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I'm new to learning music theory, so i'm sorry if the following question seems strange and obvious to some.

From what i understand, a scale is a logical combination of 8 notes. On the guitar, however, there are many more notes on the scale. For example, the G major scale pattern, root at the third fret, contains 16 notes. The first 15 notes are clear to me, as the last 8-15 are the same same notes as the first 1-8, just an octave higher. But the last note of the scale bothers me (the A notes, highest E string 5th fret). Why is it there, why not just stop at the third fret of the highest E string, which is a G note?

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You have misunderstood what a scale is. It doesn't matter what instrument you play, the scale is chosen from the 12 semitones available, and is in this case the 7 notes of the Gmajor scale, and onwards.

You can play the G major scale from G to G or you can keep going as far as you want up to the upper limit of your instrument. As long as it uses notes from that scale it is fine. Stop at that G on the E string if you want, or keep going.

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Thank you. I thought it was a strict rule that a scale is 8 notes. But as i now understand, there isn't any set number of notes in a scale. A scale just represents the notes ordered by some algorithm (i'm a programmer, so .. :D). –  geekkid Mar 30 '13 at 21:39
    
Well, there are actually lots of variations - I have described western conventional scales, which have 12 semitones, but there are a range of others in other cultures. –  Dr Mayhem Mar 30 '13 at 21:48
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Geekkid - you were fooled by the term 'octave', denoting a note of half or twice,basically, the frequency of another note.E.g. A is 440Hz, a lower A is 220 Hz and a higher A is 880Hz.Between one octave note and the next are 12 semitones and 7 of these notes in order constitute a scale- be it maj. or min.HOWEVER a pentatonic scale only uses 5 of these semitones before reaching the octave.The term octave actually refers to a diatonic scale in Western terms, and is somewhat a misnomer with regard to other scales. –  Tim Apr 3 '13 at 14:25
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In your example, you refer to 16 notes, which are all in the key of G major. But properly speaking, the G major scale has seven notes and then the octave. What you are playing is the G major scale across two octaves and a second. You are playing a slightly-more-than two-octave pattern based upon a certain scale.

A scale is a sequence of pitches that proceed, in progressive order, from a low pitch to the same pitch one octave higher. A scale, conventionally, is something that repeats at each octave.

Look up some references on scales and modes. According to the theory of contemporary Western music, there are 12 keys, and for each key, there are diatonic scales that can be constructed from each tonic key from among 7 modes (with special attention paid to the distinction between the natural minor, harmonic minor and melodic minor variations in that one mode).

Each of the Western diatonic scales has seven notes and then the octave.

There are other kinds of scales from different systems of music: for instance, various pentatonic scales, which have only 5 notes and then the octave. The whole-tone or octatonic scale has 8 notes and then the octave, and the chromatic scale has 12 notes and then the octave.

Footnote: To further complicate things, outside of the realm of contemporary Western music, there are instruments and scales with pitches in them that do not fall into the 12 pitches you can play on a modern guitar or piano (which are tuned according to the system we call equal temperament). Some of what we call non-Western music contains certain notes and pitches that are notably flatter or sharper and fall between the 12 equally-spaced chromatic pitches on the modern guitar or piano.

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If you mean this "scale pattern", 2-Octave G Major Scale
I believe the additional A at the top is for rhythmic purposes. It allows the final G to land on a beat for a more reassuring sense of finality.

Consider the result without the extra A, G Scale, no 'A'.
It just trails off. It doesn't land on the tonic, rhythmically weak. This would be difficult to execute, and troublesome to loop.

A third, slightly more rhythmically satisfying option is, G Scale, no repeated 'G'.
This puts the root on a stronger beat, but you don't get to exercise your pinky for that A; it doesn't fill the measures like the first. It doesn't emphasize the tonic as much as the first, because you've lost that 9 -> 8 change. So it doesn't exercise your ears as much either.

The third measures of the second and third examples are just too weird. You would not want to start at those spots. Unless you're going for that extra challenge. Perhaps that's the real reason: so the third measure starts on the tonic.

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MuseScore + Snipping Tool are my new friends. –  luser droog Mar 31 '13 at 5:01
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On a lot of guitar tutoring sites, 'scales' are written using the boxes guitar players visualise and use. They often contain ALL of the notes from a particular scale, e.g. the G major you ask about may even 'start' on the F#, 6th string 2nd fret,as that note is fingerable within the box.As such, it'll sound like a Locrian mode, and it could be shown to go up to an A on top(thin) string, 5th fret, finishing more like a Dorian. This is confusing to beginners,as they expect a scale to go from tonic to a higher tonic and probably back to the start again.This sounds more complete and is how scales are played in an exam situation.

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There is only one scale, the chromatic scale. All other "scales" are modes of this scale with some pitches more important than others.

Any "major scale" is actually 12 notes(actually more). The first 7 notes of the scale are the most important(the tonic triad notes are even more important).

The key of C has the notes

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

If we arrange them in a matter of importance, more or less, then

(C G E) (D A F B) (A# G# C# D# F#)

The patterns on the guitar(All the skipping and stuff) is simply avoiding the avoid notes.

There are many ways to play the 7 main notes and you can extend them several octaves up the neck.

Scales are just patterns used to develop technique and some logical concept of melodies. Melodies and music are not scales.

When someone creates a cool melody from creativity they are not using a scale to do so but may use the scale to avoid hitting those "bad notes".

Ultimately you don't have to and don't want to rely on scales but want to just have the melodies flow out. In this case you will be using the chromatic scale simply because the guitar is a fretted instrument. Usually to get close to this goal you end up having to practice scales for both a technical aspect and to reduce complexity(after all, it's easier to visualize 7 note patterns than 12).

Note that a scale doesn't have to start and end on the tonic/root. Jazz players tend to end them on the 9th. It usually helps to tend them on the tonic since it solidifies the mode. If you resolve on a clunker it will sound bad, mainly because you are emphasizing something that clashes with the tonic area.

Scales help being able to play a pattern and sound halfway like you know what your doing if you play in the right key.

Before you learn your 7 note scales work on your 3 note scales(arpeggios) and 5 note scales(pentatonic). The reason is these scales are more important in practice than 7 note scales because they encode chord information better... and most of the time you'll be playing over chords. (a chord is just a pattern with all the notes played at the same time or arpeggiated)

e.g.,

If you are playing over a C chord then the first 3 notes you need to be able to call up instantaneously are C E G(The chord tones). After that you need to be able to call up any add tones(D A F B) which you can get from your pentatonic. e.g., C major pent over a C chord gives you the D and A tones(also known as a Cmaj6/9 chord) while G major pent over a G chord gives you your B D A extensions... but guess what? C major pent and G major pent are the same patterns!!!

So essentially by learning just one major arpeggio shape you can get all kinds of music from country to jazz. It would be very rudimentary at first but if you really worked on it, it would take you further than your avg guitarist.

e.g., Over a C major chord, The G major arpeggio gives you the G B D notes which allows you to get a major9 type of sound. Ab major arpeggio gives you the notes Ab C Eb, which gives you a sort of bluesy sound if you use it right. D major arpeggio gives the notes D F# A which gives you a Cmaj13 type of sound...

But realize, all these arpeggios (shapes) are the same. Just the basic triadic arpeggio (shape). There are just a few of these major triad arpeggio shapes on the guitar. The biggest drawback to the guitar is that the B string makes us learn 3 times as many shapes but it also is what allows us to play 3 times as many chords.

But if you play likes this, unless you happen to be very advanced at it, you'll sound quite a bit polytonal and as if you are playing in the wrong key in some instances. To be able to make it work you have to add more notes.

The C major arpeggio + the G major arpeggio = C E G + G B D which gives you your Cmaj9 sound... same as a above. But this time you can learn this as a pentatonic = C E G B D scale!!! By learning this pattern you'll consolidate your visualizing into larger chunks on the fretboard... But note, it's still simply a C major arpeggio and a G major arpeggio.

The basic idea here is that you have 12 notes to work with. Most of the time you will be using 3 to 5 note "patterns" since these are easy to remember. Since it is on the guitar, if you learn one pattern you basically learn 12 since you can use it in 12 different keys by just playing it at different places on the neck. A piano player doesn't have that ability, for example.

If you know two 5 note patterns you can combine them to form new patterns. If many cases you'll not end up with a 10 note pattern but something smaller due to the patterns overlapping. e.g., C major = C D E F G A B can be thought of as a C major 7 arpeggio + a G7add13 arpeggio = C E G B + G B D F A or a C major 9 arpeggio + F major 7 = C E G B D + F A C E...

Or, Cmajor6/9 + Dmin = C E G B D A + D F A. The first can be thought of as the pentatonic.

With all these choices it becomes a matter of using the right "pattern" to draw your melodic ideas from. Using the wrong pattern can sound bad/wrong or very cool. The main point to get from all this is that you have 12 notes to choose from but you have to break them down into manageable pieces and understand how those pieces fit together.

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Down voted because there is quite a bit of incorrect information in this answer. –  ecline6 Apr 6 '13 at 16:27
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Geekkid has JUST started to learn theory.Major 7s and 9s or 6/9s are hardly beginner material.G7add 13 - G13 always has 7 in it !This answer is not particularly helpful to Geekkid - or most people ! –  Tim Apr 6 '13 at 17:12
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I disagree. It was helpful to me. @Tim A G7add13 is more commonly known as a G7/6 chord and different from a G13 as it does not imply the 11th. –  AbstractDissonance Apr 6 '13 at 20:03
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Please use chat for extended discussion. Comments are not the place for long conversations. –  NReilingh Apr 7 '13 at 19:28
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My one addition is this: The only thing wrong with this answer is that it is using a very nonstandard definition of "scale". Much of this could have been avoided by stating your alternate definition at the beginning instead of making the claim that everyone else is wrong. Instead of using ad hominem attacks in comments, asking for references and documentation is much more useful. –  NReilingh Apr 7 '13 at 19:35
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