Intervals

[Gard]

A discussion via IM with our buddy Cassanova has prompted me to be aware that the concept of "interval" is a topic which needs to be explained for at least some of our members. I will attempt to do so, as clearly and informatively as possible for my limited communication skills:

For our purposes, we will work with the key of C major, mainly because it has no sharps or flats to bother us (because in addition to being in possession of poor communication skills, I'm also lazy ).

There are two important pieces of information when describing an interval: I call one the "quantity", or the rough distance between the 2 notes (which I will underline); the other I call "quality", the exact distance. Hopefully all this will make some sense to someone...



2nds:
minor2 BC, EF
major2 AB, CD, DE, FG, GA

3rds:
minor3 AC, BD, DF, EG
major3 CE, FA, GB

4ths:
perfect4 AD, BE, CF, DG, EA, GC
augmented4 FB

5ths:
diminished5 BF
perfect5 AE, CG, DA, EB, FC, GD

6ths:
minor6 AF, BG, EC
major6 CE, DB, FD, GE

7ths:
minor7 AG, BA, DC, ED, GF
major7 CB, FE

Octave
perfect oct. each note to the next appearance of that note (i.e. C to C1)

Now, a couple of things to notice:

In each "Quantity" group, there are 7 total pairs of notes, while the number of "Quality" varies.

Some "Qualities" are referred to as major/minor, some as perfect/augmented-diminished. There is a historical reason for this difference, which we will not go into here, as it's beyond the goal of this post. Just consider it like a theorem in mathematics, it just "is" for our present purposes.

I didn't specify the distance between each interval in whole/half step distances, but that information is simple enough to discover for yourself, and worth the effort to discover (i.e. B to C is a half step, C to B is five and one half steps).

Once you "know" a certain interval from this post, you "know" many others: An explaination - C to E is a major 3rd, then C to Eb is what? A minor 3rd. The same is true for C# to E, it's "smaller" than C to E, therefore it's a minor 3rd. Conversely, E to C is a minor 6th, then E to C# would be a major 6th.

I'm certain that this will bring as many questions to people as it will answers, and of course any additional input from other members would be greatly appreciated! If you don't get something, ask, and someone will pitch in to help out, based on past experience - either myself or someone else with as much or more knowledge in this field.

[Chris Fitzgerald]

TOAST GARD,

Excellent post...I think that we (i.e. - clan TABEVIL) should make this part of a theory FAQ that stays either on the homepage or here in GI. HASBRO'S scale guide is a wonderful start, and this is a great addition.


The only thing I would add to this at all is that intervals are often easier to understand if you grasp the concept if intervallic inversion, which Gard alluded to in his post.

An inverted interval is simply an interval that is turned upside-down.

For instance, C down to B is a minor 2nd, while C up to B is a major 7th. These inverted intervals can be said to be in the same class, since they involve the same two notes.

An easy way to remember how intervals invert is to remember that all interval inversions add up to the number "9", and that all major or minor intervals flip-flop their quality when you invert them. For example, if we consider all the following intervals to be ascending, then;

C to B = Ma 7th
B to C = mi 2nd
7+2 = 9

C to Bb = mi 7th
Bb to C = Ma 2nd
7+2 = 9

C to A = Ma 6th
A to C = mi 3rd
6+3 = 9

C to Ab = mi 6th
Ab to C = Ma 3rd
6+3 = 9

C to G = Perfect 5th
G to C = Perfect 4th
5+4 = 9

C to Gb = diminished 5th
C to F# = augmented 4th
5+4 = 9

C to F = P 4th
F to C = P 5th
4+5 = 9

C to E = Ma 3rd
E to C = mi 6th
= 9

C to Eb = mi 3rd
Eb to C + Ma 6th
=9

C to D = Ma 2nd
D to C = mi 7th
=9

C to Db = mi 2nd
Db to C = Ma 7th
= 9

and hypothetically,
C to C = unison (1)
C to C = 8ve (8)
8 + 1 = 9


Notice that perfect intervals invert to perfect intervals, Major intervals invert to minors, minors to majors, and Augmenteds invert to diminished and vice versa. Another interesting characteristic of inverted intervals is that they have the same psychological effect no matter which way they are inverted...octaves are always the most consonant, and mi2nd/Ma7th intervals are always the most dissonant (this has to do with the acoustical properties of the harmonic series, but that's a topic best saved for later). For this reason, I always think of the inverted intervals as being roughly the same, which cuts in half the number of categories to remember.

So, instead of thinking of 2nds, 3rds, 4ths, 5ths, 6ths, and 7ths, you can instead simplify to:

2nds/7ths
3rds/6ths
4ths/5ths


Hope that wasn't too confusing.

[Dave Metts]

I for one think a FAQ sounds like a great idea! I know I'd learn a lot from it once I get the mechanics of my playing down.

I really hope you guys can find a way to put it all together!

btw - You guys have inspired me to start learning to read notation. I'm not so sure about sight reading pieces, but I'd at least like to be able to read so I don't have to use tAbZ anymore. So what do you think -- libster a good place to start?

[Pacman]

Excellent post, Gard.

It seems our young apprentice is making us all think. Through PM, I've been working with him on analyzing diatonic chords to see the relationships between chords and scales. He'll be a jedi in no time.

Talkbass Rocks!

[Gard]

BLISS McCHERYL -

Thanks for the compliment, and for pointing out the "Magic 9" rule. I knew I could count on the rest of CLAN TABEVIL (I was never made an official member, but...well, I am a member, aren't i? ) to pitch in and improve things.

SMACKPLAN -

It was precisely your suggestion of analyzing the diatonic chords that led to this post, so you're as responsible for it as anyone (IT'S ALL JON'S FAULT, IT'S ALL JON'S FAULT!!!! ).

MADEHIM FLEX -

A theory FAQ would be an excellent idea, I do believe SPAZZFLO's brilliant explaination of scales/modes is already posted somewhere in that vein. We could gather that up, add to it my primer on the Circle of 5ths/4ths and the interval primer (with the addition of BLISS's information) and create some good basic theory instruction.

A suggestion should be made to FEARLESS LEADER (aka Paul), hopefully it could be done fairly easily. Someone should also do a primer on reading standard notation, but I'm not sure how to do that so that it will work on the board (getting the staff, notes, etc to work with the format).

Thanks y'all....keep it comin'!!!

[JimK]

Good stuff, guys.
This interval talk reminds me of a Keller anecdote from my college daze.
Rather than looking/seeing & actually counting the interval, I was 'hearing it' & that's how I answered the professor...
Example: G to A#
I 'heard' that as a minor 3rd...so that's what I blurt out in class. Teacher says "No", I say "Yes"...back & forth, classmates sitting on their hands.
Damn, couldn't I SEE it's G-A(a 2nd) & not G-B(a 3rd)?!

[cassanova]

alright here goes nothing.

Gard if Im reading you right on this. Then I get what your talking about. Minor 2nd, 3rds etc. Are 1/2 step lower than the majors. Making that the "quality" of the interval.

The quantity would also be 2 because thats aproximatly how how many notes between that and the root.

EX:
C-D major 2nd (quality is maj2nd) quantity is 2 because its also the 2nd degree in the scale?

If its a minor 2nd its a 1/2 step lower than the major 2nd, (quality) and its quantity would also be 2, do to its rough distance from the root?

am i in the ballpark here now or still way up in the nose bleed seats?



Im not sure if im right about that, so thats why Im asking.

[Pacman]

by jove, he's got it!

[cassanova]

Originally posted by Chris Fitzgerald
TOAST GARD,

Excellent post...I think that we (i.e. - clan TABEVIL) should make this part of a theory FAQ that stays either on the homepage or here in GI. HASBRO'S scale guide is a wonderful start, and this is a great addition.


The only thing I would add to this at all is that intervals are often easier to understand if you grasp the concept if intervallic inversion, which Gard alluded to in his post.

An inverted interval is simply an interval that is turned upside-down.

For instance, C down to B is a minor 2nd, while C up to B is a major 7th. These inverted intervals can be said to be in the same class, since they involve the same two notes.

An easy way to remember how intervals invert is to remember that all interval inversions add up to the number "9", and that all major or minor intervals flip-flop their quality when you invert them. For example, if we consider all the following intervals to be ascending, then;

C to B = Ma 7th
B to C = mi 2nd
7+2 = 9

C to Bb = mi 7th
Bb to C = Ma 2nd
7+2 = 9

C to A = Ma 6th
A to C = mi 3rd
6+3 = 9

C to Ab = mi 6th
Ab to C = Ma 3rd
6+3 = 9

C to G = Perfect 5th
G to C = Perfect 4th
5+4 = 9

C to Gb = diminished 5th
C to F# = augmented 4th
5+4 = 9

C to F = P 4th
F to C = P 5th
4+5 = 9

C to E = Ma 3rd
E to C = mi 6th
= 9

C to Eb = mi 3rd
Eb to C + Ma 6th
=9

C to D = Ma 2nd
D to C = mi 7th
=9

C to Db = mi 2nd
Db to C = Ma 7th
= 9

and hypothetically,
C to C = unison (1)
C to C = 8ve (8)
8 + 1 = 9


Notice that perfect intervals invert to perfect intervals, Major intervals invert to minors, minors to majors, and Augmenteds invert to diminished and vice versa. Another interesting characteristic of inverted intervals is that they have the same psychological effect no matter which way they are inverted...octaves are always the most consonant, and mi2nd/Ma7th intervals are always the most dissonant (this has to do with the acoustical properties of the harmonic series, but that's a topic best saved for later). For this reason, I always think of the inverted intervals as being roughly the same, which cuts in half the number of categories to remember.

So, instead of thinking of 2nds, 3rds, 4ths, 5ths, 6ths, and 7ths, you can instead simplify to:

2nds/7ths
3rds/6ths
4ths/5ths


Hope that wasn't too confusing.

it was

but i just grabbed my bass and went over the scale. I see how the ma7 is B. So later when I have time, Ill go over it again and and figure out what the min 3rd is and then the maj 6th and so on.

I dont quite get the little 9 rule.

also my brother once told me and i think i read somewhere that every major has a relative minor. Is this what they were talking about? And how you go about figuring it out?

[JimK]

Originally posted by cassanova
Minor 2nd, 3rds etc. Are 1/2 step lower than the majors.

...and don't forget about the perfect intervals.
If you LOWER those a 1/2 step, they become diminished(ie, NOT "minor").
A '4th' can only be perfect, augmented(raised 1/2 step), or diminished(lowered 1/2 step).
A '5th' can only be perfect, augmented, or diminished.

2nds, 3rds, 6ths, & 7ths...
All can be major, minor, augmented, or diminished.

Each Major key has a 'relative minor' key...
Simply go DOWN a minor 3rd from the Major key's root(you know how this looks on yer bass' neck, right?)-
Example:
C Major = A minor
F Major = D minor

...or UP a minor 3rd from the minor key's root-
Example:
E minor = G major
C minor = Eb Major

D minor = ________?

A Major = ________?

[cassanova]

Originally posted by JimK


Each Major key has a 'relative minor' key...
Simply go DOWN a minor 3rd from the Major key's root(you know how this looks on yer bass' neck, right?)-
Example:
C Major = A minor
F Major = D minor

...or UP a minor 3rd from the minor key's root-
Example:
E minor = G major
C minor = Eb Major

D minor = ________?

A Major = ________?

is it F and C?

[JimK]

No.
(Hint for the D minor: "F______?). Gotta be a little more specific.

A Major = ________
Play the A note @the 2nd fret/G-string; go down a minor 3rd...(Hint: It won't be a C note).

[Jay]

Originally posted by Gard

SMACKPLAN -

It was precisely your suggestion of analyzing the diatonic chords that led to this post, so you're as responsible for it as anyone (IT'S ALL JON'S FAULT, IT'S ALL JON'S FAULT!!!! ).

[/b]

I can't hide it any longer! I taught him the circle of 5ths through IM!!!!!

::runs for the distant hills of Castle TB hoping to find refuge there::



BTW, I totally agree with a theory FAQ, excellent idea. Just my $0.02

[Pacman]

Originally posted by Gard
[b][b]SMACKPLAN -

It was precisely your suggestion of analyzing the diatonic chords that led to this post, so you're as responsible for it as anyone (IT'S ALL JON'S FAULT, IT'S ALL JON'S FAULT!!!! ).

Hey, with all the TaBz requests, it really nice to see someone interested in getting better as a musician, so if it's my fault I'm glad to be a part of it.

[Gard]

Originally posted by Pacman


Hey, with all the TaBz requests, it really nice to see someone interested in getting better as a musician, so if it's my fault I'm glad to be a part of it.

Just because it's your fault, doesn't mean I think it's a bad thing!!!

[cassanova]

Originally posted by JimK
No.
(Hint for the D minor: "F______?). Gotta be a little more specific.

A Major = ________
Play the A note @the 2nd fret/G-string; go down a minor 3rd...(Hint: It won't be a C note).

F major and F# minor.



Hey guys, does Fieldy know this crap? Cos if he does'nt then why the hell should I?

[Dave Metts]

I don't really consider myself a musician (I play more for fun than anything), but I'd still like to learn this stuff. It's a lot easier to create music with some knowledge behind you than it is by just randomly hitting notes.

[embellisher]

Very good information, LARD, GETBLITZEDGERALD, SHAQMAN and BEN GAY!

With this, the mode help that Angus has been giving me and the Time thread, I'm learning a lot.

Now if we could just find some place for the TaBz posts.

PHLEGM TABEVIL

[Gard]

Hey, I need a tAbEViL name...

[Dave Metts]

I think I may be able to pick up on theory yet! I'm going to make a promise to stay away from tab and learn how to read notation as well.

I agree though, let's turn this into a theory forum.