Monthly Archives: May 2010

How To Write Natural Minor Scales

Musical Modes

In the lesson on major key signatures, I introduced the concept of tonality or key, which is determined by what pitch sounds like the “home base” of any given passage of music. So when we say the tonality of a piece is C, we mean it is in the key of C. But how do we know if it’s C major or C minor? That’s where the term modality comes in. Put another way, tonality refers to the specific pitch (A, A-sharp, G, G-sharp, etc.)  that is the tonal center or key note of the music. Modality refers to the specific scale type. So, while the tonality of a passage might be C, it is the modality that tells us whether it is C major or C minor.

A mode is a distinct arrangement of whole steps and half steps. We’ve already learned the major scale, which is a mode, although we don’t generally refer to it that way. There are several modes in our musical system; we’ll start with the minor mode, and its related minor scales.

The minor scale exists in three forms. The first is the natural minor scale, which is a pattern of whole steps and half steps identical to the pattern of white keys on the piano keyboard beginning on A. The best way to learn the WS-HS pattern of the natural minor scale is to learn that the half steps are from , and .

A Natural Minor Musical Scale

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The Relative Minor Method for Spelling Natural Minor Scales

It’s obvious that the notes for the A natural minor scale are exactly the same as those for the C major scale, but starting on A instead of C. Every major scale has its own corresponding natural minor scale, called the relative minor. A-minor is the relative minor of C major. To find the relative minor of any major scale, simply go to of that major scale.  Spell that major scale beginning on , and the result is a natural minor scale.  In other words, of every major scale is  of a natural minor scale. If you need to spell a certain natural minor scale, say, G-sharp minor, first figure out what major scale G-sharp occurs as . This major scale is the relative major of G-sharp minor.

The easiest way to find the relative major of a minor scale is to go up a minor third (3 half steps) from the given minor scale’s key note. In this case, up a minor third from G-sharp is B. B, then, is the relative major of G-sharp minor. (Note also that G-sharp is of B major.) Now, spell a B major scale, but begin with the G-sharp. The result is a G-sharp natural minor scale:

G Sharp Minor ScaleThis audio example plays a B major scale followed by a G-sharp natural minor scale.

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If you start with a major scale, you can find its relative minor scale by going down a minor third. Below is a summary of the relationship between relative minor and relative major scales. All four points listed are saying essentially the same thing, but from different angles. Use the G-sharp minor example above as a reference. Then, try to figure out other relative major/minor relationships:

  • The relative minor of a major scale begins on of that major scale.
  • The relative minor of a major scale is a minor third below that major scale.
  • The relative major of a minor scale begins on of that minor scale.
  • The relative major of a minor scale is a minor third above that minor scale.

Now that we have this information, we can complete the circle of fifths chart with the relative minor keys.  The key signature for a minor key is the same as the key signature for its relative major as shown on the circle of fifths chart below. The lowercase letters on the inside of the circle are the relative minor keys.  (It is common to indicate minor keys with lowercase letters.)

Circle of Fifths Major and Minor Music Key Signatures

The Parallel Minor Method for Spelling Natural Minor Scales

Some people find it easier to write minor scales by converting a major scale to a minor scale. Here’s how it works: Start with a major scale, then lower , , and by a half step. Major and minor scales that have the same letter name (e.g., C major and C minor) are said to be parallel. That is, C major is the parallel major of C minor; C minor is the parallel minor of C major.

C Minor Musical Scale

If you find this method easier, just be sure that you don’t confuse this method of writing natural minor scales with the relative minor method. Furthermore, there is a common error that students make when first learning how to write minor scales using this method:

  • When lowering scale degrees 3, 6, and 7, you don’t necessarily add a flat symbol. Lowering means doing whatever is necessary to make the scale degrees a half step lower:

B Natural Minor Musical ScaleThe accidentals in parentheses (called “courtesy accidentals”) are not really necessary. I put them there to show you that, in order to create a B natural minor scale from its parallel major, we have to lower , , and . In this case lowering these scale degrees means removing the sharps from the B major scale.

In the next lesson, I’ll introduce the other two forms of the minor scale. It’s important that you thoroughly understand building natural minor scales before moving on.

Download a pdf copy of all of the minor scales.
Download a pdf copy of the circle of fifths chart.

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Minor Scales, Lesson 2

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Learning Musical Intervals: The Finale!

Interval Lessons Table of Contents

I hope you haven’t had enough of intervals, because there’s still more to learn. But take heart, this is our last lesson on visually recognizing and writing musical intervals.

Augmented and Diminished Intervals

When we make a perfect or major interval one half step larger, it becomes an augmented interval; when we make a perfect or a minor interval a half step smaller it becomes a diminished interval. The important thing to remember about augmented and diminished intervals is that the numerical value does not change. In other words, we don’t change the line or the space on which the interval is located; we change only the accidental. When you write an augmented or diminished interval, it’s best to write the notes on the proper line or space first, that is, get the numerical value right first, then add the accidentals needed to make it augmented or diminished.

Perfect Intervals

To make a perfect interval augmented either raise the top note a half step, or lower the bottom note a half step. Below are several examples of melodic and harmonic perfect intervals made into augmented intervals. Notice that, in each case, the accidentals (and consequently, the sound) of the interval change, but the numerical value stays the same:

Perfect Musical Intervals Converted to Augmented

To make a perfect interval diminished either lower the top note a half step, or raise the bottom note a half step:

Perfect Musical Intervals converted to Diminished Musical Intervals

I didn’t include the diminished unison because it exists only in theory, as there is no way to make an interval with no half steps, a half step smaller!

Major and Minor Intervals

The diagram below shows how to make major and minor intervals augmented or diminished:

Major and Minor Musical Intervals converted to Augmented and Diminished

Enharmonics and the Tritone

Do you remember enharmonics? We covered them in this lesson. Enharmonics simply are the same sounding pitch spelled a different way (e.g., E-sharp and F). Also, we saw enharmonic scales (e.g., B major and C-flat major). We frequently encounter enharmonic intervals in music as well: the same sounding interval, spelled two different ways. Below is an example of an augmented 4th and diminished 5th; they sound exactly the same, however, they are spelled differently.

Musical Tritone Interval

We commonly refer to an augmented 4th or a diminished 5th interval as a tritone (TT). It gets its name from the fact that its size is exactly three whole steps, dividing the chromatic scale in half. The tritone has been called the diabolus in musica (“the devil in music”) for a variety of reasons. You can read more about that here. The tritone is one of the most interesting intervals in music because, depending on its context, it exhibits a variety of musical tendencies and implications. I’ll have much more to say about the tritone in future lessons.

Interval Inversion

We’ll conclude our series of lessons on intervals with interval inversion. You may already have figured out interval inversion from this diagram that I presented in the last lesson. Inverting an interval means nothing more than taking the bottom note of an interval and putting it on top by moving it up an octave, or by taking the top note and making it the bottom note by moving it down an octave. When you invert an interval, it becomes a different interval, but the pattern is consistent and easy to learn. Actually, interval inversion is one of the best ways to learn the intervals, especially the 6ths and 7ths. Here’s how the intervals invert:

Inverting Musical IntervalsFrom the diagram above, we can make the following conclusions:

Quality

  • Perfect intervals invert to perfect intervals
  • Major intervals invert to minor intervals
  • Minor intervals invert to major intervals
  • Augmented intervals invert to diminished intervals (not shown)
  • Diminished intervals invert to augmented intervals (not shown)

Numerical Values

The sum of an interval and its inversion is always nine:

  • Unisons invert to octaves (1+8=9)
  • Seconds invert to sevenths (2+7=9)
  • Thirds invert to sixths (3+6=9)
  • Fourths invert to fifths (4+5=9)

Using Inversions to Write 6ths and 7ths

The easiest way to write intervals larger than a fifth is to write that interval’s inversion first, then move the bottom note up an octave. For example, say I asked you to write a major 7th with A-flat as the bottom note. Instead of trying to count 11 half steps up from A-flat, just write its inversion first, (a minor 2nd) down from A-flat, which is a G. Then move the G up an octave:

Musical Inversion Example

Wrapping Up Musical Intervals!

The chart below puts everything we have learned about intervals together. Each row has the interval, its enharmonic equivalent, the number of half steps with a keyboard diagram, its inverstion, and an audio file that plays the interval melodically then harmonically. You can download a pdf version here.

Perfect Unison Musical Interval

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Minor Second Musical Interval

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Major Second Musical Interval

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Minor Third Musical Interval

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Major third musical interval

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Perfect 4th Musical Interval

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Tritone Musical Interval

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Perfect 5th Musical Interval

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Minor 6th Musical Interval

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Major 6th Musical Interval

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Minor 7th Musical Interval

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Major 7th Musical Interval

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Perfect Octave Musical Interval

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Lesson Table of Contents

A Word about Interval Ear Training

I have considered developing online ear training exercises so readers could practice learning the sounds of the intervals. Years ago, I developed an ear training program that my students used at Vanguard University. Since I’m not much of a programmer anymore, and because there are already so many great programs out there, I’ve decided against going that route. However, I will be discussing interval sounds quite a bit, and giving you tips on how to learn them. A program that I highly recommend, and have used for years is Practica Musica (available for Windows and Mac OS). I believe it is the best ear training software on the market, and you can purchase it here:

Practica Musica

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