# Tonal harmony, counting intervals and confusing about Perfect Fifth in C Major

Distance from E to F is a half step because no other notes fall between them. Why are we using the G note as a perfect fifth in C Major chord? Shouldn't be G sharp?

• possible duplicate of What makes an interval "Perfect"? Sep 29, 2015 at 8:39
• Note that what makes something a perfect fifth is not how many keys away it is on the piano keyboard. Again, don't let the piano keyboard fool you into thinking that the piano is in charge of how music works. It's a servant like the rest of us, and it doesn't totally make sense. A perfect fifth is a specific frequency ratio. On a harmonica, it's only two holes away. On a guitar, it's one string and two frets higher. On a piano, it's always seven keys away, regardless of whether those keys are white or black. Sep 29, 2015 at 10:22
• Actually I was thinking piano is in charge of how music works. My instrument is guitar. Just because my thought I was seeking every music theory question of mine on the piano keyboard. Now I will focus on the frequency ratio. Thanks. Sep 29, 2015 at 11:44
• You need describe the thought process that made you pick G# (in what way would it be related to the semitone between E and F ?), otherwise you're just asking for the perfect fifth's definition (instead of having us show you where your process is flawed) Sep 29, 2015 at 15:44

I need to confess your question was not easy to me to understand. We normally use these concepts on western music without thinking, and you really made me think. Thank you! :)

I think the other way to ask your question is: If I hear a major third as a "perfect" interval, why a perfect fifth is made of a major third plus a minor third instead of two major thirds?

Well, let's go:

The concept of "perfect" is related to historical concepts, to the ratio between frequencies of two notes and to the way our brains hear these frequencies on an interval.

At the time the concept of "perfect" was forged, Western music had pratically only Pythagorean temperament to tune their instruments, and the consequence of the use of this way of tune was only 4 intervals were regarded as consonances: the perfect unison, perfect fourth (diatesseron), perfect fifth (diapente) and perfect octave (diapason). At that time and using that temperament the major and minor thirds were not as usable as they are on modern temperaments. I mean, subjectively, they were not as pleasant as they are today.

What made these intervals perfect is the way our brain hears these intervals. Since the ratios of frequencies on these intervals are respectively 1:1, 3:2, 4:3 and 2:1, our brains hear these intervals in a very pleasant way, as if the frequencies on these intervals "fit" one into another perfectly. Acoustlically speaking, these intervals had no beats or hammerings.

It's difficult today to really understand why these intervals are still called perfects on an instrument tuned on equal temperament, because since fourth and fifth doesn't hold that perfect ratio on these instuments anymore, our brains don't listen them as perfect also. All intervals on modern piano (except octaves) have beats. The perfect fourth and the perfect fifth hold their names for historical reasons. If you have the chance to hear a violin/viola/cello tuning their strings on perfect fifths (they can do that), you will understand why they are called perfects.

BONUS: if you want to understand more these concepts, you could study acoustic interference and musical temperaments. I think this will untie your questions a little bit and will make you more curious about the subject. :)

• First I appreciated for your answer. I have lot of questions now before I have. I also confused. I think it will worth it. Because I will keep digging. :) Thanks again. Sep 29, 2015 at 13:26
• You are welcome! But what exactly confuses you? Sep 29, 2015 at 13:48
• Interference and different musical temperaments these are based on math and physic. There are lot of formula come up when I was searching at the internet. I don't understand ratio defination (4:3, 3:2 etc...) also. Well, I have to more study about these. Sep 29, 2015 at 14:06
• The ratios part are easy. Let's get, for instance, an A 220 Hz and an E 330 Hz. The ratio between 330 and 220 is 3:2. If you get an A 440 Hz and an E 660 Hz the ratios between them will be the same. These are the frequencies of these notes on Pythagorean tuning (old system). If you put these frequencies on a frequency generator they will sound perfect. If you use equal tuning (modern), the frequencies will be 440 Hz and 659.255 Hz. I recommend you to try these pairs of frequencies on Audacity or another frequency generator to figure it out. Sep 29, 2015 at 14:41

The perfect fifth's size is 7 semitones. So, let's count them from C:

1. C-C#
2. C#-D
3. D-D#
4. D#-E
5. E-F
6. F-F#
7. F#-G.

If we count 7 semitones, we end up on G natural, and not G#.

Also, if we had a chord that consisted of C,E and G#, it wouldn't be C major; it would be C augmented. A major chord is built with a root, a major third and a perfect fifth. The aforementioned example is built with a root, a major third and a augmented fifth, which results in a different chord.

• Not always. I just realised Perfect fifth of B is F. These intervals between B and F is 6 semitones. Sep 29, 2015 at 9:20
• @oyilmaztekin B-F is a diminished 5th, not a perfect. The 7 semitones that form a perfect 5th are constant, no matter what notes you choose. B-F# would be a perfect 5th Sep 29, 2015 at 9:21
• B is the only note in the C major scale that doesn't have a perfect 5th Sep 29, 2015 at 9:23
• I will more carefully when I choose my reference next time. I could be sure before I asserting an idea. Accept my sorry and thanks for your help. Sep 29, 2015 at 9:29
• @oyilmaztekin no need to worry, we are here to help you Sep 29, 2015 at 9:37

Counting up from a note, alphabetically, using the first as number one. C-D-E-F-G. So G is number 5. Start on C# and do the same. G# is number 5. A perfect fifth is a bit of a misnomer, as is perfect fourth. I'm sure a more apposite word should have been used, but we're stuck with it now! The space between 1 and P5 is always 7 semitones. It just is. When this space is increased by one more semitone - either way - it is known as an augmented 5th. If decreased by a semitone, it becomes a diminished 5th.

• "Counting up from a note, alphabetically, using the first as number one. C-D-E-F-G. So G is number 5. Start on C# and do the same. G# is number 5" Thank you Tim. That was so simple and informative. Sep 29, 2015 at 8:22

You need to know a little bit more about perfect fifths than just how many semitones they are away from the root.

Remember F double sharp and A double flat are also seven semitones away from C but are in no way perfect fifths.

Now the word perfect tries to say two things to you. It tries to firstly indicate that these intervals have a very pure and easy listening quality to them. They generally just sound good.

Secondly it tells you that a perfect interval is a note that forms both part of the Major and minor scale of the root note. This also the case in with the interval of a second but because of this intervals dissonant quality it is not called perfect.

In your example both c Major and c minor the relative key of Eb Major has a G in the scale. Hence the title perfect. This phenomenon is present at the unison, the fourth, the fifth and the octave and also the second but because of its awkward sounding nature is not included in the list.

• "Secondly it tells you that a perfect interval is a note that forms both part of the Major and minor scale of the root note. This also the case in with the interval of a second but because of this intervals dissonant quality it is not called perfect." I think I understand now. It doesn't matter the size of half step or whole step... If root is natural, perfects 5th is too. Sep 29, 2015 at 8:17
• There is no perfect second. It is called a major second (as in C to D). And, strangely, a min.2nd (C- Db) doesn't even appear in the minor scale notes.The fact that a note appears in both maj. and min. doesn't make it 'perfect' necessarily.
– Tim
Sep 29, 2015 at 10:08