Fourths and Fifths

[zr1bill]

I am trying to get my head around this and I'm not sure what I'm missing. In a C maj scale, the fifth is a G. If you count down, descending, the G is a fourth. Am I OK so far?

My teacher told me that this would be the inverse. (I think he said inverse) He said that the sum of the two would always be 9. (4+5+9) So the third would be an E and is also the sixth descending. I find this confusing because it seems that a note can be two different degrees depending on whether you are ascending or descending. So, do you speak of degrees as either ascending or descending. Or is this just a bit of trivia that isn't really used.

If it is useful, how is this used?

Also, does this all relate to the circle of fifths, which I see referred to as circle or cycle of fourths or fifths.

I would ask my teacher but we are on hiatus and will start back up in 2 weeks.

[Djentleman]

If I'm understanding your question correctly, the answer is that you always name the scale degrees as the ascending interval. The descending intervals are not the name of the scale degree, they're simply the interval that it would be if you played the note that's lower.
If that makes sense

[Ezmar]

Useful only insofar as your understanding of theory goes. Basically just the internal understanding that a sixth up would be the same pitch class as a 3rd down. (With appropriate major/minor designations, of course.) Just sort of understanding the relationships between notes. I don't really think it has that much to do with scale degrees, I think it's more intervals. But in any case, I think it's just useful in the sense of knowing how things work.

[Russell L]

To simplify it, look at a keyboard and count the number of half-steps up and down to reach the note in question. (C up to G = 6 half-steps up; C down to G = 5 half-steps down). These numbers also have nothing to do with the scale step number (G is the 5th scale degree of the C major scale).

[AlastairWatts]

Originally Posted by Russell L

To simplify it, look at a keyboard and count the number of half-steps up and down to reach the note in question. (C up to G = 6 half-steps up; C down to G = 5 half-steps down). These numbers also have nothing to do with the scale step number (G is the 5th scale degree of the C major scale).

or 7 up...

[strappa]

scale intervals are numbered in ascending order
c = 1, d = 2, e = 3, f = 4, g = 5 up to the octave c = 8
if you count down the scale descending
you are starting from the octave 8
c = 8, b = 7, a = 6, g = 5

[zr1bill]

Originally Posted by Djentleman

...always name the scale degrees as the ascending interval.

Thank you all. This seems to be the answer.

[Fergie Fulton]

You have the info now. But I will just add, an interval is taken from the lowest note up to the next note.....never back to a note.

Inversion of a major interval produces a minor interval, inversion of a minor interval produces a major interval. Invert the 4th or the 5th and yo still have the same interval, that's what they are called perfect because they do not change when inverted.
As I said always work from the lowest note up to create the interval, never back down to one.

[MalcolmAmos]

Originally Posted by zr1bill

I am trying to get my head around this and I'm not sure what I'm missing. In a C maj scale, the fifth is a G. If you count down, descending, the G is a fourth. Am I OK so far?........................ Or is this just a bit of trivia that isn't really used. If it is useful, how is this used?

Count up, count down, what difference does it make? Intervals and scale degrees help us talk to each other so we understand what the other person is saying, so yes, it is part of the language we speak, thus you should know that language. Go over it again with your instructor. Your question revolves around -- how will you use all that scale degree stuff. Lets look down the music road a couple of months and see what they can do for you. Sometime seeing the big picture helps with the nitty-gritty of scale degrees.

I live by scale degree numbers. Understand when playing with the band I use fake chord sheet music which has the chord name and the song's lyrics. Nothing else. So here is the process I go through. Ends up that scale degrees are important in the way I play.

I look at the fake chord sheet music and decide what key the song is being played in. Why I look for the key will become clear later. Playing from any sheet music all that is necessary is you follow the notes and chord as written. That is great if the sheet music has everything you will need. Fake chord will tell you what chords and what lyrics are being used, nothing more. Sheet music is telling you to play a C chord next. OK great how much of the C chord? Just the root, or is more called for? Should I play the root of the chord, and then the 3rd scale degree of the chord, how about the 5th degree should I include that? When seeing the C chord I know that R-3-5-7 degrees of that C scale will be a good bass line under that chord. Course the music may not give you room for all of those scale degrees so you grab the root on beat 1 and then use as many of the other chord tones (degrees) as the music will allow. I end up playing a lot of roots and root-fives. WHOA, too much....... trying to give you an idea of what is coming - skim over the rest of this don't try and remember the nitty-gritty, just file it away as things that come into the picture.

Knowing the key I then decide what position I'm going to gather the notes I will be using, i.e. let's say this song is in the key of C. I can find the notes of the C scale in several places on my fretboard. The two locations I normally use are the 3rd string 3rd fret, or the 4th string 8th fret. The 4th string 8th fret normally wins out. Don't forget about the C's past the 12th fret..... Yep, gotta know where the notes are on your fretboard. I use the major scale box pattern and need to know how to position it so the notes I need are all within that four fret area.

Next thing I do when playing from fake chord I visualize my ole major scale box.

Major Scale box.

G|---2---|-------|---3---|---4---| 1st string
D|---6---|-------|---7---|---8---|
A|---3---|---4---|-------|---5---|
E|-------|---R---|-------|---2---|4th string

Notice my box does not have dots, it has numbers. Those numbers are the scale degree of the scale. Place my root over a C note on my fretboard and the notes of the C scale await me.

Now the magic.... The 2 is the second note in the scale and it is also the second chord in the key of C.
Chords in the key of C
1, 2, 3, 4, 5, 6,. 7
C, D, E, F, G, A, B, Interesting question should I know both it's name and it's scale degree? Answer, yes. Lot of things we need to know before we start playing songs.

The 3 is also the third chord in the key of C, yes, the 5 is also the fifth chord in the key of C. So..... my major scale box helps me with notes of the scale and also chords of the key. Playing just roots, this comes in handy.

Most songs I play will have the 1, 4, 5, 6 and 3 chords in their progressions, and the chord name, C, F, G, etc will be listed. So...... I add the numbers, over the chord name, on my fake chord sheet music. Why do that? I think in numbers more so than note name or chord name so in the middle of playing a song I may go blank where the Am chord is on the fretboard - but, I know where the 6 is. Course I had to know that the Am chord is the 6th chord in the key of C. Yep, lot of fundamentals that have to be stored before we can play songs.

From running my box until I can do it in my sleep, I know that the 4 chord is up one string and same fret as the root. The 5 chord is up a string, from the root, and over two frets, or just below the root on the next string down. The 3 is up a string and back a fret and the 6 is right above the 3 on the next string up. I think in scale degree numbers.

Once I get the scale degree numbers on my fake chord I visualize my box, place it on the fretboard position I like best -- and find my scale notes and or chords within my box.

That's how I use scale degree numbers. So looking down the road several months..... if you are like me and play from the major scale box pattern - then scale degree numbers are important.

Your choice, name or number.

[Fergie Fulton]

Originally Posted by MalcolmAmos

Count up, count down, what difference does it make? Intervals and scale degrees help us talk to each other so we understand what the other person is saying, so yes, it is part of the language we speak, thus you should know that language.

Unless I am mis-understanding you Malcolm (your info is always great),
surely it makes a big difference when talking intervals, C -E is a 3rd where as E -C is a 6th, if we assume we count up or down then that means we confuse the meaning, because either one of them could be seen as both being 3rds (which they are not), but only counting up to the note we only ever have one answer.

[zr1bill]

Originally Posted by Fergie Fulton

Invert the 4th or the 5th and you still have the same interval, that's what they are called perfect because they do not change when inverted.

Fergie thanks for the added information. Could you just expand on this a bit. It's a bit foggy in my head. I have always wondered where the term "perfect" came from but I'm seeing how this works.

Thanks,
Bill

[MalcolmAmos]

Originally Posted by Fergie Fulton

Unless I am mis-understanding you Malcolm (your info is always great),
surely it makes a big difference when talking intervals, C -E is a 3rd where as E -C is a 6th, if we assume we count up or down then that means we confuse the meaning, because either one of them could be seen as both being 3rds (which they are not), but only counting up to the note we only ever have one answer.

Yes it always depends on which way you are counting. That's what makes intervals so confusing, all they really are is the distance between two notes - course that depends on if you are going up scale or down........

We normally count up as you said.

[Febs]

Originally Posted by Fergie Fulton

Inversion of a major interval produces a minor interval, inversion of a minor interval produces a major interval. Invert the 4th or the 5th and yo still have the same interval, that's what they are called perfect because they do not change when inverted.

I think that you mean to say that the inversion of a perfect interval is another perfect interval (but not necessarily the same interval). Invert a perfect fourth and you get a perfect fifth:

C --> F = perfect 4th
F --> C = perfect 5th

So if you invert a perfect interval, you get another perfect interval, but it is not necessarily the same interval.

[Joe Louvar]

Always count up.

[Fergie Fulton]

Originally Posted by zr1bill

Fergie thanks for the added information. Could you just expand on this a bit. It's a bit foggy in my head. I have always wondered where the term "perfect" came from but I'm seeing how this works.

Thanks,
Bill

An interval is the gap between two notes, consider the lower note the root, and the upper note the target.
To invert an interval just means move the lower interval an octave up so to is above the the target note....they are now upside down...inverted.
Remember the number nine.

A perfect interval inverted becomes a perfect interval
A major interval inverted becomes a minor interval
A minor interval inverted becomes a Major interval
A diminished interval inverted becomes an Augmented interval.
An Augmented interval inverted becomes a Diminished interval.

So interval quality as inversion can be seem as a table that reads;
Perfect - Perfect
Major - Minor
Augmented - Diminished

The actual interval as a table is seen as
Unison - Octave
Second - Seventh
Third - Sixth
Fourth - Fifth

As you see they add up to nine, one will be major one will be minor etc.

Because when we invert 4ths and 5ths the do not change quality, we can alter them by augmenting or diminishing them, but they are still considered 4ths and 5ths, so they will still add up to 9.

[Fergie Fulton]

Originally Posted by Febs

I think that you mean to say that the inversion of a perfect interval is another perfect interval (but not necessarily the same interval). Invert a perfect fourth and you get a perfect fifth:

C --> F = perfect 4th
F --> C = perfect 5th

So if you invert a perfect interval, you get another perfect interval, but it is not necessarily the same interval.

This is the problem with such matters, yes it is in the detail. If any part of the detail is missed out, not learned or understood, then I becomes confusing.
Those that learn in the correct way do not have confusion because their learning is ordered to build on ideas.

For my sins I generally take it for-granted that ideas can be seen another way, but that is because we were only taught to see them for what they were.....any expansion on the idea came later.
I came from a time when the only information I got was from a book or a teacher, so I was very limited in where I could go with it.
This meant my teachers and tutors knew exactly what I knew, what my abilities were, and more important my weaknesses.

So when I talk theory I am like many others of that era, I just assume you know what it means....sorry for the confusion and the post above hopefully clears it up.

[Mugre]

Don't confuse interval with scale degree. Moving down a fourth lands you on the 5th of the key signature. It's that simple. On a piano, if you play a chord 4 steps below the tonic, does if function (sound) like a IV chord? No it functions like a V with it's attendant strong resolution to the I.

[Fergie Fulton]

Originally Posted by Mugre

Don't confuse interval with scale degree. Moving down a fourth lands you on the 5th of the key signature. It's that simple. On a piano, if you play a chord 4 steps below the tonic, does if function (sound) like a IV chord? No it functions like a V with it's attendant strong resolution to the I.

You make my point, it is assumed that the difference is already know...if not, then what not?
But you also expand on idea, so now the ideas of its function within the harmony, so that idea is a big leap forward on what intervals are about when learning, what you offer is info to be used when intervals have been learned.

This is why theory on the net gets confusing, no one can really control the order of the information.
It akin to asking directions when lost, you ask someone and they give them to you, only for someone to jump in and say there is a better way, and give you their ones, only for someone else to jump in with there are faster ones and give you them, only for someone to join in with easier ones and so on and on......till you just drive away and are still non the wiser for asking.

[Russell L]

Originally Posted by AlastairWatts

or 7 up...

Oops, that's right...G is 7 half-steps up from C. Sorry folks, I was sleepy.

[Russell L]

Notice on a keyboard that if you play a C and a G above it there will be three white keys between them. Then, if you play a C and a G below it you will have only two white keys between them.

I believe the key of C on a keyboard is the best way to learn intervals. You can see the major scale as all white notes, and any variations as black notes, basically. Wanna understand 1 3 5 7 9 11 13? Notice how you just skip every other note all the way (chords are based on thirds). How 'bout a #11? It's right there before your eyes.