetrachord in that scale is WWH. Next consider the second tetrachord in the scale as a second unit, and see that G to A is whole, A to B is whole, and B to C is half, so you have another WWH group in the second tetrachord. Put a whole step between those two (F to G) and you have the grouping for the Major Scale: WWH W WWH, and that same grouping can be applied from any starting note to develop all scales of the Major category.
Now, what really makes the Cycle of Fifths a valuable learning tool, is that as you link tetrachords together, you find that the two tetrachords in C are also the same as the second tetrachord of F and the first tetrachord of G, making those two scales different from C by only one note in each case. And if you maintain the one use of a letter in each spelling (modified by sharps and flats where required by the Major Scale Formula) you can build the whole array of scales by extending the tetrachords upward and downward from the C Scale until you have to start using the double flats and double sharps to complete the spelling.
First, consider just expanding upward from the GABC tetrachord (C Scale Second Tetrachord) to build the G Major Scale. You know you have to use the remaining letters DEFG and that you must use the W-WWH arrangement, so you’re left with D (Whole step from C), E (W), F# (W) and G for the second tetrachord of the G Major Scale. Thus the only note that differs between the G and C Major Scales is the F Natural in C and the F Sharp in G. All other notes are the same.
Similar logic applies going DOWN from C, using the CDEF tetrachord as the SECOND tetrachord of a new scale. You can see that the letters involved must be FGAB. You can also see that if you start on F and follow the WWH spacing, you’ll develop F to G (W), G to A (W), A to Bb (H), so the completed F Major Scale is FGABb CDEF, and that the only differing note is the Bb in F Major and the F Natural in C Major.
Another interesting thing to notice as you build upwards in tetrachords from C is that you always sharp the third note in the second tetrachord of the new scale, while maintaining any already sharpened notes from earlier tetrachords. To see that in action, just note:
C Major: C D E F G A B C
G Major: G A B C D E F# G
D Major: D E F# G A B C# D
A Major: A B C# D E F# G# A
E Major: E F# G# A B C# D# E
B Major: B C# D# E F# G# A# B
F# Major: F# G# A# B# C# D# E# F#
You can see that the order in which notes are sharpened as you go up the Cycle of Fifths (called that since the second tetrachord in each scale is the one starting on the FIFTH note of the previous scale) is: F# C# G# D# A# E# B#, and that the number of sharps in the scale goes from 1 to 7 as you progress through the Cycle Of Fifths. Also note that you can identify the scale in question from the “key signature” by looking at the rightmost sharp in the cluster and seeing that the scale involved is one half-step up from that rightmost sharp. For instance, in the A Major key signature of three sharps (F# C# G#) the rightmost sharp is on G, so the scale involved (A) is a half-step up from that G# in the signature.
Similar logic applies to going DOWN the Cycle of Fifths from C into the Flat Keys, except that in building lower scales from tetrachords, you always flatten the fourth note in the new (lower) tetrachord, maintaining any previously flattened notes as you go downward. That gives:
C Major: C D E F G A B C
F Major: F G A Bb C D E F
Bb Major: Bb C D Eb F G A Bb
Eb Major: Eb F G Ab Bb C D Eb
Ab Major: Ab Bb C Db Eb F G Ab
Db Major: Db Eb F Gb Ab Bb C Db
Gb Major: Gb Ab Bb Cb Db Eb F Gb
Cb Major: Cb Db Eb Fb Gb Ab Bb Cb
Here again, the order in which the notes are flattened as you go down the Cycle is: Bb Eb Ab Db Gb Cb Fb, the exact opposite of the sequence of sharps. Also, you can tell the key from the signature by looking at the cluster of flats and take the second from the right as the Key Note. If there’s just one flat, the key is F.
Another nice bit of trivia is that if you look at any pair of letters involving accidentals (b’s and #'s) the sum of accidentals in those keys will be seven. For example E and Eb: 4 #'s and 3 b’s. And since the C scale has no accidentals, either Cb (7 b’s) or C# (7 #'s) makes that rule of seven work twice.
Just remember the tetrachord structure and things fit together nicely.
I didn’t have time to finish proofreading my previous post because I was in a hurry to log off to avoid a storm passing through. There’s an error in the paragraph below that I have corrected (in bold):
“Similar logic applies going DOWN from C, using the CDEF tetrachord as the SECOND tetrachord of a new scale. You can see that the letters involved must be FGAB. You can also see that if you start on F and follow the WWH spacing, you’ll develop F to G (W), G to A (W), A to Bb (H), so the completed F Major Scale is FGABb CDEF, and that the only differing note is the Bb in F Major and the B Natural in C Major.”
Another point I had meant to make concerns those “enharmonic keys” referred to in the OP. They involve the keys with 5, 6, and 7 accidentals. Since C# and Db are the same notes, the Major Scales built on them involve the same notes, but with different spellings. The same holds for Cb and B, and for F# and Gb. So, even though you can create 15 separate Major Scales before running into the double flats or double sharps, by choosing the “enharmonic keys” with the least number of accidentals as the ones to identify the ones with 7 accidentals, you can reduce the 7 sharps of C# to the 5 flats of Db, or the 7 flats of Cb to the 5 sharps of B Natural. It falls for the 6 flats/6 sharps keys of F#/Gb to be used at the composer’s choice, since they are equally loaded with accidentals.
It’s possible to see chords named after those “keys” that aren’t in general use, such as A#, D#, E#, Fb, Cb, because chords are named for the notes on which they are built and from the resultant scale involved whether there are double flats or double sharps (or even triple! of them) to contend with or not. So even though you won’t see “key signatures” with more than 7 accidentals, you will find chords with weird notations at times, even some that have a mixture of sharps and flats. This can be quite confusing until you adjust to the idea that Scales (Keys) are usually discussed in reference to the “key signature” and that Chords are normally discussed in terms of their intervals. Where it gets most confusing is when the Chord/Scale relationships are intermixed, as is done a lot in Jazz.
It all gets even more worrisome once Minor Scales enter the picture. It’s good to have the Major structures well in hand before trying to make sense of the Minor Systems.
If you’d like a visual rendition of the circle of 5ths, I just threw one together in Photoshop, which you can see here.
Oh, and another way to answer your question directly is this: due to conventions of musical notation we don’t ever name the same note twice in a scale (that is, each major scale must contain each letter, ABCDEFG, once and only once, no omitions, no duplications).
The scale of A# would be as follows:
A#, B#, C##, D#, E#, F##, G##
This way, you maintain the rule of each letter only once. But, as you can imagine, this would be a fairly unwieldy scale. Why use it when you could convey your musical meaning much more clearly with the scale Bb (the enharmonic equivelant to A#).
Can you point me (us?) to web resources for piano? I’ve taken some theory, but recently trying to brush up.
Ok, another beginner question. I’m having trouble understanding time signatures, like 4:4 or 4:8. The first number refers to the number of beats per measure, that I understand. The second number refers to what note duration is assigned to a beat: 4:4 would be four beats per measure with each beat a quater note, and so forth.
The part I don’t understand is what determines which note duration you use? As far as I can tell, the only difference between 4:4 and 4:8 time is which note symbols are used to write out the score. The time signature isn’t the same as the actual speed the piece is played at, that’s the tempo. How would a measure written in 4:8 sound different than one written in 4:4?
Not particularly. As far as I know it’s a stylistic choice. Depending on the music, it might look better or read easier written in 4:8 as opposed to 4:4.
What determines the note duration? You just follow what the time signature says. As you have said the top number is the number of beats in a measure and the bottom one is the type of note that gets 1 beat. 4/8 = 4 beats in a measure with an eight note getting 1 beat. 4/4 would be 4 beats in a measure with a quarter note getting 1 beat. A measure in 4/8 will have half as many 1/8 notes as a measure in 4/4. A measure in 2/4 or 1/2 can have the same number of 1/8 notes as a measure in 4/8.
Actually there is a bit of a misconception about the bottom number. The buttom number is determined by the way the beat is subdivided. If the subdivisions are duple the bottom number is 4 and if they are triple it’s 8.
4/4 is counted: 1 & 2 & 3 & 4 &
(the 3 tends to be stronger than 2 and 4 but weaker than 1).
3/4 is counted: 1 & 2 & 3 &
In the first case there are 4 beats in each measure (cycle) and in the second there are 3 and each are divided in half (or multiples of 2). A quarter note represents one beat of time and quite nicely divides into 2 eighth notes. Want 4 subdivisions? We have 16th notes for just that purpose.
But say you wanted to divide the beats into 3 equal parts? To represent that on paper you need a note that can represent a third of a beat. Well, there really isn’t a note that does that exactly. The best they’ve come up with is to use 3 eighth notes and then a bracket joining them with a little “3” above it to let you know that they are triplets. That works fine if you need it here and there, but if the entire piece has a triplet feel all those brackets will get quite distracting very quickly.
The solution is to simply count the triplets as ordinary 8th notes. Afterall, it is pretty arbitrary what you actually call the notes. By putting an 8 on the bottom of the time sig, it tells us to count each measure according to it’s 8th notes. It does NOT, however, mean that the 8th notes are the beats. In fact the beat is actually moving in dotted quarter notes (a dotted quarter = 3 eighth notes). Hence:
6/8 is counted: 1 2 3 4 5 6
There are 2 beats and each are divided into 3. Likewise 9/8 has 3 beats and 12/8 has 4, the first beat always being stronger than the others.
Let me see if I can think of some popular examples. Everyone knows the Beatles, right?
The Sgt. Pepper reprise opens up with a solo drum intro in a very clear 4/4, with the duple subdivision explicitly stated by the bass drum on beat 3. i.e. 1 2 3 & 4
Now take Norweigen Wood. You could count it in 4/4:
I once had a girl or should I say she once had me?
1 2 3 4 1 2 3 4
But it’s much more descriptive of the rhythmic feel if you account for the triple subdivisions inherent in the music and particularly the vocal/sitar melody:
I once had a girl or should I say she once had me?
**1** 2 3 **4** 5 6 **7** 8 9 **10** 11 12 **1** 2 3 **4** 5 6 **7** 8 9 **10** 11 12
Thus it is in 12/8 by my count.
Incidentally, I don’t believe I’ve ever seen music in 4/8, nor can I, off the top of my head, think of any practical reason to use it.
Actually, I guess it would probably be: 1 2 3 4 1 2 3 4
8/8 would most commonly be counted: 1 2 3 4 5 6 7 8
I hope this is somewhat clear.
(That was a coding nightmare).
Moe, you are completely and utterly wrong.
It’s a pity you’ve never seen 4/8 or 6/4. Trust me, they exist.
::sigh::
First off, I never even mentioned 6/4. It happens to not only exist but be quite common.
Second, I never said 4/8 doesn’t exist. I did say “Incidentally, I don’t believe I’ve ever seen music in 4/8, nor can I, off the top of my head, think of any practical reason to use it.”
Please save your pity and enlighten me as to what exactly 4/8 means to you.
Finally, I can’t wait to hear just how completely and utterly wrong I am. Please explain where I went wrong (I’d also appreciate it if you could include some examples.)
I don’t think there’s any misconception about what the bottom number means, it’s the type of note that gets one beat.
What you have elaborated on is the notion of pulse. No all 4/4 music is counted or felt the way that you describe. In a lot of R&B music the strong beats are the 2 and the 4, where the snare drum hits are and where people clap their hands, or if they’re dancing it’s when their foot hits the ground.
OK everyone please settle down. You in the back, yes you, please put those drum sticks away and pay attention.
In modern music, with the breakdown of functional tonality and the breakdown of conventions of time signatures, everyone who has previously posted is right in certain conditions.
I have never seen 4:8 time, I have seen 2:8 and that is about the same amount of wierdness. Usually, not always, and with frequent exceptions if 4 is the bottom number the music will be sub-divided into groups of two, simple meter. Usually, not always, and with frequent exceptions if 8 is the bottom number the music will be sub-divided into groups of three, compound meter.
Rock, Jazz, R&B, Country and many other modern or pop music genres have the strong beat on 2 and 4. This is not written in stone there are numerous exceptions and lengthy articles in music periodicals can be fredged up to prove either side of the arguement. Western Art music usually has the strong beat on 1 and 3, or when triple meter is used the strong eat is on 1. This is not written in stone there are numerous exceptions…
Most music boils down to the following, “Alright folks let’s start at the top a 1 and a 2 and a you know what to do…” Let the theory experts hack away at the probability of 4:8, 15:16 and other time sigs, just tell me how many beats in a measure or the tempo and I’ll give you a reason to have me on the gig.
Getting back to the OP with a slight hijack, I was a bit stunned earlier this year to see a book of scales fr guitar. I was amazed to learn that there were listed in this book 131 different kinds of scales. Of course I was familiar with major, natural minor, harmonic minor, melodic minor, chromatic, diminished, whole tone and all eight of the modes. Now I need to learn only 117 other scales. This does not include the fact that each scale can be constructed on a different pitch. That would mean that I need to know over 1500 scales, ACK.
I am way behind the power curve now. Luckily, classical tuba music can be performed with my limited scale knowledge (and thank God for that, it took me long enough to master the ones I know).
The OP wants to know about scales and s/he got a great answer. Let’s not muck up the discussion with aimless rantings about time signatures.