Hello, I was asked to try to teach a child about intervals. She needs to be able to write them on the staff. She is a violin student, around 8 years old and she has difficulty learning new things in the sense that she might understand something now but 5 seconds later she doesn't seem to remember it. So far she can write all the intervals with notes and also guess them when they are written. This however only works with perfect intervals, no augmented, diminished, etc.

How would you go about explaining minor and major 3rd to this child? I just explained 2nds to her on the piano in a very interesting way*, I can also show her 3rds in some way but how do I make her recognize and build them on paper? She hasn't started with the obligatory piano in school yet so she doesn't have that image in her head to help her at the moment.

*for example I showed her all the notes that are close together like C and D. Then I explained that the notes that are close together without a black note in between are living in the same house like a family so it is a m2, the black note in between is a wall and if there is a wall then they are neighbors and it is a M2. She remembered it this way and was able to show me all the intervals I asked for this way with success mostly.

I would not get into major and minor until she understands what they look like on the paper. I usually start with thirds. I tell them they look like snowmen. I would build snowmen all oner the staff and then have her play them. I would also use the C clef to displace the C in different places to see that it is just a pattern. After she can recognize thirds and recreate them, I move on to ends, because ends are easy to see as well. After she masters the difference then move on to other intervals.

In order to understand the minors it may be easier if she already understands scales. If not, just start with the key of C and the minors and augmented are the accidentals.

This is one thing that I have taught. Additionally, since this is also a violin student, I have violin in my background.
Intervals have two aspects: what they are and how we name them. If we don't have that clear in our minds then it is hard to teach it.

For what it is: An interval is a given distance between two tones which we could measure as semitones or piano keys (each adjacent piano key is a semitone). A "major third" is one semitone (piano key) closer to the bottom note than a "minor third". An interval also *is* a distinct sound quality, where "major third" has a happier quality than its minor counterpart.

Pianists will tend to see the key distances first and then hear the sound, while violinists have to start listening from the start, and will relate the closer distance of the finger afterward. Pianists hear harmonically, while violinists will tend to pick up on intervals melodically.

The second aspect of intervals is what they are named. Here we go by how many letter names are involved. CEb involves 3 letters and is a minor 3rd, while CD# involves 2 letters, uses the same piano keys, produces the same sound, but is an augmented 2nd. If you get confused about whether an interval with 3 letters is a minor or major 3rd, it helps if you ALSO know "what it is" (how many semitones - sound quality) because you can then check yourself.

What we did when I taught this was to start with hearing qualities just to experience it for awareness. Then we explored the C major scale (white keys). We took the intervals from the tonic - 2 notes = 2nds, 3 notes = 3rds etc., and listened for the quality and saw the semitones. She picked up the pattern of intervals being: Major minor minor Perfect Perfect minor (dim) Major.

From there she got that any major key will have this pattern. This was something the theory book taught and it's useful to know. But really, all you have to is see how many semitones two intervals are apart and/or whether they sound major or minor for the thirds. If it sounds minor and you want to change it major, increase the interval by naturalling a flat, or sharping the note, and vice versa.

If there is a problem with memory, then understanding how it works will help a student work it out.

I have to get this concept across to very small children on piano. When teaching brass, it was a bit different, since USUALLY brass students were older when they started.

On brass you have to relate intervals to scales and arpeggios. Chords don't exist. So even when I was teaching brass, not piano, I always *explained* intervals on the piano.

With serious students I always said that the word "interval" is a fancy way of describing the distance between two pitches. And as you very well know, that "distance" is perceived quite differently when measured by eyes or ears or fingers or embouchure (etc.)

To me, that is just one "elephant in the room".

So for small children, I simply tell them to count how many letters, and I stick to white keys, which correspond to naturals. I don't even get into major/minor, perfect, diminished, augmented, until they get the "grosser" measurement down. They are never simply reading music, away from the piano, because I need them to be developing reading ability, and it just doesn't happen if it is separated from playing. So I THINK the understanding comes first looking at the piano, and hopefully listening while pressing keys begins to develop the ear. Then linking what is happening physically to what is happening on the page may be rather natural.

Hearing intervals is a whole different ball game with its own separate problems, as you have mentioned...

I like that, but I have to start off on a more basic level. Few of my students are serious, and they tend to get lost in a heartbeat. So I teach big 3rds and small 3rds, since this relates directly to size. Big and small 2nds. Big and small 6ths and 7ths. On piano big and small can be understood by SOME people by number of black notes skipped. As said, I always teach this on keyboard, even to people who are not keyboard players. Then they can relate it all to their main instrument(s). The problem with doing this NOT on the piano is that you can't see, immediately, that C to E skips two black keys, but D to F only skips one. And this joins three senses. You see the number of keys skipped, you feel the distance in white keys, and you (hopefully) start hearing that there is a sound difference between the big and small 3rds. And the quality of an interval will be "contaminated" by anything that has proceeded it. If, for instance, you play CE and get your "happier" response, then play EG, the second interval may be linked, subconsciously to the first as one chord (CEG), and you may then get the unexpected answer of, "That sounds happy too."

I bring up this point because 6ths sound "minor" OR "major" to me according to which note I imagine to be completing them. EC, a minor 6th, has one sound to me if I imagine there is a missing G (forming a major chord), but another if I imagine a missing A (forming a minor chord). And for this reason I will most frequently mis-hear major and minor 6ths (when listening in isolation), if I am not careful, but never miss major/minor chords

And brass players feel minor 3rds as a shorter distance because of the amount of change in the embouchure.

I only teach the more difficult names of intervals to students who have nailed down the easy ones, and in the long run that is not the hardest problem, because it is only a written problem. As you know...

At the moment I teach major and minor triads, first, even to my youngest students, and I EXTRACT major and minor 3rds from those chords, then teach perfect 5ths as the "outside" of major and minor triads. Again, this only works on keyboard. I find 6ths and 7ths more difficult to teach, because they are really 2nds and 3rds, inverted.

In fact, I would say that understanding it is everything. Without the understanding, attempting to memorize these "facts" is nearly impossible for most people, and even if they do memorize it all, I strongly doubt that it is all real for them, in sound, where music really lives.

I usually just teach intervals found in a major scale (major and perfect only). Once they grasp this, then we talk about altering the major intervals by half a step to make minor. Once they can tell the majors and minors apart, then I go into discussion about augmented and diminished.

Since this is a violin student, I would do things by ear first, but again, only as they relate to the major scale. I would use the first notes of familiar songs to help her figure out what a major 2nd sounds like (Happy Birthday), and a major 3rd (When the Saints Go Marching In, Michael Rode the Boat Ashore, Kumbaya), perfect 4th (Here Comes the Bride), perfect 5th (Twinkle Twinkle), major 6th (My Bonney Lies Over the Ocean), major 7th (Bali Hai - OK it's an octave then a 7th, but that helps them figure it out - or Maria from West Side Story). Sometimes it's a challenge with kids these days because they grow up not knowing any folk songs at all, especially in areas that have no general music programs in the schools.

My only problem is that major and minor are abstract terms, whereas big/small are not. The smaller the children, the longer it takes for them to get these abstract terms. I find the term "perfect" extremely hard to explain. How do you explain it?

I would love to hear how perfect is explained! Here's how I explain it to myself: if you count up from the bottom of a major scale vs. if you count down from the top you get different size intervals: big (major) going up and small (minor) going down. E.g. C up to D, major second; C down to B, minor second, etc. But for fourths and fifths you get the same size interval going up or down: C up to F, fourth; C down to G, same size fourth. So they're not major/minor. This is an elegant quality to have, so let's call them perfect: unchanging.

I believe there is a longtime philosophical belief (speaking generally, not music specifically) that if something is perfect, it can't change, because one state or the other must be better so if it changes it either didn't start from, or is moving away from the best state. So changing intervals like the major/minors are imperfect. It's a logical fallacy that if perfect implies unchanging, then unchanging implies perfect. But compared to the changing major/minors, the unchanging other intervals may as well be called perfect.

As a student, I don't know if this is teacher-approved, but it's what I've come up with for myself.

In fact, I do teach what you just suggested, that a perfect interval remains perfect when inverted.

All major/minor intervals "flip" names when they are inverted:

m2 to M7
M2 to m7
m3 to M6
M3 to m6

There is yet another thing to add to this:

If you measure from any note (pick C) and use only the major scale, going right is major, but going left if minor. When they are the same, there you have the perfect intervals.

Right, which is why I don't introduce those terms. I was just calling them major or perfect for clarity to the OP, but I don't say those terms with students at first. I just call it a 2nd, 3rd, 4th, etc. Then once they can play major scales for a while we talk about major and perfect.

I don't have a great explanation for "perfect", except that I say it could be a part of a major chord, or a minor chord (in the case of a 4th, of course, you have to play an inversion), and for that reason it's outside the major/minor intervals. Or if the student is a bit older, you might be able to go into what would happen if you raised or lowered the upper note of a perfect 4th or 5th. In the case of a 4th, you get a 3rd if you lower by 1/2 step, and if you raise you get another anomaly, the tritone. The 5th lowered is also the tritone (which most students when they hear it can tell it's not a major or minor sound) and raise it's a minor 6th.

But generally, I avoid getting into all that by saying "That's just it's name. Everything's gotta have a name, so "perfect" is just as good as any other."
:P

I am presently rethinking standard terms. This does not mean I stop teaching them, but I am more apt to say, "Here is what X, Y and Z are called, officially. If you want to pass musical tests, you will have to know them. But they are often about the worst way to think about why things are as they are."

My *personal* favorite reason for describing "perfect" is that 4ths, 5ths and octaves are almost completely standard in all tuning systems. Violin tunes perfect 5ths, the bottom two notes most used with any fingering on brass from a perfect 5th, and 5ths vibrate everywhere in nature. Because a 4th is just an upside-down 5th, the same tuning rules apply.

Recently I found out that 5ths tuned on keyboards in older "temperaments" were tuned just a wee bit lower than our modern tempered 5ths. 5ths on modern pianos are tuned 2 cents flat, and that is SO close to non-tempered 5ths that for most people it is not hearable. In older temperaments, they were often tuned down 4 cents, which is still very small.

But the other degrees of the scale are all over the place, depending on tuning systems, and they sound wildly different on keyboards or pianos tuned with those various temperaments.

I evade the whole problem of enharmonic intervals until I no longer can get away with it. I call augmented 4ths/diminished 5ths tritones or "half octaves". And I use for an example of why the spelling is a nuisance the fact that BF looks like a 5th, FB looks like a 4th, so if we play BFB, the spacing of the white keys fools our eyes and tells us that what we are hearing is not right, when it *is*.

The one enharmonic interval that I think we have to mention is the augmented 2nd, why it appears in scales, but not a minor chord. And why it shows up in a fully diminished chord. But I find explaining these things SO hard. Math has always been very easy for me, so such things have been very easy for me to understand almost instantly since I was a child.

Very often I say almost the same thing!