[MUSIC] In the last lecture, we defined all the possible intervals. We said Unisons, 4ths, 5ths and Octaves can be Perfect, Diminshed and Augmented. 2nds, 3rds, 6ths and 7ths can be Major, Minor, Diminished or Augmented. We saw how we can count half steps to figure out intervals. For example, a diminished 5th has 6 half steps. An augmented 7th has 12 half steps. But there are faster ways, such as using scale degree relationships, Do up to any diatonic interval is major, or perfect. And memorized referenced intervals. Let's start this lecture by practicing labeling and spelling intervals. If you have memorized your major 3rds, even just the major 3rds up from the white keys on the piano, and if you remember that all perfect intervals have the same accidentals except for the two between B and F, you can figure out any unknown interval by comparing it to a known interval. For example, what is the interval Ab up to C#? If you already know that A to C# is a major 3rd, you know that Ab to C is also a major 3rd and you can easily figure out Ab to C#. The major 3rd has been made wider so the interval is augmented. How about D# to G natural? You know that D to G is a 4th. You know that perfect 4ths have the same accidentals. So D to G is perfect, as is D# to G#. And you know that raising the bottom note or lowering the top note shrinks the interval, making it narrower. So D# to G is a diminished 4th. Remember shrinking a perfect interval gives a diminished interval, not a minor one. One more, what is an augmented 6th down from C#? First, C anything down a 6th is E something. Let's use the "Up from Do" method. Eb up to C is a major 6th. Since C natural is "La" in Eb major, three flats. And an augmented 6th is a half step wider than a major 6th. So we must lower the bottom note. So C# to Eb is an augmented 6th. I've already mentioned inversions of intervals, where we move the bottom note of an interval up an octave or the top note down an octave. Let's do it with this perfect 4th, moving the F# above the B. When we invert a perfect 4th, we get a perfect 5th. When we invert a major 6th, we get a minor 3rd. Maybe you're noticing a pattern. An interval plus its inversion always adds up to 9, 2nds to 7ths, 3rds to 6ths, and so on. Furthermore, Diminished intervals invert to Augmented intervals and vice versa, Minor and Major intervert to each other, and Perfect intervals invert to Perfect intervals. So a major 3rd, say F# up to A#, inverts to a minor 6th, A# up to F#. This is another good way to figure out large non-diatonic intervals. Let's look at C# down to Eb again. It's a big cramatic 6th, the two notes don't belong together in a key. When we invert the 6th, moving the Eb up an octave perhaps, we can get a 3rd between Eb and C#. Since you have memorized major 3rds, you know that C to E and C# to E# are major 3rds. C# to E is a minor 3rd, so C# to Eb is a diminished 3rd, two half steps. If C# up to Eb is a diminished 3rd, inverted C# down to Eb is an augmented 6th, 10 half steps. The half steps of an interval plus its inversion always adds up to 12, since that's how many half steps there are in an octave. Lets do one more, a really ugly one. What note is a diminished 6th up from E#? A diminished 6th inverts to an augmented 3rd. E# down to what note is an augmented 3rd? E# down to C# is a major third. Making that interval wider by lowering the C# gives C natural, which is an augmented 3rd. Moving the C natural up an octave makes an augmented 6th. Finally, let's use the intervallic equivalence method. A diminished 6th sounds like a perfect 5th. A perfect 5th, up from E#, is B#. When we respell B# to C natural, we have a diminished 6th. That's it for intervals. You now know several ways to figure out even the most complicated intervals. I suggest you practice. Give yourself a starting note, and figure out an interval above or below it. A# up an augmented 4th, perhaps. B# down a minor 7th. The more you practice, the faster you'll get, and you'll discover what method works best for you. In the next module, we're going to start talking about rhythm and meter. [SOUND]