So if you remember, in our Universal Encyclopedia of Scales, we map out for you guys. All 2048 scales
in music. So a bunch of people are asking us well, how do you know it's exactly 2048? how
do you know there aren't more? how do you know it's not too many? well today, we're going to talk
about how we figured out this exact number, and we're going to use the circle of fifths to show
you that... "If you're new to mDecks Music, we create music books and apps, piano arrangements, and we
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So subscribe and hit the bell, and join us for exclusive access to our ever expanding
library of Music resources..." So here, we have our handy dandy circle of fifths, with a C at the 12
o'clock position. What we're going to do, is graph the C scale on top of this circle of fifths, get
a very unique shape, and show you how that shape will find us the answer to that original question.
So, I'll just kind of like plot out here, all the notes relevant to the C scale. And you can see
I just kind of go around the circle of fifths to find all these notes... and then there's the F
over here. So there are all the notes I might find in a C scale in the circle of fifths. Now, if I just
connect these dots together, I'll get that graph -- or that very specific shape -- that I was talking about
over here, and then, I got to go all the way across right there. So what I have here is, basically, the
the major scales shape. Here's the major scale graft onto the circle of fifths, and I could have
any note at 12 o'clock. I could have D at the 12 o'clock position, and now I have the D major scale.
Or G, or F... but what you'll notice, this shape does not change because, well, a major scale is a major scale.
There's only one major scale. So, kind of what we're looking at here, is a a scale formula, all right?
There's only one whole tone scale, and that would give us a very different shape. Now, whether we can
(uh), or whether we should consider transposing those scales into (uh) all 12 or 15 Keys... that's right, I
said 15... if you want to understand that more: check out this video we'll react to Victor Wooten's 15
scale Theory. Whether we want to do that to get a another number altogether, we'll get into later.
So yes, that means using our definition any two notes, or any interval, can be considered
a scale. So, if I have the tritone interval (or scale) that's, that's what it looks like graphed
on the circle. If it's just like a straight line across. So if I wanted to do a power chord, or or
a fifth rather, it's just a straight line across the graph in that direction. Now (um) let's do... I
don't know... what if we had an augmented Triad? That's a good one, because it just creates a nice
symmetrical shape triangle, and that really reinforces the idea of symmetry in our scales.
When you see them graphed over their circle of fifths, all these properties get exposed to us. Okay,
so now that you understand how graphing scales onto the circle of fifths works, let's take the
next step. That's going to be the first step into understanding (uh) our proof for how we got to 2048.
So, as you can see it put the C scale back on the circle of fifths. So now, what I'm going to do is:
I'm going to create a sort of a binary fingerprint, or barcode (or) or number f you will. That lets us
associate this scale formula with that scale type, irrespective or irregardless of what the
root is. This is a major scales serial number. All right? Here we go... this is how we're going
to do that... I'm going to put a one next to every note starting at 12 o'clock that is in the scale,
and then a zero next to any note that is not featured in the graph -- or the scale -- so what I do
now is: I just write that over here as a 12 digit number, starting with again C our 12 o'clock note
(our root) and I'm going to get this... I'm going to get 1 1 1 1 1 1 1 is that six? yes! one two three
four five six. And I got five zeros in a row, one two three four five, and then that F over there: 1.
So now, we have here a very unique number that's specific to just the major scale type, or the major
scale formula if you will. All major scales will look like that, and we can do this for any scale
type. We can do this for any scale formula. So here we have melodic minor. Let's look at melodic minor's
unique binary number here, so now we would have one one one one ,now we have four ones in a row...
...two three four... A zero... a one again for the B... Three more zeros... one two three... a one, a zero
and well, that should be a one also. boom! So there we have (uh) our melodic minor expressed
using that binary system that we talked about so here we have the whole tones binary number
and the augmented Triads binary number so if you're stuck with us so far congratulations
it's about to start making sense here's what we're going to do now we have these 12 digits
or these 12 columns and what we're gonna what I'm going to do is we'll just block off
this first one because well it's always going to be a one there always has to be a root all right
so we're going to set that aside as something uniquely I don't know consistent it's always there
we always need a root and what that leaves us with is 11 other columns so basically what I have here
is two and then I have 11 other choices to the power of 11. there's two options within that First
Column or any column really so there's our two and I have 11 different choices to pick and choose
from as it relates to whether there is a one there or whether there is a zero and when I create that
exponential I get well you guessed it two thousand and 48 there are 2048 scale formulas in music so
the number of scale formulas in music will always be 2048. that's why we know we have all of the
scales in music within the universal Encyclopedia of skills also we can find all related modes by
grouping the scales with shifted binary codes and we can also find symmetric scales because
they have fewer modes than notes which means there are fewer binary codes than notes in the scale so
just one more point of clarification Before I Let You Go you may have noticed or as I alluded to in
earlier in the video I said there's only one type of major scale there's only one type of whole tone
scale so if we want to I guess basically for those of you who want to know how many different scales
do I have to learn how many different muscle memory patterns am I going to have to sort out
all my instrument to get through all the skills in music you always you would have to do is take
the number we came up with you multiply that by the 12 tones or pitch classes in music and that's
how you would sort out not that there are merely 2004 merely 2048 scale formulas of music but how
many scales there were actually to learn on your voice or instrument and you would see 24 576.
so 2048 scale formulas times 12 24 576 scales there you have it hope all that made sense
congratulations to you if it did if you want to learn more about the universal encyclopedia skills
check out our website and grab your copy today you can get it in hardcover or in PDF format and
of course all members of our channel will get free supplemental material based on today's lesson if
you're not a member and would like to become one just click on the join button or the link down
below if you have a different take on our 2048 skill formula proof let us know in the comments
down below and we're more than willing to hear you out thanks again for watching catch you next time
so you were saying that there are scales with less modes than notes
correct there are scales with less modes than nodes we call these symmetric scales
or scales of limited transposition limited transpositions yeah never mind that now
do you remember earlier how we got all the related modes of a scale by using the circle