I assume now that you've read part 1 and read the material I linked to.
Intervals are named by their positions on the staff (there is a lesson on Musictheory.net properly describing how intervals work. Since I cannot show you a staff here, I'll just show all the intervals in relation to a certain note as an example)
If we take the note C as our tonic (our 1) then the notes would be named as:
C 1 "Prime" "Unison" "Root Note" or "Tonic" depending on context
C#/Db b2 "Minor Second"
D 2 or bb3 "Major Second" or "Diminished Third"
D#/Eb #2 or b3 "Augmented Second" or "Minor Third"
E 3 or b4 "Major Third" or "Diminished Fourth"
F 4 "Perfect Fourth"
F#/Gb #4 or b5 "Augmented Fourth" or "Diminished Fifth"
G 5 or bb6 "Perfect Fifth" or "Diminished Sixth"
G#/Ab #5 or b6 "Augmented Fifth" or "Minor Sixth"
A 6 or bb7 "Major Sixth" or "Diminished Seventh"
A#/Bb #6 or b7 "Augmented Sixth" or "Minor Seventh"
B 7 "Major Seventh"
C 8 "Octave
C#/Db b9 "Minor Ninth"
D 9 or bb10 "Major Ninth" or "Diminished Tenth"
D#/Eb #9 or b10 "Augmented Ninth" or "Minor Tenth"
E 10 or b11 "Major Tenth" or "Diminished Eleventh"
F 11 "Perfect Eleventh"
F#/Gb #11 or b12 "Augmented Eleventh" or "Diminished Twelfth"
G 12 or bb13 "Perfect Twelfth" or "Diminished Thirteenth"
G#/Ab #12 or b13 "Augmented Twelfth" or "Minor Thirteenth"
A 13 or bb14 "Major Thirteenth" or "Diminished Fourteenth"
A#/Bb #13 or b14 "Augmented Thirteenth" or "Minor Fourteenth"
B 14 "Major Fourteenth"
If we take A as our tonic:
A 1 "Prime" "Unison" "Root Note" or "Tonic" depending on context
A#/Bb b2 "Minor Second"
B 2 or bb3 "Major Second" or "Diminished Third"
C #2 or b3 "Augmented Second" or "Minor Third"
C#/Db 3 or b4 "Major Third" or "Diminished Fourth"
D 4 "Perfect Fourth"
D#/Eb #4 or b5 "Augmented Fourth" or "Diminished Fifth"
E 5 or bb6 "Perfect Fifth" or "Diminished Sixth"
F #5 or b6 "Augmented Fifth" or "Minor Sixth"
F#/Gb 6 or bb7 "Major Sixth" or "Diminished Seventh"
G #6 or b7 "Augmented Sixth" or "Minor Seventh"
G#/Ab 7 "Major Seventh"
A 8 "Octave
A#/Bb b9 "Minor Ninth"
B 9 or bb10 "Major Ninth" or "Diminished Tenth"
C #9 or b10 "Augmented Ninth" or "Minor Tenth"
C#/Db 10 or b11 "Major Tenth" or "Diminished Eleventh"
D 11 "Perfect Eleventh"
D#/Eb #11 or b12 "Augmented Eleventh" or "Diminished Twelfth"
E 12 or bb13 "Perfect Twelfth" or "Diminished Thirteenth"
F #12 or b13 "Augmented Twelfth" or "Minor Thirteenth"
F#/Gb 13 or bb14 "Major Thirteenth" or "Diminished Fourteenth"
G #13 or b14 "Augmented Thirteenth" or "Minor Fourteenth"
G#/Ab 14 "Major Fourteenth"
And so on. Homework: Watch the videos on Musictheory.net under the category "Intervals."
A mode is an intervallic structure that can be applied to any note and turned into a scale. A scale is a mode with a decided tonic. This means that if we have a mode made of the intervals 1, 3, 5, and 6 and you apply the tonic A, you're scale will be A, C#, E, F#. Often times people use the terms "scale" and "mode" interchangeably, it really isn't anything to freak out about.
The first scale you'll learn is very simple, and has the same notes no matter what tonic you choose. It's called the chromatic scale, and it is made up of all 12 notes. It's intervallic structure would be 1-b2-2-b3-3-4-#4/b5-5-#5/b6-6-b7-7. If you apply this mode to the tonic D# you end up with:
You can now apply "scale degrees" to this scale. Scale degrees are an informal, quick way to express which note of the scale you're referring to.
Often times people confuse intervals and scale degrees. DO NOT DO THAT.
Section 3--The Overtone Series, The Circle of Fifths, and The Major Pentatonic Scale
to understand the "overtone series" before moving on.
The "circle of fifths" is what happens if you take a tonic, find it's 5th, turn that 5th into your new tonic, find it's fifth, and keep going until you've completed a circle. Starting on C:
C, G (5 of C), D (5 of G), A (5 of D), E, B, F#, Db, Ab, Eb, Bb, F, and back to C.
The circle backwards is the circle of fourths:
C, F (4th of C), Bb (4th of F), Eb, Ab, Db, F#, B, E, A, D, G, C.
At some point in very early music, various cultures simultaneously discovered "pentatonic scales" (scales made of 5 notes). The most common was the major pentatonic scale (1-2-3-5-6). These notes are the first 5 notes of the circle of fifths. There isn't much of an explanation for why multiple cultures with no relation to each other developed this scale simultaneously, when the circle of fifths hadn't even come into use yet. One theory is that since it is the first 5 notes of the overtone series condensed into one octave, people subconsciously knew it would sound very consonant*. Theorists actually argue intensely over where the scale came from, and to give you a taste of what it's like to be a theorist,** here is an argument over the pentatonic scale (with a link provided to an interesting video I highly recommend you watch mostly for pure entertainment, it's on the 4th post "One supporting example"):
http://forum.emusictheory.com/read.php?5,7858 They also use the term "harmonic series" as a synonym to the "overtone series," just a heads up.
*Consonant-Pretty sounding as apposed to harsh sounding; harmony as apposed to acrimony.
**I hope all readers understand that you don't have to be a music theorist to be a musician, knowing general theory can help you greatly in the art of creating sound, but there is a difference between a music performer (one who plays music on stage), a composer (one who creates/writes music), a music theorist (one who specializes in studying music, the history of music, how/why music works the way it does, ect.) and an acoustic scientist (one who studies sound waves and how sound works). They are all amazing and respectable careers and I'd like to think I'm giving a decent start for anyone interested in any of them, but in the end, especially if you want to be a theorist or acoustic scientist, you'll need much more formal training in this sort of thing than I can give you.
The pentatonic scale is a good source for simple, pretty melodies. Some musicians make a whole career out of it. Almost every song by Foster the People uses almost exclusively notes in this scale (and I think they use it very well). Blues and rock guitar players including Jimi Hendrix use it very frequently (although Hendrix is good enough to where it never sounds like he's playing a scale, and typically blues involves a lot more than the major pentatonic scale). Take Me Out to the Ballgame has a phrase or two which fit in the scale, and so do many other classic American jingles.
Play around with the scale yourself; there's no doubt you'll quickly come up with a catchy, easily-enjoyable melody.
Section 4--Harmony and Triads
This is the very beginning of a long journey in learning all about harmony. Actually, you're journey can be made MUCH shorter if you pay attention to a reliable source (I may be biased, but I think I'm reliable).
Harmony is playing multiple notes at the same time to create chords and chord progressions. An English professor may assume that the opposite of harmony (which means an agreement of sounds) would be acrimony (sharp sounds), but musicians prefer to refer to ALL combinations of notes as harmony, and use the terms consonance and dissonance to refer to whether it sounds pleasant or harsh. Dissonance definitely DOES have it's place in music. Too much dissonance can make a song sound difficult to listen to...But hey, sometimes the only way to make your statement heard is to stab your audience in the ear?
For a proper education on harmony, I would suggest you read multiple books (most or all of them named simply "Harmony") starting with the book that created our modern sense of harmony. This book is Treatise on Harmony by Jean-Phillipe Rameau, published in 1722. This book talks a lot about acoustics. In some cases Rameau is actually wrong about many of his acoustical theories, but you can see how those assumptions led him to create his theories and systems on music which are still the most commonly used in composition today. Other books that could be important for getting multiple different theorists' perspectives on harmony would be:
Harmony Simplified by Hugo Riemann
Theory of Harmony by Arnold Schoenberg
Harmony by Heinrich Schenker
Harmony by Walter Piston
All of these authors also have other great books.
WARNING: These books are EXTREMELY dry and often difficult to understand, theorists even argue sometimes about the meanings of certain things these authors have said.
Okay, so now on to some very basic harmony, beginning with vocabulary:
Chords-Three or more notes played at the same time
Tertian harmony-The technique of creating chords by "stacking thirds" (which will be explained)
Triad-A three-note tertian chord
How do we "stack thirds?" Well we start by choosing a root note. I'll use C.
We want to use the generic interval of a 3rd. This means we choose a minor or major 3rd away from C, so either Eb or E. I'll use E.
So our chord so far is made of C and E. Now we use the minor or major 3rd from E, which is G or G#. I'll choose G.
So now we have the triad: C-E-G. To review: C, major 3rd E, minor 3rd G. Or if you prefer to think of it all in terms of C, G is a perfect 5th away from C, so C-E-G is 1-3-5. This is a Cmajor triad, or Cmajor chord. Why is it major? Because we used the major 3rd and perfect 5th, or because we used the major 3rd and the minor 3rd of that note.
Now let's make a minor chord. We'll use the root note A. The minor 3rd of A is C, and the major third of C is E. A-C-E, or 1-b3-5.
Now let's make a diminished chord. We'll use B. The minor third of B is D. The minor 3rd of D is F. B-D-F, or 1-b3-b5.
Finally, the augmented chord, using C again. The major 3rd of C is E. The major 3rd of E is G#. C-E-G#, or 1-3-#5.
So in review:
To make a major chord, play any root note, it's major 3rd, and that note's minor 3rd. 1-3-5
To make a minor chord, play any root note, it's minor 3rd, and that note's major 3rd. 1-b3-5
To make a diminished chord, play any root note, it's minor 3rd, and that note's minor 3rd. 1-b3-b5.
To make an augmented chord, play any root note, it's major 3rd, and that note's major 3rd. 1-3-#5.
Major chords are the most consonant, minor chords slightly dissonant, and diminished and augmented chords are harshly dissonant. At the end of the day though, the way the chord sounds depends on the context, how it is used in the song.
Stay tuned for Part 3, where I'll cover more about harmony and introduce the major and minor scales.