Possibly a Very Stupid Question

[dough_mouse]

Hi,
This is a question thats been bothering me for a while and Im sorry if its stupid. I was just wondering, whats the theory behind accidentals in a piece? Whenever I'm improvising or something, if I play a note not in the scale, I can tell it sounds off and wrong. But when I read a real piece in F Minor, for example, sometimes there are flats/sharps/naturals that create notes that are not in the F Minor scale - yet the piece stays in the same key. I was just wondering what allows a composer to use accidentals and still stay in the same key and if theres any theory that explains why there are accidentals in a piece that don't sound wrong. How come composers can use notes out of scale and I can't? Thanks in advance.

[preludium]

This is no stupid question at all. It's way too complex a topic to cover in one post and has both a harmonic and a melodic aspect. Let's start with the melodic part.

The set of notes can be extended by grace notes. They resolve chromatically to their target. There is a bunch of different names in German language for grace notes, based on the context, like whether they appear on a stressed or an unstressed beat, but there seem to be no English counterparts, so I have to leave it like that. Grace notes on stressed beats are an important feature of Mozart's style. In this context they have no harmonic meaning, but in other cases things can be quite ambiguous. Chromatic scales like in many Chopin pieces are of a similar nature. In German the out-of-key notes in such a context would be called transitional notes, but I'm not sure whether this notion is used in English.

Now to the harmonic part. Harmonically the set of notes can be extended by dominant chords. Like grace notes for melodies a dominant creates tension in a harmonic context. The root of a dominant lies a 4th below (= a 5th above) the root of the chord to which it is expected to resolve. The 3rd with respect to the root of the dominant is major and the 7th minor - there is nothing to understand about it, since it is just a definition. Within the constraints of a key there is only one such chord. In the key of C major this would be G7 (G - B - D - F). You can prepare the transition to another chord build by the notes of the C major scale by inserting such a dominant. Say you want to go to the e minor chord in the key of C, the corresponding dominant would be B7. This introduces D# as the major 3rd of the B7 chord (and F# as the 5th of B7 as well, but whether the 5th belongs to the definition of the dominant depends on the style of music; in classic it does, in Jazz it doesn't). Likewise you can use an E7 to go to the a minor chord. E7 introduces G#. Such dominants are often played with their 3rd in the bass, so that you get a chromatic ascending line (G# - A in the last example). You can use double dominants (dominants to dominants) and chain them that way.

Since both grace notes and dominants create tension you can combine them. This leads to the notion of altered dominants. In fact, as long as you have the 3 notes that define a dominant you can add any other note to such a chord as long as it resolves chromatically to a target. You have the whole chromatic scale covered (except for one particular note) by diminishing and augmenting the 5th and 9th. The exception is the major 7th, which is not allowed, since it would destroy the dominant function. Diminished 9ths are quite common in early romantic works. Augmented 5ths are often not seen as alteration, because they belong to the key if you assume to resolve to a minor chord an exchange them enharmonically by the minor 6th. The earliest occurence of the augmented 9th that is known to me is in the Tristan motive of Wagner's "Tristan und Isolde".

Don't expect to understand this stuff in one day. As I said it's complex and there still is more, like dominants where the root doesn't appear. One example for this is Schumann's "Von fremden Laendern und Menschen" where the 2nd half of the first bar is an altered double dominant chord without root (A7b9). The amazing thing is that it looks like a diminished chord at the first glance, but this interpretation doesn't reveal its function which is clearly audible. The same rootless X7b9 chords can be found in many Bach pieces. Then chords can be inverted, which can add some ambiguity. In Jazz there is a particular inversion called tritone substitution, which again creates chromatic bass lines, but this time in descending direction. Okay, I'll stop it now. It would take much more space to get all these things sorted.

[Bob]

That's a big question.

From the reading and printing perspective, using a key signature makes it easier to read and uses less ink. 

Accidentals mean you're using notes that aren't part of the scale -- the scale indicated by the key signature.  If you're using major or minor (or whatever scale you want) anything that's not in that scale would be an alteration -- not 'part of the key' anymore.

I tend to think there is just one major/minor scale.  Steps 1, 2, 4, and 5 (maybe 7) are the same in both.  3 and 6 (and 7) are just raised or lowered between major and minor.  And then since minor is unstable and changes on the conditions, I see it like a version of major, maybe a compressed major scale.

It depends how you hear things and the style.  Very generally, each tone has a pull or wants to move in certain directions.  Step 1 pulls everything toward it and is very stable.  5 and 7 want to move to 1.  4 to 3, or to 5.  6 down to 5. 2 down to 1, but maybe 3.    That's the major/minor scale again.  IF you follow the idea of scales and IF you hear things that way -- because with extended chords or exotic scales a note might sound right and not necessarily follow those rules. 

With the major/minor scale idea and that pull back to step 1, the more accidentals (the more chormatic note) you use, the more you blur that tonal center.  For example, if you use #2, that wants to go to 3.  When you use a chromatic note, you put a little more weight toward another note that is not the tonic (step 1).  Tonality is blurred a little bit.  The more you use chromatic notes, the less stable that tonal center is.

There are different amounts of how tonal a piece is.  Some can be very tonal and follow the rules that pull back to step 1 very closely.  Other pieces use more chromatic note or go off into other keys enough that that piece is much less tied to a certain tonal center.  Some pieces blur the tonal center so much you can say it doesn't have any key (tonal center) at all.

If you're a student and you want to learn about music theory, you have to start somewhere.  A teacher or a textbook has to have somewhere to start to explain what things are "correct."  Music theory is only ideas though -- You can do whatever you want.  We've had 3-400 years of music history developing ideas about tonality though -- discovering it and developing it and then moving away from it -- so it is good to know what's been going on and what's been done before.

And then there are rules about writing parts out -- maintaining a certain number of voice parts consistently and keeping them independent so two or more voices don't blur into one single voice.  IF you follow those rules, then there are right and wrong notes and things you shouldn't do if you want to maintain that independence of voices.


There a lots of types of chords.  You can use a chord that has accidentals in it (notes out of the key) and it can still sound good and right with the piece.  It depends on the style and how the chord is used.  A dominant chords (5 chord) goes to I, the tonic.  You can build a dom5 going to the dom5 of that same I chord.  V/V to V to I.  That V/V chord would have an accidental in it but it would sound ok.  You could also have some tall extendend chord that sounds good (depending on the style) but that chord could have lots of accidentals -- It still sound ok, but it has notes that are outside of the key.  Even with that, I wonder -- how true are the laws built up around a plain vanilla tonal center, I wonder.

[preludium]

You can do whatever you want.

dough_mouse has apparently discovered that this is not necessarily true. I'm cautious to say something like this easily, because it sends the message that you don't need to learn anything. You can break the rules you know and the result will be completely different than if you don't have a clue. Listen to Debussy - he breaks all the rules, but he studied at the Paris Conservatoire for 12 years and you can hear that in every bar. Knowledge gives freedom, not ignorance. The key to the problem is that you can do what you want after you've learned the lessons because you will want something different then.

"It is sad that the idea 'today one can write everything' keeps so many young people from learning something decent, understanding the classics, gaining culture." (Arnold Schönberg)

[dough_mouse]

Huh. I really appreciate the help and time you guys put into your post but I dont really think I...understand...all of that...eek. So I have some more questions!

First, what are grace notes? Because I thought grace notes were the little fast notes that you played before another note that didnt count towards the meter, but that definition doesnt sound right in this context. And what does "chromatically resolve to the target" mean? Does that mean if I'm going to play a certain note I can play a note a half-step under it and it will resolve to that note? Also, preludium, are you saying that I can use a dominant chord to play notes not in the scale and then use the dominant of that dominant to play more new notes indefinitely? And, what is E7 and B7? Thanks a bunch.

[preludium]

First, what are grace notes? Because I thought grace notes were the little fast notes that you played before another note that didnt count towards the meter, but that definition doesnt sound right in this context.

Well, I actually wanted to avoid the notion "leading note", since it is used for the 7th note of the major scale in English, so that could be confusing. With your idea of grace notes you're perfectly right. I'm not a native English speaker and you can't find such things in standard dictionaries. So let's stick to the more correct term "leading notes" and make clear that this is a more general concept that has no direct relation to the major scale. It is actually a note that has a strong tendency towards another one. This always depends on the context. To resolve chromatically means that the leading note always is a halftone below or above the one to which it wants to go. To make that clear lets look at Schumann's piece "Von fremden Laendern und Menschen" that I mentioned above, because it contains a lot of stuff within a short section.

https://www.mutopiaproject.org/ftp/SchumannR/O15/SchumannOp15No01/SchumannOp15No01-a4.pdf

We are in the key of G major here. The first half of the first bar is based on the G major chord (only G, B, and D occur), so this is the tonic. The second half of the bar is another chord, but this is a tricky one. We have the notes C#, Bb, E, and G. At the first glance this is a diminished chord - it consists of minor thirds only. You can see that if you "unspread" it, i.e. play all notes as closely together as possible, like C# - E - G - Bb within the same octave. Now, these diminished chords never fit into any key. There is at least one note that is alien to the key. Here it's even two: neither C# nor Bb belong to the key of G major. At the end of the first bar it's not clear what that means harmonically. We have to go on to the next bar and see what happens.

The whole 2nd bar is a D7 chord, i.e. a D major with additional minor 7th. So we have the notes D, F#, A, and C available. There is an E in the right hand, but Schumann makes quite clear that this is melody only by making it the shortest note in the bar and putting it on a unstressed beat. Don't get fooled by the fact that the lowest note in the 2nd half of the bar is F#! It still is the D7 chord but its third is in the bass. The 3rd bar repeats
the 1st, so this is a G major chord again and the D7 before was its dominant. The F# in the bass before acts as leading note to the root of the G major chord in the 3rd bar.

Now back to the diminished chord again. Its lowest note C# resolves to the root of D7, so again a leading note, but this time it's one that doesn't belong to the key. The second lowest of the diminished chord Bb resolves to the A of the D7. Again, the leading note is out of the key, but this one resolves downwards. If you look at it from the beginning of the 1st bar you even get a chromatic line B - Bb - A, so this Bb could be called a
transitional note, i.e. a chromatic note that connects two notes from the key of G major. Very nice by Schumann that he introduces two leading notes at the same time that resolve in opposite directions. Okay, so with this diminished chord we have something that "wants" to resolve to the D7, and in a harmonic context this can be done by a dominant. Since every dominant comes from the 4th below (identical with the 5th above) by definition, this diminished chord must be an A7 in disguise. The C# is its major 3rd, the E its 5th, the G its minor 7th, and the Bb a diminished 9th. This A7b9 is a double dominant, because it resolves to another dominant D7.

HTH

[soliloquy]

Oh my.  While this is slightly off-topic, I am going to have to impugn some of Bob's remarks on the "similarities and differences" between the major and minor scales.  This doesn't really have much to do with the actual question, but I wouldn't want someone reading that and getting their information wrong.


Major Scale:

scale degrees 1-2: diatonic whole step
scale degrees 2-3: diatonic whole step
scale degrees 3-4: diatonic half step
scale degrees 4-5: diatonic whole step
scale degrees 5-6: diatonic whole step
scale degrees 6-7: diatonic whole step
scale degrees 7-8: diatonic half step


Harmonic Minor Scale:

scale degrees 1-2: diatonic whole step
scale degrees 2-3: diatonic half step
scale degrees 3-4: diatonic whole step
scale degrees 4-5: diatonic whole step
scale degrees 5-6: diatonic half step
scale degrees 6-7: augmented second
scale degrees 7-8: diatonic half step


Melodic Minor Ascending Scale:

scale degrees 1-2: diatonic whole step
scale degrees 2-3: diatonic half step
scale degrees 3-4: diatonic whole step
scale degrees 4-5: diatonic whole step
scale degrees 5-6: diatonic whole step
scale degrees 6-7: diatonic whole step
scale degrees 7-8: diatonic half step


Melodic Minor Descending Scale:

scale degrees 8-7: diatonic whole step
scale degrees 7-6: diatonic whole step
scale degrees 6-5: diatonic half step
scale degrees 5-4: diatonic whole step
scale degrees 4-3: diatonic whole step
scale degrees 3-2: diatonic half step
scale degrees 2-1: diatonic whole step


Natural Minor Scale:

scale degrees 1-2: diatonic whole step
scale degrees 2-3: diatonic half step
scale degrees 3-4: diatonic whole step
scale degrees 4-5: diatonic whole step
scale degrees 5-6: diatonic half step
scale degrees 6-7: diatonic whole step
scale degrees 7-8: diatonic whole step


Anyway, in fully tonal music IE pre-Scriabin/Ravel/Debussy, accidentals will occur 99.99% of the time due to one of the following:

Chromatic Scales
Appoggiaturas/Suspensions
Counterpoint
On chords that function in the scale but use other notes
To illustrate the function of double notes IE where it would be easier to read as a 2nd, it is written as a 3rd
Unmarked key changes
Ornamentations