Re-confused on intervals/circle of 5ths

Theory
#1

I think i had asked this before but I Can’t find the thread. I had this figured out but my son is now doing piano and I re-confused myself…anyways

He is doing perfect fifths. We were working on Star Wars. C4 to G4 is a perfect 5th. He asked if it is the same in reverse. G4 to C4…logically it has to be yes…its the same distance between the notes–same number of keys…same frequencies in a chord.

But according to my cycle of 4ths/5ths chart, starting at G and going to a C is a fourth.

And then that got me comparing it to bass. Starting on C on the a-string, we say that G on the d-string is a fifth. But if we start on G on the d-string, we say that a fifth down is D on the a-string. Yet, i also know the bass strings are tuned in 4ths, so how can that be?

Can someone help me out on this…mind is swimming.

1 Like
#2

It’s because there’s 12 semitones in an octave scale, and a perfect fifth is seven semitones. A fourth is five. So, going up seven semitones is a perfect fifth (in the same octave). Going down five semitones from the root gets you to the same note in the previous octave - 12-5=7, so going down by five semitones gets you to the seventh semitone from the previous octave’s root. So if you start on that note as a new root, and go up five semitones, it’s a fourth, not a fifth; five semitones is a perfect fourth interval.

The same is true on your bass, of course, and is immediately apparent when fretting. Going up one string in the same fret is a perfect fourth. The bass is tuned in ascending fourths. Going down one string is a perfect fifth :slight_smile:

1 Like
#3

You assume a symmetry that is not quite there…

When you write out the notes of a scale:

C - D - E - F - G - A - B - C

then you can see there is no perfect “center/middle” note from which the distance to either end of the scale is equal. The only way to divide this is in unequal parts:

E.g., for “your” case:

C-F (fourth) and then F-C (fifth) or
C- G (fifth) and then G-C (fourth)

In other words, the direction of the interval is important as well - C to F (upwards) is the same as F to C (downwards), namely a fourth. But, it is not the same interval as C to F (downwards), which, however, is the same as F to C (upwards), namely a fifth.

The root of the confusion is that the same term is used to describe the interval (=distance between notes; a fifth) and to describe the degree in the scale (the fifth note).

Just think of other relationships in that scale: C up to E is a (major) third (interval), while C down to E is indeed a (minor) sixth (interval), but E is still the third degree/note in the scale, and thus commonly referred to as THE third, i.e. the note defining major or minor for that scale.

This distinction is perhaps more obvious in the C-E example, while it is almost not there for the C-F or C-G examples and thus even more confusing.

1 Like
#4

Just to add to what the others have said, if you Google search for a Youtube clip on “Inversions” (from a content creator that you know and trust) that may help clarify it more for you.

2 Likes
#5

They’re inversions and they always sum up to 9. Here’s some info “Dolmetsch Online - Music Theory Online - Inversion of Intervals” Dolmetsch Online - Music Theory Online - Inversion of Intervals

Maybe seeing it on a staff will make it more obvious what’s going on:

20220224_025509
20220224_025509432×592 29 KB

Or this (not the same notes as above)

20220224_044737
20220224_044737912×698 56.2 KB

And to see why it’s always 9, move the C to a D.

1 Like
#6

The root of the confusion is that the same term is used to describe the interval (=distance between notes; a fifth) and to describe the degree in the scale (the fifth note).

But, if we are constructing triads based on the root of a scale, the “third” is in fact a “major third” and the “fifth”, is, in fact a “perfect fifth”

#7

Ok. but in the first picture you have, the distance remains the same between the two notes regardless of direction, correct? A down to E is a perfect forth. But starting on the same E and going up to the same A is also a perfect fourth, right? Likewise, A up to E is a perfect fifth, but taking that same E back down to the A is also a perfect fifth, right?

image

And I guess the “root” of my confusion can be shown in the second example you have. the C up to the G is a perfect fifth. But we also say that you can “play the fifth an octave lower” on the E string. Even though the interval distance between the C and the lower G is a fourth, we still say its the fifth for the scale degree.

image
image755×430 89.9 KB

#8

Yes, that was my point about the “language/choice of words” not helping. The fifth degree above is indeed the interval of a fifth away. The fifth degree played below is an interval of a fourth away.

The third degree above is an interval of a third away. The third degree below is an interval of a sixth away.

And so on…

Other languages use latin-derived words for the intervals, such as “quart” or “quint” etc. to avoid some of that confusion. (English seems to only have retained the octave in that vein.)

2 Likes
#9

Yes, the scale degree is the position of the note in the scale, relative to the tonic (of that octave). Degree (music) - Wikipedia

The interval is the distance up or down between two notes.

If i start on the tonic and count up to the 7, it’s a 7th.

If i start on the 1 and count down to the 7, it’s a 2nd.

image
image1070×111 32.3 KB

When you talk about notes in the following octave, you keep counting so the 2 becomes a 9. A 2 is quite dissonant with the root note but it sounds less dissonant when it’s an octave away. Extended intervals eg 9, 11, 13 are common in jazz.

1 Like
#10

Ok, I get that…thanks. Can you please confirm that if you play the 7th–the D–and then go BACK DOWN to the tonic–E–that interval is still a seventh?

#11

Yes. The interval is a distance, it has to be the same or you wont end up in the same place you started :slight_smile:

If you’re standing at the bottom of the stairs and you go up 7 steps, you have to come back down 7 steps to be where you started.

3 Likes
#12

There is an interval of a perfect fourth between G4 and C5 (G4-A4: 2 ht, A4-B4: 2 ht, B4-C5: 1 ht for a total of 5 half-tones).
G is the fifth degree if you start counting from C, and (in fact) there is an interval of a perfect fifth between C5 and G5 (C - 2ht - D - 2 ht - E - 1ht - F - 2ht - G = 7 ht)

As @shadowbass said, we are using similar sounding names for different things, mostly for traditional reasons…

2 Likes
#13

Thanks everyone… I “THINK” I am sorted.

3 Likes
#14

Excellent :slight_smile:

We all basically said the same things above, using different terminology. The key reason here is because the fifth is more than halfway in to the octave, so going down to that note from the root is a different interval distance than going up to it.

This is another thing that would have been immediately apparent using a keyboard and just counting the interval or semitones between the specific notes.

3 Likes
#15

This was also confusing to me in the beginning, I made sense of it by fretting patterns:
To get to the fifth below the root, I think of it this way:
Going to the fifth above: 1 string up, 2 frets up.
Then down an octave: 2 strings down, 2 frets down.
So I end up on the same fret, 1 string below.

2 Likes
#16

Intervals are different than how notes are operating musically within a key.
C to G and G to C are both root to fifth, or fifth to root in the key of C.

But the actual INTERVAL between C up to G (a perfect fifth) and a G up to a C (a perfect fourth) are very different.

If you count piano keys or bass frets between each, you can see the difference.

Hope this is helpful!

3 Likes