Wednesday, July 16, 2014

Key Signature Calculation (via MusicTheory.net)

Lesson from MusicTheory.net

Recently I found myself in a situation quite common for me: purposelessly browsing musictheory.net and aimlessly clicking through the site's many lessons and exercises (yes, really). One lesson I came across was called Key Signature Calculation, and it explained a handy method of calculating key signatures with minimal rote memorization required.

I have previously written about key signatures in a post where I shared a visual aid (a variation on the standard Circle of Fifths) that can be used to remember the number of sharps or flats in a particular key. This tool covers 12 major keys, and by extension, 12 minor keys. That's a total of 24 keys, and when you account for enharmonic keys, there are actually 30 possible key signatures.

Instead of struggling to memorize all these key signatures, this calculation method can be used with minimal memorization. All the information that must be memorized to use this method is summarized in the following image, which I lifted from musictheory.net:





The Method

The top row of the image shows the seven notes of a C major scale (C, D, E, F, G, A, B) with their respective key-signature-numbers. The absolute value of the numbers refers to the number of sharps (positive) or flats (negative).

The next few bits of information (bottom row) show three possible calculations you can use to get from a key from the top line to a different key not on the top line:
  • Major key to parallel minor: subtract 3  (C major to c minor: 0-3=-3
  • Key to half step lower: subtract 7 (C major to Cb major: 0-7=-7)
  • Key to half step higher: add 7 (C major to C# major: 0+7=7)
The method is simple: apply the appropriate operation (from the image's bottom row) to a (top-row) numeric value.


Application

Once that information is committed to memory, it is now possible to quickly and easily calculate any key signature. Let's practice:


1. Desired key signature: Eb major

  • E's numeric value is 4, then we subtract 7, yielding -3
  • -3 translates to 3 flats (Bb, Eb, Ab). Voila.
2. Desired key signature: G minor

  • G's numeric value is 1 (1 sharp). To get to its parallel minor, subtract 3, yielding -2.
  • -2 translates to 2 flats (Bb, Eb). Boom.
3. Desired key signature: F# major

  • F's numeric value is -1 (1 flat). To go up a half step, add 7, which yields 6.
  • 6 translates to 6 sharps (F#, C#, G#, D#, A#, E#). Piece of cake.

Final Words

That's about it. Commit those seven key-signature-numbers (from the top row of the image) to memory, then either subtract 3 (to get to the key's parallel minor), add 7 (to go up a half step), or subtract 7 (to go down a half step). The resulting number tells you the number of sharps (positive number) or flats (negative number) in your desired key. If you want more key signature information, check out this circle of fifths visual I made.

Monday, March 24, 2014

Modes of thinking of modes

 The basics of modes


In music theory, a scale is a pitch collection comprised of 7 different pitches, where each pitch is either a whole step or half step away from the next. Typically, there are 5 whole steps and 2 half steps. A good starting point to understand scales and modes is the major scale, which I explained in an earlier post (click to read).

After we understand the interval make-up of the major scale, we can continue onward and look at different modes of the major scale.

I will be using solfeggio names to address certain scale degrees of the major scale:
  1. Do
  2. Re
  3. Mi
  4. Fa
  5. Sol
  6. La
  7. Ti
  8. Do (octave higher)
*Note that the half steps occur between scale degrees 3-4 (mi-fa) and 7-8 (ti-do).

Now let's get into the modes. There are seven different modes, corresponding to the seven different pitches found in a major scale (listed above). The major scale is also known as the Ionian mode (achieved by playing a scale beginning on the first scale degree, do). And by starting on different scale degrees, we get the rest of the modes, each with their own unique sound. Here are their names:
  1. Ionian (major scale)
  2. Dorian
  3. Phrygian
  4. Lydian
  5. Mixolydian
  6. Aeolian (natural minor scale)
  7. Locrian
And that is how they are typically arranged, in order of the major scale's pitches, 1-7. But there's another nifty way of organizing the modes, and it's an idea I first heard about in a master class by Gary Burton.

Another way: Bright to dark

 

The arrangement of modes that Burton explained is one which orders the modes based on each of their unique aural qualities. Scales/modes can be described as sounding happy or bright (major scale), or as sad or dark (minor scale). The brightest mode is Lydian, and by continuing through the modes via a cycle of descending fourths, the modes get darker and darker, finally reaching Locrian—the darkest of modes.

If that didn't make sense (did it?), perhaps this table will make things clearer...

Modes, arranged from 'bright' to 'dark'

Mode
Sol-feg syllable of first note
Alterations to the major scale
Chords
Lydian
fa
#4
Cmaj7(#11)
Ionian (Major scale)
do
[unaltered]
Cmaj7, C6
Mixolydian
sol
b7
C7
Dorian
re
b3, b7
C-, C-6
Aeolian (Natural minor scale)
la
b3, b6, b7
C-7
Phrygian
mi
b2, b3, b6, b7
Csus4(b9)
Locrian
ti
b2, b3, b5, b6, b7
C-7(b5)

The first column gives you the order of the modes from brightest to darkest, and the second column gives you the corresponding sol-feg syllable of that mode.

The third column shows how each mode is related back to a major scale. For example, to turn a C major scale (Ionian mode) into a C Dorian scale, you lower the third and the seventh scale degree (Eb and Bb).

In the fourth column I listed one or two chords which correspond to the modes. In other words, if someone were playing a C7 chord on the piano, you would find that if you played Mixolydian scale along with that chord, it would sound pleasing to the ear.

Why?

 

What's the point of arranging the modes in different ways like this? Valid question.

The first arrangement of modes I listed above (Ionian, Dorian, Phrygian...) is very helpful in showing how each mode relates to the Ionian mode (major scale). Once you realize each mode is comprised of the same notes as the other (one just starts on a different scale degree than the other), you may very well let out a big sigh of relief. And this has important applications to the world of music improvisation, too (it's much easier to improvise when you know which modes to use and when).

The second (newer for me) arrangement (bright to dark) is, I think, just inherently interesting. It makes you more aware of each mode's unique sound quality. If you hear a bright/happy song, familiarity with the modes' aural quality can help you identify which mode the song is in (Lydian or Ionian). But if you hear a darker-sounding piece of music, you'll consider perhaps the Dorian or Aeolian modes.

Of course there is no one correct way to conceptualize the modes, but I reckon that familiarity with as many ways of thinking about them will prove to be beneficial regardless. Do you have another way you think of scales/modes? Tell me about it in a comment below!


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