More Intervals

author: CPDmusic date: 07/16/2010 category: the basics
rating: 6.4 / votes: 5 
Intro: Hello, and welcome to another CPDmusic lesson! Today we will expand on our lesson on major and minor intervals by learning about augmented, diminished, and compound musical intervals. You will need to have some knowledge on the major and minor intervals, so if you haven't read my lesson on them already, you can do so here. So, lets get down to business! Augmented Intervals: First of all, what is an augmented interval? Well, an augmented interval is when a major or perfect interval is sharpened (raised) by half a step (one semitone). There are eight types of augmented intervals: an augmented unison, second, third, fourth, fifth, sixth, seventh, and octave. So, lets start by looking at the augmented unison. As we know from the last musical interval lesson, unison is when the two notes are exactly the same, like this:
E||------------||
B||------------||
G||------------||
D||------------||
A||------------||
E||--0----0----||
Now, we also know that and augmented interval is when a major or perfect interval is sharpened by half a step (a unison interval being a perfect interval) meaning that an augmented unison would be this:
E||------------||
B||------------||
G||------------||
D||------------||
A||------------||
E||--0----1----||
Now, you may have noticed that this is the same as the minor second interval; one semitone. That is correct, the two are enharmonic intervals, meaning that they sound exactly the same. So than, what's the point of having two names for the same two intervals? Well, the main use of augmented intervals is in augmented chords. We will get into this idea later, in an upcoming lesson on using intervals to construct chords. So, now that we get the idea, lets look at the remaining augmented intervals, in order from smallest range to largest range (in order from augmented second to augmented octave):
E||--0----3---|--0----5---|--0----6---|--0----8---|
  
  |--0----10---|--0----12--|--0----13---||
So, those are the augmented intervals! We will use these when creating augmented chords in an upcoming lesson, so don't forget them! Diminished Intervals: To start off, diminished intervals are much like augmented intervals, except instead of raising a major or perfect interval by a semitone, diminished interval are when a MINOR or perfect interval is LOWERED by a semitone. Like the augmented intervals, there are diminished unison (well, that is debatable), second, third, forth, fifth, sixth, seventh, and octave intervals. So, lets look at these intervals, starting with the diminished unison. First of all, I said above that this interval is debatable. This is because some musical theorists do not consider it a legitimate interval, because it breaks the rule that all dyadic intervals are named from the lower note, and instead call the interval an augmented unison. To better explain that lets look at, for example, the minor second interval.
E||------------||
B||------------||
G||------------||
D||------------||
A||--0----1----||
E||------------||
This interval is named a minor second because the higher note is a half step above the lower note. But, a diminished unison interval looks like this:
E||------------||
B||------------||
G||------------||
D||------------||
A||--0---------||
E||-------4----||
It is an A going DOWN to a G#. Now, as I said above, some music theorists strictly follow the rule that a musical interval is named from the lower note, being G# in this case. So, G# to A would be an augmented unison. So, there's your little lesson in music theology for today. Anyway, lets look at the rest of the diminished interval (which are all totally legitimate) in the same fashion as with the augmented intervals (diminished second, third, fourth).
A||--0----0---|--0----2---|--0----4---|--0----6---|
  
  |--0----7---|--0----9---|--0----11--||
So, those are diminished intervals. They are used when constructingdiminished chords. (Once again, wait for the next lesson) Compound Intervals: Compound intervals are pretty simple, an octave PLUS another interval. So then, theoretically, there are an infinite number of compound intervals. But, for the sake of time, we will only look at the three that we will use in our lesson on chord theory, the ninth interval (used to make ninth chords), the eleventh interval (used to make eleventh chords) and the thirteenth interval (used to make thirteenth chords). So, lets look at the ninth interval to start. A ninth interval is an octave plus a second. This means that there are both major ninth and minor ninth intervals, depending on whether you add a major or minor second. So, a minor ninth would be an octave plus a minor second, or 12 semitones plus one semitone, resulting in 13 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------------||
E||--0----13----||
And a major ninth would be 12 semitones plus two semitones, making 14 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------------||
E||--0----14----||
Now, an eleventh interval is an octave plus a fourth, meaning there are both perfect and augmented eleventh intervals. A perfect eleventh would be an octave, or 12 semitones, plus a perfect fourth, or 5 semitones, resulting in 17 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------------||
E||--0----17----||
An augmented eleventh is an octave plus an augmented fourth, resulting in 18 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------------||
E||--0----18----||
And finally, the thirteenth intervals. A thirteenth interval is an octave plus a sixth, meaning that there are major and minor thirteenth intervals. A minor thirteenth interval would be 20 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------15----||
E||--0----------||
And a major thirteenth interval would be 21 semitones:
E||-------------||
B||-------------||
G||-------------||
D||-------------||
A||-------16----||
E||--0----------||
So, those are the main compound intervals you need to know, although there are many, many, many more. Outro: So, that's all for today's lesson. We now know major, minor, perfect, augmented, diminished, and compound intervals. We will use this knowledge in an upcoming lesson on chord theory, and using these intervals to construct major, minor, augmented, diminished, ninth, eleventh, and thirteenth chords and arpeggios. This may seem like a lot, but it's a lot easier than it may seem, and is well worth it in the long run. Did You Like This Lesson? Check Out My Last Lesson, Unorthodox Tonalities. More Lessons Coming Soon!
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