I’m starting to think that I learned my intervals in the wrong order.
You probably learned your musical intervals like this:
C-Db m2
C-D M2
C-Eb m3
C-E M3
C-F P4
C-F# Tritone
C-G P5
Intervals refer to note (excuse me) frequency relationships. Everything in music can be reduced to intervals, the molecules of musical matter.
This may seem like the right order because the intervals get “bigger'“ but music doesn’t exactly make sense from “small to big”. Why are 4ths “perfect” while thirds can be major or minor?
I propose a solution, let’s leave behind the piano for now and think of music the way Pythagoras of Samos did. For Pythagoras music, science and religion were all interconnected. He built a whole cult based on math. He didn’t have a piano with 230 strings to work with, he figured out how music worked just fine with one string. We can take that string and change it’s length and therefore the frequency of that string just like those nutty Pythagoreans did. In Lesson 1 we discussed replacing the idea of notes with frequencies. Let’s expand upon that. let’s call this system, “Intervals: From Order to Chaos”
(Note: I will not get into the minutiae of Just intonation vs. equal temperament or any other tuning systems for this video. We’ll keep things simple for today)
People like using A 44o as a template because it’s a nice, round number. I’m going to use the C string on my six-string bass because it allows us to use C as a reference pitch and it justifies me owning a six-string bass. I said in the last video that C3 vibrates at 130.81 Hz, but there is no need to keep track of this number. We will be studying intervals which are relationships between frequencies and the actual numbers don’t matter as much as the relationships.
The first interval we should learn is the unison. It’s a ratio of 1:1
It’s the state of unmoving. It’s stasis. It’s what’s known as “The Monad” As the universe was in the moment before it’s creation. When all was one, a singularity.
Next up is the Perfect Octave, having a ratio of 2:1. Take a string of any length and split it in half and you will get an Octave. Octaves exists in most musical cultures around the world. It’s why you have two dots on your twelfth fret. The octave is so consonant that when you play it, you haven’t “gone anywhere” so it could still be considered “The Monad”. Play one harmonically with your volume all the way down and raise the volume as you sustain it. If your instrument is perfectly in tune, it will sound like a single note.
The next interval in this system is the Perfect 5th. The ratio is 3:2, A third the length of your string. This is when you can say that the intervals actually “go somewhere”. It’s the first true “diad”. This importance can’t be understated. If I take this old metronome and set it to eighth notes and triplets simultaneously, it’s now playing a very slow perfect 5th. Think of the 5th as a “balance point” this is important in future lessons.
Next up is the perfect 4th. A ratio of 4:3. Consonant enough to be considered Perfect, as the 5th is. Now considering that an octave is considered consonant enough to be practically a singularity, let’s consider the interesting relationship between the 4th and 5th.
A 5th is a 4th and a 4th is a 5th. They invert to each other so they can be considered the same interval. This allows us to create a relationship pattern that yields 12 tones. It also allows us to create the circle of 5ths, otherwise known as the cycle of 4ths which forms a perfect lattice of tones. We do well to study and understand this lattice.
I categorize the Perfect intervals as the Foundational intervals. They represent pure Order in their mathematical simplicity. As the foundations of the earth were here before the dawn of man, the perfect intervals have been and always will be.
The next interval is the Major 3rd. A ratio of 5:4 it is considered consonant but imperfect. I call it the Yang interval. It is bright and warm, not unemotional and solid like the perfect intervals.
The minor 3rd is next with a ratio of 6:5. Minor 3rds stand as a counterpart to Major 3rds, The minor 3rd is dark and sad. I actually even call it the Yin to the Major 3rd’s Yang. An interesting feature of these intervals is that they invert to their tonal counterparts. A Major 3rd inverts to a minor 6th. A minor 3rd inverts to a Major 6th. Like the eye of the serpent in the supreme ultimate, in Yin there is Yang and in Yang there is Yin.
I call these the corporeal intervals because I feel like they have a material and tangible form, like our bodies. They are the light and dark elements of music.
As the complexity of these intervals increases the notes actually move closer together. A Major 2nd is pushing the limits of harmonic stability having a ratio of 9:8. The Major 2nd inverts to a minor 7th. The minor 2nd edges closer to dissonance than ever. It’s ratio is 16:15. Minor 2nds inverts to major 7ths which were until recently considered dissonant. I call these the adjacent intervals because, well they are next to each other. Their closeness creates a sense of motion, hence we tend to run scales in 2nds.
Now we get to the most complex intervals. The tritone has a ratio of 45:32 and is the proverbial “fly in the ointment” of harmony. It stands as the counterpart of the stability of the perfect 5th and sits somewhat ironically a half step away from the perfect 5th. The tritone inverts symmetrically, which is another interesting feature.
There is one more interval we will discuss, It’s the b9. It’s the counterpart of the octave. The b9 is extremely unstable as it expands one semitone beyond the octave. We reach a sufficient level of chaos at this point and we’ve created a spectrum of chaos and order to work with.
Consider that the numbers 666 and 13 are unlucky numbers. The 6th fret from the open string is the tritone and the 13th fret from the open string would create a b9. In numerology, the number 5 is the number of power while seven is a lucky number. the fifth fret creates a perfect 4th and the 7th fret creates a perfect 5th.
This is a more organized system of naming the intervals. It involves the ear far more because it is far easier to distinguish a tritone when it’s thought of as “complex” and to hear a Perfect 5th when we feel that it’s “secure and simple”. If I had started learning in this manner, then perhaps I would not have run into as many problems as I did when I was starting out.
So, let’s try learning the intervals in this manner and see how it works out. If we keep compounding these intervals, we get all the usual elements of chords and scales that we are accustomed to. I will continue building upon these elements in the next video. Please like and subscribe and tell me what you think in the comments below. Thank you.