Monday update 10/20

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How intervals work: minor-seconds and major-sevenths

Do you have a swagger in your step? I mean, you’ve mastered nearly every interval in music. So why wouldn’t you be feeling good?

But there’s one more pair of intervals to look at before you can say you’re a true music theory ninja. And these intervals are easy because they’re directly on either side of the tonic (1). Immediately to the right of the tonic (in a clockwise direction) is the minor-second (b2). And to the left (in a counter-clockwise direction) is the major-seventh (7).

In the key of C, for example, these are notes Db and B:

Minor-second and major-seventh intervals on ColorMusic piano

Both of these notes sound very dissonant with the tonic. After all, they’re the respective dominant and subdominant notes of the tonic’s tritone. (They are positioned next to the tonic because of the rearrangement from the circle of fifths to the chromatic scale.) But they do show up in the tonic’s key to differing degrees.

The major-seventh (7) note, for example, is used a fair amount in any given key. And that’s because it is part of the key’s major scale. So it’s often used in melodies written in that key. For instance, B often appears in the key of C because it’s part of the C major scale. And because it’s also the major-third of C’s dominant note (G), the major-seventh holds a favored position in many songs.

Major-seventh interval in key of C on ColorMusic piano

The minor-second (b2), on the other hand, gets relatively far less play. So you’re less likely to hear it in the tonic’s key. For example, Db rarely shows up in the key of C because it’s dissonant with the tonic … and because it doesn’t sound very good with other notes in the key of C. So it usually gets benched come game time.

As usual, these intervals are also symmetrical in every key. And, as you can see, each tonic connects with its minor-second (b2) in a clockwise direction and with its major-seventh note (7) in a counter-clockwise direction.

Minor-second and major-seventh intervals in ColorMusic

And because these intervals are really just a series of half steps, you could say the entire chromatic scale is simply a sequence of both minor-second and major-seventh intervals. Yeah!

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How intervals work: major-seconds and minor-sevenths

Let’s play a word association game, shall we?

If you say “Beatles,” I immediately think of the word “brilliant.” And if I say “Little,” you might say “Richard” without stopping to think. Some ideas just go together naturally.

So if I say the phrase “music theory,” what’s the first thing that comes to mind? In the past, you might have answered with something like “complex” … or worse, “useless.” But by now, you’re more likely to see the word “symmetry” flash through your brain.

After all, if music theory is anything at all it is symmetrical.

We’ve seen the symmetry of a tonic with its tritone. And we’ve dissected the symmetrical layout of subdominants and dominants in every key … not to mention the symmetry of major-thirds and minor-sixths … and minor-thirds and major-sixths.

So it shouldn’t come as a surprise that the symmetry continues. Spaced on either side of the tonic – at whole-tone intervals – are the major-second (2) and minor-seventh (b7) of a key. In the key of C, for example, these notes are D and Bb:

Major-second and minor-seventh intervals on ColorMusic piano

Both of these notes sound fairly stable with the tonic. And both are spaced pretty closely to the tonic (in the circle of fifths, as well as in the chromatic scale).

The major-second (D) note has the honor of being in the key’s major scale. So it gets along well with the tonic (C). It’s also harmonically close to the tonic’s dominant note (G), so this note shows up more in songs than its cousin the minor-seventh (Bb).

But the minor-seventh still has a special place in a lot of music. Especially blues music, which relies heavily on the slightly tense sound the minor-seventh note creates in a tune. And because it’s positioned so closely to the tonic, the minor-seventh is often used as a landing point as musicians work their way to and from the tonic in scales, melodies, and instrumental solos.

As you would expect, the minor-seventh and major-second are perfectly symmetrical in every key. Each tonic note connects with its major-second (2) in a clockwise direction and with its minor-seventh (b7) in a counterclockwise direction.

Major-second and minor-seventh intervals in ColorMusic

Oh, yeah … and because these intervals are really just whole-steps, there are only two groups of major-seconds or minor-sevenths. There’s one group of squares and one group of circles. Easy!

Two sets of major-second and minor-seventh intervals in ColorMusic

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How intervals work: minor-thirds and major-sixths

The symmetry in every key is astounding. You’ve already seen how a tonic is positioned directly opposite its tritone. And you know that the subdominant and dominant notes in a key flank the tritone.

Not only that, but you’ve also seen how the major-third and minor-sixth form a perfect triangle with the tonic. But did you know this same powerful symmetry continues? Yes, sir (… or madam).

On either side of a tonic’s major-third (3) and minor-sixth (b6) notes are its minor-third (b3) and major-sixth (6) notes. In the key of C, for example, these notes are Eb and A:

Minor-third and major-sixth intervals on ColorMusic piano

These two notes – Eb and A – are tritones in their own right. And together, they form a perpendicular cross with the tonic (C) and its own tritone (F#/Gb). Like this:

Minor-third and major-sixth intervals in ColorMusic

As a result, this equidistant positioning gives all four notes (1–b3–b5–6) a special love-hate relationship with one another.

For example, the tonic (1) sounds good when played with either the minor-third (b3) or major-sixth (6). But both of these notes also get along well with the tonic’s tritone and arch-nemisis (#4/b5). And this dual affinity between notes creates some surprisingly satisfying tension.

I mean, imagine if a couple of your good friends – who you resonate well with – also sometimes hung out with your enemy. You’d have a strange, conflicted relationship, right? Well, it’s the same with these intervals in any given key. The tonic plays nicely with the minor-third and minor-sixth notes … but there’s always a little tension between them – because they’re also friends with the tonic’s tritone.

And what’s beautiful is this same symmetry exists in all keys. It’s fascinating!

In total, the chromatic scale has three groups of minor-thirds or major-sixths. Each group includes two pairs of tritones. And each note in these groups connects with its minor-third moving in a clockwise direction and with its major-sixth note in the opposite direction.

Three sets of minor-third and major-sixth intervals in ColorMusic

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How enharmonic intervals work

Okay, so scale degree names can get wacky. Just like the letter names for notes, the numbers we use to label scale degrees can go by different enharmonic names. And the term you use to describe a scale degree depends on how sharp or flat it is.

For example, here’s a lovely graphic that summarizes every possible scale degree in music. Double-sharp (x) numbers are in the outer ring, followed by the different sharp (#), natural, flat (b), and double-flat (bb) numbers for various intervals in the chromatic scale.

All enharmonic intervals in the chromatic scale

Looking at the scale degree “3,” for example, you might just refer to this interval as “3” … or as “##2″ … or maybe you’d call it “b4.” But it doesn’t really matter because these different number names describe the same interval in a given key—that is, one that’s two whole steps above the tonic note. So no matter what you call it, you’re describing the exact same interval.

Of course, some of these scale degree names are a little obscure. For example, I can’t think of anyone who calls scale degree “1” “#7″ or “bb2.” After all, the tonic is the tonic (!), so it usually just goes by the name “1.” And 7 hardly ever goes by the names “b1″ or “x6.”

So, for simplicity, these are the most common scale degree numbers you’ll hear musicians use music. The better you get at learning these musical terms, the better you’ll be at playing songs.

Common scale degree numbers in the chromatic scale

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Why use squares and circles?

Some of you have asked why we use squares and circles in ColorMusic. And it’s a good question. This video gives you the quick answer. You can also find an illustrated explanation in the blog post, “Why the shape code works.” Keep the questions coming!



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How intervals work: Major-thirds and Minor-sixths

You hear it all the time … major-thirds have all the fun. But minor-sixths get the cold shoulder!!

Okay, maybe you don’t hear that all the time. (Unless you hang out exclusively with mega-music nerds.) But if you step back and think about it, that’s a really good question. Why does the interval of a minor-sixth get less play than its cousin, the major-third? After all, both of these notes are spaced at equal intervals from the tonic note of a key.

In the key of C, for example, the major-third (E) and minor-sixth (Ab) are both spaced at two whole-tone intervals from the tonic. The E note is just below the subdominant (F), while Ab is just above the dominant (G).

Major-third and minor-sixth intervals in a ColorMusic piano chromatic scale

Yet the major-third (E) is honored with much more of a presence in the key of C … while the minor-sixth (Ab) hardly shows up at all.

Well, this has to do with the consonance and dissonance of each note. And how good each pitch sounds when paired with the tonic. Or, better said, how nicely each note plays with the other pitches in key.

E (M3) sounds great when paired with both C (1) and G (5) in a major chord … and that’s important. Because it means the major-third is friends with both the tonic and its dominant – which are, decidedly, the most powerful kids on the block in a given key. So M3 is naturally favored in the songs of that key.

Major-third and perfect-fifth intervals in a ColorMusic piano chromatic scale

Ab (m6), on the other hand, sounds good with C (1), but downright crummy with G (5). And, as a result, it doesn’t get invited to as many musical parties when C is the host/tonic. (It’s all about who’s friends with who, you know?)

Minor-sixth and perfect-fifth intervals in a ColorMusic piano chromatic scale

As you might expect by now, it’s easy to see this pattern of major-thirds and minor-sixths in every key. Take a minute to soak it in – noting the fascinating symmetry of pitches in the chromatic scale.

All major-third and minor-sixth intervals in a ColorMusic chromatic scale

In total, the chromatic scale has four groups of major-thirds or major-sixths. There are two groups of squares and two groups of circles. The squares include all of the primary colors and secondary colors … while the circles include all of the tertiary colors.

Major-third and minor-sixth intervals in ColorMusic

Oh yeah, and each note connects with its major-third in a clockwise direction and with its minor-sixth in a counterclockwise direction. So, so cool, my friends. If you get a lay of the land by understanding these patterns, you’ll advance very quickly in your mastery of music theory and its use in the art of writing songs.

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Proof that tritones are dissonant

Okay, so in an earlier video about tritones, I mentioned that a given tonic and its tritone are rarely paired together. And it’s true … because these two notes are highly dissonant.

In the key of C, for example, the tonic (C) and its tritone (F#/Gb) are like polar opposites. ColorMusic makes this super easy to see, of course, because these two notes are complementary colors.

ColorMusic tritones in the chromatic scale

And because they’re very dissonant, they sound extremely tense together. But what would you expect?

After all, they are polar opposites.

I mean, imagine putting two mismatched musicians together in the same studio … like, say, Weezy and Rod Stewart. The resulting sound wouldn’t be too pretty, right?

Weezy and Rod Stewart are like tritonesWell, it’s the same with a tonic and its tritone. Because each note sounds so different from the other, people rarely try to combine them into a single harmony. It’s just not what most people want to hear.

To see what I mean, check out this list of chords in the key of C. Of course, a note like G shows up all the time because it’s the tonic’s favored dominant note. But the tritone? You find it in only a handful of chords … and even those are relatively obscure. Out of a full 62 different chords – only 17 include the note F#/Gb. That’s only 27% … wow!

Tritones in ColorMusic chord chart

So if anybody ever tells you the tritone sounds good with the tonic, you’ll know they’re lying. Or worse, maybe they’re crazy. Otherwise, you’d hear these two notes paired a lot more often.

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Latin note names in all 12 keys

Without a doubt, it’s good to know the Latin terms that musicians use each day. That way, you’ll know how to navigate the mean streets of music vocabulary.

For example, if you’re sitting in a jam session, and one of your buddies calls out “move to the dominant chord!” you’ll know exactly what to do. If you’ve already studied Latin terms, then you can swiftly move to the fifth chord without missing a beat.

dominant fifth is the fifth chord in a key

Or if somebody shouts “hit the minor submediant!” you’ll simply slide to the sixth with total confidence … knowing that your killer music theory skills just earned you an invite back to the next session. But to truly master these terms, you must know how they apply in all 12 keys. In a previous post, I explained how they work in the key of C. But what about other keys … tlike G, D, A, etc.? To answer that question, here’s a more complete look at how these note names apply to every key in music:

all Latin note names in ColorMusic

Because the Latin terms are like scale degrees, they are consistent in each key. For example, the tonic is always the first note … the supertonic is always the second note … and so on. Seriously, you should commit this information to memory. Because it’s super useful to know. After all, music theory is civilized pursuit. And with a solid understanding of these Latin terms, you’ll know how to communicate with ease – like the high-class gentleman or lady that you are.

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The royal drama of subdominants and dominants

In every musical key, there are special relationships between the notes. And all these relationships evolve around a central – and uber-powerful – tonic note. In the key of C, for example, the C note acts as the tonic … the tonal center of the key that presides over all the other pitches in its kingly domain.

No, really … the tonic note of a key truly is like the lord of the castle. It exerts a strong influence on the other notes, which act as its subservient subjects.

Royal tonic with subdominant, dominant, and tritone in ColorMusic chromatic scale

Taking this analogy a bit further, you can find all sorts of royal intrigue in a key. Some of the tonic king’s courtiers hold more sway than others – while others act as the king’s foes. The tritone, for example, is the tonic’s arch nemesis. It sounds highly dissonant when paired with the tonic … and therefore, rarely gets invited to the king’s parties.

But the tonic’s close relatives – the subdominant and dominant notes – are favored kin. So they are often seen cavorting with the royal king. In the key of C, for example, the subdominant (F) and dominant (G) even share the tonic’s “red blood” … so they sound very consonant when played with the tonic. In fact, you might even say they sound downright beautiful together.

The tonic is closely related to the subdominant and dominant because these notes are all neighbors in the circle of fifths. So the royal C note feels nice and snug when nestled between F and G.

Royal tonic note in ColorMusic circle of fifths and chromatic scale

But when the circle of fifths pattern is rearranged into the chromatic scale, the subdominant (4) and dominant (5) notes are moved to straddle the tonic king’s tritone (#4/b5). And that makes for some fascinating royal intrigue. As a result, all of these tonal friends and enemies in the chromatic scale are forced to be in close quarters … which heightens the musical drama.

But wait – it gets even better!

That’s because every note can have its day in the sun. That is, every note in music can serve as the king of its own key. And because the relationships between notes are symmetrical in each key, the connections between pitches are super rich and intriguing.

To see what I mean, check out this illustration of the chromatic scale – with lines connecting every tonic with its respective subdominants and dominants. The symmetry is astounding. And the multiple layers of tonal relationships are, frankly, mind-blowing.

All subominant and dominant notes in ColorMusic chromatic scale

Ahhh, the ever-compelling story of music theory. The ongoing battles for consonance and dissonance. The shifts in tonal power. The harmonic loyalties, and conflicting betrayals. It’s images like this that give meaning to the phrase, “Oh, what a tangled web we weave.”

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