About Fourths and Fifths

[ozboomer]

Another (probably dumb) theory question...

Premise 1: An interval of a Perfect 5th is defined as 7 semitones
- start at "A"
- moving upwards by 7 semitones (a Fifth) gives E
- moving downwards by 7 semitones (a Fifth) gives D

Premise 2: Moving clockwise around the 'Circle of Fifths' defines an interval of a Fifth; moving anticlockwise defines an interval of a Fourth.
- start at "A"
- moving clockwise to the next note on the circle (a Fifth) gives E
- moving anticlockwise to the next note on the circle (a Fourth) gives D

Problem: A (descending) 'Fifth' interval is different if you go by the '7 semitones' definition compared to the way the 'Circle of Fifths' works.

Please explain.

Observation: An 'ascending Fifth' note is the same as a 'descending Fourth' note, owing to the way the major scale is built (and I guess, by virtue of Equal Temperament)... and is akin to the 'Circle of Fifths' way of working. This is the same whatever interval is used- an 'ascending Third' note is the same as a 'descending Sixth' note.

Thanks.

[stevewf]

An interval can be both a fourth and a fifth only if we incorrectly apply "octave equivalency," which treats any note and all notes that are integer multiples of ocataves apart from it as being the same note. For example, we could treat all "D" notes, regardless of which octave it's being played in, as being just that: a "D".

That being said, treating the "A" without octave equivalency while treating all the other notes with octave equivalency is inconsistent and makes a fourth the same as a fifth. The "D" that's the lower-freq neighbor of the reference "A" is a fifth apart froim the "A"; the "D" that's the higher-freq neighbor is a fourth higher - but it's not the next note in the circle of fifths. If we decide that clockwise around the circle of fifth is higher frequency, then the next CW note is "E", a fifth higher than the "A"; if we decide the opposite direction is higher freq, then the next CW note is a "D", a fifth lower than the "A". Only after defining which direction is which and then taking one or more steps around the circle, and apply the octave equivalency in the same direction as the circle steps can we consistently say either a fifth or a fourth.

In short, Premise 2 is incorrect: Better written would perhaps be:
- start at "A"
- moving clockwise gives a higher "E". We refrain from equating this "E" with the "E" that's lower in freq than the starting "A", as this is in treating as though we're moving anticlockwise, which is the opposite of what we really did.
- moving anticlockwise gives a lower "D". We refrain from equating this "D" with the "D" that's higher in freq than the starting "A".

[sumgai]

ozzy,


Stop mixing your Fifths and Fourths. Every time you say "Fourth" while descending seven semitones, you're referring to the name given while ascending - don't do that.

To keep it clear in your head whilst counting off semitones, don't name it as a reference, just count it out. Once you've arrived at the next note, you can then give it the proper note name. Then, and only then, should you give it a reference or relation to the root.

And yes, most folks, beginner and advanced alike, do refer to notes as if everything always ascended, and never descended. But being able to go in either direction without having to 'stop to do the math' is what separates the musician from the wannabe.

tl;dr:

It's a simple matter of semantics, that's all.



HTH





sumgai

[ozboomer]

Okie, that's as clear as mud in a beer bottle... but I'm kinda slow anyway, so let me think about the suggestions some more...

...but I'd ask if my 'Observation' is correct, specifically to this example (sorry Sumgai... but y'know wot I'm like )... and talking about the Major Scale....

An 'ascending Fifth' note (A, B, C#, D, E) has the same note name as a 'descending Fourth' note (A, G, F#, E) (see 'Intervals' in Inversion (music), which sortof speaks to stevewf's points about a change in octaves... but just further confuses me [at present]).

Hmm??

All this stems from somebody saying that, while playing an "A" they 'moved down a 5th, to D'... which confused me... and led me down this rabbit hole of theory (again).  I can see how you'd 'move UP a 5th' if you were playing a "D" and you moved UP to "A"... but not the other direction... 

[reTrEaD]

May 5, 2024 21:30:48 GMT -5 ozboomer said:

...but I'd ask if my 'Observation' is correct, specifically to this example (sorry Sumgai... but y'know wot I'm like )... and talking about the Major Scale....

An 'ascending Fifth' note (A, B, C#, D, E) has the same note name as a 'descending Fourth' note (A, G, F#, E) (see 'Intervals' in Inversion (music), which sortof speaks to stevewf 's points about a change in octaves... but just further confuses me [at present]).

This is sloppy terminology which is the root of your confusion. However, a do have a tonic for that.

The term 'fifth' has two meanings which are not interchangeable.

• If we use that word to mean an interval (or distance), a perfect fifth is seven semitones.
• If we use that word to mean the degree of a scale, that is a destination, not an interval.

A perfect fifth is the fifth note of the scale is when we start from the tonic and ascend seven semitones.
But a perfect fifth is the sixth note of the scale when we start on the second degree of the scale and ascend seven semitones.

Likewise, if we start at the tonic and descend a perfect fifth, we will arrive at the fourth note of the scale.
Put another way, if we start at the tonic descend to the fourth note of the major scale, the distance is seven semitones ... a perfect fifth.

Use 'note' to indicate the destination.
Do not use 'note' to indicate an interval.

[ozboomer]

After some hours of bending my brain, I've taken a step back...

My current (simplified) thinking is:
- the circle (as an 'interval' reference) shows notes that are always 'a perfect fifth apart' (7 semitones) (independent of 'left' and 'right', clockwise, anticlockwise)
- the circle (as a 'scale' reference) shows the degrees of a scale; for a selected note being 'I', 'IV" will be to the left, 'V" will be to the right, etc (and this is where the clockwise => move by fifths [degrees], anticlockwise => move by fourths [degrees] makes sense)

My error came from applying the 'scale' usage in an 'interval' context... I think.

[stevewf]

I think that like many concepts that are ascribed to "math" but are really logic, the answer lies on a web of paths, converging at the point we're investigating.
What?
In other words, reTrEaD, sumgai and I are each saying the same thing.

Start with a note. A. If you go "up" a fifth, that's an interval. You went up. Don't (yet) name that note, because other notes (octaves) have that same name. You have a fifth interval.

Now you may name that note and make it the base of your next interval to be studied. E.

Now consider this choice:
a) moving up a fifth gets an aggregate 14 semitones (a major 9th). Now you're at B.
or
b) moving down a fifth returns to a familiar spot. Now you're back a A.

What you don't get to do is move a fifth in one direction, name the note, then take that same named note but in a different octave, and only then evaluate the interval.