The Armchair Harmonist

Tchaikovsky and the Triad – Part 6

Posted on May 24, 2016 by The Armchair Harmonist

Yes, believe it or not, we’re still talking about triads. We’re almost done though. Maybe one or two more posts. Triads are the basic building blocks of Western diatonic harmony, so it makes sense that we’d be spending a considerable amount of time on them.

In the last post we discussed how common tones between triads can be used to progress from one unique triad or chord to another. While this is probably the easiest and most logical way to move between triads, there are certainly other ways of doing so. Let’s take a look!

There are several ways we can move from one triad to another. One such way is called parallel motion, or the movement of two tones in the same direction–upwards or downwards:

parallel

One can also move in oblique motion, in which one tone stays the same while the other voice moves upwards or downwards. This is the motion typically used when a common tone is maintained:

oblique

And finally we have contrary motion, where both voices move in opposite directions–one moves up, the other moves down:

contrary

Now, if you think you can move tones willy-nilly using any one of the above motions, think again. Moving tones correctly can be especially difficult when dealing with parallel motion. Tchaikovsky states that moving tones in parallel motion by second or fourth intervals is allowable, just so long as both tones move by the same interval (ignore the third bar in the example because it’s bad–you’ll soon find out why):

parallels

The thing that must be absolutely avoided is moving from a fifth or octave into another fifth or octave using parallel motion:

parallels2

Wait, but why? What’s so wrong with this kind of motion? Well, for one, it just sounds terrible when dealing with sparse four-part harmonic writing. Or if you want the long answer, here’s what Prof. T has to say about parallel fifths and octaves:

remark

Ugh, so many rules, right?? Well, this is just the tip of the iceberg, friends. Don’t get discouraged–let’s keep going!

So, we want to move from one chord to another without using a common tone. Hmm, how should we approach this. Well, I guess we could move all the tones of the chord up or down by a second interval. Would that work?

parallelsecond

Oopsy! Extra credit to anyone who can tell me what’s wrong here! So many things wrong…First of all, we have both an octave AND a fifth moving in parallel motion. For shame! This won’t do at all. So how about this?

contraryprog

Ahh, this is much better. My ears have finally stopped screaming. Now this is what a chord progression is supposed to look like. The best way to avoid those nasty parallel octaves and fifths is just to simply move tones in contrary motion, as you can see above.

Instead of moving the tonic C up by a second interval, you can avoid parallel fifths and octaves while still moving to the same new chord (D minor) by lowering the tonic by the interval of a seventh to the D below. But is this really the best solution? Remember, basses don’t like those big jumps! Very unmelodious, as Tchaikovsky puts it.

So how about this?

contraryprog2

And there we have it: the most correct answer. Isn’t that a beautiful sight to behold? I’m sure it sounds even better! In this example, not only do we avoid those terrible parallels, but we also give the bass a nice and relaxing second interval to sing. See how things change yet still remain essentially the same? Welcome to the wonders of harmony!

One thing to remember when working with four-part harmony is that contrary motion is your best friend. Sure the other motions are useful, but none quite so commonly used as contrary motion–take it from me, it’ll save your life some day!

Important Stuff:

Parallel motion – the movement of two tone upwards or downwards in the same direction.
Oblique motion – one tone moves upward or downward while the second tone stays put.
Contrary motion – the movement of two tones in opposite directions–one moves up, the other moves down.

Tchaikovsky and the Triad – Part 5

Posted on May 21, 2016 by The Armchair Harmonist

How are we doing? Still managing to keep up? Sure you are! This is fun, right? Now things are starting to get interesting. Heck, at the end of this post you’ll have the tools you need to compose an actual piece of music!

So, up to this point in our discussion of triads we’ve learned that a triad shares a common tone with several other unique triads. What this means is that instead of playing various inversions of C major like a gifted toddler at the piano, we can now navigate from C major to G major, or even A minor just by maintaining one or more common tones in the same voice between the two triads! Woohoo!

Let’s look at another one of Prof. T’s examples:

progression

Ok, so here we have an actual example of what a harmonic progression looks like. Doesn’t look all that bad, now does it? What we’re looking at here are various triads we can travel to using common tones with C major:

C major shares its fifth, G, with the tonic of its dominant triad G major. In the above example, the fifth is in the alto voice and the same tone and voice is maintained in the G major triad. The soprano moves down to B, the tenor moves down to D, and bass moves all the way up to G.
C major also shares its fourth, F, with the tonic of its sub-dominant triad F major. In the above example, the octave is in the soprano and the same tone and voice is maintained in the F major triad. The alto moves up to A, the tenor moves up to F, and the bass also moves up to the F an octave below the tenor.
C major also shares its tonic, C, with the third of its relative minor A minor. In the above example, the octave is in the soprano and the same tone and voice is maintained in the A minor triad. The alto moves up to A, the tenor also maintains the same tone and voice, and the bass moves down to A.
C major shares its fifth AND third, E and G, with the tonic and third of its mediant triad E minor. In the above example, fifth is in the alto and the third is in the tenor. Both tones and voices are maintained in the E minor triad. The soprano moves down to B and the bass moves up to E.

Hello? Is anybody out there? If the above verbosity didn’t scare you away then you’re probably getting the knack of this. Let’s keep going!

progexamp

What is this, now? Tchaikovsky has just supplied us with examples of progressions that are good, better, and less good. Take a moment to look at this and try to figure out what’s going on here. I’ll give you a few moments.

(Cue Final Jeopardy! music)

Ok, let’s compare notes.

Our first good progression involves moving from a C major chord to a G major chord (remember, if it has more than three tones it’s a chord not a triad) with the bass note going from C to G (not A, as the typo would lead you to believe). The second example is almost exactly the same, except instead of moving down to G, the C in the bass moves up to G.
Our better progression moves from a C major chord to an A minor chord. Why is it better, you ask? Well, from a voice leading perspective, moving from C major to A minor is a cinch! A minor shares two common tones with C major, requiring the movement of only two voices–in this case, the alto and the bass. But…
The less good–or “lessgood”–progression just verges on being naughty. Can you tell the class why? Well the triad looks fine; two common tones with the G moving up a step to A like the previous example. But the problem lies in the bass–as it so often does. Having the bass tone jump the interval of a sixth is just, well, for lack of a better word: lessgood.

Important Stuff:

Mediant – Whoa where did this come from? The mediant is a shadowy and mysterious triad built upon the third scale degree of any key. In major the mediant is minor, in minor, the mediant is major. Now say that 10 times fast.
Voice leading – I foresee this concept taking up a considerable amount of posts in our future. For now, simply know it as the “direction” voices move in harmony. A key (no pun) thing to remember: voices hate jumping and moving around.

Tchaikovsky and the Triad – Part 4

Posted on May 21, 2016 by The Armchair Harmonist

Since this discussion about triads is pretty hefty, let’s take a moment to recap. We know that triads are comprised of three tones built upon the degrees of a scale. We also know that triads become chords in four-part harmony. We’ve learned how to change the position of triads by switching or inverting intervals. Now what?

Now we delve into one of the most important features of four-part harmony: common tones. Henceforth, the following shall be our golden rule (forgiving, of course, the spelling errors):

triadconnect

Now, we could for all intents-and-purposes write a piece of music using only the various positions of a C major triad, but that’s hardly music in the end. Go ahead, try it. Not that interesting, right? In order for there to be “color” in music, there needs to be some transition from one unique chord to the next–this is where things get wild and crazy. I’m not going to tell you what this process is called just yet. But don’t you worry, we’ll be going through an entire book on the subject when we’re finished with Tchaikovsky.

Anyway, back to common tones. Prof. T, in his infinite wisdom, teaches us that there’s yet another relationship between the triads and that has to do with the tones they share. Yep, that’s right. The C major chord shares tones with not one, not two, but five unique triads! But is it practical to move from a C major triad directly to any one of those triads? Remember the golden rule: the common tone of the following triad must remain in the same voice. Don’t worry, this will eventually become clear. At least I think it will.

Let’s take a look at Tchaikovsky’s self-explanatory chart to help us understand:

commontones

Umm…well, maybe not that self-explanatory..

So what does it all mean? Is this differential calculus all of a sudden? While it would seem like that’s the case, understanding this is actually easier than it looks. Let’s consider it this way:

C Major (keep in mind that Tchaikovsky differentiates minor triads by lower-casing their letters) is made up of the tones C, E, and G. So, if we are in the key of C, the shared triads will be E minor (E, G, B) and G major (G, B, D).
The parallel minor, C minor (lowercase c in the above chart), is the only common tone triad that will add tones outside of the key. In this case, E-flat. But E-flat in no way shares a common tone with C major. It’s difficult to grasp, I know…
This is why in the context of C major, a C minor triad can only correctly move to G major, C major, or A minor triad.
Perhaps the second most important minor triad relationship to C major is A minor (A, C, E), which, like C minor, shares no less than two tones with C major and is known as its relative minor.

The above chart now looks more like a road map of common tones that can be generated from a C major triad. I know we didn’t discuss it all (and neither did Tchaikovsky for that matter), but just gaze longingly at it for a while and let all of the above sink in. I promise it’ll make sense sooner or later.

Important Stuff

Common tone – a tone shared between two unique triads.
Parallel minor/major – A minor triad built upon the same tonic as the major key or visa versa. For example, C minor is the parallel minor of C major.
Relative minor/major – The triad built upon the sixth scale degree of a major key or the third scale degree of a minor key.

Tchaikovsky and the Triad – Part 3

Posted on May 18, 2016 by The Armchair Harmonist

The triad in musical harmony is a huge deal and will probably take a few more posts for us to cover. Hang in there!

Now we’re going to start picking up the pace as we delve into the whimsical wonders of four-part harmony. Fun times. Up until now we’ve only dealt with harmonizing three tones. Unfortunately, limiting ourselves to three doesn’t maximize music’s potential in the realm of harmony, so adding one more tone tends to make things sound more “complete” I guess. Let’s find out.

In four-part harmony, or “four-voiced writing” as Tchaikovsky puts it, we have a separation of tones based on their relationship to the human voice: Bass, Tenor, Alto, and Soprano. Bass is the lowest outer voice, and soprano is the highest outer voice. Tenor is the lowest inner voice, and alto is the highest inner voice. If you’re an opera singer or familiar with operatic music, you know that there are several more vocal range categories, but for our purposes we’ll just be dealing with these four.

If there are four tones how can they still be considered triads? Well, they’re not–they’re considered chords. The triad exists though, usually in the three voices above the bass. The chord can also be transformed into various positions, which we’ll go into here shortly.

It’s important to note that in basic four-part writing, one of the tones will be repeated in a higher or lower register (e.g. the bass is the tonic and the soprano is the octave), so you will still only have three distinct tones sounding together. It’s also important in basic harmony to ensure that the inner voices (alto and tenor) are as close as possible to the upper voice (soprano). Take a look at this:

fourpart

This is a complete C major chord with C in the bass and also in the soprano.
This is an inverted C major chord with C in the bass and in the alto.
This is another inversion of the C major chord with C in the bass and in the tenor voice (examples like these probably confuse the whole human voice analogy, but oh well).

As you can see, C is the constant root tone in each example and it is repeated, or doubled, in either the soprano, alto, or tenor depending on the triad’s position. Is this always the case, though? “By no means!” Tchaikovsky answers. Doubling the fifth or third can be done, but only by clever armchair harmonists. We’re far from clever at this point.

Uh oh, things are starting to look altogether…different. Ooh, scary! But never fear, I’m sure Prof. T will guide us through.

Important Stuff:

Four-part harmony – four tones (soprano, alto, tenor, and bass) sounding simultaneously.
Soprano – The highest outer voice or tone in a four-part chord.
Alto – The highest inner voice or tone in a four-part chord.
Tenor – The lowest inner voice or tone in a four-part chord.
Bass – The lowest outer voice or tone in a four-part chord.
Chord – two or more tones sounding simultaneously. Unlike triads, chords are not limited to three tones.
Position – the state of a given chord, which can fluctuate while still being the same chord.
Doubling – The repetition of two tones (usually the tonic) in order to complete a four-part chord.

Tchaikovsky and the Triad – Part 2

Posted on May 18, 2016 by The Armchair Harmonist

Next up in our discussion of Tchaikovsky’s text has to do with triads that are built using major scales. We’ll keep things simple and use the C major scale for our examples. Take a look at this lovely snippet and commit it to memory:

majortriads

What we have here are triads built upon each scale degree of the C major scale. So what? Looks pretty basic to me. There aren’t even any sharps or flats! What does this mean and how does this affect me?

Well, Tchaikovsky gets a bit convoluted here so I’ll try to explain as best (and as correctly) as I can. Let’s first take a look at the two pure intervals. Do you remember what those are? That’s right, the fourth and fifth (4 and 5 on the snippet). These triads form what is known as the sub-dominant and dominant respectively. Don’t worry if these terms seem foreign to you (in the world of music, at least)–we’ll learn more about them–much, much more…

145

What is interesting about triads built upon the fourth and fifth scale degree is the fact that they also act as tonic major triads for their respective keys. I know that sounds a bit confusing, but I can’t really simplify the concept further. For example, the fourth and fifth degree of the C major scale is F and G. The triads they form are complete major triads: the F major triad and the G major triad. This is why these triads and the tonic triad tend to be the strongest forces in tonal harmony. Ever heard of the “Circle of Fifths”? Sure you have. We’ll get more into that when we talk about chord progressions.

Can other scale degrees also act as major triads for their respective keys? No. Why not? Let’s keep reading.

236

Tchaikovsky goes on to explain that triads built upon the second, third, and sixth scale degree are minor triads and are harmonically weaker than the major triads discussed above (the tonic, sub-dominant, and dominant). Looking at the C major scale again, the second scale degree is a D minor triad, the third is E minor, and the sixth is A minor. Triads built on these scale degrees still serve a very important purpose in harmony, though not as important as their “pure” counterparts. Elitists…

So what is their purpose? Prof. T tells us that “they furnish us with a beautiful contrast to [major triads], emphasizing their strength!” So, in other words, these triads can serve as a kind of supporting harmony to the major triads along the scale. Phew…I guess this is all starting to come together.

To conclude this post, I’d like to let our dear mentor speak for himself on the relationships between minor and major triads along a major scale–and even give us a hint about what’s to come:

minormajor

Important Stuff:

Dominant – the triad built upon the fifth scale degree. This is always a major triad and the strongest harmonic relative to the tonic.
Sub-dominant – the triad built upon the fourth scale degree. This is also always a major triad and is the strongest harmonic relative to the dominant.

Tchaikovsky and the Triad – Part 1

Posted on May 17, 2016 by The Armchair Harmonist

Ok, if you’ve managed to get through intervals, now we’re ready to move on to the main part of Tchaikovsky’s text, headed thusly:

harmony

So here we have a definition of harmony: Combining multiple tones in two different ways, either separately (melody) or together (harmony). Stir these together with a dash of rhythm and you’ll have one tasty musical concoction. That said, Tchaikovsky doesn’t give a flying flip about melody and rhythm in this text (though he is arguably the world’s greatest master of both), and neither do we at this point. All we’re concerned with now (and maybe forever) is sweet, sweet harmony. Let’s see where Prof. T takes us.

Since we aren’t going to talk about melody or rhythm in this text, it’s safe to assume that we’ll be learning how to properly combine tones together. The combination of three distinct tones is called a triad. And no, not like the criminal organization. Though I’ll admit that the name is pretty badass.

The basic structure of a triad always includes three tones with the following intervals played simultaneously: the tonic (“fundamental tone”), a major or minor third, and a perfect (pure), augmented, or diminished fifth.
triads

Oh hello there! Isn’t this a darling little snippet. Why, these are triads! What do those letters above them mean? Nothing really–the just correspond to something Tchaikovsky is writing about in the text–allow me to paraphrase:

a) the first triad (with a tonic of C) has intervals of a major third (the note E), and a perfect fifth (the note G). This is a major triad.
b) the second triad (with a tonic of A) has intervals of a minor third (the note C) and a perfect fifth (the note E). This is a minor triad
c) the third triad (with a tonic of B) has intervals of a minor third (the note D) and a diminished fifth (the note F). This is a diminished triad.

What does all this mean?! Don’t fret–we’ll find out next time.

Important Stuff:

Harmony – two or more tones sounding simultaneously.
Melody – two or more tones sounding separately.
Rhythm – the forward motion of melody and harmony.
Triad – The tonic, major or minor third, and perfect, augmented or diminished fifth interval sounding simultaneously.
Major Triad – Tonic, major third, perfect fifth.
Minor Triad – Tonic, minor third, perfect fifth.
Diminished Triad – Tonic, minor third, diminished fifth. Probably the most depressed of the triads.

Intervals According to Tchaikovsky – Part 3

Posted on May 17, 2016 by The Armchair Harmonist

Let’s see now, where were we? Oh yes, intervals. This will be my last post on the topic as discussed in Tchaikovsky’s text–but you can be sure they’ll be discussed more in the future through the lens of other texts we’ll be exploring.

Henceforth we’ll be discussing the inversion of intervals–a concept I’ve always had a difficult time grasping. Let’s see if Tchaikovsky can clarify it any further for us.

So, to parse Prof. T’s tricky language, inverting an interval simply requires moving the upper tone to the octave below OR moving the tonic (“fundamental tone”) to the octave above. There’s a whole series of symbols and fractions that are typically employed in music analysis to identify intervals and their inversions–but we’ll save that discussion for a later post.

Here’s a series of examples from the text–hopefully I’ll be able to elucidate some of it:

inversion

So, what is this all about? My brain is already cluttered with ordinal numbers, I’m not sure if I can go on. But I’ll try.

I guess one key thing to remember when dealing with interval inversions is that every interval inverts into its opposite–e.g. the tonic becomes the octave, major becomes minor, diminished becomes augmented, etc. What about pure intervals? The inversion of these intervals can only result in another pure interval. There are only two so it shouldn’t be that hard to remember. The inversion of the fourth is the fifth, and visa versa.

Now that we have a basic understanding of interval inversion, the question now becomes: how does this change things in the music?

Well, according to Tchaikovsky these inversions can lead to consonance or dissonance. A consonance, for example, is something that sounds complete in itself, kind of like the last chord of a song. A dissonance, on the other hand, sounds harsh or even incomplete–in the world of basic music, dissonances typically resolve into consonances.

These inversions are considered consonances:

Tonics (or “Primes”)
Major or minor thirds
Fifths
Major or minor sixths

One note about the above. Tchaikovsky found it important to separate tonics and fifths into “perfect consonances” and major or minor thirds and sixths into “imperfect consonances.” I guess we’ll find out why at some point in the future.

Here are the inversions that are considered dissonances:

Seconds
Sevenths
All diminished and augmented intervals (not major or minor intervals)

Remember a post or two back I mentioned the leading tone that exists in harmonic minor scales? This tone, which is an augmented seventh, is used to strengthen the scale’s resolution to the octave. Wait, that’s still might be a little too complicated to grasp. Let’s put this discussion on the back-burner. Just as long as you know that dissonances are typically used as a “lead-in” to consonances you’ll be safe. For now…bwahahah!

Important Stuff:

Inversion – Raising the tonic OR lowering the upper tone by one octave in order to invert the existing interval. Think of it as an interval’s “mirror image.”
Consonance – A stable harmonic relationship between two sounds. Think of it as two tones that “sound right” together.
Dissonance – An unstable relationship between tones, often with a very strong inclination to “move” or resolve toward a consonant tone. Think if it as two tones that “sound wrong” together.
Leading Tone – a dissonant tone, such as the augmented seventh in a minor scale, that leads strongly toward a consonant resolution.

Musical Musings: Chopin and Schumann I

Posted on May 17, 2016 by The Armchair Harmonist

The personal and professional relationship between Frederic Chopin and Robert Schumann has always fascinated me. I guess I ended the title with a roman numeral in expectation of this becoming a multi-part discussion. Though it may not.

kreisler

Of major interest to me are the dedications of music they made to each other. Schumann had dedicated arguably his most important work, Kreisleriana, Op. 16, to Chopin in 1834.

In a predictable response due to his cool, and perhaps condescending reception of Schumann as a friend and colleague, Chopin had apparently complemented the design on the sheet music cover and nothing more.

ballade

Chopin returned the favor, however, in 1839 with the publication of his Ballade No. 2 in F Major, Op 38 dedicated to Robert Schumann. Unlike Kreisleriana, Chopin’s second ballade isn’t usually celebrated as one of his best piano works–because it isn’t. Though I will say that some of his best music can be found in the coda.

Anyway, I was playing through Kreisleriana today when I noticed something in the sixth movement:

kreisl1 kreisl2

This rhythmic sequence is employed throughout almost all of Chopin’s second ballade, such as here:

balla2

Methinks Chopin had a far deeper relationship with Schumann’s work than he would have cared to admit. At least this shows that he may have been inspired by a small part of it.

Although to his complement on the cover design for the first edition of Kreisleriana, one can’t really argue with it. It’s a pretty awesome sheet music cover. Look at this design on top:

kreisleriana cover page

That’s a picture of Schumann surrounded by an angel and some sort of Bacchus satyr man. There’s even a monkey sitting in a French horn playing the violin upside down. The letters of the title look like they’re carved out of onyx and float on top of the water. That cover art blows my mind.

Even the movement Roman numeral headings are fun to look at:

Intervals According to Tchaikovsky – Part 2

Posted on May 16, 2016 by The Armchair Harmonist

I ended my last post with a basic overview of what intervals are and how they can be raised and lowered between tones in order to achieve the desired harmonic effect–or just for fun!

Tchaikovsky continues his discussion of intervals by separating them into two groups. The first group includes the second, third, sixth, and seventh intervals. The second group includes only the tonic, fourth and fifth intervals, and the octave. I’m not entirely sure why he separates them into these two groups, but maybe we’ll find out as we read more. Onward!

Below is a lovely chart of intervals with a note by our friend Tchaikovsky:

Tchaichart

Goodness gracious–looks like something you’d feed into an old Fortran machine. But no, this is actually a fairly cut-and-dry chart expressing all possible interval permutations with C as the tonic (“fundamental tone”).

Let’s take a further look at how the Tchaikovsky’s interval “groups” appear on this chart. So, we see that the first group (seconds, thirds, sixths, and sevenths) include all interval permutations except pure intervals. That’s right, these intervals are impure! No, not really in that sense. The second group (tonic, fourths, fifths, and octaves) are pure intervals that can be augmented (raised one half step above a pure or major interval) or diminished (lowered one half step below a pure or minor interval), BUT they cannot be expressed as a major or minor interval…

AHHHHHH!!! Sorry, had to scream a little bit.

moreintervals

Oh, Tchaikovsky! What did you just say? Let me try to figure this out. So in addition to raising or lowering an upper tone in a scale, you can also raise or lower the tonic to create the desired effect? Hmm, something doesn’t seem right about this to me, or maybe I’m missing something. Does that mean there isn’t a root? But if that’s true, what’s keeping the tones from floating away? I guess this is something we’ll have to learn about later…

I also included a snippet on intervals that go beyond the octave just to give you an idea that, yes, these intervals do exist, but we won’t be talking about them just yet.

Important Stuff:

Second – One interval above the tonic. Can be major, minor, augmented, or diminished.
Third – Two intervals above the tonic. Can be major, minor, augmented, or diminished.
Fourth – Three intervals above the tonic. Can be pure, augmented (naughty!), or diminished.
Fifth – Four intervals above the tonic. Can be pure, augmented, or diminished.
Sixth – Five intervals above the tonic. Can be major, minor, augmented, or diminished. (Anyone starting to see patterns here? Or is it just me?).
Seventh – Six intervals above the tonic. Can be major, minor, augmented, or diminished.
Octave – Seven intervals above the tonic. Can be pure, augmented, or diminished.
Pure intervals – Intervals that can’t be expressed as major or minor intervals between tones. Think of these intervals as the unwavering “backbone” diatonic music. Only the fourth and the fifth, are pure (or “perfect”) intervals.
Augmented interval – one half-step (or semi-tone) above a pure or major interval.
Diminished interval – one half-step below a pure or major interval.

Intervals According to Tchaikovsky – Part 1

Posted on May 16, 2016 by The Armchair Harmonist

I’ll spare you the biographical details, though I will preface this post with a brief explanation on how Tchaikovsky’s Guide to the Practical Study of Harmony came about. The text of about 137 pages was produced in 1871 by Tchaikovsky following his tenure as Professor of Music Theory at the fledgling Moscow Conservatory. It is said that the text was based on lecture notes written by one of his students at the conservatory. In fact, it reads a heck of a lot like lecture notes now that I think about it.

The text begins with a discussion of the most basic aspects of music theory: intervals.

tchai1

Those of us who have a basic familiarity with music theory understand intervals as merely the spaces between tones on a scale. For example, a C major scale will start with C as the tonic (Tchaikovsky calls it the “prime” or “fundamental tone”). The second interval would be D, the third, E , and so on.

Tchaikovsky goes on to explain that even when intervals following the tonic are raised or lowered, they still go by the same name (second, third, etc.) only the sound of the scale will be fundamentally changed. This is how we get major and minor scales, as well as modes–this is also how we get whole-tone scales, and blues scales, all of which will be discussed with different texts much, much later.

Here’s an example of an E major scale:

From The Virtuoso Pianist by Charles-Louis Hanon

This scale differs from the C major scale used in Tchaikovsky’s example in that the location of major intervals are in different locations. A major interval is represents a space of two half tones (or a whole tone). A minor interval represents a space of only one half tone. In the case of this scale, the second, third, sixth, and seventh intervals (F, G, C, and D) are major intervals, creating a scale that, when beginning on E, sounds like the E major scale we all know and love.

What if we don’t raise those four tones while still using E as the tonic, you ask? Well, then we get into the murky waters of church modes which we won’t discuss here just yet.

Now, what about another scale–let’s say, D minor–a favorite key of one of Tchaikovsky’s favorite students, Sergei Rachmaninoff. What does this scale look like? Oh here!

From The Virtuoso Pianist by Charles-Louis Hanon

Instead of having sharps in the key signature, this key has one flat. So whenever you see flats in the key signature you know that the scale will rely on one minor interval to achieve it’s uniquely desperate sound. In the case of D minor, the sixth interval, B, lowered by one half step thereby creating two minor intervals: E to F and A to B-flat.

But wait, isn’t there also an raised C in the D minor scale shown above? Wow, that’s perceptive! Yes, the augmented seventh interval is used in harmonic minor scales. Why? Well, we’ll get into that later. But I will say that it has to do with what is known as the elusive and mysterious (not really) leading tone. If we’re lucky, maybe we’ll even get into a discussion of melodic minor scales. No promises though.

Important Stuff:

Scale – A series of tones separated by intervals.
Tonic – the root, prime, fundamental tone, the first note of a scale–whatever you want to call it.
Major intervals – One whole step between tones (or two half steps–however you want to think about it).
Minor intervals – One half step between tones.