I had a question from one of my students on friday (who is doing her grade 5 theory on thursday) that got me questioning myself:

Referring to intervals - how do you explain the difference between an augmented and a diminished interval?

For example: if you are given the the notes Eb and F# above, would you call it a diminshed 3rd, or an augmented 2nd? And how do you explain why that is the case, when to her it looks the same?

P.S: Please don't go all derisive and ridicule me for not knowing basic theory, because I saw how people responded to dcmbarton's post about leading notes and it's not necessary - we're both in a situation where we've realised that we're not sure about something, and instead of giving our students the wrong information, we're seeking out the correct answers.

I'm no expert, but, wouldn't it be an augmented 2nd because its F sharp, and would be a diminished 3rd if the note was G flat. Im sure there will be someone to correct me if im wrong.

To work out intervals this summary makes them easier to remember:

largest --> INTERVAL --> smallest
augmented --> MAJOR --> minor
major --> MINOR --> diminished
minor --> PERFECT --> diminished

This is how I tend to work out intervals in my head:

I usually work out the notes of the Eb major scale (Eb, F, G, etc.). You know that Eb to G is a major 3rd. Eb to F# is an augmented 2nd as it is a semitone above the major interval. In this case a minor 3rd would be Eb to Gb as it is a semitone below the major 3rd interval, meaning a further semitone below that is the interval of a diminished 3rd, which is Eb to F.

Car Expert

I can see how the confusion would arise if you were working out the interval at the keyboard but not if it werewritten on manuscript paper.

When naming intervals ask your student to count the numerical value first. E to F has to be a second.
Then work out the type of interval. Failsafe and simple!

Thank you for your advice - but this made even me more confused!



Phew, I do know what I'm talking about afterall! She just kept saying to me "but it's the same note, just written differently, so it's the same interval, just written differently!" and even though she knows about enharmonics, I still started to think that maybe I had it wrong ... I haven't been teaching all that long so I'm not 100% confident on everything.




Good point - Usually I do most of the work at the piano, but I guess it would be clearer if we worked with written out examples. We have 2 more lessons before the exam, so I will see if this method makes things easiernfor her!

I've just started teaching theory, and i just can't get them to understand that 1 note can have two names.

As a simple explanation for enharmonics (this would be similar) I tell my students that the name depends on the job the note is doing at the time.
For younger ones I point out that I am known by different names according to what my 'job' is at any given time so I might be Mrs Sbhoa, mum, grandma.....
With intervals I find that explaining that it's the spelling that makes the difference can help as has been covered in previous replies.

It might not be so easy to show on other instruments, I don't know, but with piano I've found that simply playing for example, G and then saying "play me Gb" and then playing F and saying "play me F#" illicits a response of wonderment that they didn't notice it before!




By this, do you mean pointing out whether the top note is defined as a sharp or a flat and then getting them to read it accordingly? As this is what most of them seem to have trouble with, especially when it is the bottom note that isn't 'clean' (i.e: has a natural/sharp/flat sign) - that really throws them and I don't know what I can do about that.

Yes, i learnt while learning piano and i think i picked it up alot quicker, but the pupil is a violinist and it doesn't help at all.

Here's my two happorth - how I teach intervals:

Looking at a keyboard, or listening to the notes, there are 12 sounding intervals in an octave

C - Db (semitone = minor 2nd)
C - D (tone = major 2nd)
C - Eb (minor 3rd or 3 semitones)
C - E (major 3rd)
C - F (perfect 4th)
C - Gb (tritone)
C - G (perfect 5th)
C - Ab (minor 6th)
C - A (major 6th)
C - Bb (minor 7th)
C - B (major 7th)
C - C (octave / unison)

These intervals can be written down in a variety of different ways using the various enharmonic equivalents. The different ways of writing them are known as different spellings.
To work out the interval -

1) Count the number of notes - count bottom and top and all notes in between - to get the number
2) Ignore all information about what key you are in, key signatures etc - just work from the bottom note and treat this as the tonic.
3) Think of what the top note would be in the major scale starting on the tonic - if you have that note, then it is either a major or perfect interval, depending on the number

2nds, 3rds, 6ths and 7ths can be diminished, minor, major or augmented.
Unisons, 4ths, 5ths and octaves can be perfect, augmented or diminished.

4) Anything else - work out if the interval is bigger or smaller than the major interval - check accidentals carefully.
If interval is one semitone larger than the major /perfect interval it is augmented.
One semitone smaller than perfect = diminished
One semitone smaller than major = minor
Two semitones smaller than major = diminished

5) if your bottom note is something really unfriendly like a C sharp, A sharp etc, work the interval out for a C or A etc instead and then remember to readjust your final answer by allowing for the extra semitone (does that make sense?!)

Works for me and my students....

I understand the confusion over 'but its the same interval' = you just have to get across that sounding intervals are one thing, written intervals are another and the same sounding interval can be spelt in a number of different ways and can get called different names as a result eg a semitone could be spelt as an augmented unison, a minor 2nd, etc

Hope that helps!

Not quite.
I mean go by the letter names FIRST to get the number of the interval as Petrat said.
E to F anything is a 2nd (involves 2 letters... remind them to include 1st and last when counting) E to G anything is a 3rd (E,F,G = 3 letters).

Measure everything against the major scale. so you start with major and perfect as Sue HM has listed.

Sorry, Cadence, but this is really very basic indeed and, in my opinion, if you don't know this you shouldn't be teaching theory. I would be concerned if a Grade 5 theory student didn't know this, never mind the teacher. Your subsequent posts suggest that you don't even understand the basic principle behind calculating intervals which is very worrying.

The very first thing to do when working out an interval is to count the letters between the notes. See the section on intervals in Piano Time Book One, for students who have been learning for about three months!

I'll now sit back and await the tide of invective...

Cadence, I'm going to ignore Czerny's comment and just say to you that I as a student, I would be happier learning with you - a teacher who's willing to ask questions, even when they suspect they may be shot down in flames - than have some of the other teachers on this board, no matter how knowledgeable they are. I hope you and others will keep asking questions - there are enough of us who are interested in both the questions and the answers, and who believe that anyone is entitled to ask anything without being shot down in flames. Good luck to you

An interesting way of ignoring it when you quote it in its entirety.

Actually I'm asking questions all the time - reading articles, looking things up, listening to new pieces of music, doing courses. But just how little information is it acceptable for a music teacher to have at their disposal? What would be the response if I were, for example, to ask a question saying "how many crotchets equal a minim??". In fact, I may do just that and we'll see.

It may seem I'm being spiteful and derisive for the sake of it, but it actually concerns me when teachers lack such basic knowledge as it's reasonable to suspect this is indicative of their level of knowledge in other areas and that they may teaching their students erroneous facts.

Perhaps you should tell her that the piano is a limited instrument, because it only has 12 notes to the octave, so it has to use the same key for the two or three (e.g. Dx, E, Fb) different notes. A 17th C. organ or harpsichord with split black keys would have one of a so-called enharmonic pair tuned to the sharp and the other to the flat. The standard orchestral strings and wind are tuned on the fly according to the ears of the player, to provide chords that sound smooth. This provides the same effect: if we are good enough to play in tune, we automatically play Ab as the fifth of a Db major chord and G# sharp as the third of E major.

Yes, I feel very much the same.

But that's the whole point!!!! What do you think theory is, exactly?! It's the stuff that's written down as opposed to what we hear.

So in this example it categorically isn't the same note - that's the crux of the matter. In terms of theory, Bb is absolutely not the same note as A# or Cbb, and it's vital that this is explained otherwise the pupil could develop a fundamental misunderstanding.

Please, let's respect the OP's request and avoid yet another rehearsal of views on what teachers should and shouldn't know.

Thank you to the people who have have posted helpful advice in response to my post.

To the people who have commented about my lack of knowledge:

I appreciate your concern for my pupils and the potentially erroneous information I have been providing them with. As it happens, I have done no such thing.

I myself know quite well the principles of theory and how to recognise intervals. Being relatively new to teaching, what I was hoping to gain from this thread was advice on how to articulate and impart this knowledge to my student in a clear manner, so that she fully understands.

You will notice that in my opening post on this thread, I wrote "how do you explain why that is the case, when to her it looks the same?"

That being: I understand, but I am having difficulty demonstrating to her why the intervals are the way they are. I have never been in a situation where I had to "calculate intervals" because I have been studying music for years and know them intuitively.

I have in fact been provided with a lot of useful ideas to help explain clearly to student the reasons behind intervals being augmented or diminished, thanks to the responses on this thread and thanks to some members of the forum who felt it necessary to PM me due to the ensuing tone of a thread that started simply to ask advice from what I thought were sympathetic peers.

I am actually a bit shocked and upset to log back in and find that people had felt the need to judge my level of knowledge and competency on the basis of one query for clarification. But I know that I am a good pianist and teacher, especially due to the feedback from my students, their parents, my own professor, and audiences at our student recitals, all of whom have been impressed by the results and progress I have promoted from my students.

I will no longer be taking part in this particular thread, so if anyone wishes to raise more concerns about my teaching practices, please feel free to PM me.
C x

Those commenting saying you are basically not a very good teacher, should examine themselves, as evidently they are unable to read, or not understand the meaning of the orginal question, asking how to explain it.
Feel free to PM me if you don't agree!

In my opinion, some of the best teachers are the ones who know when to say "I'm not sure, I'll get back to you". I am a teacher (not a music teacher) and I say it all the time! I can't believe the meaness of some of the teachers posting on here. Talk about undermining people's confidence.

Not that this applies to Cadence anyway as she (he?) was asking how to explain something - surely this is the point of a forum - if everybody already knew everything before posting then we could just close all the threads apart from the café!

I do it too (like you I am a teacher but not a music teacher). My students (I teach in a university) have often told me that this is one of the things I like about my teaching. Over the years I have learnt that it is often very hard to explain something that you know instinctivly and/or something that you have known for so long that you can no longer remember how it was first taught to you.

I agree.

Here is what I do.

• First there is the groundwork. Students I am teaching this stuff to already have a (near) foolproof method of working out key signatures and writing scales. When teaching theory, this is the first area of knowledge I address. Anybody interested can email me at pianodoodler@hotmail.com for the method. I will pass it on freely. I would add it here as an attachment, but cannot work out how.
• So, granted that the student can identify keys and key sigs, given an interval to identify, here is what they do:
  • Count the letter names to get the basic interval.
  • Treat the bottom note of the interval as the first note of a major scale, then look at the top note:
    • The interval is a 4th, 5th or 8th; work out the 4th, 5th, 8th note of the major scale:
      • The top note of the interval is the same - interval is perfect.
      • The top note is higher - interval is augmented.
      • The top note is lower - interval is diminished/
    • The interval is a 2nd, 3rd, 6th, 7th, work out the :2nd, 3rd, 6th, 7th note of the major scale:
      • The top note of the interval is the same - interval is major.
      • The top note is higher - interval is augmented.
      • The top note is a semitone lower - interval is minor.
      • The top note is a tone lower - interval is diminished.

Hope this makes sense. It is easier to work through with a pupil than it is to describe.

I do agree with both these points. However...

1) There is surely a level of knowledge below which our pupils should not expect us to be constantly reaching for the reference books.

2) As teachers, it is surely precisely our job to work out ways of explaining things we know instinctively (in fact a lot of what we're teaching to others certainly *should* be instinctive to us, but if we can't pass on that information clearly and succinctly we're not much use to our students). It shouldn't really matter how they were taught to us in the first place, unless we remember a particularly helpful teaching method.

As regards point 2), I think it is fair to expect new teacher to take a while to build up their repertoire of ways of teaching certain practical and theoretical aspects.

Yes, and the OP was looking for advice on precisely that point (how to get the information across), not the actual factual material.

Unless you have something new to say, could you please let this go now?

Apologies for coming back to this old post, but I haven't seen a correction of this last bit ... yes, Eb to Gb is a minor 3rd, but Eb to F must be a major second; it's only a diminished 3rd when you spell the notes Eb to Gbb.

I read it as that was the question which the pupil had asked.

Wouldn't it be better to let the thread die now

If people play the different notes differently on the instruments that can make the distinction, some of us can hear the difference.

On the subject of Asharp/Bflat I recently pointed out to my teacher that I loved the sound of a particular Asharp in the 1st movement of moonlight sonata, it "tinged" kind of like a triangle would. I said to her that it sounded nothing whatsoever like a deep soft Alison Moyetesque Bflat, to which she informed me that on her violin it is a completely different note and thus played differently

This I thought was a very interesting snippet of information!

I'm about to do grade 5 theory too and would say personally that intervals do have the capabilty of actually "cooking" ones brain!!

Can't wait for that sunk in feeling when you can't understand what you didn't get to start with!!!