[Present Vin:] Hmm… I wonder what scale is hidden within the major scale. Let’s extract some invisible scales.
Musical scales are very interesting things. There are so many types. We've got major scales, minor scales, diminished scales, augmented scales, Neapolitan scales, scales for jazz and the blues, and even— invisible scales?! Well, invisible scales aren’t exactly invisible, per se. These kinds of scales are hidden in plain sight within other scales, tucked into the gaps between notes.
Quick vocab lesson before I move on. Diatonic notes are the ones already in the scale, and non-diatonic notes are the ones in between. Invisible scales are kinda both, if you think about it.
If we start with C major [in blue] and make all the non-diatonic notes red, we get this. Let’s extract the red notes. Now, let’s fill in the blanks with generic note letters. I found, after going through this same exact process with many iterations of C major and C minor scales, F#, the tritone, had been extracted from all of them, meaning that they’re the farthest apart from one another two notes can possibly be on the piano keyboard. Let’s rearrange the resulting set of notes to begin with F#. And now, we’re left with something called F# Mixolydian mode.
[Future Vin:] Psst… Modes are just scales that start on different notes. There are many different kinds of modes, both major and minor, but that’s something I don’t have time to explain right now. If you wanna learn more about modes, check out Signals Music Studio. He has fantastic videos about modes. Anyway…
[Present Vin:] I added in E and B because those went missing somehow. All the red notes, excluding E and B, were originally non-diatonic to C major, but are now diatonic to F# Mixolydian mode. But, since all these notes form a unique scale, I can now call all of them diatonic. If you transpose this back to C, you get something called C Mixolydian mode. Comparing C Mixolydian to C Major, you may notice one significant difference: the B has become a Bb.
[Future Vin:] Hmm… where’d that come from?
[Present Vin:] I was wondering the same thing when I decided to experiment with finding invisible scales. My goal in this video is to show you how each invisible scale compares to and relates to its original scale, for example how C Mixolydian relates to C Major.
In order to do this, I started with different variations of major scales and minor scales and charted them out. Let’s get started!
[a polyphonic procession of explanations of charts which illustrate my failed experiment]
*groan* Okay— I may have gone overboard on this.
You see, my initial goal was to take ten scales, extract their invisible scales, and proceed to compare each original scale with its respective invisible scale. I was hoping to find some kind of pattern that remained among all the scales. Turns out that things aren’t always that simple. There was no apparent rhyme or reason to anything. Yes, maybe there were a couple of interesting things that I found for one scale or another scale, but there was no overall pattern. There’s not a singular magical word that will [show you? 3:12] what pattern or quality every single one of these invisible scales has in common as compared to their original scales.
Where did I go wrong? Let’s back up and take it step by step. If you’re confused by the end of this video— good. I want you to be as deep into this process as I was. It started with a simple concept…
[Past Vin:] I wonder what’ll happen if I try to put together all the notes in between the notes of a scale. Oh, look, there are two notes missing. I’ll just add them back in as generic notes to fill in the blank. What’s this scale? F# Mixolydian? Cool, but why is it F# Mixolydian? Oh, I see… because no matter what major scale I start with, as long as it’s in C, F# will certainly never be a diatonic note of that scale because it’s a tritone. Okay. Now it may be easier to compare these two scales if I start both of them from the same note, C. Now I wanna see what happens with another kind of major scale… maybe something called the harmonic major scale. Oh, what about minor scales? There’s a bunch of those. I should create a chart so everything is laid out in front of me.
Wow, I can easily find a pattern showing how all these scales are related to one another. Of course, I have to start small. I saw this video once by David Bennett Piano on YouTube about the brightness and darkness of modes. If you add flats, it gets darker; if you add sharps, it gets brighter. This should be perfect. I can figure out how dark or how bright each scale has gotten, using a simple spectrum, and make a chart for comparisons. I’ll put the original scales, in C, in the top row of the chart and the invisible ones in the bottom row, from darkest to brightest. Then, I should add a column to my first chart showing where each scale falls. The difference between the originals and the invisible scales can be the same for most or all of them. That would show it’s simply a matter of brightness and darkness.
*reviewing my mess of a chart* These numbers are all over the place! I don’t see any simple relationships between the invisible scales and their original scale counterparts! Here, I’ll simplify this a bit. For each individual set of scales, I just wanna see how many flats or sharps I’ve added or taken away. Maybe it’s the same for all these scales.
*reviewing my other mess of a chart* Oh, maybe not. This chart’s kinda messy, although it is easier to compare the scales. I see a bunch of flatted sevens, but there are too many other factors getting in the way. Plus, where did these flatted sevens come from anyway? I know that B is the 7 [seventh degree] for C major, and there’s no Bb in C major, but why are all the other notes still exactly the same?
Wait, hold up… oh my God, I’ve been doing it all wrong! Of course— Ian Ring!
Ian Ring has an amazing website called Ian Ring’s Exciting Universe of Music Theory, where he compares thousands of scales and outlines intricate, exact details about each scale, front to back, left to right. I can’t possibly find the answer without using that resource. I’ll gather as much relevant information as I can and see where that takes me.
Oh, I have plenty of information here. I don’t understand all of it, but that doesn’t matter. When I don’t understand something, I can always look it up on the website.
[Present Vin:] Which is linked in the description by the way.
[Past Vin:] I’m looking for numbers that show similarities between the original scales and their invisible scale counterparts. I know that the brightness spectrum didn’t help me too much earlier, if at all, but I’ll include it here just in case.
Ooh, this is something! The imperfections column is sticking out to me. Because, with some of the scale pairs, the number of imperfections of each scale is the same.
[Present Vin:] Quick vocab lesson. A scale has an imperfection when one of its notes does not have a counterpart exactly seven piano keys away from it, also known as a perfect fifth.
[Past Vin:] So looking closer at the pairs Ionian and Mixolydian, Melodic Minor and Mixolydian b13, Aeolian and Phrygian, and finally Harmonic Minor and Phrygian b11, comparing all those on the farthest right column of this chart, I can see that some of these pairs are actually the same scale. For example, Harmonic Minor and Phrygian b11 both share the same notes because they’re both part of the mode called C Ultralocrian.
Yes! I finally have something that relates some of these scales.
That’s not enough. I wanna know if there’s a surefire way to relate all invisible scales ever to all original scales ever.
[Subconscious of Past Vin:] You know, self, there is another way to analyze scales. Chords. You love chords.
[Past Vin:] That’s right, I do love chords. I should analyze the chords of each of these scales using Roman numerals.
[Present Vin:] Roman numerals are a fancier way of saying that, for example, in C major here, the sixth note is A, and if we make a chord starting from A, we get A, C, and E, which just happens to be A minor. Since the sixth chord of C major is a minor chord, I can write a Roman numeral for 6, which is vi, but lowercase, to show that it’s minor or diminished.
[Past Vin:] That way, it’s all numbers and not letters. Numbers are easier to look at, right?
*exasperated sigh* Nevermind. These are crazy and super unhelpful to me right now. In fact, this may be the worst thing I’ve done so far. These Roman numerals are helpful in a different context, but in this case, I still don’t know why they may be the same for each set of scales, if they are at all…
[Present Vin:] Hey viewer, I can tell at this point that you’re confused. To be frank, I’m confused as well. I’m way too deep in the weeds right now. I need to take a break from this and come back with a fresh mind.
*a sequence wherein I play the chords that I had developed earlier*
I’m back. I realized that I’ve been overthinking this process quite a bit. There are a couple parts of this process that I skipped over for the sake of this video because I don’t want this video to be any longer or any more confusing than it already is… probably. I’m glad you’re still watching this, because this is where I learn my lesson.
Okay, my original goal was to show you how each invisible scale compares to and relates to its original scale. Sure, I found some insight along the way, with the imperfections and some of the primary modes, but what does it all mean? What does any of this actually mean for me? In the end, I’m not thinking about music anymore. I’m thinking about analysis and algorithms. That’s not what I set out for at the beginning of my experiment.
My conclusion is I should see that there is an invisible scale and leave it be, treat each scale equally, say, “Wow, it’s interesting that I can extract, like, Ultralocrian from Double Harmonic Major; maybe I should just, you know, pair them together in a composition or something and see what happens.”
I believe that sometimes it's more intriguing to find no answers at all, because it leaves room for others to figure it out as well. The thing that I wanted to, extract, from all this confusion, pun intended, is that if you see or hear a composer pair together a scale with its invisible scale counterpart for a piece, and you have the background knowledge to understand that process and how it works, then you get a little closer to understanding the piece as a whole.
That’s it. That’s the answer.
Comments