Remembering where we left off with half-steps, we are going to define our distances with the name, as well as their distance in half-steps. There are five types of interval, Major, Minor, Perfect, Augmented, and Diminished. Perfect intervals are the easiest to explain, because it is the smallest subset. A perfect interval is one which when inverted, remains Perfect, is perfectly consonant, and appears early in the harmonic series. The question now becomes, what the heck does that mean? An inversion is when you change the organization of a set of tones, such that the lowest (or bass voice) tone has changed, while preserving the initial tone set. I'm not really simplifying this very well, am I? With examples it quickly becomes clear. I should add that this is an overly complicated explanation for a very simple concept.
The first perfect interval is P1, or the perfect unison. Lets use C for our example note. Our plucky musician plays a C, then plays the exact same C a bit later. He has represented P1 (P for perfect, 1 for unison) well, perfectly. The measurement here is zero half-steps, it is the same note. Since it is the same note, it cannot be possessed of any natural dissonance above and beyond what is present in the sound generated by the sound source itself. This is initially somewhat confusing, because there is a trend towards thinking that a measurement of zero is nothing, but that is not the case here. Unison functions in a very specific manner in music, and thus is not nothing.
The second perfect interval is P8, or the perfect octave. Using our C from the previous example, our musician hammers away at a C one octave higher, playing both notes simultaneously. Two notes played in tandem is called a dyad(I think that is how it is spelled). Since both notes are the same note, just an octave apart, this too cannot be possessed of any natural dissonance. Now that we have two simple intervals, lets revisit that inversion business and see what we can figure out.
In our perfect unison example, we have 2 instances of the same note. Let us now assume that both notes have been played simultaneously by 2 players, so we have a dyad. To invert this interval, we take the bass note and move it up an octave. Since both notes are the same, one of our players just begins playing a note an octave higher. Our P1 has now become a P8, meaning the intervals retained perfect status through inversion. OH MY GOD IT IS LIKE HE SELECTED THE COMPLETELY RANDOM EXAMPLES SPECIFICALLY FOR THIS PURPOSE!!!! Wheels within wheels, maaaaaaaaan. Now the really interesting thing to note about this is when you add the numbers up, you come up with 9. It is tough to keep track of all of the wheels in motion here!
That's all easy to follow, so lets elaborate. Same set up with two musicians. First musician plays a C, second plays the G above that C.
This is a perfect 5th. We can identify this in a couple ways. The easiest is to count note names: C, D, E, F, G. C is the first note, G is the last, there's a total of five. We can also count half steps (go ahead and count, I'll wait!), of which there are seven total. This is transitive across any dyad, it doesn't just work for C to G. The perfect fifth is one of the most important intervals there is, and has perfect consonance. Which leads us into an excellent opportunity to explain consonance and dissonance. If you want to talk about concepts that have really defined and shaped western music through history, these are two of the biggies. Consonance is the listening state of being at rest, and means that your sonic quality does not have any warbling or beating to it. Dissonance is, conversely, the listening state of being in motion, and means that your sonic quality does have beating. To explain, being at rest means that your ear is completely satisfied with that which it has been presented, and does not feel like it needs to continue musical motion (whether or not further musical motion is presented). To hear this we should consult a master. Go to this website and click to listen to the Minuet in F Major. Direct linking appears to be disabled.
This piece is in 3/4. Listen to the melody, and how it seems to express a musical thought over the course of 4 measures. This then repeats through the work. At the end of every set of 4, notice how your ear doesn't seem to like that held half note at the end, but much prefers the last quarter note when played. This is especially noticeable at the end, as our second to last set of 4 does not end in a satisfactory manner, instead we have to wait for the last 4, which is then held for a longer period of time and feels like a proper ending. That feeling at the end! That is rest. We have brief periods of rest at the end of every 4 measures, but they are de-emphasized in order to keep the work light and fanciful. Those held notes that seem to pull you to the final note in the set, those are in motion. They're pulling you towards the end, which establishes a good sense of inevitability. Remember that one from AC/DC? Now, this is not to say that ending in motion is bad or not acceptable, it is just a different sound that is unsatisfying to the listener. Sometimes you can't get no satisfaction. Please also note that consonance and dissonance are somewhat of a sliding scale. The perfect intervals are as consonant as it is possible to get, and all other intervals are of relatively increasing levels of dissonance.
Onwards and upwards, our next interval is the P4. Composed of 5 half steps, it functions differently than all of the perfect intervals.
Before we discuss how it functions differently, lets talk about inversions again! The inversion of the P4 is, naturally, the P5 and vice versa (oh look, they add up to 9). This is good to keep in the back of your head, because the P5 will take a major center stage in the near future, while the P4 lies forgotten by the roadside, having to scrape together cash by begging on the street. Sure the P5 is going to occasionally kick some cash P4's way and they'll both pretend they're ok with how things have turned out but really P4 keeps on plugging away trying to make the chords work, while P5 is covetous of P4's laidback lifestyle. The main thing that's interesting about P4 is that it is a restful state when approached in one manner (Herbal Tea) and is in motion when approached in another (Coffee). Approached in this case means stuff played before we get to the the P4. This means that it possesses perfect consonance, as is required of a perfect interval, but can be used as dissonance when prepared properly. The reasons for this have to do with the harmonic series gobbletygook I posted about above and which I'll explain at some point.That takes us out of perfect intervals, and onto the other 4, which are more complicated, but will be quicker to explain. Most of their complication will take place in subsequent lessons.
One point that needs clarification is that to define an interval one defines the note by the scale number and position first. Because our starting point was defined as C for this, that is the first note, or the 1. The 2 would then be a variation of D, the 3 would be a variation of E, etc etc. Since we're using the chromatic scale, when ascending (Remember it is notated differently depending on directionality) the C# would be defined as a 1 also.
The Major intervals are M2, M3, M6, M7. M2 would be C to D and possesses 2 half steps. M2 is a dissonant interval, and is one of the most dissonant intervals. M3 is C to E, is 4 half steps, and is a consonant interval. M6 is C to A, 9 half steps, and is a consonant interval. M7 is C to B, 11 half steps, and is a dissonant interval.
The Minor intervals are m2, m3, m6, m7. Looks familiar doesn't it? Please notice that the m's have become lowercase, that is to distinguish between major and minor. Minor intervals are simply Major intervals that have been diminished by a half step, and function similarly. Thus, m2 is D♭. Remember, defined by scale position first, so even though this could be called a C#, it doesn't function as one. m2 is one half step, is a dissonant interval, and is even more dissonant than M2. m3 is C to E♭, is 3 half steps, and is a consonant interval. m6 is C to A♭, is 8 half steps, and is a consonant interval. m7 is C to B♭, is 10 half steps, and is a dissonant interval (technically).
Inversions for Major and Minor intervals function a bit differently than Perfect intervals, since Perfect intervals invert to other Perfects. Major intervals invert to Minor intervals, and vice versa. Don't believe me? Lets look at M3! M3 is C to E, 4 half steps. E to C is how many half steps? That's right, it is 8 half steps, which is m6. What is major, now is minor. The other conversions should be easy to figure out.
Finally we get to discuss Augmented and Diminished intervals! I'm sure you're on the edge of your seat waiting to see how all of this will resolve. Augmented intervals are ones that have had their pitch raised. Diminished intervals are ones that have had their pitch lowered. So if we have a M3 that is then diminished, we get an m3. If we then take that m3 and diminish it further, we get what would ordinarily function as an M2, but is in fact a d3 in this case. Now we're discussing actual theory! Things that are technically correct but practically useless! Function before form! I'm only half joking here. There are very good reasons why a dim3 would be used instead of a notation that would make more sense at a first parse. Those, however, are much more advanced than we're going into this lesson, and so just take my word at face value, as you must do with creation science as well.
More applicably, were we to wish to modify a perfect interval, it always immediately goes to a diminished character. Some of you may have noticed that we are missing the G♭ from these examples. This fine young gentleman is the diminished 5th (d5), the augmented 4th, also known as the tritone, or the diabolis in musica. Weighing in at a middleweight of 6 half steps, it acts as its own inversion (4.5 + 4.5 =???). The tritone has a lush, storied history. It is considered the most dissonant interval (which I personally disagree with), and is indeed so horrifically dissonant that it was COMPLETELY BANNED FROM USE IN MUSIC BY THE CATHOLIC CHURCH FOR A COUPLE HUNDRED YEARS. Music that had a single tritone in it was considered Satanic and heretical. You call yourself a person of conviction? Are you willing to be excommunicated for your music? Needless to say, as the cultural domination of the Catholic church weakened in Europe, the tritone went from being entirely unused to being a staple of modern music and even ended up defining a genre.
Augmented intervals are the opposite of diminished ones. a4 is our good buddy the tritone that we just talked about. a5 is the same tone as m6, but functions differently depending on situation. A lot of these conditional situations are going to be in subsequent lessons, so just internalize that they exist. I don't want you scoundrels thinking that an m6 is an a5 and then going out and spraypainting that on a wall somewhere!
As always, questions, comments, and further instructional material are appreciated.
Where can I find a diminished 5th in modern music?
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