I've been helping my friend out in learning theory, and I was helping yesterday when we got a bit stuck (on grade 3!).

When I was at grade 3 level, I didn't really understand intervals, and guessed at them really (the minor/major bit anyway). But since then my teacher told me a way to work out intervals, which makes me understand them perfectly (taking the lowest note and 'pretending' that's the key it's in, and then seeing if the higher note is in that key...if it is it's major, if it's 1 semitone less it's minor etc).

So I was showing my friend this way, and then we did one exercise and, to check, looked in my old theory book...only to see that I had put a different answer (four times!) and my teacher had marked them both correct!! So now I'm really confused...either the method I was shown that now makes so much sense is wrong, or my teacher marked 3 or 4 questions in a row wrong...

Anyway, here's the question - hopefully you can help me clear this up!

* The key sig has a Bb and an Eb (above says G minor), the lowest note is a G, and the higher note is an F (natural).

Now I initally put major 7th (and my teacher marked this correct), but since looking at it recently, I think it's a minor 7th, because if I take the lower note and 'pretend' it's in G major, then the F would be F# if it was a major interval...but it's not!!

Basically, am I right (with the minor 7th) and is my teacher wrong, or is my teacher right and I've learnt completely the wrong method?!!!

Please help!!

Laura

You're right, Laura, it's a minor 7th!

Oh my gosh, thank you so much!! haha! I'm really pleased about that...I was getting so confused!

You are correct G-F is a Minor 7th. G-F# is a Major 7th



Must type faster!!

That's great, thanks for your reply too, MadTom!!

Hi Laura

You are right it is minor 7th. I was actually taught to work out things the same way, if it is in the major key then it is major and if not then it is minor. Of course after Grade 3 then you move on to augmented and diminished. A perfect that is no longer a perfect either becomes augmented or dimished.

I always draw myself a keyboard to work out the intervals, that way I can see if it gets bigger or smaller.

When I did Grade 4 I hadn't really sussed out intervals it was only when I did Grade 5 it all fell into place.

I am helping my son with his Grade 3 now and it is a lot of fun going back to it. However, sometimes we get to a question and I think thats a bit hard for Grade 3 and I have to stop and think.

Yes that was exactly the same with me...I always hated intervals until I did grade 5 and then they suddenly became clear! I think for grade 3 (and maybe 4 too) it was much easier to just 'take a guess' at the intervals, as they were just major and minor, but this of course meant they were often wrong!! Then for grade 5 you're required to think about them more and actually work them out due to the dim and aug stuff!! Interesting!!

Laura

This applies to 2nds, 3rds, 6ths and 7ths. 4ths and 5ths in the key of the lower note would be perfect. Note also that in a minor key, the 3rd and 6th are minor, but the 2nd and 7th are still major.

I just tested myself on how long it took me to work out that it was a minor 7th using the method I've quoted above - it took just under one minute, including jotting down a keyboard diagram. Simple!

Perhaps Skylark would like to work out the names of the following intervals, lower note first:

C# - Eb
A# - Db
Eb - F#
D - Gb
G# - C
C - E#
C# - Gb
B# - Gb
B - Ab
Cb - A#
F - E#

The OP is stuck on intervals at G3 level and the method I've given in my post (which I learnt from a well-known recommended theory book), is suitable for working out intervals up to G5. I suspect your examples involve doubly-diminished intervals and all sorts of other variations which aren't applicable up to G5. For the 30,000 or so people who take Grades 3 to 5, the method I've given is extremely quick and easy, in my opinion. Those who find it as useful as I did up to Grade 5 are welcome to use it - why would I keep it to myself when I've found it so useful ! But I honestly don't think it's doing any favours to the majority of people who just want to learn G3 intervals to complicate matters by discussing intervals on a G3 thread which won't crop up even at G5 level (double dims etc).

I'll save her the trouble

C# - Eb Diminished 3rd
A# - Db Doubly diminished 4th
Eb - F# Augmented 2nd
D - Gb Diminished 4th
G# - C Diminished 4th
C - E# Augmented 3rd
C# - Gb Doubly diminished 5th
B# - Gb Doubly diminished 6th
B - Ab Diminished 7th
Cb - A# Doubly augmented 6th
F - E# Augmented 7th

Interesting academic exercise. Low musical value. The names do not reflect how you would hear most of these intervals. Genuine doubly diminished/augmented intervals are rare in real compositions.

I don't know what method you used to work these out, but they're the answers that the "semitones" method would return, so I'm not quite sure why kenm has a problem with it, if indeed he does. Although I still think that any discussion about the higher reaches of theory including double dim/aug intervals would be better on a separate thread rather than on a Grade 3 thread. But that's just my opinion!

I agree. As I said:

Rare, but I have come across them: doubly augmented unison in the Brahms Horn Trio; doubly diminished fourth in Elgar's "Sing unto the Lord", both melodic.

Two things worry me about the semitone method:

1) It reinforces the limited view of the pitch system that pianists so easily acquire: that there are 12 notes to the octave, some of them with more than one name, for some peculiar reason.

2) It fails to cope with the differences between the minor third and the augmented second and between the augmented fourth and the diminished fifth. all of which intervals occur in the harmonic minor scale. The ear usually has no difficulty making these distinctions in a tonal context.

Skylark, if I've understood your method correctly then working out kenm's puzzles will work (I've only actually worked out one or two using your method, so don't know about the rest). If I'm right then as I see it you'd work it out as follows:

Interval C# to Eb

1. Count letter names C, D, E gives you a third, so our interval C# to Eb is a third of some sort.
2. Count semitones. If the interval has 4 semitones it's a major third (which is skylark's starting point), if it has 3 semitones it's a minor third, if it has 2 semitones (as in our example) it's a diminished third. And if it has 5 semitones it's an augmented third.


Interval A# to Db
Counting letter names (A to D) gives you a 4th of some sort.
Counting semitones (A# to Db) gives you 3 semitones. A perfect 4th has 5 semitones, a diminished 4th has 4 semitones, a doubly diminished 4th would give you 3 semitones. So it works for these as well.

At first I thought kenm's reasoning was correct and it wouldn't work for counting semitones, but when I looked more closely at the way you work it out, and tried it out, I could see it does work. It isn't the method I use for teaching or working out intervals myself as I don't think I could remember how many semitones each major/perfect interval has, but it seems a perfectly valid way of doing it. Of course the OP is only asking about Grade 3 and at that level you won't encounter Diminished or augmented intervals; at grade 5 you don't encounter doubly diminished intervals; and even in all the past papers/exercises, and the exam I did for Grades 6/7/8 there were no doubly diminished interval to be identified, so I think they are more likely to be studied at university/diploma level.

I would be interested to see a pair of notes where the semitone method doesn't work because up to Grade 5 I've done dozens of these examples, and I haven't come across any which haven't worked. But there's always a first time for everything!

I don't see how anyone could mistake a third for a second, or a fourth for fifth, unless they can't count letter names



Yes I checked the semitone method against all of Mad Tom's answers, and assuming MT is correct (and I think the odds are in his favour ), then the semitone method works for all of kenm's examples, most of which would not in any event be encountered at G3, or even as you've said, probably until university/diploma level.

Once you've remembered the pattern of semitones for each major/perfect interval (which isn't really difficult, it's only 2-4-5-7-9-11-12), then the formula can be quickly and easily applied to *any* given interval, as far as I am aware. And as I said in an earlier post, once you've remembered the number of semitones and can automatically recall them, it takes less than a minute, including jotting down a keyboard diagram (which is essential to the method), to apply the formula to any interval. It works for me anyway! (And speaking as a clarinet player, you don't have to be a pianist to know how the keys are laid out on a keyboard - it's been invaluable to me up to Grade 5 to know the piano keyboard).

The way in which you've worked it out jm-hamilton is the logic I use. I found the method in the "Take 5 and Pass First Time" book and if anybody is struggling to understand intervals, I recommend they get this book and study the author's method - he also gives a very helpful diagram to clarify the method.

I'm in complete agreement with kenm on this - I know I've posted on this very subject before, but counting semitones to work out intervals is not a safe way to do this, and if someone has learnt it this way, they're going to have to relearn it another way for more complicated intervals. Bach does diminished 3rds all over the place (see the F minor 3-part Invention, for instance), but using the semitone method these would come out as major 2nds. The Black Pearl Goldberg variation is plastered with strange intervals, if you want further proof that kenm's instances aren't just academic.

The two people that I've taken on at the last minute for Grade 5 who had learnt it he 'counting semintones' way were both very confused.

EDIT - I stand corrected, as I see there's a refinement to the method that I hadn't absorbed (counting the letter names) - but I still think there's more risk of confusion with counting semitones than the alternative method of working from the template of the major scale built on the lower note of an interval. The simple list of semitones & intervals you quote, skylark, needs a major 'health warning' saying that this is not the whole story!

It seems that a significant number of people find the extra learning involved in the 'semitone' method is easier than knowing the major scales.
My concern would be that with that amount of extra learning there is potential for something to be remembered incorrectly when you really need it.
I think that working out intervals by using the major scale as a starting point demonstrates an understanding intervals more than memorising a list.

It might take less than a minute with the semitone method but for most intervals it can take less than 10 seconds if you know major scales.

As I asked earlier, how is to possible to mistake a 3rd for a 2nd, unless you can't count letter names which would be more than a little bizarre. Until someone gives an example of this, then it's difficult to convince me of the possibility of making this mistake.



"Strange intervals" are not within the province of G3, G5 or as posted earlier, probably pre-University/Diploma. Around 30,000 people a year just want to pass G3-G5, compared with a relative handful who want to do the higher grades and even fewer do University/Diploma.


It's fair comment for anybody to say that other methods may be *preferable* in order to gain a deeper understanding of the structure of music, and if someone wants to apply themselves to this, then that is their choice. But for someone who wants a quick and easy method in order just to pass the exam, then the semitone method (in my opinion) fits the bill. What I feel is not fair is to make out that the semitone method doesn't work as I've yet to see an example of this.




EDIT. I see you've edited your post briantrumpet, so perhaps kenm hadn't properly absorbed the semitone method either and hadn't realised that counting letter names is integral to the method.

Yes, I wouldn't say it doesn't work though I'd not necessarily agree about it being quick and easy.
And yes, for someone who finds it an easier way to pass the exam it will fit the bill.

I know there's not going to be agreement on this, skylark. However, I'd suggest that your above comment - I don't think I've unfairly taken it out of context - reinforces my preference for the 'major scales' method. My disillusionment with 'education' in its current status is that it uses quick fixes in place of real education and deep understanding. I'd rather someone risked getting the wrong answer using the method that promotes deep understanding than getting the right answer using a method that does not promote that understanding. I'd suggest that the 'counting semitones' method falls into the latter category, hence my dislike of it. Sorry.

That's fair enough, everybody has different views on the matter! It's the statement which kenm put forward and which you initially agreed with that the semitone method *doesn't work* that I take issue with, not people's differing views on which method is best!

Well, I think both kenm's & my thinking that your method doesn't work was caused by your simple list of semitones and intervals - quoted without qualification, this will cause misunderstanding, as we both demonstrated. And we know something about intervals.

Yes I'm well aware that you both know a lot more about intervals than I do, but I did actually put in my original post to "count the letter names", which jm-hamilton did and which I mentioned again subsequently. I don't see how I can be held responsible for people misinterpreting my posts through not reading them properly!



Shall we draw a line under this discussion?

Not the one you'd hoped I suspect. Sorry

I imagine my RH playing a (major) scale on the piano starting from the lower note. I stop when I hit the degree of the scale with the same letter name as the second note. That gives me the type of interval - 2nd 3rd, 6th whatever. I then adjust it up or down one or two semitones if necessary to get the actual note.

You can train yourself to inwardly hear the notes as you do this. And it is very quick. Some intervals you can work out the name pretty much instantly. At worst it takes a second or two - certainly not a minute.

I think he semitone method works fine, but I find my method quicker and easier and more closely related to understanding intervals in a musical context. You have to know all the major scales - including unusual ones like B sharp major! But apart from that you just need to know that:

In the major scale 4ths, 5ths and octaves are Perfect. All other basic intervals are major
maj->min->diminished
maj->augmented->doubly augmented
perfect->diminished->doubly diminished
perfect->augmented->doubly augmented

I didn't hope anything - it was just a simple statement of fact...


It's bad enough when what I say is misinterpreted without having my thoughts misinterpreted as well

Do you think there is no intrinsic value, in the sense of adding to one's general music education, in learning how many semitones there are in a given interval then?

And do you think I don't know major scales? Hmmm

Just because I find the semitone method quicker and easier than the "major scale" method does not mean I don't know major scales. Nor that I don't know the "major scale" method of working out intervals. I happen to prefer the semitone method as described in the "Take 5" book and find it more convenient. I see no reason not to recommend it to others, who are perfectly entitled to take it or leave it. But to say that someone who uses the semitone method doesn't know major scales is no more valid than my saying that someone who uses the major scale method can't count

skylark
Founder of the "I love scales" club and "I love theory" club

I don't think you do really... if you get something more obscure as a starting note then make it something easier.
Do the same to top and bottom note and it still gets the same answer. Just don't change the letter....unless you are confident of handling it.

Having thought about it a bit, I realise that knowing how many semitones there are between two notes, one of which was a double sharp or flat, might help me to sing them. If they were in the same major or minor scale, the semitones would not be necessary, because I would know the sound of the interval more directly. Another circumstance in which one needs to know the number of semitones between two notes is in analysis of atonal music by the methods described in Allen Forte's book.* In the neither case is it necessary to know the relationship between the name of the interval and the number of semitones, in the first because semitones and interval names would be alternative sight -singing strategies; in the second because Forte assumes that all atonal music is serial and dodecaphonic, and traditional interval names are not used in analysing dodecaphonic music.

* Not a rewarding exercise, because it seems to bear little relationship to the features of atonal music that make it sound better or worse.

If they were in the same major or minor scale, the semitones would not be necessary, because I would know the sound of the interval more directly

Yes.

I don't think I've ever seen a B# major scale, and certain I've never seen its key signature. The occurrence would be very memorable, though I suspect the key signature itself, with its five double sharps, would be a bit more difficult. Most composers (Mozart and Chopin, for example) would change to flats around F# +- 1, to avoid the double sharps. You might find lots of double sharps or double flats in Poulenc: he seems to dislike this sort of enharmonic change.

sbhoa's method reduces the number of scales you have to know.

Like Briantrumpet, I was misled by the list of semitones and interval names, but got the point from later contributions. Recognising the intervals of at least the home keys by sight, and also knowing their sounds, provides an extremely useful facility for sight singing, conducting and score reading, and playing the horn, but each interval needs to take less than a second. Its usefulness is rather like that of memorised multiplication tables.

You weren't misled. You misread it. Your fault, not mine, although neither of you have had the grace to admit that and both of you have instead tried to blame me for not being clear

I said it in June and I said it early on in this thread... i



In what way is "count the letter names" misleading

Sorry if I sound tetchy, but I've seen various posts in the past dissing the semitone method from several erudite people, for the reason that they thought - incorrectly - that it failed to distinguish between intervals like aug 4th and dim 5ths etc. It seems that none of you had grasped, even though I have consistently said it, that letter names need to be counted. And now *you're* trying to blame *me* for being misleading

Skylark, yes, I misread it, but I misread it because my eyes alighted on the simple list that you quote (I guess you've taken this direct from the book:

2 s/t = major 2nd
4 s/t = major 3rd
5 s/t = perfect 4th
7 s/t = perfect 5th
9 s/t = major 6th
11 s/t = major 7th
12 s/t = (perfect) octave

I now know this has to be qualified by the sentence below the list, but the list at first glance appears to be unqualified.

I have politely said why I don't like the method. I'm very quick to admit mistakes (as I did in my earlier post's edit). As you know I personally don't like this list because of its potential for misinterpretation (proved by kenm's & my misunderstanding), but it works for you and others, so fine. Please, before you accuse us of a lack of grace, try to understand why we misinterpreted your method. Then we can all live in harmony.

Why didn't you repeat my quote in full... DIRECTLY after the list you've quoted above came the phrase:



In what way could it have been made any plainer than to put directly after the list that you "count the letter names" If you just "glanced" at it, then it is your fault for drawing an incorrect conclusion as a result of not properly reading the method. And that conclusion - had I not been willing to stand my ground in the face of far more knowledgeable people than myself - could have put people off learning a method which many other people find useful.


There's only potential for misinterpretation and misunderstanding if people don't properly read the method And that applies to any method.

Earlier in the thread I took pains not to rub anybody's nose in misreading it and suggested that we draw a line under it. But I'm sorry - since you are both persisting in saying that my post wasn't clear, then I will persist in saying that it was, and that the pair of you have been extremely ungracious in trying to blame me for the fact that neither of you bothered to read it properly

I don't think I've ever used a "bah" on this forum before but I'm using it now

I think that qualifies you for membership of GOW, skylark...

Thank you for making me laugh Cyrilla


(but I must admit I'm still at blame being shifted)

I didn't misread skylark's post because I read it thoroughly before answering.

All arguments aside as to whose fault it is that skylark's post was misinterpreted (and I know whose side I am on...)

I can see the benefit in both methods - 'intervals counted by note-name and then semitone' (very useful and foolproof method for teaching interval recognition for exam purposes up to grade 5 and beyond, no doubt), and the 'major scale - bottom note as key-note' method (which develops a deeper understanding of intervals and their context).

A colleague of mine has used the 'note-name and semitone-counting' method with her theory students for over twenty years, without encountering problems in its use as a technique for exam preparation. Personally, I was taught the old-school 'major-scale' method, and still use it to this day.

With my advanced theory students, both methods are used by them - those using the 'semitones' method take slightly longer, but the end results appear equally reliable.

denmark

p.s. Isn't this thread, as I understand it, originally about grade 3 interval recognition, not advanced interval analysis?