Table of intervals: part 1

Hello and welcome to this 2-part blog post on intervals. I mean intervals such as “major third” and “augmented fifth”, things like this. Extremely important building block in Music Theory. You need intervals to transpose stuff for example. Or, much more importantly, to figure out how to make chords (triads or more complicated ones).

Eventually with practice you should have these intervals memorized but to get off the ground you need some help.

(psst, do you want to learn about the Circle of fifths too?)

Tl;DR

Starting with the end in mind, here’s all you need in order to figure out any interval ever:

In this first post you’ll learn how to draw most of this table, in the second – how to finish and use it.

You should be able to draw this on your own so you don’t rely on referring to a piece of paper (that you lost last week, most likely) and also so that you memorize the intervals sooner. DIY FTW!

Mother’s little helpers

You’ll need some aids. The first one is the C major scale. Pancakes all the way!

From C to shiny C:

Next, you need a keyboard. You know how to draw a keyboard, right? Rectangles for the white keys, then the black keys go in groups of 2, nothing, 3, nothing, 2, nothing, 3, nothing… Finally the white key next to the group of 2 (that look like Chopsticks) is C. The white key next to the cluster of 3 (that look like a Fork) is F. Chopsticks – C, Fork – F. Fill in the rest using your mad alphabet skills.

So there – these are the visual aids: a staff with C major and a keyboard:

The table of intervals

Time for the table. It starts with two groups. The intervals belong to one of the two groups.

Each group gets two more columns: “#” for “number of lines and spaces on the staff” and “d” for distance in terms of semitones on the keyboard.

Now you need to put the numbers 1 through 8 in the # column. 1 goes first on top left.

2 is top right.

3 goes under 2.

4 goes to the left of 3.

5 is under 4.

6 is to the right of 5.

7 under 6.

And finally 8 is bottom left.

Did you see a pattern? It’s a snake!

Why 8 do you ask? 8 is the number of lines and spaces between C and C. More on that later.

Let’s add some names to those numbers, starting with the oddballs: 1 is called unison and 8 is called an octave.

Unison means “the same sound”. So the first C and the first C are the same, the interval between them is a unison. Why 1 and not 0? Because when you count the number of lines and spaces you start with the first note. You put your finger on the first note and say “one”. As you move up, you increment. Don’t worry, you’ll see a lot more of this later.

Next, let’s fill in the rest of the interval names in the left column (group 1). They are pretty boring: fourth and fifth.

Now the right column (group 2). It’s all-too-boring too. Second, third, sixth, seventh.

Back to the discussion above, let’s learn to count lines and spaces.

Put your finger on the first note, say “one” and as you move up you increment for each line or space. So C is 1 and it’s on a line. You move up – it’s a space. You increment 1 – it’s a 2. The note there is D.

Next one up is E. It’s 3. F – 4. And so on.

Now it’s time to populate the last column left – the one with distances in terms of semitones.

First is the unison. It’s the same C note. There are 0 semitones between the C and the same C. So put a 0.

Next comes the second interval called “second” (wow!).

The number of lines and spaces between C and D is 2, we already established this and put in the # column.

Now what about the distance in semitones? From C you go to C♯ which is one semitone, they you go to D which is another semitone. Two in total.

So since there are two semitones between C and D, you put 2 in the table.

Next, the third interval. Between C and E. (BTW, we use C major to figure out the table because it’s the easiest, but these intervals then apply to any scale or starting point.)

There are 3 lines/spaces when you start from C and count C = 1, D = 2, E = 3.

And there are 4 semitones between C and E (C♯, D, D♯, E).

The semitone distance from C to E is 4 and that’s the number that goes in the table.

Next number if 5. Why? Look at the keyboard above and count the semitones between C and F.

Next number is 7. Why? There are C♯, D, D♯, E, F, F♯, G (7 in total) semitones between C and G.

The distance from C to A is 9 semitones as you can see keyboard picture above.

To wrap it up – C to B is 11 semitones and C to C is 12.

“Group 1” and “group 2” aren’t particularly cool names. We need something better. Let’s put a P in the left group.

P stands for “perfect”. Let’s call the whole group the perfect group.

The second group is called the Major group.

Now let’s stop here for now and see how to use what we have so fat in the next post.

Adios!

Aside: Why the name Perfect? Cool story.

Imagine a string. Pluck it. Now another string that’s exactly half as long the first. Pluck. The twice-as-short string makes a very similar sound only higher (an octave above). If you play the two together, they sound good even to the pre-historic human. Perfect actually. (Today we call it Perfect 8th.)

Now the unison is two strings of the same length vibrating. They sound the same and they sound good together. Boo-boo the Conqueror of the Cave as well as Bach both will agree they sound perfect together. (Only Bach would say the two sounds are in a perfect unison.)

If you shorten the second string to be 1/3 of the length of the first, the two still sound good together. A perfect 5th. Ask all heavy metal and punk guitar players – this interval is just perfect for most songs. When you play C and G together with a distorted guitar it sounds awesome. C and G#? Not so much.

If you shorten the string by a 1/4 and you play both they still sound good, albeit borderline. Pushing the limit of what your ear would call perfect. This is the perfect forth. Anything else is not so perfect. Therefore it needs a different name – let’s go with Major.

Guitar harmonics

Octave, fifth and fourth (the perfect) also happen to coincide (well, no coincidence really) with where the harmonics of a guitar string are easiest to produce. Harmonics is when you hold your finger but not press on the string above 12th, 7th and 5th fret. 12th fret (the octave) is the easiest and perfectiest, the 5th fret is borderline (the perfect fourth interval).

12th fret of the guitar is exactly the middle of the string, so no surprise.

Pentatonic? ‘nother cool story.

Pentatonic scale is 5 (penta) notes before you reach an octave. For the longest time in human history it was the only scale before our ears became sophisticated enough to find a few more notes musical. All Chinese music, all Scottish, all blues, all everything for a long while just used a pentatonic.

Example, common in blues guitar – A C D E G. 5. You know what’s cool? You make up this scale only using perfect 5th intervals.

C to G. G to D, D to A, A to E.

Think about this.

Circle of fifths: a quick test

(If you’ve come to this page out of nowhere, please see the Circle of fifths explanations part 1, part 2, part 3)

Now that you know all there is to know about the Circle of fifths, it’s time for a little test… Identify the key signatures that you see in the pictures below. Every picture has a corresponding major and a minor key. Figure out one or better yet, both of them. To check your answers, click on an image. If I got any of them wrong, let me know I’m an idiot.

F major / d minor

Gb major / e flat minor

E major / c# minor

F# major / d# minor

Db major / b flat minor

Eb major / c minor

C# major / a# minor

Cb major / a flat minor

Bb major / g minor

B major / g# minor

A major / f# minor

Ab major / f minor

G major / e minor

D major / b minor

Circle of fifths part 3: minor scales

So far you know how to draw the circle of fifths using the old FCGDAEB (Fat Cats Go Down And Eat Breakfast).

You also know how to figure out which ♯s and ♭s you need to make up a major scale.

Goodie.

Now it’s time for minor scales.

Good news: you already know all there is to know. You use the same ol’ circle.

TL;DR: The only thing different is that the top of the circle (the North pole) is a (meaning a minor) instead of C (C major).

You picked up on Majors being Uppercase and minors being lowercase? Gooood.

K, let’s back up a bit.

Here’s the circle of fifths that you’ve learned to love and cherish (and draw by yourself too!):

Now instead of C at the top, you put an a. But on the inside of the circle:

It makes sense, doesn’t it?

C major scale is CDEFGABC – all the white keys on the piano. a minor is the same notes without any ♯s or ♭s. Still all the white keys on the piano. Only it starts from A not C. So the a minor scale is ABCDEFGA. But you probably knew that already.

So Major scales go outside the circle, minor scales go inside. They are minor. Fragile. In need of protection. Keep ’em inside.

Moving on.

If a is where C is, then a♯ should be where C♯ is and a♭ is with C♭.

Now go back up and finish “..And Eat Breakfast”.

Since you run out of the fat cat sentence, you start over with f. Only that all are sharp now (because you just finished with non-sharp, nor flat ones). In other words you write f♯, c♯, g♯, d♯.

a♯/a♭ is already there, you continue with Eat Breakfast (e♭, b♭). They are flat because they are on the flat side of the circle.

Then you start over with non-sharp/non-flats – f, c, g, d.

This is actually the full circle. It shows both Major and minor scales.

Almost. The problem is I forgot to take a photo of the numbers next to each minor letter. But you’re a smart cookie, you can figure those out. They are exactly the same as the Majors. a has 0 flats/0 sharps. Just like C. Then you move to the right and put 1 next to e. 1 sharp in e minor. (Just like 1 sharp in G major). And so on…

Now it’s test time. What is the signature of a minor?

Find it in the circle. Look at the number. It’s 0. No flats, not sharps.

There you go:

Something more interesting? f♯ minor.

Find it in the circle. It’s on the sharp side. And has the number 3.

So f♯ minor scale should have 3 sharps? Which ones? Back to the Fat Cat… (FCGDAEB).

The first three are F, C, G.

Therefore the signature looks like:

Or if you want to spell out the whole scale…

Thanks for reading!

Now you know how to draw the circle of fifths. And figure out ♯s and ♭s in all the major and minor scales. Hooray!

(Psst, practice now!)

Want some other things to practice?

Practice saying ABCDEFG aloud. You probably have no problem with this. It’s the alphabet.

Now start with B = BCDEFGA. Now start with C. And so on.

Now the same but backwards. Say quickly GFEDCBA. DCBA. DBA. DCBAGFED. And random stuff like this.

Now FCGDAEB. (Fat cat…)

Now BEADGCF.

Circle of fifths: part 2

(part 1, you are here, part 3, test)

In the previous post you learned how to draw the circle of fifths yourself. You practiced a coupla times. You have it down. Fat cats did what again?

Now it’s time to put the circle to good use. In other words, find which sharps or flats are in a major scale (minor scales in the next post, promise).

The circle

As a reminder, here’s the circle you learn to draw in the previous post.

Now, here’s a question: what sharps/flats are in E major scale?

First, you explore the circle (The Circle!) looking for E. Ah, gotcha! It says 4. And it’s on the ♯ side. This means that E major scale has 4 sharps.

Which sharps thought? You look at the FCGDAEB area and count 4 letters.

So here’s your answer. E major scale has 4 ♯s and they are F, C, G and D.

Put them on the staff….

Fat:

Cats:

Go:

Down:

And this (above) is your scale signature. So your scale has the notes E F♯ G♯ A B C♯ D♯ E. There you go.

By the way, the ♯s and ♭s have designated places on the staff. You can’t for example put the G♯ on the second line. I mean you can, but giving such a signature to other folks to play may cause confusion. Followed by ridicule. Followed by mutiny!

How do you remember the positions of the ♯ and ♭? Dunno. I just go by the “Fat cat…” again and have a mental picture memorized of where stuff goes. Here’s a picture or two for you too.

Now, let’s go through the exercise again. B♭ major, shall we?

Found it! Two ♭s.

Which two ♭s you ask? Well look at the flat list (the reversed fat cat):

So B♭ major has two flats…

And they are B and E.

On the staff:

To be continued…

Next time: minor scales.

Meanwhile you go draw some circles. And practice figuring out ♯s and ♭s in major scales.

Need prompts? OK, tell me which ♯s or ♭s are in…

  • C major
  • D major
  • C major
  • F major
  • A♭ major

Overachiever? Draw these ♯s and ♭s on the staff in bass clef. Bye!

Circle of fifths: part 1

This is the first in a series of posts I’d like to call “What I learned in Music Theory 1”. I took this class in Santa Monica College recently and had a great experience and a great professor. Highly recommended. He showed us a few diagrams that make so much sense and make learning a breeze. I’ll try to share some of the things I’ve learned.

(part 2, part 3, test)

Intro and tl;dr

Circle of fifths, eh? What it is, why, the story… there’s always Wikipedia for all this. For the purposes of this discussion, the circle of 5ths helps you figure out how many sharps or flats are in a major or minor scale, and also which ones. That’s all.

I’ve seen several videos and read several explanations of the phenomenon known as “circle of fifths” but none of them stuck. This one that you’re going to see did stuck. It’s also different than any other one I see when searching for images on the web. I mean look at this. None of these images have C♯ and C♭ at the bottom.

Anyway, to cut a long story short… here’s the final result:

Now let’s see how you draw this yourself…

Before we begin, memorize this: Fat Cats Go Down And Eat Breakfast. Got it?

DIY: a circle and some fifths

Unsurprisingly you start with a circle…

You split the circle in half. The right-hand side is the sharp (♯) side and the left is the flat (♭).

Do your best to split the right-hand (sharp) side with six ticks. If you imagine a vertical line through (like the earth’s equator), three ticks should be in the upper half (north) and three in the lower (south). I say “do your best”, but there’s no need to break a finger (you need those for playing!) trying too hard. Doesn’t matter all that much.

Same thing (6 ticks) go on the left (flat, aka East) side.

Now the North pole becomes C, while the South pole is both C♯ and C♭. C major scale has no sharps, nor flats (all white keys) on the piano. C♯ has all sharps and C♭ has all (7) flats.

Next you need to put all other notes on the circle. They are all a 5th apart (not that it matters). How do you know where to put them? That’s where the magical FCGDAEB comes into the picture. How are you going to remember? Fat Cats Go Down And Eat Breakfast.

Write these magical letters somewhere while mumbling…. Fat. Cats. Go. Down. And. Eat. Breakfast.

Then write the same “Fat cats…” only backwards. BEADGCF.

Beautiful. Check if you’ve made a mistake. Fat… cats… go… down… and… eat… breakfast. K.

You already have C (cat), so add the F (fat) right before it. Fat cat.

Keep going… G, D, A, E, B.

Now you’ve run out of letter. Start over. But because you already have an F, you need a sharp or a flat. And since you’re still on the Sharp (right-hand) side, make it an F♯.

Next, keep going with the fat cat. You run out of letters (Breakfast) right on time.

But since you already have FCGDAEB and you cannot repeat yourself and you’re on the flat side, you make these new ones flat. G♭, D♭, A♭, E♭, B♭.

Done with all the letters. These are all the major scales there are. If someone asks for something not on the circle, like G♯, you tell them they are an imbecile and give them A♭ which is on the circle.

As I said, done with letters, now you need some numbers.

Start with the North pole, the C. C has no flats. Nor sharps. In other words 0 sharps and 0 flats. So 0 it is.

Now you start with the circle and write consecutive numbers 1, 2, 3, 4, 5, 6, 7. The letter G gets a 1, D is 2 and so on. Easy-peasy.

C♯ has all 7 sharps, C♭ has all 7 flats. Write 7 then for C♭ too.

Fill out the rest with 1, 2, 3, 4, 5, 6. Or if you want to count backwards – 6, 5, 4, 3, 2, 1, up to you.

Voilà, le circle est complet!

Probably messed it up in French, but I mean – there you go, the circle is complete.

Practice drawing this yourself. Fat cat… and so on. 1 to 7.

In the next post you’ll see how to use the circle you just drew.