What is a perfect fifth?

Question

I have gone through many documents, but don't understand what a perfect fifth is. Can somebody please explain with an example? (An example is important!)

I have already found these explanations, but I don't understand what they mean:

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

...and this one...

In classical music from Western culture, a fifth is the interval from the first to the last of five consecutive notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C

Answer 1

An interval is just the distance between two notes. The name perfect 5th comes from the idea of a scale. For example the C major scale consists of the following notes:

C D E F G A B

The 5th note of the scale is G hence the 5th of the C major scale is G.

A 5th that is 7 semitones up from the root is perfect, but where the term perfect from is a bit debatable.*

The ratio is the ratio of the distance between the notes in hertz. For example A440 is 440 Hz and if you multiple 440 by 3/2 you get 660 Hz which is an E which also fits the description based on the scales as defined above. Thus A to E is a perfect 5th.

*_{5ths, 4ths and unison/octaves are the only intervals that can be perfect that have one "typical" spot. Whether this is due to purity of ratios of the interval or a side effect of choosing 7 notes out of a possible 12 with an ordered structure is up for debate, but it does not change what it's called.}

Answer 2

The term "Perfect Fifth" is used to define an interval between two notes in a diatonic scale in Western Music. It's confusing because "fifth" sounds like a fraction (as in one fifth of 100 = 20). But while there is a ratio involved (the frequency ratio of the sound waves between the bass and high note) the term fifth as used in "Perfect Fifth" does not refer to the fraction 1/5. There are two parts to the phrase "perfect fifth" and each part is a descriptor of the interval between two notes. "Perfect" refers to the quality of the interval and "Fifth" refers to the number of the interval. Let me define each part separately. It will be easier to explain if we start with the number. The number (in this case 5) defines the number of staff positions a particular interval occupies (inclusive of the bass note and the higher note) on a musical staff. For example - in the key of C major - the interval between E and B is described as a Fifth because if you put a E and B on a musical staff and count the lines each note is on and the line and two spaces between them - that interval controls 5 staff positions thus is a "Fifth" interval. An easier way to think of it is the interval number is equal to the number of notes in the particular key (using only the 7 notes of the diatonic scale in that key) that are occupied from the bass note to the higher note (inclusive). So in the above example the interval from E to B is 5 because it encompass (or spans) E F G A B = 5 notes. Similarly the interval between C and G in the key of C major is also a Fifth because C D E F G = 5 notes in the diatonic C major scale. So that's what makes the interval a "Fifth".

Now let's talk about what makes it "perfect". Setting aside all arguments about quantification to achieve even temperament so an instrument such as a piano can play in all keys and almost be in tune and how that makes almost every ratio technically imperfect - in common practice the term "perfect" as used in "Perfect Fifth" means that the higher note of the interval is exactly 7 semitones above the bass note. One semitone is represented by one white or black key on the piano or one fret on the guitar (on the same string). There are 12 semitones in a chromatic scale but only 7 notes in a diatonic scale (key of C has 7 notes, Key of D has 7 notes etc.). There are perfect fifths and there are diminished fifths. Almost all fifths are perfect because if you play the bass note and the high note of a 5th interval ie: C and G and you count the number of white keys and black keys on a piano (semitones) from the C to the G starting with C# and ending on G there are 7. Every Fifth Interval with 7 semitones between the bass note and high note is referred to as a "perfect" fifth. Same from D to A (perfect fifth) E to B (perfect fifth) F to C is a perfect fifth, as is G to D and A to E. But if you look at a piano and count all the white and black keys between B and F (a 5th interval) there are only 6. Six semitones in a 5th interval makes it a "Diminished" Fifth instead of a perfect Fifth.

The reason there is not a perfect 3rd (only a major 3rd or a minor 3rd) is because there is no consistent number of semitones between the two notes comprising a 3rd. The interval comprised of C and E is a 3rd because from C to E there is C D and E = 3 counting only the diatonic notes in the scale. Counting all the notes in the chromatic scale (white keys and black keys) starting with C# and ending with E there are 4 which make that interval a "Major" 3rd. But the next 3rd interval in the key of C is comprised of D and F which is a "Minor" 3rd because counting from D to F starting with D# and ending on F there are only 3 semitones or 3 keys on the piano. It's a Third interval because from D to F spans D E and F in the C major diatonic scale = 3 notes = "Third". The 3 semitones we count to determine if it's a minor 3rd or major 3rd is the number of keys between D and F starting on D# (NOT including D). The thirds intervals alternate back and forth between major and minor (3 keys or 4 keys on the piano) so there are no "perfect thirds".

Most Fifth intervals are perfect but there is the occasional Diminished Fifth (6 keys vs 7). Most Fourths are perfect (exactly 5 semitones - or keys on piano including black and white) but there is the occasional "Augmented" (6 semitones) Fourth. Octaves are all perfect, sixths are either major or minor like thirds, second and seventh intervals are also either major or minor depending on the number of semitones (or black and white keys on the piano) that separate the bass note from the high note.

Answer 3

A Semitone is the next physical adjacent note on a piano after a given pitch. Semitones are also often called "half-steps". If you pick a note on the piano, and count seven half-steps higher or lower, it will result in a perfect-fifth.

For Example:

A given fundamental note is "C". "C" to "C#" is one semitone.

C->C#, C#->D, D->D#, D#->E, E->F, F->F#, F#->G

If you count each grouping separated by commas, you will see that there are seven groups. Seven groups, seven semitones = perfect-fifth.

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A perfect-fifth is one of the Class 1 intervals: perfect-octave, perfect-unison, perfect-fifth, perfect-forth.

They are described as perfect because their wavelengths perfectly coincide with the wavelength of the fundamental tone.

Class 2 intervals are consonant (major/minor 3rd, major/minor 6th) because they only partially align with the fundamental.

Class 3 intervals are dissonant (major/minor 2nd, major/minor 7th) because they do not align with the fundamental.

The frequency ratio which you describe refers to the correlation between crests and troughs in the amplitudes of each sound wave for each pitch. A ratio of 3:2 describes one in which the top note of a perfect-fifth interval produces three crests for every two crests of the fundamental pitch.

Answer 4

To make it simple: There are two kinds of intervals in music theory:

Primes, Fourths, Fifths and Octaves are perfect. Seconds, Thirds, Sixths and Sevenths can be major or minor.

The reason for this may be, that in tonal music you have much more alterations (relative to the key's scale you are in) on the major/minor intervals as you have on the perfect ones. But whatever reason, it is like it is, and in this case, the reason is not at all an important detail of music theory to be understood.

Are perfect or minor intervals alterated by a b, they are called diminished. Are prefact or major intervals alterated by a #, they are called augmented.

If you have a guitar string tuned in c', and then part it in two exact halves, both halves give you a c'', which is an octave over c'. Frequency c'':c' is 522 Hz:261 Hz = 2:1.

If you part the string at 2/3rds of its length, it gives you a g' on the longer part, which is a perfect fifth over c'. Frequency g':c' is ~392 Hz:261 Hz which is ~ 3:2 or 1,5 (in well temperament).

Answer 5

The problem with the definitions you dug up is that they refer to different things. The usual meaning of "perfect fifth" is in contrast to a "tempered fifth".

In relation to a guitar, a perfect fifth is the interval you get between the first harmonic (over fret 12) and the second harmonic (over fret 7).

When tuning, the most pleasing interval between most strings is a perfect fourth. When you play empty strings tuned to a perfect fourth, you get a single sound without beating. Unfortunately, stacking one perfect fourth after the other (which you can do by comparing 3rd harmonic over fret 5 on one string and 2nd harmonic on the next) does not work.

So instead one uses tempered intervals. These days, equal temper is almost universally used which makes all semitones equally wide.

With regard to frequency (inversely proportional to string length given the same string and idealizing a bit), a perfect fifth has the frequency relation 3:2 compared to the base note. An equal-tempered fifth has the frequency relation 2^(7/12) which is 2 cents flat compared to the perfect fifth. The difference is quite small, but there is a slight bit of well-defined beating if you talk about instruments with fixed tuning and clear sound, like tubular bells or an organ or accordion fresh from a good tuner.

With a guitar, the difference is small. Basically you want to stop tuning a fourth preferedly when you are slightly sharp rather than slightly flat as compared to the perfect fourth.

So much for the one "perfect fifth". Now the other use case talks about "perfect fifth" in comparison to "augmented" or "diminuished" fifth. I would strongly discourage using "perfect" in this context since it really is reserved for consonant intervals with a "perfect" rather than "tempered" frequency ratio.

I'd have called this a "proper fifth" or "plain fifth" instead because "perfect" has different connotations.

Answer 6

Interval quality naming conventions have been around for centuries so it stands to reason that their are subtle changes in meaning. While trained musicians generally know the conventions, they often don't understand the particular reasoning, whether Church-based, or based on Helmholz and other researchers.

To put it simply there are two classes of intervals: perfect and imperfect.

Perfect intervals are the set of intervals which were determined to be consonant by religious authorities until roughly the 15 century (this is fuzzy, and obviously most people were unaware of the controversy, and I imagine there were outliers ). This set of Perfect intervals includes unisons (1), fourths (4), fifths (5), and the octave (8) plus their octave transpositions. A simple way of defining this set is the unison, the fifth, plus all inversions and octave tranpositions. Think of it this way, in the first place these Perfect intervals, when sounded simultaneously and tuned justly, beat very little. Psychoacoustically we hear pitches relative to the harmonic series (see the "case of the missing fundamental"), so one can imagine that we might subconsciously be evaluating the tonal qualities of pitches relative to their octave-reduced position within the harmonic series anyway. [Psychoacoustically we hear octaves as similar even though they grow progressively wider as they move up.] And this series goes root [octave span] octave, [Perfect Fifth span] Perfect Fifth [Perfect Fourth Span] double octave, [M3 span], Major third, [m3 span] octave of Perfect Fifth, etc. As you can see the Perfect intervals come first, followed by the consonant ones. Next are the dissonant intervals.

https://en.wikipedia.org/wiki/Interval_(music)#/media/File:Harmonic_series_intervals.png

Imperfect intervals are intervals that don't sound quite as harmonious (and introduce a little bit more of an interesting spin to the pendulum between P4th, root, and P5th) as the perfect intervals. They fall into the two groups above (of consonant or dissonant) depending on their accepted consonance/dissonance quality:

consonant imperfect intervals: Major/minor third, Major/minor sixth.

(as spans in the harmonic series, these come next after the Perfect Intervals).

dissonant imperfect intervals: Major/minor second, Major/minor seventh.

(as spans in the harmonic series, these come still further along in the harmonic series, as it generates spans that get closer and closer).

Answer 7

In order to understand the definition you wrote, you must first understand half step and whole step.

A half step is the musical distance from any key to the very next key up or down . For example, C and C# are half step away from each other, as are C and Cb.

A whole step is equal to 2 half steps. For example in piano, keys which are whole step away have one key in between.

Now, notes with perfect fifth distance have six half steps between them (exclusive). For instance, G and D form a perfect fifth, because if you list all half steps between them, you'll have:

G, G#, A, A#, B, C, C#, D

As another example, B and F# form a perfect fifth too, since you have:

B, C, C#, D, D#, E, F, F#

If you're interested to listen to perfect fifth in a song, check out Twinkle Twinkle. The first two notes form a perfect fifth (C to G).

Answer 8

I am not a musician, so my answer might be completely wrong, but... if I am correct, here is the answer I would have wanted someone to give me. What musicians call a “fifth” is a note that is either approximately or “perfectly” 150% greater than another note; a root note. So, the first answer you showed from you research was actually not bad... except... who can easily visualize what a 3:2 ratio is? Personally, I don’t think that way. For my mind, I think it’s much clearer to say that a fifth is 150% or 1.5 greater than a root note. If you understand that an octave note is twice the frequency of a root note, or 200%, then saying that a fifth is 150% of that same root note tells you that a fifth is exactly half way between a root note and its octave note. That’s important to visualize, because... if you want something... anything... to be harmonious with an original, it is a good idea to make it the exact same pattern, only perfectly doubled, in the case of the octave note, or... perfectly half as much greater, in the case of the fifth. So a “perfect” “fifth” is a note that is EXACTLY 150% of another, and as a result is beautifully harmonious because the patterns line up well. In the 12 tone system of Western Musical Notation, a fifth is pretty close to exact. C4 is about 261.62556hz, and if I am correct, moving over a fifth would put you at a G4 which is about 391.99543hz, which is 149.8307% greater. So... darn near “perfect” ... almost exactly half way between C4 and C5 in the frequency pattern... 0.1693 off. The same is true for what musicians call a “third” if I continue to be correct. A third is important because it is approximately half way between the root and the half way point of the “fifth” or... 125% or 1.25 or 1/4 greater than the root note. If I have this correct, then from C4 to a “third” would put us at E4 which is about 329.62755hz which is 125.992% greater... 0.992 off. That’s 0.8227 less “perfect” that the 149.8307% “fifth” note, but so close as to sound good when part of a triad chord. And I believe that when someone talks about something being augmented or diminished they are referring to notes that are directly adjacent to these “perfect” harmonious percentages, and are thereby not quite as good - augmented means you went beyond that perfect 150% mark to the next note higher, and diminished means that you were just short of the perfect 150% mark to the note just below. The second answer you noted from your research is the kind of answer I see much more often, where someone just tells you it’s this or that many notes away from another... or this many semitones or staff bars for you to count, as if it doesn’t matter what is actually happening - being exactly half way between or one quarter along - just count the notes and memorize the terminology. I’m not a musician, so I was not interested in jumping into the terminology, I just wanted to know what was happening. Hope I got it right!

Answer 9

Ok. A perfect fifth is a fifth (ex: C to G) that is not augmented (half step larger) or diminished (half step smaller). For example, from C to G is a fifth. A fifth is seven half steps between the two notes (a half step is the smallest distance between two notes). As previously stated, the distance from notes C to G is a fifth. -more specifically a perfect fifth.

There are a total of five lines and spaces between these two notes (including the lines the notes are on). This makes it a fifth. What makes it a PERFECT fifth is the fact that the notes are in the key of each other. In the C major scale, there is a G natural. In the G major scale, there is a C natural. The two notes in this example are C and G. Since they are a fifth apart and they are in the keys of each other, this is a perfect fifth. If this were a half step larger, (if it was a G# and C or if it was G and Cb) this would be an augmented fifth. If it were a half step smaller, (if it were Gb and C or C# and G) It would be a diminished fifth.

Answer 10

A perfect fifth occurs when the fifth interval, the fifth note in a scale, contains seven semitones. For example, in the case of the scale that starts with C, G is the fifth interval because it is the fifth note from C.

G is also a perfect fifth because there are seven semitones from C to G. Count them up:

• C-D (a tone=2 semitones)
• D-E(a tone=2 semitones)
• E-F(semitone)
• F-G(tone=2 semitones)

which equals 7 semintones. Thus G is a perfect fifth.

Answer 11

Maybe if I quote the Oxford companion to music saying the same thing as I then maybe people will believe me then.

Intervals: By an interval in music is meant the difference in pitch between any two notes. Precise measurements of such difference is expressible acoustically by statement if vibration numbers, but for ordinary purposes which concern only the notes found in the various Major and minor keys. The major scale is take as the most convenient measuring-rod.

The intervals between the keynote and the fourth, fifth and octave of the scale are all called PERFECT: they have a hollowness (and perhaps we might say purity.) that is quite different from the effect of the other (Imperfect) intervals.

The remaining intervals from the keynote (ie second third, sixth and seventh) are all MAJOR:

Answer 12

If you pluck a string you hear a note. If you make the string half as long, you hear the same note, twice as high. If you remove only one-third of the original strings length, you get a note in between these two notes, called a perfect 5th. The same goes for pipes. It's a harmonic you often hear in nature.

To be precise: the fifth you'll hear from most instruments is slightly tempered with, but it's still called a perfect fifth.

The reason it's called fifth is historical: it happens to be the fifth note of some scales.

The reason it's called perfect is also historical, and people's explanation for it seems to differ.