3rds and 6ths - can someone explain

clive swindell · From: Huddersfield, West Yorkshire, UK

OK, so I understand that a scale on strings 5&6 is 3rds and that the inverse ie the scale played on strings 3&5 is in 6ths.

Same with a scale on strings 5&8 (6ths) and 4&5 (3rds) etc, but why are the intervals called 3rds & 6ths?

Is it the number of 1/2 tones in the separaration? or the number of whole tones? or what?.

Sometimes I lie awake at night trying to figure out the answer!

Nicholas Dedring · From: Beacon, New York, USA

How exactly are you playing the scale? If you are pedalling down, then you have a changing interval...

however, a major sixth is 9 half-steps. It's a note, plus an interval one full tone above the fifth.

A major third is four half-steps. Minor thirds are three half-steps. A major chord is a major third, then a minor third.

I don't know what exactly you want to know, though... with pedals, the intervals are not remaining sixths or thirds... on strings six and five, you make a minor third into a major third with A&B down. on 3&5, you go from a 9 half step, to an 8 half-step interval when you pedal down.

[This message was edited by Nicholas Dedring on 04 March 2004 at 06:15 AM.]

John McGann · From: Boston, Massachusetts, USA * R.I.P.

Hi Clive-

Here's the basis of "diatonic" (meaning in a major key) harmony. In every scale, each note has a particular function, signified by a number. The root of the scale (or chord) is always note #1.

Imagine a C scale, CDEFGAB.
If you measure in either 1/2 or whole steps, between each note (the space called an 'interval") you get W W 1/2 W W W 1/2.

Now, if you measure from the root C to each note you get the following:

C to D major 2nd
C to E major 3rd
C to F perfect 4th
C to G perfect 5th
C to A major 6th
C to B major 7th

So, C to E is a third. It's known as a MAJOR third to distinguish it from the non-diatonic (out of the key) Eb. C to Eb would be a MINOR third.

So, our C to E is a third. But if we invert it, and put the E on the bottom and C on top, it becomes a MINOR sixth.

So, each interval INVERTS to a different interval. Without going way out in the theory zone, if you see and hear that 3rds and 6ths are the most common and "consonant" (pleasing to the ear) harmony interval, then you are in business.

Now, if you measure some scale intervals internally, for example "going up the scale in thirds" means that some intervals will be MAJOR thirds and some will be MINOR, because of the way the 1/2 steps occur naturally within the scale. (re-read that a few times!)

1. CE (maj 3)
2. DF (min 3)
3. EG (min 3)
4. FA (maj 3)
5. GB (maj 3)
6. AC (min 3)
7. BD (min 3)

Now you'll see why the 1,4 and 5 chords themselves are major and 2,3 and 6 are minor (7 is diminshed, which is mionr on the bottom and a b5 on top). Play the above sequence over a C chord and you have a harmonized scale in 3rds in the key of C. Invert the intervals to 6ths and you'll have the same thing, as far as the relationship of the notes against the chords, but a WIDER interval as the 6ths are further apart from each other than the thirds.

Email me if I can be of further help (if that was any help at all!)

[This message was edited by John McGann on 04 March 2004 at 06:21 AM.]

C Dixon · From: Duluth, GA USA



C D EF G A BC D E 


1 2 34 5 6 78 9 10

The reason C to E is called a 3rd and E to G is called a 3rd is because of the note counts, NOT the spaces. IE, C D E or 123; E F G or 123. But follow along...

Note: there is a count of 4 between C and E; and there is a count of 3 between E and G, IF you count the notes AND the spaces. (Spaces=frets too!)

The first interval (C-E) is called a "major" third; the second (E-G) is called a "minor third. Now you know "why".

Now lets play with some more numbers. See if you can see the following:

C-D is a 2nd. Simply begin counting with the C and only count notes.

C-D (above the octave) is a 9th.

D-C is a 7th

D-A is a 5th

G-C is a 4th

C-G is a 5th

C-E is a 3rd

C-B is a 7th (major 7th in our country)

C-A is a 6th

A-C is a 3rd

B-E is a 4th

E-B is a 5th

E-A is a 4th

and so on.

It then becomes evident that C-E is a 3rd, yet E-C is a 6th.

Hope this helps,

carl

[This message was edited by C Dixon on 04 March 2004 at 09:12 AM.]

Nate LaPointe · From: Los Angeles, California, USA

Carl's explanation is a good one. Each interval has a quality(Major, minor, diminished, augmented) and a number(3rd, 6th, etc) Carl walked you through the numbers and inversions. One tip for figuring out it's quality(this works for 2nd's, 3rd's, 6th's, and 7th's)...
If the higher of the 2 notes is in the key of the lower note, it's major. ie C-E=Maj3
If it's not in the key, it's minor, dim, or aug(you can figure that out by counting it's distance from the Major interval) ie E-C=min6
For Perfect intervals(4th's and 5th's), they are both in eachother's keys.
i.e. C-G is a 5th, G-C is a 4th.
If you make a perfect interval smaller(raise the first pitch or lower the second pitch) the interval becomes diminished. If you make a perfect interval larger(lower the first pitch or raise the second pitch) the interval becomes augmented.
ie C-Gb dim5, C-F# aug4
C-G# aug5, C-Ab min6
Whew, sounds like a foreign language course!
Nate

[This message was edited by Nate LaPointe on 04 March 2004 at 10:21 AM.]

Dave Van Allen · From: Souderton, PA , US , Earth

Time for my M.A. meeting...
Musician's Anonymous™ .. it's a 12 half-step program.

(c)David Van Allen

[This message was edited by Dave Van Allen on 04 March 2004 at 11:14 AM.]

Ray Minich · From: Bradford, Pa. Frozen Tundra

Wow, I'm digesting this bit of musical infusion, my head is still spinning. I have another question along this same line... and this place seems the logical time to ask it.

Is there a musical key for each of the 12 half tones per octave? Are there 11 keys or 12. The reason I ask is that in the "Circle of Fifths" dissertation that Bill Keith wrote about in Winnie's 1975 Oak Book on the PSG, he stated there were 11 keys. Where's the 12th one? Is there a duplicate? Couldn't one start to play a 1-4-5 chord set from any starting fret? and there'd be 12 starting frets in an octave.

Not meaning to hijaak the thread, just seemed the right place to ask this question. Thanks.

C Dixon · From: Duluth, GA USA

There ARE 12 discrete keys.

1 C
2 C# or Db
3 D
4 D# or Eb
5 E
6 F
7 F# or Gb
8 G
9 G# or Ab
10 A
11 A# or Bb
12 B

While there CAN be an E# (or B#) note there is NO E# (or B#) key. Confusing huh?

Every one of the 12 keys has a I, IIM, IIIM, IV, V, VIM and a DIM (V7 actually) chord in it. And they are spaced according to the same tone tone half-tone tone tone tone half-tone scenario spoken of earlier in this thread.

The one caveat to the learner is the fact that between E and F (and B and C) there is only a half a tone, whereas all others there is a whole tone between them. Keep this in mind.

What determines whether it is a sharp key or flat key is more in the mind of the composer. But musical notation simplicity, along with the limitations of certain musical instruments like the saxophone, flutes etc, tend to dictate whether a tune is in the key of G# or Ab as an example.

Without going into it really deep, the above should be sufficient to explain it from a practical point of view.

carl

Ray Minich · From: Bradford, Pa. Frozen Tundra

Thanks Carl, you've answered my question and confirmed what I thought to be the order of things. I think what Bill Keith meant to write was that there were "eleven more..." keys, maybe it was just a typo.

Had me going for a while. Thanks again.

Nate LaPointe · From: Los Angeles, California, USA

Technically, there are 15 major keys, let me explain...
If you go through the circle of 5ths, you'll notice the number of sharps in that key increases by one as you go up by 5ths, and increases by one flat going in 4ths.
C-0
G-1#
D-2#
A-3#
E-4#
B-5#
F#-6#
C#-7#

F-1b
Bb-2b
Eb-3b
Ab-4b
Db-5b
Gb-6b
Cb-7b

as you see, there are a few scales that are enharmonic(Db=C#, Gb=F#, Cb=B). This is what accounts for the extra 3 scales totalling 15.
This is the kind of stuff they teach you in music school. It sounds bogus, but believe it or not, I'm thankful to know the difference and be comfortable with both F# and Gb. Same key, but they mean different things, especially to horn players!

Ray Minich · From: Bradford, Pa. Frozen Tundra

New Words Alright Already!!! I had to go to a dictionary printed in 1934 (big two volume Noah Webster version) for this...

Enharmonic:
1) Of or pertaining to that one of the three kinds of genus or scale (diatonic, chromatic, enharmonic) which employed dieses, or quarter tones.
2) Pertaining to a change of notes to the eye where a keyed instrument can mark no difference to the ear, as the substitution of Ab for G#; as an enharmonic interval.
3) Pertaining to a scale of perfect intonation (uh-oh) which recongnizes all the notes and intervals that result from the exact tuning of diatonic scales and their transposition into other keys.

I had to look it up, just thought I'd save the rest some work :>)

Really, Nate and Carl, thanks for the info.

[This message was edited by Ray Minich on 05 March 2004 at 12:37 PM.]

Robert Porri · From: Windsor, Connecticut, USA

Number 2 of that Webster definition of enharmonic works for me. Sounds the same, "spelled" different.

Definitions 1 and 3, for me anyways, just sound confusing.

Bob P.

[This message was edited by Robert Porri on 05 March 2004 at 11:24 PM.]

Ray Minich · From: Bradford, Pa. Frozen Tundra

Great idea Robert...

A Musical Homonym, whooda thought? great metaphor...

[This message was edited by Ray Minich on 07 March 2004 at 08:28 AM.]

clive swindell · From: Huddersfield, West Yorkshire, UK

Thanks guys, I think I understand it now, at least I now have something to refer to.

Bruce Clarke · From: Spain

Nate, if you were taught that there are 15 major keys, you went to the wrong school.

Nate LaPointe · From: Los Angeles, California, USA

Obviously Bruce, there are really only 12 major scales to the ear. But if you approach it from the standpoint of key signatures, you'll see there are technically 15 major scales. Ask any horn player, he'll tell you that F# and Gb are different keys.
Ask a classical violinist and he'll tell you if the peice is in Gb, he wants to see Cb's.
Being a jazz guitarist, if I see Abmi7-Db7, I know I'm in Gb Major. However, if I see G#mi7-C#7 I know I'm in F# Major.
Yes, they are enharmonic, but the approach on the instrument is sometimes different.
I went to CalArts Bruce, where did you go to music school?

Bruce Clarke · From: Spain

Nate, yes there are 12 Major scales to the ear, but if you approach it from the standpoint of key signatures you will see that each of the 12 has its enharmonic equivalent. Only a few of these are ever used in practice, the others being unnecessary, and the complexities involved in writing and reading are considerable. As an example, try writing out the scale of E# major. If you were not required to do this sort of thing during your studies, to get you started I will point out that you will need 11 sharps in the key signature, and this will involve the use of double sharps.

I don't want to state where I went to school, I might be accused of boasting, and it was a long time ago anyway, although I still regard myself as a perpetual student.

I replied to your post only because when beginners come to the forum asking questions about music theory I think we should be absolutely accurate in replying, otherwise we are not helping at all. to state that there are 15 major keys is just plain wrong, and misleading.

C Dixon · From: Duluth, GA USA

Mega Dittos Bruce.

Mike Delaney · From: Fort Madison, IA

This sounds like a riddle, but it isn't at all. Just rules of thumb.

1-Inversions always add up to 9.
2-Major becomes minor, minor becomes major.
3-Perfect remains perfect.

For example, C to E is a major 3rd. E to C is a minor 6th. 3+6=9, major 3rd became minor 6th.

C to Eb is a minor 3rd. Eb to C is a major 6th. 3+6=9, minor became major.

C to G is a perfect 5th. G to C is a perfect 4th. 5+4=9, perfect remains perfect.

Hope this will help make some sense of it.

John McGann · From: Boston, Massachusetts, USA * R.I.P.

(quote) to state that there are 15 major keys is just plain wrong, and misleading. (unquote)

Bruce- I'm afraid it's you who is in error here. Check out the circle of fifths in any basic theory book, and here are the keys that you'll find.

C
F
Bb
Eb
Ab
Db
Gb
Cb
G
D
A
E
B
F#
C#

That's 15 discreet keys, with no double sharps or flats involved. All commonly used keys. No E# key or B# key.

Carl lists D# and A# as keys, but they don't exist in terms of standard notation key signatures that have been in use since the time of J.S. Bach (and maybe before for all I know)...They are not the same thing as Eb and Bb. Ask any non-guitar player musician.

The fact that these keys exist and are in constant use will be proven by looking in any music store at any given batch of sheet music.

It doesn't matter where you went to school, or IF you went to school. This is the standard practice of the music world at large. If it doesn't matter to you, it doesn't matter...

[This message was edited by John McGann on 10 March 2004 at 12:50 PM.]

Nate LaPointe · From: Los Angeles, California, USA

I agree, I think we should be absolutely accurate in replying, which is exactly why I support John's argument for the circle of fiths/fourths. When speaking of diatonic major scale harmony, I believe the circle has become the standard, and for very good reason. Not only does it allow the student to learn his/her major scales and the order of sharps and flats, but it provides the professional with tools to compose and interpret music. I agree, the key of E# is useless and far too complex to be practical. But is the understanding of 3 enharmonic keys(C#/Db, F#/Gb, B/Cb) really a problem? Like John said,

"This is the standard practice of the music world at large"

so why limit yourself?

Bruce Clarke · From: Spain

Nate, I first gained an understanding of the three enharmonic keys that you mention, plus all the others, when I started to write arrangements for the big bands that I was working with as a pro piano player. As you imply,no use writing for the sax section in F#.

John, when I was employed by the Yamaha Music Corporation as an organ instructor I too found the circle of fifths thing to be useful. It's a bit limited though, for instance while it tells you that the key signature for D major has two sharps, F# and C#, it does'nt explain why. I had to know why in case someone asked me.

Nate, if in your original post you had stated that there are 15 key signatures in general use, you would have been correct. You in fact stated that there are 15 major keys, and that is a very different statement, and an incorrect one, and still incorrect no matter how many times it is repeated.
I guess you were just a bit careless with the terminology, but the guy who asked the question did not know that, and he may be a mite more confused than before, so it's nice that we agree, that in this situation we should get it right.

John McGann · From: Boston, Massachusetts, USA * R.I.P.

For the curious, the "why" of F# and C# in the key of D (or why there are sharps and flats in different keys) is to retain the interval sequence from the root:

W W 1/2 W W W 1/2

that defines the major scale. HALF STEPS between 3 + 4 and 7 + 8

If you write out D E F G A B C (remember 1/2 steps are between E + F and B + C) you'll see the half steps fall in the wrong place. Raise the F's and C's and you have what's required. This what all the key signatures do- put the 1/2 steps in the right places for each key.

------

Bruce, no offense intended, but regarding your refusal of the fact that there ARE 15 keys, why else would there be 15 key signatures? Any 9th grade music student who was asked to "write all the key signatures" and only wrote 12 would be wrong-anywhere! If you leave out C# or Cb or whatever, you'd be incomplete. It's the truth, no matter how you slice it.

I have also written for string orchestras, jazz orchestras, blah blah blah. As you know, writing jazz charts requires a lot of transpositions, so you get to work in lots of keys.

Checking facts in ANY theory book before posting info that can confuse beginners, as you suggested to Nate, is great advice, but you should take it yourself, especially before being so heavy handed about it.

I agree that C# may be used less often than Db as a key, and Db is easier to read, but you'd have to rewrite history to say the two don't co-exist! As someone who has spent a lot of time with written standard notation, I'd think you'd be well aware of this.

Just because they are the same keys on the piano (or frets on a guitar) doesn't mean they are the same thing on non-fretted instruments-most classical bowed instrument players would agree. If you work with written standard notation and especially music that modulates a lot, you'll understand why the keys of C# and Db are different and their relationship to other keys. They are different conceptually.

PS- in the big picture, playing music, not reading it- on a bar gig- does it matter? Probably not. But since this thread was started by someone looking for clarification of confusing theory, I figured this explanation really was worth the effort. Again, sorry if it rubs you the wrong way.

[This message was edited by John McGann on 11 March 2004 at 11:08 AM.]

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