Hi

Sorry to bother you but can someone just give me quick explanation of intervals - up to Grade 3.

I know a 4th, 5th and octave are Perfect Intervals - but why? What makes them "Perfect"?

I'm only up to dealing with Major, Minor and Perfect at the moment. Could someone give me a base rule to work with please?

Thanks for your help.

4th, 5th and 8ve are perfect because when they are inverted (bottom note put to the top) they remain the same quality. However a major interval would turn to minor and vica versa.

Ahhhhh, I see. I'll go back to it then. Thanks!

Intervals are also perfect because they are the same in both major and minor scales. For example, F to C is the perfect 5th in both F major and F minor and the same with the perfect 4th - F to Bb. If you alter perfect intervals by a semitone they go straight to a diminished or augmented interval without ever becoming major or minor.

I'm sure someone will be along to correct me if I've made any errors

I think I read somewhere that they were originally so named in medieval times, when unisons, fourths, fifths and octaves (but not augmented fourths or diminished fifths) were "perfect" consonances and thirds and sixths were "imperfect" consonances. By about 1400, English composers were using thirds and sixths more freely; when the style arrived in France, it was known as the "contenance angloise".

Also, is it not connected to harmonics too? If you hold down a note on the piano and play the note a perfect ovtave below it, the note you are holding will resonate. Same with a compound perfect 5th. That doesn't happen with a major/ minor interval.
I too thought it came from the way instruments were tuned/ played in medieval times.

I think John is the nearest in the reason why they are called perfect, even though they were used in medieval music. I have just found in an old theory book 'the only intervals which do not change are the perfect intervals, that is why they are called perfect...' (The New Road to Theory of Music by M. Dawe, Bk 2, p12). It took a long time for thirds and sixths to be commonly used I think - and became a device in Italian music for violin parts to be a third or sixth apart.

I've heard something about perfect time in medieval music - 3/4 the perfect 3 representing the Trinity (complete circle) whereas 4/4 time was imperfect - hence the half circle for Common Time, which I thought was interesting. I used to think the C stood for the Common.

Occur early in the harmonic sequence
Are the same when inverted
Are the same in major and minor scales

to which I would add - they sound stable and at rest. They do not create a feeling of needing to move or resolve onto a different interval.

Is it not the combination of all these things (rather than any one of them) that earns the label perfect

It doesn't happen with thirds and sixths, but it does (faintly) with major 17ths. Piano hammers are designed and located to minimise the fifth component of the motion of the string, because it is not exactly the same frequency as the equal tempered (ET) 17th above the fundamental. The second, third and fourth components are strong. Well trained piano tuners make the nominal octave exactly the same pitch as the second component,* and the third and fourth components are better in tune with the ET 12th and 15th.

* The frequency of the second component is slightly more than twice that of the first, so that when your piano sounds at its best your electronic tuner will show you that its upper register is sharp and the lower register flat compared with the middle.

I agree with mad Tom on this one, it's the combined qualities of inversion, harmonic series and equality between the major and minor scales which make perfect intervals perfect. Plus of course they sound stable and at rest.

As for the problems of reaching a compromise when using equal temperament, I'm afraid that issue is way over my head. But I can see how slight differences between tuning as regards true 'perfect' fifths, fourths and so on would create stronger harmonics compared to compromised fifths etc. I certainly become aware of this when tuning the strings of my violin (in fifths of course...)

But what about the controversy over the perfect fourth? By any reckoning based on the harmonic series, it should be classed as a perfect consonance, but in music it is usually treated as a dissonance, and resolved accordingly (normally to a major or minor third)...? So is it a consonance, or a dissonance?

denmark

At the risk of sounding rude or aggressive - which is not my intention ...

I don't buy the idea that the term "perfect" is about the same notes appearing in the major and minor scales. That would require a major second to be called a perfect second.

I don't think the explanation involving resonances and the harmonic series can be right. Listen to the harmonics of a lowish piano note: you hear an octave, then a twelfth, then a fifteenth then a two octaves above (a) a third, (b) a fifth, (c ) a minor seventh (roughly), etc, the intervals between successive harmonics getting smaller and smaller. Resonances will happen when the harmonics of the resonating strings are close to the harmonics of the "exciting" string: press the E below middle-C down silently and then play the C below it loud and staccato - you'll hear a resonating E.

And I don't see that it explains anything to say that reducing fourths and fifths by a semitone yields diminished intervals - isn't that just applying a definition, and not explaining a definition?

I don't know where the people quoting these ideas first came across them, but, to me they seem like something that someone (put "on the spot" with a question) once made up rather than admit they didn't know the answer.

Hi Chab - that is why I said John must be the closest - that the 4ths and 5ths remain perfect when inverted. A major 2nd inverted changes to a minor 7th. I was taught that perfect 4th and 5ths are the same in both major and minor scales which is correct. However, this discussion has got me thinking that this is not a reason why they are called perfect which I said in my first post. It's the fact they don't change - I also quoted from a theory book

I think I'm missing the point here:

C-F is a fourth. But inverted (F-C) it is a fifth - and the (heard) quality of these intervals is quote different. So in what sense is the interval 'the same'?

I had always assumed that the name 'perfect' went back to Pythagoras' experiments with string hamonics ...?

nick

Okay - a perfect interval remains perfect when it is inverted - even though a 4th becomes a 5th and vv. Major inverted becomes minor and minor becomes major, and aug becomes dim and vv.

Sorry - in haste

Impeccable logic and accurate observation, destroying the hypotheses based on the harmonic sequence and the "same in major and minor" theory. Leaving just the "same when inverted" reason.

Right - much clearer, thank you.

NJ