Piano World Home Page Forums Our Most Popular Forums Piano Teachers Forum Alternate names for intervals

You are exactly right! The Beethoven example could have been written several ways, and his spelling there is illogical vertically but very logical horizontally. That's where the weird intervals occur, when two or more voices are moving chromatically, often in opposite directions.

In a strange way this is consistent. We know, for instance, that a M3 and a dim4 are both common. You don't have to go any farther than C E Ab to see that, Caug, which is correct spelling if the next chord is C F Ab - Caug to Fm/C.

In the same manner, you can have this:

D-G moving outward to Db-G# to C-A. I can't think of a practical place to do that, but I'm sure sooner or later I will find it.

I think in general that the moment we think something is too weird to be used, someone uses it, and effectively. That said, I can't think of any standard interval, by number that is TRIPLY shrunk of expanded.

Cb E# would be a doubly augmented 3rd. Would anyone use that. Hmm...

I can't think of a place where I have seen that.

I THINK we can content ourselves with sticky to intervals that have two common ways of being written, with roughtly equal frequency, and others that have two ways where one is far more common that that other but where the uncommon one is still used a LOT and is very useful.

For the latter idea, m7/aug6 is probably a good example. C-Bb is going to be much more common than C-A#, but C-A# is important for augmented 6th chords, and those appear quite frequently.

Musical math:

3+3=5
3+3+3=7
3+3+3+3=9

The reason is that our weird tradional system double counts notes. It is like saying, "Take three steps," then counting your starting place as the first step. It is counter-intuitive, but we are stuck with it.

It is safe to say that anything else is going to be highly unusual, but don't rule it out! Just be ready to curse.

That is correct.

this is all above my head. I never learned any of this stuff. I can easily recognize 4ths, 6ths, 5ths.. that's about it. I don't know why that is even important unless one is a singer.

For the "naming" system, which is the one that is usually taught first traditionally, I count how many notes are involved in terms of note names. It is not complicated. CE involves 3 notes C,D,E. EC involves 6 notes. We don't have to worry about sharps or flats for counting how many notes are involved: E,F,G,A,B,C = 6. It is as simple as counting a row of toys. This little trick of 6 + 3 = 9 is handy for checking yourself since it is faster to count to 3 than to count to 6, but really, it isn't necessary.

I've had this idea of 3 + 3 = 5 presented to me before. Here is what I see: A family comes to visit: John, Mary, and Dot. John and Mary are husband and wife: 2 people. Mary and Dot are mother and daughter: 2 people. There are 3 people all together: 2 + 2 = 3. Same thing, no? But I would never think of it this way, because it would be confusing, and it doesn't help me. Yes, in CEG you have a major 3rd from C to E, and a minor 3rd from E to G, and P5 from C to G, but to me that is like John, Mary, and Dot. We've already counted the E; and to find the interval of C to G I don't have to add the two thirds, I can just see how far G is from C.

I can see, however, how a student might look at our CEG and say "Wait a minute. I know CE is a major 3rd, EG is a minor 3rd, CG is a P5 - so a third and another third makes a 5th? That doesn't add up."

For anyone mystified by the math:

3+3=5 is referring to something like this: CEG: CE = major 3, EG = minor 3, CG = P5. We have a major 3rd plus a minor 3rd in the chord but altogether the chord spans a P5.

3+3+3=7. CEGB. same as above, plus GB = a major 3rd. From the lowest note to the top note we have a major7, since CB is maj7.

I've never added up intervals. To me it's like they are lined up in a row and if I want to see the distance between any two notes, I look at that distance. I don't think about it a lot, I just do it. The beauty about music is that even though it can look complicated, it usually has some simple principals sitting underneath.

A lot of the things in this thread look complicated. Stuff in theory books can look complicated too. When working with harmony theory we work with chords, and chords have intervals; voice leading rules involve intervals. We can't get away from them. But I believe that if we can get to a basic understanding first, then we can always go back to some very simple things. However it seems that theory often seems to spend next to no time on the rudiments, glossing over them, so we don't get that first solid thing to rely on.

I'd go for two fundamental things, and this is how I taught it for getting at those fundations:

First fundamental: The most basic and fundamental thing is what intervals actually are. They are a distance between two notes. If we use an actual measuring device such as semitones / half steps (two names for the same thing), then we can see this distance. We can hear this: BC, F#G, AbA or G#A - strike two adjacent piano keys and we hear a common quality to this tiny interval. We hear what is the same about it regardless of where we play it.

For the "what it is" we can also explore the intervals before learning to name them anything. CD, CE, CF, CG.... how does each of them "feel" to you? Do they all feel the same? Is one more or less pleasant? This is very fundamental, but maybe if someone plays CF# and then feels relief with CG, later things in music make sense. What about encouraging exploration from a very early time. Then later when music gets complicated, go back to this same simple exploration to get one's bearings. Essentially that's the tack I tried when we went to complicated theory, and it seemed to work.

I believe it is absolutely essential to distinguish between what an interval is, getting in touch with the reality of it, and on the other hand, how intervals get named. I know the subject is "alternate names for intervals", but before we can even go there we have to look at intervals in the raw. Otherwise it is easy to get lost. On the other hand, if we have a firm foothold on the "what it is" side, we have something to fall back on.

Second fundamental: Naming: The fact that there are naming conventions which have to do with the grammar of written notation. Otherwise we can be stuck with learning early on that the sound we hear "is" a major 3rd, and later when we hear that same sound it "is" an augmented 2nd, with a hasty note that, well, we call these "enharmonic equivalents". If on some level we have a grasp that this quality of sound is what it is as per above, and that it is clothed in different names, then it's not a big deal. But if we think that the name defines it 100%, it can muddy up everything.

There is a different fundamental principal going on with the naming of intervals. It is very simple. We count how many note names are involved - nothing more than that at its simplest level. If there are 3, then it's a 3rd. If there are 5, then it's a 5th. The biggest problem is in overthinking it, and trying to see meaning in it. There isn't any. That's it.

Then we go about memorizing or in some way learning what major and perfect intervals are, which is easiest done via a C major scale, always counting up from the tonic. Anything a half step below a major is a minor. The perfects are I, IV, V & octave. Getting at diminished and augmented is a next stage, simply a matter of one more half step.
------------------
If we have these two sides of it, then we can wend our way through all the complicated grammar rules that come up. The "obvious and simple things" sitting at the bottom are what helps make sense of everything else.

When we got to the more complicated theory, the temptation was to get cerebral. But that was the time to go right back to the beginning, and get at it from these two points of view.

I only have one student right now who can glance at a solid interval, and name it immediately just by how it is shaped visually on the staff. My others either count the lines and spaces between the notes, or name the two notes and then figure out how far apart they are. I don't know how to get them to that next stage of instant recognition. Maybe just through repetition?

(As background info, none of my students have been studying for more than 2 years)

My situation is not different at all, really, with those who have only played two years or less.

I THINK that people learn to play things, and that makes a link between what they feel and what they hear.

For instance, if you can get your young students to play major and minor chords, triads, in all keys, just by feel, two things may happen:

1) They may start to associate the sound of major/minor with the feel of these chords.

2) They may develop a primitive understand of intervals through the chords themselves, separate from notation.

I find that most people will pick up the idea that the "outside" of these root positoin triads are perfect 5ths. They can "extract" the 5th from the chords. From that they can easily learn that all P5s are the same color except for Bb-F and B-F# - two white keys or two black keys.

From there we can count black keys and reason out why F-B and B-F are actually the same "size", and why they need to be "adjusted" to make the 5ths we need for major/minor chords.

Once the P5 is in place, major and minor triads allow us to point out that we have two different sized 3rds, a big one and a small one. Again, we can count keys. I teach major/minor as a 3rd finger toggle, all keys, both hands.

From there it seems easy. I don't give a hoot about interval names, the traditional ones - in the beginning. I think they are horrendously confusing if taught FIRST. Later they become necessary.

Instead, we say as my students are reading music: "Oh, what do we have here? Can you see how that is an Eb major chord, but SCRAMBLED? Look, I'll play the chord, the simple way. Now, you compare your chord with mine. Can you find an Eb? And a G? And a Bb? We can spread them all over the place. We can clone them. We can put any of those three notes on the bottom, any on the top. We can space them out wide. We can both play them at the same time. We can run them up and down the whole keyboard."

That approach seems to get the essence of what major and minor chords are, and how to begin recognizing that they can be scrambled in a near infinity of ways.

When THAT knowledge is in place, then I worry about naming the intervals.

Does that make any sense?

That makes lots of sense. It's completely backwards from how we traditionally teach, but that makes it even more appealing to me! lol

I have one student, okay maybe my *favorite* student, who is exactly how I was as a beginner. You can't teach him any 'rules' unless he knows why he's doing it. He constantly asks "why?" and I LOVE it. It's an especially awesome lesson if he manages to stump me and I have to tell him I'll find out and get back to him at his next lesson. We learn the theory stuff in his little method book, but he asks so many questions that we're actually getting into fairly advanced concepts considering he's in book 1 of his method series. He would latch on to major and minor triads in under five minutes, and I think he would have a lot of fun with them. I can already predict that he will dislike major triads but enjoy playing minor triads fortissimo at the low end of the piano .

My others are just starting to learn about whole steps and half steps in their method book. It would probably be a perfect time to introduce major and minor triads for them. I'll give it a try next week and report back .



I've been forcing myself to play in key signatures with lots of sharps because I'm scared of them, and have been playing more 20th c music lately, so I'm going to keep a look out for the AA3rd. I wouldn't be surprised to find one .. composers do some crazy stuff.

I don't believe great teachers, teaching little children, EVER taught in the way we are told is traditional. I doubt there was much tradional about how Mozart's father taught young Mozart.

Where teachers go wrong, in my opinion, is that they find things that are logical to young children, then assume they will not be logical to older kids and adults.

I LOVE being stumped. It means I get to learn something new!

If you can teach anyone all the majors and minor at once, that is highly unusual. I have to teach them by groups, color and feel, then work towards chromatic playing. And for minors, I have to teach them first as a "morph" from major - this includes the really smart students of all ages.

But people definitely have feelings about chords. Many of my students like experimenting with minors played randomly, because ANY combination sounds like some freaky TV show or movie they have seen.

I would do it this way: the moment they are able to play a simply C major chord, give them G and F. They all feel the same, so there is no coordination problem. And that is I IV and V.

Next teach A, D and E. It is easy for people to extend their longest finger to a black key, and this gives I IV and V in the key of A - which you don't even have to mention.


I've heard other people say that sharps are harder. I THINK that may be because the V7 of sharp keys are less common. That said, there are SO many famous pieces in C# minor, and there are many more than four sharps that actually show up in such pieces.

Yeah, they are already playing pentascales in C and G, so I don't think picking out 1-3-5 will be too tough. And I like the idea of adding the "major-minor toggle".



I always thought it was because I played in wind ensembles for so many years -- winds tend to play in keys with flats. It was a challenge when I played with a full orchestra -- playing sharp keys on the trombone felt really weird. I love flats -- I would take 6 or 7 flats over 5 sharps any day. I need to find someone to transpose Bach's P&Fs in C# major into Db for me.... I could do it myself, but it seems like a lot of work.

I just got the significance of this and went back to find the quote:

First off, a couple of years ago I ran into a new idea - getting a sense of theory via the instrument which fuses what we hear, feel in our hands, and theory from that angle as one thing.

Well, I know intellectually that an m3 (or aug2 etc.) is 1 1/2 whole tones, 3 semitones, the middle of C minor, and has a particular sound. I also know that 4 in a row give me a diminished 7 chord.

But here is another way of "perceiving it". First we have our "half octave" which cuts our octave directly in half, right at the tritone. Then when I have that tritone, I cut it in half again and I get a minor third. Instead of building a dim7 from a row of minor thirds, or some other way, I start with my octave, and slice it twice from big to little.

It's nice to think of this mathematically. We have an octave made of 12 semi-tones. So how many ways can we divide it evenly?

- 6 whole tones (whole tone scale)
- 4 minor thirds (dim7 plus octave)
- 3 major thirds (augmented major triad plus octave)
- 2 tritones
- 1 octave

very nifty

update -- I had two students today -- both have been with me for two years now. We had talked about half steps last week, and we did whole steps this week. They both already know their C and G pentascales by rote, but we analyzed them using whole steps and half steps and then built the F pentascale using the pattern. Then we built triads from the pentascales and I demonstrated happy triads and sad triads and how you could make the happy chord sad by lowering the 3 -- and wow, that was a hit lol. I had them show me their "happy" triads in C, F and G and then make them "sad".

One funny thing is that I'd already introduced flats and sharps to one of these girls but not the other. It was actually easier building the F pentascale with the one who *didn't* know about flats or sharps yet. She was completely focused on half steps and whole steps and not what the notes were 'called'. Maybe all these labels just get in the way of understanding patterns. Of course, we need something to call them eventually, but I'm starting to think I'll teach the concepts first and add the labels afterwards.

Another thing I have issues with is calling major and minor triads happy and sad... it's how I was taught when i was their age (7 or 8), and my students like it, but if the minor chord sounds sad, does the dim chord sound *really* sad? LOL! Anyway.. I think I will replace the happy and sad labels with major and minor next week to avoid all that confusion.

Diminished chords sound "scary" and "evil."

Whatever works. Some kids are so tone deaf, nothing will get them to hear major/minor/diminished/augmented. Try getting them to hear the different 7th chords.

for my students the diminished chords sound 'magical' and there's a reference to the D minor Fantasy (Mozart... the first 'run' which ends up in CEbF#A... :D).

Same reason we have 12 months and 12 (24) hours in the day. Not to mention the 'dozen' and the fact that 13 is considered an extremely unlucky number in most societies!

________________

But...

Thing is that the one thing that I find fundamentally wrong in how we deal with intervals, and their definitions, is the fact that the first and the last note are included. I mean C - E is a third, because it's C, D, E... Then E - G is another third (E, F, G) and this is why if you turn it into math it screws up our brains (3+3=5, etc...). It's like those old twisted questions my father used to say, to prove that we had 11 fingers, instead of 10! (Count from 10 down to 6, including 10, and you have 1 hand left. Then ad the other 5 fingers bingo: You're up to 11! :D).

Yeah, that messes up my students too. I always have to remind them to count the first and last note.

I only had one student (this year) ask why two thirds, C-E and E-G, didn't equal a sixth. He's very mathematical, so when I pointed out that his calculations were counting the E twice, he understood why 3+3=5. phew!

I lost a job when I first moved into this area, working as "an assistant" to someone who probably was running a business like the typical music-school-sweat-shop. I'm glad I didn't get it, since soon afterwards I built up my own student base and worked for myself, but what got me rejected?

I didn't know the term "tetrachord". Well, DUH!!! Of COURSE the first four notes of any major scale are also the last of another, and vica versa. But it never occurred to me to name the concept. I absolutely tortured my brass students with major scales, because they are always on exams. How students play those scales makes or breaks an audition for "chairs" from middle school on, and knowing them for the greatest range possible also has a huge impact on power, tone, flexibility and so on.

But to this day I have never taught tetrachords except in passing.

Now I see "pentachord" is very popular. Was it always so? It seems to be used for what I think of as five-finger positions, the first five notes of major scales, and could also be the first five notes of minor scales, with just the 3rd lowered. But I honestly don't know. So I'm getting that out of the way first.

haha thanks for clearing that up. My pedagogy teacher talks about tetrachords sometimes but I had no idea what she was talking about until now.

And yes, I think the pentascale is a relatively new thing. I mean, it always existed, but seems to be more commonly taught in early piano now. I certainly was never taught any pentascales when I first started out. They are now part of the technical requirements for the preparatory RCM (Royal Conservatory of Music in Canada) exams, which may explain why they have been more commonplace.

Edit -- and yes, there are minor and major pentascales. Since they only use the first 5 notes of the scale, we don't have to worry about harmonic, melodic and natural minors.

heh... I will admit that I wasn't fully aware of what a tetrachord was either... :$ ... I have used it in my compositions thought!

Gary: About the pentachord: I would assume that it's the last five notes that provide an issue here... The melodic minor scale (upwards) has the same five notes as the major scale with the same name!... Perhaps this has something to do with it?