CHAPTER 5:
  How Keys and Modes REALLY Work
  _______________________________
  
  5.2 The Modes: Scales of the
  Diatonic Order

 
PAGE INDEX
  

5.2.1 The Diatonic Order: A Distinctive Pattern of Tones and Semitones

5.2.2 Flavours of the Diatonic Order

5.2.3 Church a la Mode

5.2.4 Some Popular Songs with Church Mode Melodies

5.2.5 More Scales Than a Catfish (2,047 to be Exact)

5.2.6 Why the Church Modes Didn’t Make the Big Time

~ • ~ • ~ • ~

5.2.1

THE DIATONIC ORDER: A DISTINCTIVE PATTERN OF TONES AND SEMITONES

Chapter 4 discussed how the major diatonic scale with which Westerners are so familiar developed from the application of simple ratios of frequencies.

     Historically, this scale did not emerge quickly or easily. The “do-re-mi” major scale pattern of five tones and two semitones took centuries of tinkering. Recall from Chapter 4 the order of tones and semitones for the major scale—the white keys on the piano beginning and ending with C:

● tone ● tone ● semitone ● tone ● tone ● tone ● semitone ●

     Two whole tones, then a semitone, then three whole tones, then another semitone: this pattern of tones and semitones is called the diatonic order.

5.2.2
FLAVOURS OF THE DIATONIC ORDER

Now, suppose that, instead of playing

C – D – E – F – G – A – B – C,

you were to start on a different white key of the piano, such as D, like this:

D – E – F – G – A – B – C – D.

The pattern of tones and semitones shifts to:

● tone ● semitone ● tone ● tone ● tone ● semitone ● tone ●

Is this still the so-called “diatonic order”?

     Yes it is. You still have five tones and two semitones. They're still spaced the same way.

     But when you play this scale, it no longer sounds like the familiar “do-re mi” scale. It sounds a little weird, a little strange. By starting on a different note—D—you change the order of the frequency ratios of several of the notes of the scale with respect to the tonal centre.

     It's a different staircase.

     Recall the pattern of curved arrows near the end of Chapter 4, representing the dynamic relationships among the tones that make up the “do-re-mi” major scale. That pattern of curved arrows does not apply to this new scale.

     Suppose you were to play all the white keys starting with E, like this:

E – F – G – A – B – C – D – E.

Now the pattern has shifts to:

● semitone ● tone ● tone ● tone ● semitone ● tone ● tone ●

     Again, it's the diatonic order: five tones and two semitones, all spaced the same way. But again, with a different tonal centre, this scale sounds different from both the C-based scale and the D-based scale. The E-based scale sounds Spanish. Or maybe Middle Eastern.

     You can keep doing this, playing a different scale on the white keys only, starting on a different key each time—a different tonal centre each time.

     Next comes this one:

F – G – A – B – C – D – E – F

Then:

G – A – B – C – D – E – F – G

Then:

A – B – C – D – E – F – G – A

And finally:

B – C – D – E – F – G – A – B

     At this point, you've run out of scale possibilities—the next one would be a repetition of the C-based scale, the one you started with.

     So ... seven variants of the diatonic order, each starting on a different white key of the piano. What's the musical significance?

5.2.3

CHURCH A LA MODE

When the diatonic order was being sorted out several centuries ago, composers and musicians were working with many scales. But it took quite a while to settle on one or two favourites, for reasons ultimately having to do with simple frequency ratios, harmony, and something called tonality (coming up later in this chapter).

     In medieval times, there were eight modes called the Church modes or Gregorian modes. As the diatonic order gradually became more entrenched, seven “modern” modes were recognized—the seven variants of the diatonic order you just played on the keyboard, each beginning on a different white key.

     The seven modes have names. The scale you get when you play the white keys on the piano starting and ending with C is called the Ionian mode. The modern name for the Ionian mode is simply the major scale—your basic familiar “do-re-mi” scale.

     The scale you get when you play the white keys on the piano starting and ending with D is called the Dorian mode. And so on.

     You can play any of these modal scales anywhere on your guitar or piano (i. e., starting on any note), as long as you preserve the interval order for the mode.

     Figure 31 below shows all seven modes and the interval orders for each. These modes will be referred to henceforth as the “Church modes” (which will no doubt irritate some history-of-music-theory purists). Note that in Figure 31

                                           T = Tone

                                           S = Semitone

FIGURE 31  The Seven Church Modes (7 Intervals, 8 Notes), Each a Different “Cut” of the Diatonic Order

Ionian Mode (now known as the major scale)

Dorian Mode

Phrygian Mode

Lydian Mode

Mixolydian Mode

Aeolian Mode (now known as the natural minor scale)

Locrian Mode

5.2.4

SOME POPULAR SONGS WITH CHURCH MODE MELODIES

Of the seven Church modes, two are no longer thought of as such—the Ionian and Aeolian modes—because the great majority of the music of the West uses these two scales, now called the major and minor, respectively.

     As for the other Church modes, they faded into disuse roughly around the Shakespearean era, some 400 years ago. Today, you can hear some of the Church modes in some genres, such as heavy metal, some British and Celtic folk music, and some so-called “art” music.

     Chapter 6 discusses the inherent properties of the Church modes that make it difficult for musicians to use them to create palatable chord progressions. Chapter 9 discusses how you can use Church mode scales to create compelling melodies, while using chord progressions derived from the two modes now referred to as the major and minor scales.

     The Church modes have occasionally found their way into popular songwriting. Here are a few examples of tunes that use Church modes as scales (some recordings of these songs may be in keys other than the original modal key):

Dorian mode (D to D, white piano keys only)

     •   “The End” (The Doors)

     •   “What Shall We Do With A Drunken Sailor” (traditional)

     •   “Scarborough Fair” (folk song popularized by Simon and Garfunkel)

     •   “Smoke On The Water” (Deep Purple)

     •   “The Way I Feel” (Gordon Lightfoot)

     •   “Green Onions” (Booker T & the MG's)

     •   “Oye Como Va", "Evil Ways", and numerous others as performed by Carlos Santana ("King of the Dorian Mode")

Phrygian mode (E to E, white piano keys only)

     •   “White Rabbit” (Jefferson Airplane)

Lydian mode (F to F, white piano keys only)

     •   “The Simpsons” theme

Mixolydian mode (G to G, white piano keys only)

     •   “Norwegian Wood” (The Beatles)

     •   "Satisfaction" (Rolling Stones)

     •   “The Wreck of the Edmund Fitzgerald" (Gordon Lightfoot)

     •   “Sweet Home Alabama” (Lynyrd Skynyrd)

     If you're unfamiliar with some of these songs, go to the Gold Standard Song List. The website www.GoldStandardSongList.com has details on how to get the lyrics and how to listen to excerpts.

Locrian mode (B to B, white piano keys only)

     •   The Locrian is a theoretical mode, too unsettled-sounding for practical melodic use. It differs from all of the other modes in that its fifth degree is not a perfect fifth interval (which usually imparts some cohesion to a scale). It's a diminished fifth—the dreaded tritone.
  
 

5.2.5
MORE SCALES THAN A CATFISH (2,047 TO BE EXACT)

In theory, how many different scales could there be?

     More than you'll find on the skin of your average catfish.

     Why so many?

     Because scales are combinatorial. You start with a finite number of items (all the notes of a chromatic scale), plus some rules about picking and combining the items (the notes you choose from the chromatic scale to make up your own scale). The more notes in your original chromatic scale, the more “sub-scales” you can create.

     Here are some scale construction “rules”:

     •   Start with an equal-interval chromatic scale. It can have any number of notes, up to a maximum of, say, 30 in the octave. (The more notes to the octave, the harder it is for your brain to distinguish adjacent notes.) In the diatonic system, there are only 13 notes in the chromatic octave, including the first and last notes. But other musical systems divide the octave into more than 13 notes. In theory, you could start with a chromatic scale of, say, 30 notes to the octave, instead of 13.

     •   Pick any number of notes from the chromatic scale to create a scale of your own. However, your scale must have a minimum of three notes—the first and last notes of the octave, plus one other note in between. The maximum number of notes would be all the notes in the full chromatic scale.

     •   The scale must be confined to one octave, with no notes repeated except the prime and octave notes at each end.

     Suppose you start with a chromatic scale of only three notes. Call the notes A, B, and A, where the two “A” notes are the notes at each end of the scale. According to the above rules, you could only have one scale, comprised of three notes.

                                     A B A

     Now suppose you start with a chromatic scale of four equally-spaced notes, A, B, C, and A (three equal intervals). According to the rules, you could create two scales comprised of three notes and one scale with four notes:

                                     A B A

                                     A C A

                                     A B C A

     Next, start with a chromatic scale of 5 equally-spaced notes, A, B, C, D, and A. The number of possible scales you could create more than doubles to seven:

                                     A B A       A B C A   A B C D A

                                     A C A      A C D A

                                     A D A      A B D A

     Next, try a chromatic scale of 6 notes, A, B, C, D, E, and A. The number of possible scales more than doubles again, to 15:

          A B A       A E A       A B E A   A D E A         A B C E A

          A C A      A B C A   A C D A   A B C D A     A B D E A

          A D A      A B D A   A C E A   A C D E A     A B C D E A

     And so it goes:

          Chromatic scale of 7 notes      =   31 possible scales

          Chromatic scale of 8 notes      =   63 possible scales

                                                     . . .

          Chromatic scale of 13 notes    =   2,047 possible scales

     As you know, the chromatic scale of 13 notes is the one from which all Western musical scales are drawn. Here's a breakdown of the 2,047 possible scales you can create using the 13-note (12 semitone) Western chromatic scale (Table 22):

TABLE 22  Number of Possible Scales Using a 13-Note, 12-Interval Chromatic Scale

     So ... the familiar 8-note “do-re-mi” major scale is only one of 462 possible 8-note scales you could construct by selecting 8 notes from the 13-note chromatic scale.

     There are 330 possible pentatonic scales. (Recall that the number of notes in a pentatonic scale is not five; it is six, because the octave note occurs twice.)

     Of all the 2,047 possible scales, only a small number lend themselves easily to modulation (key changes) and harmony. Those are the ones you'll find most useful.

     Roedy Black's Guitar and Keyboard Scales Poster, available at www.CompleteChords.com, displays guitar and keyboard fingering diagrams in all keys for five of the most useful, commonly used scales:

     •   Major scale

     •   Minor scale

     •   Major pentatonic scale

     •   Minor pentatonic scale

     •   Blues scale

Now, just for fun . . .

     Q: How many scales could you theoretically create if you started with a chromatic scale of 30 notes to the octave?

     A: Precisely 268,435,455 possible scales. When you die, if there is a hell, and you end up there because you've been bad, they will have a 30-note chromatic scale. You will have to memorize all the possible scales you could create from it. On the other hand, if you've been good and you go to heaven, you will meet Maurice Ravel, who will try to get you interested in learning how to compose heavenly music with the whole tone scale, which you may or may not find appealing, depending on how long eternity lasts.

5.2.6

WHY THE CHURCH MODES DIDN’T MAKE THE BIG TIME

For purposes of creating harmony, the five Church modes that fell into disuse lacked the vigour and dynamism of the scales that stuck around.

     A “successful” scale (as far as your brain is concerned) needs a mixture of two kinds of intervals:

     1.  Easily-processed simple-frequency-ratio intervals. These intervals provide your ear with a sense of tonal recognition, a “home,” a centre of gravity.

A note associated with the next-simplest frequency ratio after the octave, namely, ratio 3:2 (scale degree 5) must be positioned in the middle of the scale. It functions as a stable counterweight to the tonic note.

At scale degree 5, a tune has travelled as far away from “home” as it can get. Now it can only proceed either downwards towards scale degree 1, or upwards towards scale degree 1 (8).

Table 23 shows the first few overtones in the harmonic series—the strongest overtones. You can see that the overtones with frequency ratios associated with the consonant scale degrees, 1 and 5 especially, and also 3, appear most prominently.

Only at the sixth overtone does a dissonance finally make an appearance. More on these phenomena in Chapter 6.

TABLE 23  Fundamental and First 9 Overtones of the “Middle C” Overtone Series

     2.  Highly unstable, unbalanced intervals, especially a “leading tone.” They function as pointers, directly or indirectly, to “home.” In particular, a highly unbalanced interval between scale degrees 7 and 1 (8) is required to propel the tune upwards to that “home on high,” scale degree 1 (8).

Unstable, dissonant intervals give a tune (melody) note-to-note impetus. As previously mentioned, unstable intervals make it possible to create a tune that sounds like it has a "sense of purpose" or "story." A road trip.

     As a musical scale, the chromatic scale fails miserably. It has 12 semitones—all highly unbalanced intervals. Way, way too many to function as a musical scale. To be sure, the chromatic scale also contains all the simple-frequency-ratio intervals. But your brain can't resolve them amid the din and cacophony of 12 dissonant semitones.

     The Church modes don't succeed because:

     •   All of them except the Lydian wimp out at scale degree 7, the all-important leading tone. Instead of a semitone pointing strongly at 1 (8), they have a much-less-dissonant whole tone. Not enough tension and propulsion to establish 1 (8) as the note-of-notes, the alpha dog, the head honcho, the top banana, the big cheese, the great enchilada, the prime kahuna: Elvis, King of Scale Degrees.

If you're a musical mode on the make, and you can't even recognize that the cab driver showing you around Muscle Shoals is Elvis, how can you expect anybody to take you seriously enough to buy your music?

     •   Two of them, the Lydian and Locrian, form a tritone interval with the tonic at scale degree 4. There's no counter-balancing middle tone in these scales.

     More on Church modes and harmony towards the end of Chapter 6.

~ • ~ • ~ • ~

~ • ~ • ~ • ~

 TABLE OF
 CONTENTS

 PART I

 The Big Picture
   Introduction

   1. W-5 of Music
   2. Pop Music
       Industry
  
 PART II
 Essential
 Building Blocks
 of Music
   3. Tones/Overtones
   4. Scales/Intervals
   5. Keys/Modes
 
 PART III
 How to Create
 Emotionally
 Powerful Music
 and Lyrics
   6. Chords/
        Progressions

   7. Pulse/Meter/
        Tempo/Rhythm
   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
        Performance

 PART IV
 Making a
 Living In Music
 12. Business of
        Music
 
 Appendixes

 Notes

 References

 Index
  

   Top

 TABLE OF
 CONTENTS

 PART I

 The Big Picture
   Introduction

   1. W-5 of Music
   2. Pop Music
       Industry
  
 PART II
 Essential
 Building Blocks
 of Music
   3. Tones/Overtones
   4. Scales/Intervals
   5. Keys/Modes
 
 PART III
 How to Create
 Emotionally
 Powerful Music
 and Lyrics
   6. Chords/
        Progressions

   7. Pulse/Meter/
        Tempo/Rhythm
   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
        Performance

 PART IV
 Making a
 Living In Music
 12. Business of
        Music
 
 Appendixes

 Notes

 References

 Index
  

   Top

 TABLE OF
 CONTENTS

 PART I

 The Big Picture
   Introduction

   1. W-5 of Music
   2. Pop Music
       Industry
  
 PART II
 Essential
 Building Blocks
 of Music
   3. Tones/Overtones
   4. Scales/Intervals
   5. Keys/Modes
 
 PART III
 How to Create
 Emotionally
 Powerful Music
 and Lyrics
   6. Chords/
        Progressions

   7. Pulse/Meter/
        Tempo/Rhythm
   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
        Performance

 PART IV
 Making a
 Living In Music
 12. Business of
        Music
 
 Appendixes

 Notes

 References

 Index
  

   Top

 TABLE OF
 CONTENTS

 PART I

 The Big Picture
   Introduction

   1. W-5 of Music
   2. Pop Music
       Industry
  
 PART II
 Essential
 Building Blocks
 of Music
   3. Tones/Overtones
   4. Scales/Intervals
   5. Keys/Modes
 
 PART III
 How to Create
 Emotionally
 Powerful Music
 and Lyrics
   6. Chords/
        Progressions

   7. Pulse/Meter/
        Tempo/Rhythm
   8. Phrase/Form
   9. Melody
 10. Lyrics
 11. Repertoire/
        Performance

 PART IV
 Making a
 Living In Music
 12. Business of
        Music
 
 Appendixes

 Notes

 References

 Index
  

   Top