This lesson contains all the other stuff I've been meaning to cover, but just haven't got around to until now. So here it goes (and in no particular order)...
 

The idea of tendency tones is another one of those simple, yet powerful ideas in music. To illustrate this idea, let's think about a major scale as being a river for a moment.

As you know, water has the tendency to flow from a higher elevation to a lower elevation and a river pretty much works in this way - water flows downward seeking lower or more stable ground. It yearns for a place to rest and will employ movement until it gets there, a kind of irony in a way.

Notes within most scales work similarly, that is, certain notes have a tendency to flow towards more stable notes within the scale or key. Let's look at the major scale.

The root is the most stable note followed by the 5th and then the 3rd. These notes act as "lower ground" using our river/water analogy. The other 4 notes in the scale have a tendency to move to one of these more stable notes. Check it out:

As the diagram above illustrates, D, the 2nd note, has a tendency to resolve towards the root, the C. The 4th, the F, has a tendency to resolve towards the 3rd note of the scale, the E. Why not the G? Because G is a whole step away, whereas E is only a half step away. So our notes act like water and take the quickest and easiest way towards stability - they'll move a half step rather than a whole step if they can - the path of least resistence, if you will.

If we look at the upper part of the major scale, we find that the 6th has a tendency to resolve towards the 5th and that the 7th has a tendency to rise upwards toward the root.

By the way, the 7th note of a scale is sometimes referred to as the "leading tone" and it almost always wants to resolve upward a half step to the root. (This is just how music works.)

Why are these ideas important? Because when you are soloing or constructing a melody for a song, you'll want to resolve your tendency tones in the right places and at the right time. Otherwise, if you ignore these natural tendencies then your music will sound, um, un-natural.

These same ideas work for minor scales/keys/intervals as well.

   b2  ==>  Root
   4    ==>  b3
   b6  ==>  5
   b7  ==>  upward  ==>  Root

Now I may have stated this before, but I can't keep track of what's been said at this point (the book's too damn long, but what the hell, some things are worth repeating.) The strongest way to establish a key (or tonal center) for a major key is to play the five-chord followed by the one-chord. (I believe) this is called a traditional standard cadence. It's used all the time in classical music. V⁷/I ---> I

Now, if we just play guide tones (3rds and 7ths of each chord) and root notes we can voice this simple cadence in the following way...

The root of the G7 chord, the G note, resolves to the C, the root note of the C major triad. What I find interesting here is that we see tendency tone movement in this cadence...

The gory details: The b7 of the G7 chord, the F note, resolves down a half step to the E which is the third of C major. And the 3rd of the G7, the B note, resolves upward a half step to the C, the root of the one chord.

Note: The interval formed by the F and the B notes in the G7 chord is a tritone, arguably the most unstable sounding interval in music. This tension, or dissonance, is resolved by going to the one chord (and employing tendency tone resolution)... the E and C notes on the resolved one chord form a nice minor 6th interval which gives us a sense of completion, a sense of rest. I find this interesting, don't you? Tendency tone resolution within a harmonic cadence.
 

I've shown you patterns for major scales using position playing rules. Most of those fingerings/patterns are pretty useful/practical. Now, I want to show you 3-note per string patterns as these are a nice way to play a lot of notes without having to cover a lot of fingerboard real estate.

For What It's Worth: I've deliberately left the fingerings for these patterns blank as I think this is something you should finger out on your own at this point. My preference is to use my second finger over my third if a first finger stretch is involved AND I'm playing below the 12th fret. If I'm playing higher than the 12th fret, then the third finger feels more natural to me when performing 1st finger stretches.
 

Since we're on a role with scale patterns, let's look at the C Harmonic Minor scale using strict position playing. We get seven patterns:

Note: The fingerings (1s, 2, 3, 4s) are written on the side of each diagram. Pay close attention to these as they are dictated by the Roman numerals in each diagram. (Consult Lesson 13 if you forget the rules on position playing.)

What makes this scale so unique is that it contains a minor 3rd interval between the 6th and 7th scale degrees (between the b6 and the raised 7th.) This scale alteration (take a natual minor scale and raise the 7th degree by a half step) was done by classical composers for harmonic reasons, hence the name of the scale... harmonic minor.

Classical composers altered the natural minor scale so that they could squeak out a V7 major chord instead of a v-7 chord. (In natural minor, the five chords are: v- and v-7) Why did they want a major V7 chord instead of the minor v-7?

Because they wanted that strong major sounding traditional cadence (V7 to I) in their music! (They were very accustomed to that sound and felt it should exist in their music - even in minor key "tunes".)

A Side Note: The Picardy Third is a device used in classical music and it comes out of Medieval organ church music. You see, when a tune ended on a minor chord, the overtone series and the natural harmonics generated from the minor chord reverberated profusely in the churches of Europe, so to speak. The only "problem" with it was that the overtones clashed with each other creating quite a bit of dissonance. Composers were somewhat disturbed by this - Hey... it was Medieval Europe, they didn't like tritones either. Dissonance was considered evil... the Devil's music. Composers were constantly exorcising their music... sanitizing it in the hopes of making it more "pure" such that God wouldn't be offended by it.

(*MAN* do we live on the planet of the apes or what???)

To lessen these daker and more disturbing frequencies... composers would end their minor key tunes on the one minor, but then shortly afterwards they would raise the 3rd of the final chord transforming it into a major chord instead.

The (meta)physics behind this, or rather, the end result was that the harmonic overtones generated were more consonent sounding or more pleasing to the ear when that minor 3rd interval was raised upward by a half step.

Plus, (and this is just my idea) but i think this compositional device helped to invoke the whole Christain sentiment that one dies (analogous to a big F-in' minor chord), but one can be saved or be reborn, if you will, through the big F-in' major chord Jesus Christ Picardy Third (Holy Trinity) Savior trip.

Pretty tricky, eh? The church inducing religious emotion and ideology through the clever use of music. Hey... it was the rock concert of the day. You went to church for a religious experience, to be reborn, to get transformed and so on.

This technique is known as the Picardy 3rd (for some reason - I forget why at this point) and is used in modern popular music as well. It's a nice touch. The Beatles have used it in their music as so have many other great songwriters. It's a nice way to lessen the harshness (or sadness) of a minor tune.

It gives the listener a sense of hope.

And with all that said... let's get back on track and look at the scale formula and diatonic harmony for a C harmonic minor scale.

Practical applications? Play a harmonic minor scale starting on the 5th degree to get a nice Spanish sounding mode called Phrygian Major. This is used quite a bit in Flamenco music and the scale sounds great over a dom.7(^b9) chord progressing to a one minor. In C minor... you'd play C harmonic minor over G7(^b9) to Cm.

In Jazz, just start this sequence on the two chord like so: D-7(^b5) to G7(^b9) to Cm.

Interestingly, the G7(^b9) chord has the same notes as an Ab diminished 7th chord (minus the root). Check it out:

I might have mentioned this before, but a diminished 7th chord is a symetric shape. It's 4 notes separated by minor thirds. What this means is that there are only 3 different diminished 7th chords. What this also implies is that once you have a shape for a diminished 7th chord figured out on the guitar, you can move it around (up/down 3 frets) and get the same diminished chord again. Finally, any note in the chord can be considered the root. Why? Because it's a symetric pattern. Remember the lesson describing augmented triads? The thing is at work here.
 

And here's a quick review of the melodic minor scales. I'm presenting them here again for your convenience so you can compare them to the Harmonic minor fingerings/patterns presented above.

And here's the diatonic harmonry for a C melodic minor scale:

Here's a doc I came across recently which I feel has some cool stuff. Arpeggios in C major (mostly in 7th position). Most of the fingerings are pretty useful. Play them and see for yourself. There are other good fingerings which are not listed here, but I encourage you to find them on your own.

A Good Exercise: Now... pick another position, say second position. Then find all the diatonic arpeggios for C major (both triads and 7th chords). You should find some more cool shapes. Work through different positions and see what YOU can come up with. NOTE: It's okay if you break position to find a better fingering pattern. The point of the exercise is to come up with some good fingerings/patterns for major scale diatonic arpeggios. Once you've done this, write these patterns down so you can see them. Now repeate the exercise, but use a melodic or harmonic minor scale and so on.