SCALES COURSE: Let's Get Interval! Hold on to your butts.
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Old 01-19-2017, 03:17 AM   #1
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SCALES COURSE: Let's Get Interval! Hold on to your butts.

WARNING - YOU WILL NEED QUIET TIME TO SERIOUSLY READ THE FOLLOWING

INTRODUCTION
Lots of folks try to wrap their heads around scales.
I'm sure it's been all over these forums (I've seen quite a few already in my short time here), and you can find it constantly everywhere there is some community or resource for music - some sort of question about trying to wrap their head around scales.

There are thousands (probably millions at this point) of write-up's attempting to help people understand this.
They'll explain it in many ways, but two things that I find rather consistent is that they will explain them in music theory formats that people are not yet familiar with, and/or they will digress into tangents of relativism prematurely.
Thirdly, all have one thing in common that I've seen: They don't really dig at the underlying pattern that governs all scales, but instead spend the time going over the upper layer of scales themselves.
This means someone has to remember crap like, "Minor is like Major, but with the 3rd, 6th, and 7th flat", etc...

While that is easy enough when you are talking about two scales in total, once you start throwing out all the names of scales at someone learning, which themselves are confusing taxonomically (meaning, the naming conventions aren't really good at describing the function of the scale; they appear to learners as rather arbitrary unless you get into music history), you end up with a dizzying set of archetypes to recall by memory or you have to refer to a chart regularly to get your navigation settings - which really gets in the way of the artistic flow of the music composition process.

While the upper-snub might be the idea that someone shouldn't compose until they can wield such information, that's just not going to happen and shouldn't - in my opinion - be required.
As close to Toaster Level Easy as is possible is what information dissemination should aim for; that's my motto. Don't demand users get better, demand the information gets better.

Furthermore, I prefer looking at any complex system by determining what principally governs the root of all subsequent layers of expression and then employing that, rather than learning the external layers and working backwards - like fractals.

And quite like fractals, music theory actually does have a core pattern that all of this spawns from.

We're going to refer to the chart at the bottom a lot, but I will go through different parts of it while explaining.

I will begin with a description of the semitone (so absolute beginners don't get lost), then move on to the core pattern, then show it in the standard set of scales, followed by expanded scales, and then a final thoughts wrap up.

DISCLAIMER
This is not to say that you can make every conceivable scale using this method, no. That is not the point.
The point here is to show a beginning and amateur approach to wielding standard sets of scales regularly employed in Western music without having to strain memorization or slow down creative processes.

NOTE:
Because most people around here are using DAWs, I will show things when needed on a Piano Roll styling rather than a normal horizontal piano.
I will also outline notes as flats or sharps correctly first, but then only as sharps following because most DAWs don't have flats in the piano roll and instead just have sharp annotations by default.

THE SEMITONE
In our use, we will employ the standard definition of a Semitone.
The Semitone is most easily outlined by looking at a piano roll.
In this diagram (Fig 1) we have an example of ONE (1) SEMITONE and TWO (2) SEMITONE intervals.
For our purposes here, the easiest way to think of semitone intervals is "one semitone equals one key on a piano roll" regardless if that key is white or black.

When we say to move ONE semitone, that means we start on a key (let's say C) and go ONE key up or down (we'll say up for this example; which would be C#).

So when we see 2 1, that is not a list of TWO keys (notes), but instead is a list of THREE keys (notes).
That is because if we start on C and then go TWO (2) semitones UP, then we would be on the D key.
If we then go 1 semitone from there, then we would be on D#.

As such, we understand that an interval number is not a note itself, but describes the distance BETWEEN two notes (think of it like counting the valley's between your knuckles - you have 3 valleys, so you therefore have 4 knuckles).

THE CORE PATTERN
Now that we have an agreed understanding of our term of "semitone" and what concretely we mean when saying that inside of your DAW environment, we can take a look at the core pattern that will underpin everything else.

The pattern is expressed in SEMITONE.
Code:
2 2 1 2 2
That's it. That's the core pattern.
Almost.

There's an extra tag-along.
Code:
2 1
We'll refer to this extra pair as the APPENDAGE.
Now, THIS [2 1] will move around and that's kind of what describes the scale: where this extra pair of intervals (3 notes) is within the alignment of the core pattern of [2 2 1 2 2]

Imagine a stereoscope toy (if you don't know what that is, look it up), but imagine that it doesn't have a spinning wheel.
Instead, it has a single horizontal card. On that card are the numbers: [2 1] [2 2 1 2 2]
Now, imagine that card is a strip of paper and wrapped into the stereoscope so that the beginning and end are joined in a loop on both sides of the ribbon, so that you have [2 1] [2 2 1 2 2] [2 1] [2 2 1 2 2]

Further imagine that at all times 7 numbers will be visible when you look in and slide around the ribbon.
And lastly imagine that there is a center mark on the lens of the stereoscope toy so that you always know where "center" is.

When you pull that ribbon back and forth, you will see the pattern of those intervals move left and right and each time you move the whole set one number placeholder to the right or left, you have CHANGED SCALE.

This is what is being represented in the first part of the chart at the bottom which shows Major, Dorian, Phrygian, Lydian, Mixolydian, Minor, and Locrian scales.

The red part that is boxed in is the core pattern [2 2 1 2 2]. The remaining [2 1] in green is the appendage.

All that's happening as we move to each scale is that the whole pattern set is sliding to the left by one number placement holder each time until we have made our way from Major (which starts the migration with the appendage at the right of the core pattern) to Minor (which ends the migration with the appendage at the left of the core pattern).
Locrian is the scale where the core pattern is dead in the middle and basically is the loop point between Major and Minor in only ONE shuffle to the right or the left (if that didn't make sense, let me know).

You COULD also draw up this same diagram so that Locrian is in the middle vertically and your set is then as the following image:
From this perspective, UP from Locrian would be shuffling to the RIGHT, while DOWN from Locrian would be moving to the LEFT.

This, then, is a reasonable definition of the CORE PATTERN and its APPENDAGE.

THE STANDARD SET OF SCALES
The standard set (those outlined in the CORE PATTERN) reveal a numerical rule:

RULE 1: the SUM of the INTERVAL VALUES must equal 12.

All of the standard set accomplish this.

Further, the standard set also accomplishes a SUM of 12 vertically as well. This BALANCED relationship between all symmetries of the scales is what causes these to be related and typically thought of as your "standard scales".

When you look at each standard set and count how many times each value occurs, you end up at another starting point rule:

RULE 2: TWO 1's and five 2's must exist in each scale.

We then add a third rule that isn't visible from this chart, but does indeed exist implicitly in the nature of the intervals themselves.

RULE 3: Each letter must exist ONCE in the scale.


Now, with all three rules together, we can outline any scale that we feel like without knowing its name.
We simply must start on any given note on the piano roll key and then pick any order of five 2's and two 1's AS LONG AS we have made every note exist ONCE in our total set of 7 notes whose total interval arrangement sums to 12.

That is the fundamental bottom line.
That might sounds hard to some folks, but it's very easy.

Keep in mind that your CORE PATTERN is [2 2 1 2 2] and you're just really figuring out where you want to slap in the APPENDAGE of [2 1], so you just say I'm going start on the SECOND 2 of the CORE PATTERN.
So that means our ENTIRE pattern is [2 1 2 2] [2 1] [2] (<-this last "2" was moved over to the end because we pushed our core pattern to the left by one slot).

So, let's start on C.
We now need to go up TWO semitones, so that would land us at D.
Next, we move ONE semitone up so that we're at D# on the DAW.
However, according to the rule, we need to have one of each letter, so that can't be D# since we ALREADY have a D, so we know that should be Eb.
So we have C, D, Eb so far (C, D, D# on your DAW).
Next, we move another 2 from Eb and land at F.
Then we go another 2 from F and land at G.
Then we move 2 from G and land at A.

Now we have C, D, Eb, F, G, A (C, D, D#, F, G, A on your DAW).

So then we go 1 from A to an A#, but according to the rule of ONE letter, we change that to a Bb (same key on the keyboard, though, remember).

So now we have:
Regular Expression: C, D, Eb, F, G, A, Bb
DAW Expression: C, D, D#, F, G, A, A#

That's it. We now have 7 notes and that means we have a standard scale!

What about that last 2, you might be asking. We only did [2 1 2 2] [2 1] so far. Where's the last [2]?
That is our interval for getting back to C.

So our full description of [2 1 2 2] [2 1] [2] starting on C is:
Regular Expression: C, D, Eb, F, G, A, Bb, C
DAW Expression: C, D, D#, F, G, A, A#, C

TADA! You just made C Dorian using SCALE BY NUMBERS (like paint by numbers, but for music theory)!

THE EXPANDED SET OF SCALES
Now that we have a foundation beneath us we can play around and ruin the rules a bit and get more interesting scales.

With this set, the whole rule of "two 1's and five 2's" goes out the door.
HOWEVER, not entirely.

With augmented scales, there are still an attendance to that math. You just DESTROY a bit to make things happen, and we all love destruction!

The new rule:
RULE 2.Amendment 1: You can have 3's at the expense of turning a 2 and a 1 into that 3*.
* = and some other exceptions in melodic, harmonic, and diminished that we'll get into

That sounds confusing possibly, but it's really simple.
Take the Major scale:
[2 2 1 2 2] [2 1]

PENTATONIC
Now, I want to make that into a Major Pentatonic scale.
So I take the 1 and 2 and collapse them into a 3.
[2 2 3 2] [2 1]

Now I take the other 2 and 1 set and collapse them.
[2 2 3 2] [3]

Now, the minor version of this behaves the same way the minor does in the standard set; as a mirror of major:
[3] [2 2 3 2]

That's because the regular Minor is
[2 1] [2 2 1 2 2]

So that becomes
[3] [2 2 1 2 2]

And finally
[3] [2 2 3 2]

How do you know which 1 and 2 to collapse?
Within the CORE PATTERN, you collapse ALWAYS [...2 1...], so the 2 before the 1 is what collapses with the 2 and in their place is left a 3.
In the APPENDAGE you collapse ALWAYS both (even separate).

This will generate you any given pentatonic that you want.

MELODICS
For Melodic's, the only difference here is that we broke the CORE PATTERN and APPENDAGE definitions.
Now it's [2 1 2 2] for the CORE PATTERN and [2 2 1] for the APPENDAGE, but this follows the same rules in every other way.
You can think of Melodics as Interval Inversions of their normal setup.
You'll notice that in Melodics, Major's APPENDAGE is to the left of the CORE PATTERN, while Minor is on the right.
You'll also notice that if I do this
[2 2 1 2] [1 2 2]
[2 2 1 2] [2 2 1]
You can easily spot that the APPENDAGE is defined by its inversion of the Interval Pattern of the three intervals of the standard Major scale.
(if that doesn't make sense, let me know)

HARMONICS
Harmonics combine both rules above and throw us into a blender.
Our CORE PATTERN of [2 2 1 2 2] is now collapsed into a three stolen from a 2 and made into [2 1 3 1 2].
Our APPENDAGE becomes [2 1] and our APPENDAGE inverts to define the difference between Major or Minor while everything else remains the same.
So a Major Harmonic has an APPENDAGE of [2 1], while a Minor Harmonic has an APPENDAGE of [1 2].

Lastly of the "But! But!" exceptions is the Diminished Octatonic.
Here we throw all rules out except for the first rule that all values must tally to 12.
In fact, that is the ONLY rule that remains consistent through all - that they all end up tallying to 12.

Here the rule is dead simple, you ONLY have a one CORE PATTERN and no APPENDAGE.
That pattern is [2 1]. You just repeat that endlessly until you have 8 total notes.


FINAL THOUGHTS
Note: on the form below that's been referenced in the above discussion, you'll notice a section called "SYMMETRICAL COUNTERPART VIEW OF SEMITONE PATTERNS".
This shows which scale is the mirror of which other scale in regards to SEMITONE INTERVALS.

You'll note that LOCRIAN is its OWN mirror and has not counterpart.
That's why it is the CENTER of the migration between MAJOR and MINOR (see above chart where LOCRIAN is shown in the center).

Also, Also Wic:
I don't pretend that this solves EVERY scale knowledge problem; again, that's really not the point.
The primary point is to make it a bit easier to start with for MOST of your common scale conceptions.

Mostly, you just need [2 2 1 2 2] and [2 1] and to move around where you are starting, and making sure whatever you move off of the left, you append to the end of the right.

That's my 2 nuyen,
Cheers!

I'm interested what folks will discuss here.

Long Chart For Reference Up Above:

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Old 01-19-2017, 06:35 AM   #2
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

I'm printing this off and you can't do anything about it

As always, good quality material.
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Old 01-19-2017, 07:26 AM   #3
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

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).

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Old 01-19-2017, 07:55 AM   #4
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Quote:
Originally Posted by Treyt0r View Post
I'm printing this off and you can't do anything about it

As always, good quality material.
Ha! Cheers!

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Old 01-19-2017, 10:43 AM   #5
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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!!
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.
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:
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.
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; 01-19-2017 at 11:18 AM..

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Old 01-19-2017, 01:04 PM   #6
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Some good stuff man! Seems you put in quite a lot of effort! You have my respect for that sir!

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Old 01-19-2017, 06:22 PM   #7
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Wow.. I really admire the amount of work you put into this. Way to go.

and now for me to put on my music snob hat.

I think this is interesting, but I think there is a reason conventional music theory has not been upended and replaced.

I've encountered this sort of approach before, and the thing that concerns me is that it is a little misleading for the novice. You've stated that your point was to come up with a system that amateurs can employ to come up with scales without having to "strain to memorize" stuff. In my opinion, this method requires a lot more legwork than a conventional approach.


If one only wants to learn a minimal yet useful amount of music theory without memorizing a bunch of stuff, that is entirely possible. And also, it should be noted that, by using your method, someone is in fact studying and "memorizing" music theory, it's just your own personal music theory.


IMO the only scale that needs to be memorized is the major scale. It is the most common scale, and it is our (westerners) frame of reference. Once you learn how to construct this scale, your time would be best spend learning what each of the scale degrees sound like. This is a process that is never really finished.

Once you know what the fifth note sounds like, learn what the fifth note sounds like flatted. It is not necessary to know the name of what scale this would create (I don't), but I can hear how it would sound in my head.

In this way, you can create whatever scale you want using your own sense of musicality instead of a formula. You will begin to see that scale degrees provide certain flavors when they are altered, and then you will be able combine them to create "recipes".


I see a lot of emphasis on scales in music theory.. as if discovering scales is a big part of it. This is kind of odd considering 95% of tonal harmony ("music theory") is contained in the major scale, melodic minor, and harmonic minor scales. That is where the bulk of studying would be done.

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Old 01-19-2017, 11:00 PM   #8
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Quote:
Originally Posted by mnkvolcno View Post
Wow.. I really admire the amount of work you put into this. Way to go.

and now for me to put on my music snob hat.
HAHA, alright, let's have some fun!

Quote:
I think this is interesting, but I think there is a reason conventional music theory has not been upended and replaced.

I've encountered this sort of approach before, and the thing that concerns me is that it is a little misleading for the novice.
Let me be clear here. I am not showing my own theory. This is regular music theory.
The way of explaining things is what's different here.
Intervals are a regular part of music theory courses, it's just that it takes a back seat to describing things as degrees, however degree focused teaching doesn't give a physical object to grab and say "AHA! That's why!". Instead, it's a conceptual lesson relative to the major scale.
You have 1 2 3 4 5 6 7 degree and then you learn 1 2 3b 4 5 6b 7b is a minor scale, but when you ask why is the 3, 6, and 7 flat, you get answers about harmony and a note that we'll get back to that later.

But that's not actually why because we didn't start with harmonies and chords and get scales from that.
No, the medieval period had melodic theory and the baroque period focused on how to align multiple melodies in motion simultaneously and from that enterprise developed chordal harmony as a result of multiple layered melodies.

The reason for those flats isn't an issue of harmony, but instead, a preservation of equal distance.
In the standard scales, you have an interval of 2 2 1 2 2 2 1 and that total distance must still exist, so it is not that the minor flattened the 3rd degree, no.
It's that the physical interval placement 2 interval distance is being preserved so that the total distance is 12 physical intervals...because (getting to this in the next bit)...

Quote:
You've stated that your point was to come up with a system that amateurs can employ to come up with scales without having to "strain to memorize" stuff. In my opinion, this method requires a lot more legwork than a conventional approach.
Not at all.
It only seems that way because it takes a lot of discussion to show HOW and WHY this approach works.
I'm not a fan of just saying "Here's a script; follow it". Metaphorically, I don't like showing how to fix a problem on a car. I prefer to show how a car works and that way you can fix any given car problem due to the knowledge of how the car works, via deduction.

To explain how things work physically, and why they do, takes a lot of text.
HOWEVER, all you HAVE to remember is one thing and one thing only (for 90% of music that you hear).
2 2 1 2 2 2 1

That's it.
Just that simple 7 numbers will be all you need.

Skipping the identities of which scale is what name, all you need to change scales is to move that sequence around such that if you take a number from the left and move it to the end on the right, or if you take a number off of the right you move it to the beginning of the left.

Like so...
Taking from the left and moving to the right:
Code:
2 2 1 2 2 2 1
2 1 2 2 2 1 2
1 2 2 2 1 2 2
2 2 2 1 2 2 1
2 2 1 2 2 1 2
2 1 2 2 1 2 2
1 2 2 1 2 2 2
and back to the beginning
2 2 1 2 2 2 1
Taking from the right and moving to the left:
Code:
2 2 1 2 2 2 1
1 2 2 1 2 2 2
2 1 2 2 1 2 2
2 2 1 2 2 1 2
2 2 2 1 2 2 1
1 2 2 2 1 2 2
2 1 2 2 2 1 2
and back to the beginning
2 2 1 2 2 2 1
So the only thing you HAVE to remember is 2 2 1 2 2 2 1
I only broke them up and gave them part names as "Core pattern" and "Appendage" because I find that makes it easier to remember the whole pattern because then you just have to remember 2 2 1 2 2, which is symmetrical so easy to remember, and then you only have to remember 2 1 as an extra set; also rather easy to remember.

Breaking them up in this way is also mostly done so that I can show WHY it's happening and WHAT is happening, because then you can watch the pattern migrate more easily by just following the red or green blocking around as it moves through the scales.

BUT, you don't need to remember all of that to get into your DAW and feel like you know where to go for your next note instead of guessing or trying to recall the Major scale and then flattening the 3rd, which can get confusing when you're sitting there on E and thinking, my Major is G# for the 3rd note/degree, so my minor is an G# flat...err...so a G. Wait, my FLAT is a natural?
GAH!

That can get confusing very quickly for folks just getting going.
Whereas it's entirely simple to say that your pattern is [2 1] [2 2 1 2 2] for a minor and so your third note (degree) will be G not because it's a Major's 3rd flattened, but because it's 3 keys (intervals) away from the root.
Because E + 2 = F# and F# + 1 = G, so naturally E + 3 = G.

And you can see and touch this concretely on a piano keyboard or virtually on a DAW piano scroll.

You can't do that with JUST degrees.
With degrees, you have to keep remembering which degree is flat and sharp for that scale (mostly just flats relative to the major).

So, I understand the impression that that wall of text is a lot to memorize, and yes, it would be.
But that's not what has to be remembered.

All that has to be remembered is [2 2 1 2 2][2 1] and from there...just slide that back and forth left to right.

Quote:
If one only wants to learn a minimal yet useful amount of music theory without memorizing a bunch of stuff, that is entirely possible. And also, it should be noted that, by using your method, someone is in fact studying and "memorizing" music theory, it's just your own personal music theory.
I want to clarify again, just to be sure; this isn't my personal music theory.
This is regular music theory.
For example, see the following link: [Only registered and activated users can see links. Click here to register]

Replace "T" with 2 and "s" with 1 - I'm writing numbers instead of things like "W" "H" or "T" and "s" because an actual number is far easier than shorthand letters.

What I did was digest a ton and change the way we talk about the same theory.
This interval information is a regular part of music theory and you really hit into it heavily when you study baroque counterpoint theory and why they developed what they did and how that was built from the shoulders of medieval melodic and tonic theories.
Intervals were a HUGE part of that period and so was the math of intervals.

Over time, that became a given fundamental component of music theory and because harmony became a major focus by the end of the period and onward (since now the groundwork had been accomplished to understand why certain notes work together and how) that degrees became the favored method of reference.

However, it's FAR easier if you START at intervals (like we did in history) and then MOVE to degrees, and then move to Harmonies.
By doing this, you'll have followed the same path of logical deduction that was used to derive these things in the first place.


Quote:
IMO the only scale that needs to be memorized is the major scale. It is the most common scale, and it is our (westerners) frame of reference. Once you learn how to construct this scale, your time would be best spend learning what each of the scale degrees sound like. This is a process that is never really finished.

Once you know what the fifth note sounds like, learn what the fifth note sounds like flatted. It is not necessary to know the name of what scale this would create (I don't), but I can hear how it would sound in my head.
Yeah, but that's the point.
Spending all that time trying to memorize sounds when what a "5th" sounds like is entirely relative is going to take a very long time.

Conversely, you can toss that out and just remember that a 5th is always 7 intervals/keys from the root, and that's REALLY easy to remember because you just to look at 2 2 1 2 2 2 1 and note that 2+2+1+2 = 7.

What's your 6th degree from D in Minor?
It's 8 Intervals (keys) from our root; D, which would be G#.

How about a 7th?
That's 10 Intervals (keys) from the root, A#

And how easy or hard is that to remember?
You don't have to remember anything.
You just take your scale, in this case:
[2 1] [2 2 1 2 2] and pick which degree you want to know the note of (after having picked a root of course), we'll say the 6th again, and subtract 1 from the degree number, so 5.
Then you count along your pattern thusly
Code:
2 1 2 2 [1] 2 2
1 2 3 4 [5]
That's our 6th note, or degree. So without knowing the rest of the notes, how can I easily spot it?
Sum all notes before it:
2+1+2+2+1 = 8

Therefore, we just start at our root and count one key (black and white both) upward 8 times from there and we'll be on our 6th degree/note.


Quote:
In this way, you can create whatever scale you want using your own sense of musicality instead of a formula. You will begin to see that scale degrees provide certain flavors when they are altered, and then you will be able combine them to create "recipes".
You can do that anyways even easier than all of this.

Pick a note, any note. Now pick any 6 additional notes and make sure you have one letter each in the scale.
TADA! That's easier than Intervals or Degrees.

Heck, my little daughters can do that; that was how they learned the concept of what a scale was in the first place: a set of 7 notes with each letter occurring only once.

(yes, there are scales that differ, but as a starting point for the standard set of scales...that's sufficient)

However, if you want to know an easy way to know the relationship BETWEEN picking scales and the degrees they will map to, Intervals is the easiest and best way because that's what it literally was originally created for in the first place. That's where we started.

And all you have to recall is just 7 little values: [2 2 1 2 2] [2 1]

Quote:
I see a lot of emphasis on scales in music theory.. as if discovering scales is a big part of it. This is kind of odd considering 95% of tonal harmony ("music theory") is contained in the major scale, melodic minor, and harmonic minor scales. That is where the bulk of studying would be done.
It is a big part of it.
All that harmony is worthless without understanding WHY those harmonies work in the first place, and to understand why they work, you need to understand the physical properties of sound - not degree theory.
And that is only possible by looking at the interval and frequency.
The interval will tell you where to go to get to the right frequency movement away from the root as it was designed to align in Western theory based on the 3:2 ratio that we started on in the Grecian period.

The reason that certain tones sound good together has to do with their oscillations and their phase coherence in wave propagation, and that lines up with a repeated division in ratio, root to 5th is 1.5.
From root to 3rd, 1.25.
Root to 6th, ~1.66 (1.66 to 1.68, depending on what period of history you are in).

These are all extractions from the initial ratio pattern outlined way back in the Grecian period as to frequency patterns and relations.

With the emergence of scoping these onto a set of instruments consistently, this became Intervals.
Eventually you had a set of intervals and you would move that around the instrument.
Then names evolved for each variation of moving the interval set around.
Then came studying melodic theory of why and how to place two melodic notes over each other without causing problems: how to write two melodies without creating one that conflicts the other.
And that lead to degree and harmony.

But you really SHOULDN'T get into harmony theory without first understanding WHY the notes are moved around the way they are firstly, imo.

That's my 2 nuyen,
Cheers!

Last edited by TheStumps; 01-19-2017 at 11:48 PM..

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Old 01-20-2017, 12:07 AM   #9
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

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Originally Posted by professurreal View Post
Some good stuff man! Seems you put in quite a lot of effort! You have my respect for that sir!
Cheers!

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Old 01-20-2017, 04:14 PM   #10
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

Thanks for taking the time to respond to my points. I hear where you are coming from. Maybe I don't completely get your perspective yet. Going let this stew for a bit

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Old 01-21-2017, 01:05 AM   #11
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Re: SCALES COURSE: Let's Get Interval! Hold on to your butts.

I've got this fantastic update to do...probably going to toss it as a new discussion.
I just finished creating an excel book built for analyzing harmony of a chord using wave propagation.

It's pretty friggen awesome!

It'll take some time to write up a presentation, but I'll post it up as soon as I can either tonight or sometime this weekend.

Last edited by TheStumps; 01-21-2017 at 01:18 AM..

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