More Intervals

Today we will expand on our lesson on major and minor intervals by learning about augmented, diminished, and compound musical intervals.

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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!

9 comments sorted by best / new / date

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    AeolianWolf
    hate to take issue with what you wrote again, friend, but i have to - i simply don't agree with everything you've said.
    There are eight types of augmented intervals: an augmented unison, second, third, fourth, fifth, sixth, seventh, and octave.
    there is also such a thing as an augmented ninth. and it goes on -- augmented tenth, augmented eleventh -- to infinity, really. why not just say "all intervals can be made augmented"? the same is true for diminished intervals. it's strange, because you mention compound augmented intervals.
    Well, the main use of augmented intervals is in augmented chords.
    i don't know if i'd say the "main" use. and really, there's only one augmented interval in an augmented chord - the augmented fifth. there is no other augmented interval -- in fact, the construction of an augmented chord is simply the stacking of two major thirds. the same thing applies for what you said about diminished chords. the only diminished interval in a diminished chord is the diminished fifth (and a diminished seventh in a diminished seventh chord).
    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.
    no. G# to A is a minor second. G# to Gx (G double sharp) is an augmented unison. proper interval notation is focused on how music is written on paper, and less on how it sounds. i don't always follow the rule that intervals should be named from the bottom note -- it is beneficial to musicians to be able to recognize descending intervals as well. A down to G# is still a minor second. A down to Ab is a diminished unison.
    mrddrm
    I agree with AeolianWolf. Especially on the fact that I had to learn intervals up and down at university, not just up. When building chords you may have to do the base then up, but otherwise, it's free reign. And mentioning chords, it is easier (much easier) to simply look at chords as combinations of M3 and m3. M3+m3=Major Chord m3+M3=Minor Chord M3+M3=Augmented Chord m3+m3=Diminished Chord Easy. None of this "Well... there is a major third followed by a augmented fifth to make an augmented chord..." Sooo much more confusing (but good to know the theory behind.)
    King Nothin
    u need to go back to GCSE music or something, it is just the basics that you dont understand. let alone posting lessons. weird.
    crazysam23_Atax
    Yeah, I really don't get how this helps. Again, you really kind of butchered this. Same way you did with the modes.
    CPDmusic
    crazysam23_Atax wrote: Yeah, I really don't get how this helps. Again, you really kind of butchered this. Same way you did with the modes.
    Modes? I've never done anything involving modes...
    aaronq1222
    So, a minor ninth would be an octave plus a minor second, or 12 semitones plus one semitone, resulting in 13 semitones
    Incorrect. The ninth in a minor ninth chord is a major ninth, 9 (A whole tone up from the octave). What you described is the chord known as the minor seven flat nine chord, m7b9, or just b9 (A semi-tone up from the octave).
    aaronq1222
    My bad. I looked back and realized you were just talking about the interval, not the chord. You're right.
    Music One
    There's common theory and advanced theory of intervals. We are used to the common theory. For an example, 1rst, 2nd's, 3rd's 4th's 5th's 6th's and 7th's. Proper terminology in the musical language is to pronounce it as 1rst is a "perfect 1rst", "major 1rst" or "natural 1rst". For flats and sharps, (flat= b/sharps=#) b-2nd's which is minor 2nd's b-3rd's which is minor 3rd's 4th's which is perfect 4th b-5th's which is flat-5th and also is a diminish 5th #-5th which is sharp-5th and also augmented 5th 6th's which is perfect 6th b-7th which is flat-7th and also is minor 7th natural 7th is perfect 7th and major 7th 8th's is octave to it's tonic 1rst We don't use 8th's in the musical language only used in advanced theory. If we compare enharmonics with intervals 1rst to 2nd's - flat 2nd's or sharp 1rst's would compare up to the same note. It's only used in advanced theory. Enharmonics is legally B to C or C to B, B# and Cb are the same note. For an example, B# is C, Cb is B.