Perfect Intervals

[keyofc]

How do you define the difference between perfect and major intervals?
Other than explaining the amount of half steps involved.
I would like a better way to explain and understand why one is called Perfect and the other is not, besides just teaching memorizing.

[cjp_piano]

4ths, 5ths, and 8ths can be perfect, diminished, or augmented.

2nds, 3rds, 6ths, and 7ths can be major, minor, diminished, or augmented.

There's no such thing as a major 5th or a perfect 3rd. 


C - G:  Per 5th

C - Gb: dim 5th

C - G#: aug 5th


F - A: Major 3rd

F - Ab: minor 3rd

F#-Ab: dim 3rd

F - A#: aug 3rd

[steve jones]

Yeah, cuz both major and minor chords have perfect 5ths. While the thirds have the power to determine the quality of the chord (ie, whether or not its major or minor), hence they called major and minor 3rds!

The minor 3rd is 3 semitones, the major 3rd is 4 semitones, the perfect 5th is 7 semitones. Try it out on your piano:

- Take a root note

- Count 3 semitones up

- Count 7 semitones up (from the root again)


Now you have a minor triad, whoot!

Then try the same, but raise the 3rd by a semitone. Now you have a major triad, whoot some more!!!

SJ

[timothy42b]

It is confusing terminology and I believe the term perfect should be dropped.  It adds no information.

Perfect as a term dates to before major and minor were invented in the 17th century.  It doesn't really make sense anymore.

Perfect as a description would refer to a beatless interval, one where the ratios of frequencies would be small integers.  With equal temperament, even fourths and fifths are not perfect, so again this is a reason not to use the term.  (With the stretch of the piano, no temperament can be beatless anyway.)

[keyofc]

Thanks for your comments,

When I took theory - I think they said if you play a P4 - you can hear an octave in it.
I couldn't hear it though, and everyone acted like, "Oh, yeah, I can hear, it's perfect"

A perfect fourth is made up of two notes which are both in each others key.
For instance C-G, Perfect fifth, C is in the scale of G, and G is in the scale of C.

A major interval, say a Major 3rd - C to E, C is not in E, though C is in E.
Maybe that's why?

[nicco]

C is not in E, though C is in E.

?

[keyofc]

Nicco,
What I mean is if you take a perfect interval
any one -
let's try another one to see if I can be more clear in what I'm saying
A perfect 5th - D to A
I noticed that both notes are in the keys of the keys represented by the notes
D is in the key of A
A is in the key of D
but when you try this with a major interval
Like a major third,
D-F#
this same interaction doesn't take place
F# is in the key of D
but D is not in the key of F#

[steve jones]

I think you need to consider it another way. Think about the formula of the major scale:

T T S T T T S

(T = tone, S = semitone)


Major 3rd = 4 semitones (4 x S)

Minor 3rd = 3 semitones (3 x S)


From this we can see that major thirds can be built upon:

- Tonic (I)
- Subdominant (IV)
- Dominant (V)

Minor thirds occur on all the other degrees of the scale.


So lets take D to contiune with your example:

D, E, F#, G, A, B, C#

The 1st degree (D) will have a major third above it, F#, 4 semitones.


Now lets take a look at the F# scale:

F#, G#, A#, B, C#, D#, E#

The 1st degree (F#) has a major 3rd above it, A#.


Do you see the point here? Intervals are derived from scales, they dont occur in isolation. So the scale dictates which intervals will occur and where. It is all ruled by the formula of the scales - T T S T T T S.

SJ

[keyofc]

Perfect and major imply two different qualities though

[icarus89]

It mainly has to do with frequencies. You should know that when you double a frequency, you get an octave. Now, if you double that, you get a pitch a fifth above the octave. Double that, and you get an octave. Double it once more, and it's a 4th. These perfect intervals are called harmonics. The original pitch is called the fundamental. After that, the octave is 2nd harmonic, the 3rd harmonic (5th),4th harmonic (2nd octave), and the 5th harmonic (4th).

Got it?

p.s: Mistake. I meant that you keep on multiplyin the frequencies by the fundamental. sry.

[Bob]

It mainly has to do with frequencies. You should know that when you double a frequency, you get an octave. Now, if you double that, you get a pitch a fifth above the octave. Double that, and you get an octave. Double it once more, and it's a 4th. These perfect intervals are called harmonics. The original pitch is called the fundamental. After that, the octave is 2nd harmonic, the 3rd harmonic (5th),4th harmonic (2nd octave), and the 5th harmonic (4th).

Got it?

Isn't it..?...
If you double any frequency, it equals an octaver higher.

Double the fundamental to get an octave above.
Triple the fundamental to get the fifth (plus then octave)
x 4  ... would to two octaves up.
x 5  and so on...

All multiples of the fundamental right?

[steve jones]

Harmonic partials are multiples of the fundamental, yes.

This is where the concept of consonance and dissonance originate, to the best of my knowledge atleast. They identified that certain intervals 'fit' the harmonic series better than others, and that these intervals sounded closer to one another.

Indeed, it could be theoretically suggested that octaves are the one and the same note, with the fundamental of the higher note representing a formant in the lower notes spectra. We get occurances like this all the time in less harmonic timbres, such as the idiophones in the percussion section of the orchestra. Seriously, listen to a big gong and you'll hear many resonant peaks (formants) that will ring out like individual notes. But as we recognise the sound of a piano as being the timbres produced by playing one note, we are able to detect the seperation in the octave.

Interesting subject though. If anyone here is into music technology, then you'll probably know that there are some amazing things possible these days. For example, you can analyse a piece of digital audio (a stream of digital samples) and then reconstruct it out of sine waves. Its really cool, as you can scale the pitch and time of the sound too with far less artifacts than when using time domain techniques. Its all based on Fourier's theorum, and the derived family of Fourier analysis algorithms.

But thats way ot... so I'll shut up now! 

SJ

[prometheus]

?

He must have meant: C is not in E, but E is in C.


As for the whole discussion, they happen on different degrees. Some degrees have minor and major qualities. Others have only one perfect one wiht two dissonant ones just above and below it.

[keyofc]

oops! yes, that is what I meant.  Didn't notice until now that I wrote it down like that.
As if writing about music is not complicated enough!

[BoliverAllmon]

I thought perfect intervals were called such because of the over tone series.