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Old 19-01-2017, 09:43 AM   #5
TheStumps
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Quote:
Originally Posted by White Noise View Post
It seems to me the next logical step would be to talk about how to transition from one scale to another, if that is a thing (I may be thinking of keys, and those may be a different thing), which could be useful in trying to come up with a live set or an album that flows naturally. I remember there being some rule about the upper and lower tetrads (when counting notes, not intervals) moving around in a predictable fashion in the major scale as you followed the circle of fifths, which is part of why that is such a thing. Are there other tricks that can get you out of some of those more advanced scales and into your comfort zone (which for me is either C major or C minor pentatonic, those are the only two I know by ear and heart).
You could easily use semitone mapping as described above to lend a hand in mapping both a scale change or a key change.

Key change is simple. You keep the same interval map but start on a different note.
Which note to move to is a matter of choice usually informed by scale degree.
The first note is degree 1, from there you move your first interval number to get to degree 2...etc...(make sense?)

So a Key change would be having a semitone map like [2 2 1 2 2] [2 1] and starting that out on C, and then sometime later starting out on G (5th of C - we'll get into that in just a second).

So you were running C, D, E, F, G, A and then we jumped Key change to G, A, B, C, D, E, F#.
The notes in our scale shifted, but the intervals remained the same.

So we switched our KEY, but not our SCALE (we're still in the Major scale).


However, what if you want to shift the SCALE, but (for example) keep the same exact notes?
Well, in that case we can shift not only the KEY, but also the SCALE (kind of have to if you want to keep the same notes, but change key).

Let's stick to the basics and we'll switch from a Major scale to a Minor scale and keep the same notes in place.

We were on C for our Major.
Now, keep in mind that our notes are C D E F G A B.
Also keep in mind that our Major interval map is [2 2 1 2 2] [2 1]
Now, ALSO keep in mind that our Minor interval map is [2 1] [2 2 1 2 2]

Now we want to switch scales, but keep the same notes, so that means we need to pick a note to start upon which will produce the same series of notes as our C Major.

In this case, it happens to be A.
Is there a rapid way of knowing that?
Yes, in fact, there is.

You start at your root, and you count up until you are on your 6th note.
C D E F G [A]

That also works for Minor to Major with the same notes.
In that case, you take the 3rd note.
Major to Minor, 6th note.
Minor to Major, 3rd note.

This works because, take a look at C Major and A Minor, as an example.
Code:
 2 1 2 2 1 2 2
A B C D E F G A B C
     2 2 1 2 2 2 1
So here you can see that the Minor map of 2 1 2 2 1 2 2 is sympathetic to the Major map of 2 2 1 2 2 2 1 when we pick A Minor scale and C Major scale.

Let me know if that part made sense or not.


Now that we know how to plop around using intervals as our navigator between Keys and Scales, let's then address how to PICK which note to jump to.

One way is the way we outlined above - by keeping the same notes of the scale.
That locks down the options pretty quickly.

However, you don't HAVE to lock in that way.
So how do you pick THAT way?


Well, let's take a moment to learn our degrees, as we'll need to know how they relate to each other a bit to make good picks.
Now, degrees are noticed (meaning, we favor and disfavor certain degrees) by their waiver (oscillation) from the ROOT (Key).

Since we're all DAW, Module, or Synth users here, stop for a moment and think of setting an oscillator to a standard sine wave (sideways S).
Right, now turn on your second oscillator and line it up to be IN PHASE with your first oscillator, but at a different tone/pitch/frequency (same thing, different names).

By IN PHASE we mean that the PEAKS and TROTHS of those sine waves line up in a supporting way; the sound isn't getting cut out, but reinforced by the second oscillator.

Make sense so far? Hope so (let me know if it doesn't).

To be specific, the degrees which have compatible oscillations are Harmonious and the ones that have disparate phased oscillations are Disharmonious.

Let's map our IN PHASE oscillations first.

Take your 7 notes (7 degrees) and call 5 "middle".
1234[5]678.
Your Key/Root is 1 and that 8 is the same as that 1, just an octave up.

So with our Major scale in C, that is


Code:
Degree   |1 2 3 4 5 6 7 8
Notes    |C D E F G A B C
Interval | 2 2 1 2 2 2 1
So G is our 5th degree.
1, 5, 8 are sympathetic frequencies; in phase with each other.
Why?

Well, let's do some SCIENCE! MOOWAHAHAHAHA!!
Code:
Content visible to registered users only.
OK, firstly, let's look at in phase oscillations and to keep it simple, we're going to go WAY down to 16.33 Hz for our C note.
We're this low so that it's easier to see the waves of our oscillations in a moment, as higher frequencies get so tight it becomes hard to see fine detail, but since octaves are just a factor of 2 (two times or a division of 2) from the same note in another octave, we can just drop all the way down and be just fine.

Now, like I said, C in this example is at 16.33 (the decimals vary, but here we're going to set them solid at 16.33 for C).

We move up to that 5th, G (look back up at that block of "code" if you need a reminder).

What's G's frequency in this octave?
It's 1.5 times that of C; in fact, that's always the 5th. 1.5 times the frequency of the root in oscillation.
So what does it look like when we put C and G over the top of each other?

Sympathetic oscillations.
Code:
Content visible to registered users only.
Now, for a frame of reference, let's look at the SECOND degree of our scale playing alongside our root.
So in this case, that would be what?
If you said C and D (see above block of code for a reminder), then you're right!

So let's see what C and D looks like in layered oscillation:
Code:
Content visible to registered users only.
Well look at that!
That second one is UUUUUGLY by comparison to the first map.

See how in the first one, you have this nice even spacing with very few gaps, while in the second one (C and D) you have two heavy pockets on either side and an emptiness in the middle?

That's why the 5th is so "pretty" to the ear, or so "loud", or "harmonious" with the root, while the 2nd doesn't make our ears tickle in the pleasant way (typically).

OKEE DOKEE, so that's our reason for root and 5th. Clear? (hope so)

So let's look at our degrees again and highlight these strongest sympathies.

[1]234[5]67[8]

That is, C G C (second C is an octave higher)

Hey! Guess what?
You now have a power chord.
Code:
Content visible to registered users only.
Alright, so one way is the all common "Circle of 5ths"...you just pick a 5th from your Root and head on that way.
Well, that gets a little boring after a while, plus everyone else is doing it (and that makes sense, I mean...the oscillations are so compatible).

So let's look further.

Let's go to the middle between the root and the 5th; cutting our oscillation in half.
[1]2(3)4[5]67[8]

Let's do this again on the other side; a bit ungainly, but the middle is 6.
[1]2(3)4[5](6)7[8]

Let's explore these as well.

These have the same kind of nature as we saw with 5ths in regards to oscillations.
2, 4, and 7 have the same as what we saw above with C and D, except that 7 is more well distributed than seconds or 4ths (which is why they get used so often)...remember, better EQUAL distribution of wave oscillations with few clustered and empty spots created as a result of the combination; ergo 7ths are somewhere between a 5th and a 2nd (conceptually) in the behavior of the oscillation spread across the root.

So, an easy round of picking is 1, 3, 5, and 6.
Off of C Major, that's C E G A.

So we can CHOOSE to spin on our heels from C to E, or G, or A and it will likely be pleasing.
Now, whether we slide over to Major, Minor, etc... some other scale is entirely up to your picking.


I hope this was helpful,
Cheers!

Last edited by TheStumps; 19-01-2017 at 10:18 AM..

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