Domain Rules: four subversive piano lessons
, unchecked, not tested
Copyright 2004, 2005 by Brian Fraser
P.O.Box 427
Scottsdale, Arizona 85252
January 19 interim edition 2005 d


Good problem solvers like to keep things simple. They do this in part by learning the "domain rules" for each problem. If you want to fly a plane, you learn the domain rules for piloting planes. If all you have is a gold plated roller skate, then you learn the domain rules for piloting a roller skate. The concept of piloting remains the same. Only the domain rules change.

Use of domain rules can turn complex problems into simple ones because they tend to pack a lot of practical utility into a very compact package.

Rather than trying to illustrate this concept by solving some arcane mathematical or scientific problem, I have chosen something many people want to do at some point in their life: learn how to play the piano. For most people, this is very difficult, but I am trying to teach it here in four lessons, after which you should become "self-propelled" and will be able to teach yourself the rest (well, maybe with a little coaching). The lesson here is written for people who want to PLAY the piano without having to learn all the clutter that usually comes with formal piano lessons.

These four lessons will definitely not make you an expert, but if you learn what is presented here you will be amazed at what you can play, and will probably be motivated to learn a lot more.

Try to spot some of the domain rules used below:

1. Humans like simplicity.
2. Simplicity reproduces and propagates well.
3. Recognition of patterns can make complex things simple.
4. Humans like to have fun.
5. Learning a skill feels good, and tends to drive itself to completion.
6. A good plan now can be more useful than a perfect plan later.
7. A skill that is practiced is not easily forgotten.


Your first piano lesson:

Here is your first piano lesson. Go to a piano and press down a key. There, you have played the piano!

That was easy, wasn't it? If I asked you to do that on a clarinet or a saxophone or guitar, you would have much more difficulty playing that same note. And when different people play the same note on the same instrument, the sound might be different too. But not so on the piano. It gives the same sound every time, regardless of who presses the key. It also has a much broader range of tones than say a cello, trumpet, or flute ( the piano is practically an orchestra at your finger tips). And there is no problem hitting the high notes or the low notes on a piano. One key is just as easy to press as any other key.

Playing the piano is easy! Most people give up on the piano, not because they cannot play the instrument, but because they cannot read the music. But the need for reading music can be kept to a minimum if you are playing "popular" music.

Your second piano lesson:

You need to know how to read the 5 lines of the treble clef staff and (maybe) the five lines of the bass clef staff. The bottom line of the treble clef staff is Middle E. The traditional acrostic used to remember them is Every Good Boy Does Fine Always Cee (I have embellished that a little bit). This was obviously invented by female teachers for their male students, who, no doubt did not like the "girl method" of learning the piano. J  The spaces between the lines denote notes too, and are remembered with the acrostic FACE. Have someone show you this on a piano with a piece of sheet music. You need to be able to match up the lines to the keys.

Treble clef staff and notes:

treble_scale.gif (4266 bytes)

Bass clef staff and notes:

bass_notes2.gif (4270 bytes)

How some treble clef staff notes correspond to piano keys:

treblestaff2keyboard.gif (8675 bytes)

one C octave of piano keys

The bass clef staff, another set of 5 lines below the treble clef staff, is similar, but the acrostic shifts downward by one line. The bottom line is therefore G. Just remember where the E begins in both cases, and it will be Easy to remember. Find the two Es on the keyboard that correspond with the bottom Es on the treble and bass clefs. Touch and remember! Find middle C too.

The treble clef notes are played by the right hand, and those in the bass clef by the left hand. These clefs denote piano keys that are in the middle third or so of the piano keyboard, where most of the playing is done.

The space between the two clefs is occupied by an undrawn line which (line) represents a single note: Middle C. You may see other notes in this "middle C-space"; you can think of them as overlapping extensions of the treble and bass clefs. They depict which notes are played by the right hand, and which by the left. (Sometimes the hands cross over into each other's usual territory)

So now in principle, you know how to read notes on a sheet of music ( ABCDEFG on the treble and bass clefs). In highschool band, students master this one during the first week. It is EASY, but of course requires practice.

(For more on music notation see: )

Your Third Piano lesson:

The third lesson is about how to construct scales, and how to use scales to construct chords.

First, some definitions:

1. The physical keys on a piano are separated by a "half-step". It does not matter whether the key is black or white, only that they are immediately adjacent to each other. (The tonal difference of a half-step is the same (as a percentage) for all keys, black or white, on the piano. The raised black keys simply shorten the physical length of the keyboard. If the black keys were the same width as white keys, you would need BIG hands to play the pianoand an office chair with wheels so you could scoot back and forth as you play.)

2. A "whole-step" is comprised of two half-steps.

3. A "tetrachord" is comprised of four physical keys that are separated by a whole-step, whole-step, and half-step.

4. A major scale is comprised of two tetrachords that are linked by a whole-step.

Example: Construct the C major scale from two tetrachords:

a. Place your right thumb on middle C. This will be the "root key" for this scale.

b. Note which key is one whole-step to the right of the key your thumb is on. Press it with your first finger. (It is D)

c. Note which key is one whole-step to the right of the key your first finger is on. Press it with your middle finger (It is E)

d. Note which key is one half-step to the right of the key your middle finger is on. Press it with your ring finger. (It is F)

You have just constructed one tetrachord, which is one half of a scale. Play the keys in sequence and let your ear learn the "color" or "flavor" of this sequence. Next construct the remaining tetrachord.

e. Note which key is one whole step away from the one your ring finger is on. Lift up your hand and put your thumb on it (It is G).

f. Note which key is one whole-step to the right of the key your thumb is on. Press it with your first finger. (It is A)

g. Note which key is one whole-step to the right of the key your first finger is on. Press it with your middle finger (It is B)

h. Note which key is one half-step to the right of the key your middle finger is on. Press it with your ring finger. (It is C)

These two tetrachords comprise the C major scale. Note that in this case it just happens that they are ALL WHITE KEYS. If you forget how to construct a scale from tetrachords, you can go to a piano and just re-derive the tetrachord rules for scales by using the ALL WHITE KEYS of the C major scale. Let the piano do your remembering!

All twelve scales are constructed by using the very same rules. So once you know how to construct the C major scale, you know, in principle, all twelve scales. Try it! Just put your thumb on a different starting (root) key. This time you will get some black keys somewhere in the tetrachords. Remember the "color" (sound) of that sequence. You will get so you can recognize it by ear.

The scales are not useful for much by themselves. In piano music you play chords, not scales. But chords are constructed from rules that are based on scales. Professionals use a number system to make creating chords from scales easy. The first key in a scale is given the number 1, the second is 2, and so forth up to 8. A half-step DOWN from a particular key is denoted by prefixing a minus sign in front of the number (like -3) and denotes a "flat". A half-step UP is denoted by prefixing the number with a plus sign (like +5) and denotes a "sharp". Most people think of sharps and flats as the black keys. But be forewarned:  in some cases they can be white keys too.

There are all sorts of chords. The basic chord is a triad (three keys). The C triad is C,E, G and is denoted professionally as 1,3,5 in the C major scale. All triads in all other major scales follow the same rules. So a G triad is 1,3,5 using the G major scale. An F triad is 1,3,5 using the F major scale. And so forth. If you learn one chord in the C major scale, you have, in principle, learned all twelve such chords. And again, if you forget the rules, you can use the C major scale to re-derive the rules on the spot.

5. Chords are constructed from the major scales as follows:

Chord name Numeric notation Example in C Example in F
triad 1,3,5 C,E,G F,A,C
minor 1,-3,5 C,Eb,G F,Ab,C
sus[pended]  (sus4)


1,4,5 (usually followed by a major triad or dominant 7th. Could also be a 1,2,5 C,F,G




augmented (or +) 1,3,+5 C,E,G#    
6th 1,3,6 (compare with minor) or 3,5,6,8 C,E,A  
major 7th 1,3,5,7 C,E,G,B  
dominant7th 1,3,5,-7 C,E,G,Bb  
dim[inished] 1,-3,-5,6 C,Eb,Gb,A  
half-diminished 7th 1,-3,-5,-7 C,Eb,Gb,Bb  
major diminished 7th 1,-3,-5,7 C,Eb,Gb,B  
octave 1,8 C,C  
dominant ninth 3,-7,9 (the 9th is usually a melody note; if so, don't play root (1) in right hand) E,Bb,D  
tenth 1,10 (a long reach) C,E (more than an octave)  
13th L: 1,-7; R: 3,6,8 (the 13th is thought of as a 7th plus a 6th; hence the name) L: C,Bb     R: E,A,C

(note the inversion in the right hand)

11th L: 1,-7; R: 4,-7,8 L: C,Bb    R: F,Bb,C L: F,Eb   R: A,Eb,G,Bb
augmented 11th (?) L: 1,-7; R: 3,-7,9,+4 L: C,Bb   R: E,Bb,D,F# L: F,Eb   R: A,Eb,G,B
six-nine L: 1,5,6; R: 3,6,9 (no 7th in right hand)    
add nine L: 1,5,(8) R: 2,3,5,8 or 3,5,9; if 9th is melody note, do not play root (1 or 8) in right had. A root note within a whole step of a 9th obscures melody note.    
b lower the following note a half-step    
# raise the following note a half-step    
add2, add9 add the note specified    
no 3rd eliminate the third    

Learn these in the C major scale and you will then know, in principle, 192 chords! (12 scales x16 chords). That is not bad for the first week! Of course you won't be proficient in them. But if I asked you to play C sharp diminished (or some other unfamiliar chord ), you could figure it out with nothing more than a piano and what you know at this point. (In fact you could play C diminished and then just move all notes up a half-step and you will have C sharp diminished! See diminished chords below.)

Each piece of music is usually based on just a few chords, (say C, F, and G chords for most jazz). So it is really not as complicated as it looks. But plenty of patience and practice are required in order to play well.

You can also invert chords. The first inversion has the root on top. In the C scale that would be E, G, C (instead of C,E,G). The second inversion has the root in the middle.  In the C scale that would be  G, C, E. These are just different ways of playing a chord, and give very similar sounds. (The C chord is customarily inverted in the bass and is usually played as G,C,E with the left hand)

If you know chords, your reading of music can be kept to a minimum. All you need is the melody note in the right hand, and then fill in with chords in the right and left hand. You really don't have to know how to read the bass clef. You can play some really beautiful music and still have very little "formal" knowledge about how to play a piano!

You might also check out the "chord finder" utilities on the Internet such as this one:

chordfinder.gif (20507 bytes)
See also:

This particular illustration shows the piano keys that you would press to play a C Minor Major 7th. To get the keys, you make a selection from the Root column first, then from the Chords column, then click the Display button to see the piano keys to play. If you want to see the scale (the keys that make up the two linked tetrachords) click the Scale button instead (for our purposes, we use only the Major scale). See Links below for other chord finders, including ones that you can have with you at the piano.

Incidentally, while all of this is a very good beginning, you will eventually encounter much more complex notation. Some examples:

Cm7-5: This is an ordinary C minor seventh chord with the 5th, G, lowered to G(C,Eb,Gb,Bb)
C7 -9-5 This is B
b,Db,Gb. The Bbis played below middle C (the C would be 10, B would be 9, and -9 is therefore Bb).
CdimMaj7) C,D#,F#,B
Ab 13-9 sus4
b 9+11
G7 -9+5
G7 -9-5

You can find pages and pages of these in various "Chord Study" books or Piano chord charts.

There are also chord finders for the guitar. A reader suggests:

Ultimate Scale Finder
Ultimate Chord Finder
Reference Tuner

Your Fourth Piano lesson:

Think of a song you would really like to play on the piano. Then go buy the piano sheet music for it. Make sure the music is in the "popular" style and has chord notations above the treble clef staff. Chord notation looks like Cm7, Fmaj7, F, Gdim, C6, E11+, and so forth. (Sometimes this kind of music also has notation for the guitar.)

If your very favorite piece is available only in the classical notation, your task will be more complicated. You will have to translate the classical notation into the popular notation. In the treble clef staff, the top note of a vertical stack of notes will be the melody note, so picking out the melody notes should be easy. But for the bass notes, you will have to "analyze the chords" and then annotate the page to include the popular notations. If you are a beginner this will be quite a task, but you can use a "chord finder" (see Links) to make the deciphering go faster. Just type in the bass notes (read the directions first) and then see what the name of the chord is.

Chord analysis can also be done by moving each note in the chord up (or down) a half-step at a time until it becomes something you recognize in a different scale; for beginners, that will usually be a chord in the C, G, or F scales. Here again, you can use the piano to help you figure  things out as you learn, instead of attempting to memorize dozens of chords which you will soon forget.

Probably the best approach is to create a lead sheet from the classical music. A lead sheet is a bare bones skeleton version of the original music. It has only the treble clef staff with single notes for the melody (no chords in the right hand), chord symbols (for the left hand) written above each measure, and lyrics below. Lead sheets for different tunes are often complied into fake books, and so the lead sheet scheme is very common in the world of popular music.  See below for an example of a lead sheet.

After you have the music in popular notation, look through the music and make a list of all the different chords that are used. Usually there are less than a dozen in the entire piece. Then make a list of what keys each chord consists of. If you don't already know them, you can derive them on the spot by using the scheme in item #5 from lesson #3. Then educate your left hand to play each one. Play the root key a couple of octaves down from middle C, then play the chord somewhere near middle C or lower. Play the root, then play the chord. Use only your left hand. Repeat this pattern twice per measure if the piece is 4/4 time.  ( The rhythm for waltz (3/4 time) is different. For each measure, play the root, and then the chord twice. )

Now look at the notes on the treble clef staff.  They should all be single melody notes at this point. But if not, then the music has some chords in the right hand.  The top note will be the melody note.  For now just play the melody note. This way you can "play the tune" but keep things as simple as possible.  Practice this with your right hand until you are comfortable playing it. (Later, when you become more proficient, you can play the right hand just as it is written;  generally, this means you will be playing single chords, instead of single notes.)

Now comes the part that is both hard and fun. You have to get both hands working together. In general the procedure is to play the root in the left hand, along with a single melody note (or set of notes if required by the timing) in the right hand. Then play the chord in the left-hand, and the next melody note(s) in the right hand. You repeat this (root,chord, root, chord for 4/4 time) through the measure and all through the piece.

You are now playing the piano, and should be able to produce some fairly respectable music!  Hopefully you will have fun doing it, and will readily spend time "playing around" and experimenting with it. You can make your fun more purposeful and productive with some good literature on the subject, as well as getting an occasional tip from a more experienced player.  You might even want to learn classical some day!



Here are some measures from Que Sera, Sera, a 1950's hit song sung by Doris Day.  It is written in the "lead sheet" style as mentioned above, except I have added some special notation for some bass notes. Note that this piece is a waltz (3 beats to a measure, with each quarter note counted as one beat).

quesera.gif (6443 bytes)

A partial "lead sheet" for Que Sera, Sera. See text (below) about the special notation. The
lyrics can be found on the internet (e.g.:   )

sera_chords.gif (2028 bytes)

Chords (left hand) for the above music. Read them bottom-to-top.
Example: for C, the left-hand fingering is 5,2,1 for G,C,E. These keys
are near the middle of the keyboard and sometimes overlap with the
melody notes.

Look at the lead sheet illustration above. Note that each measure has a chord for the left-hand written above the measure. The chords are not written explicitly above every measure, but only when the chord changes. This reduces visual clutter.

Lead sheets usually do not say anything about the bass notes. You are supposed to derive them from the chords as you are playing. For example, the bass note for a C chord would be C or E (the root or the 5th). For a piece like this one, with several contiguous C chord measures, you might want to add some variety in the bass by playing, say, the root, or a fifth, or the root as an octave or the root as a tenth. Just experiment a little and see what sounds good.

For this example I have added some special notation to suggest which bass key to play. You will NOT see this kind of notation (keys with numeric subscripts) in any music. A piano with a full keyboard has 88 keys. Its tonal range is from A0 (27.5 Hertz) to C8 (4186 Hertz).  In this scheme, middle C is  denoted as C4.  The piano key board has eight C keys (C1 to C8). The ones you play as a root key for the bass, are at the left end of the keyboard, about two octaves down (leftward) from Middle C. This is the general location of the C2, C#2, D2, and G2 keys.

Follow the usual procedure for learning to play a piece on the piano. First, practice the melody with the right hand. Then practice the chords with the left hand (the waltz rhythm is root, chord, chord,   root, chord chord,   and so on for each measure). Then play the whole thing with both hands.

To play the first actual measure with both hands:

1. Press C2 (left little finger) and G (as shown on the staff) with the right little finger. Continue to hold G down.
2. Play the C triad (G,C,E) with the left hand (note the inversion of the chord). Then release G in the right hand.
3. Play the C triad (G,C,E) again with the left hand, along with E (use the right middle finger). The fingers overlap here.

If this is your very first attempt at playing the piano, playing this portion of Que Sera, Sera will seem like a bit of a struggle at first. But this is an easy piece and  you will catch on quickly. It is just a sample of what you can do with very limited knowledge. If you like what you hear, I hope you will want to learn more. Learn at your own speed, with your own favorite music, and HAVE FUN doing it!

NOTE: I did not know about various existing notation systems when I wrote the special notation.     See reference:  


Fingering for the piano

"Fingering" addresses the issue of what note in a melody should be played with which finger. (For now we will consider only the melody, but the same ideas apply to the bass notes.)

When you first started playing the piano, you probably used the  "hunt and peck" system. You looked at the music, then at the keyboard and went  "plinking" with  your favorite couple of fingers. Playing the piano was basically target practice. But this soon became frustrating and very limiting.  The melody  usually has 3 or 4 and sometimes 5 notes to play at once in the right hand. And the left hand has to play notes too. How could you get all those fingers going and playing all those different keys, one set immediately after another?   You realized that there must be a better way of doing this. We call it "correct fingering".

The first step in learning correct fingering is to learn chords. Teach your eye to recognize chords in the written music, and teach your hand to play the corresponding set of keys on the keyboard. Then when you see the notation "C7", or a cluster of notes that your eye recognizes as C7, then your hand will automatically know what to do.

If you know the C chords, try this experiment. Put your thumb on middle C, close your eyes, and then play in sequence, a C triad, then Cminor, then Cdim, then C7 major, then a C octave.  You should easily be able to do this. Now think about the implications. You had to look at the keyboard once to position your thumb. After that you were able to play five chords without even looking at the keys!  And if you did not get one of the notes right, your hand probably "knew" how to correct the error without you having to look at the keyboard or even think about it very much. Instead of having to look at the keyboard, your eyes could have been looking at the music to see what was ahead.  (If you are in an adventurous mood, repeat this exercise using the F or G chords which you probably know by now)

Of course,  you cannot play an entire melody while keeping  your thumb on middle C. There are lots of other chords, and your hand must move up and down the keyboard. Correct fingering enables you to play the notes with the most ease and economy of motion. It positions your fingers over the keys you are about to play, and also helps get your hand into position to transition to the next set of notes.

Example: try this simple sequence with the "hunt and peck" system:  middle C,  F#, A, and then upper C & E (together). You probably hit each of these keys with your index finger, and the final C&E with your thumb and middle finger. But if you were following written music, you would have to look back and forth from the music to the keyboard each time.

Now try this alternative for the same sequence:  play middle C with your thumb, hit F# with your index finger, then move your thumb underneath your hand to hit A, then hit upper C and E simultaneously with your middle finger and little finger. Practice it a few times. Then do the same thing without looking at the keyboard. You should be able to convince yourself that your hand can walk from one note (or chord) to another, and even keep track of where it is, as well as correct itself when it makes a mistake.

Eventually this skill becomes subconscious and automatic. You won't even need to think about it. You'll  get to the point where you can play an entire melody with your right hand and only occasionally glance down at the actual keys. It is like learning "touch typing" except it is for the piano. (And once you finally learned touch typing,  you probably would not even consider going back to the hunt and peck system)

Classical music sometimes has the fingering written above selected notes, but other kinds of music, like popular, usually omit it altogether. Fingering is denoted by numbers (1 through 5) above the notes. The thumb is 1, the middle finger is 3,  and little finger is 5. This applies to either hand. Usually the numbers appear above just a few notes where the fingering is not obvious. The fingering for the unnumbered notes is supposed to be self-evident for an experienced player.

When you are first learning how to play a piece of music, sit down at the piano and spend some time figuring out how to get your fingers to walk through the progression of notes and chords with the most ease and economy of motion. Then write the fingering onto your sheet of music so that you won't forget it. This will allow you to practice playing a piece of music exactly the same correct way each time, and your subsequent practice sessions will be more productive. Remember that not just any kind of practice will make you a good piano player. It is only perfect practice that will make you perfect.

(For more on the theme of doing things right the first time, and on keeping the gains you have acquired, see the Four Values article.)

Diminished Chords

The following table shows all twelve diminished chords:

Diminished Chords                   Example
Cdim  Ebdim   Gbdim   Adim C, Eb, Gb, A
C#dim  Edim  Gdim  Bbdim C#, E, G, Bb
Ddim  Fdim  Abdim   Bdim D, F, Ab, B

There are really only three diminished chords, despite the appearance of twelve. The twelve are actually inversions of only three. For example, Cdim is C, Eb, Gb, A, and if you invert it once, you get  Eb, Gb, A, C,  but this will probably be designated  Eb diminished. Invert it again and you get Gb, A, C, Eb,  which is Gb diminished, and so forth.

Just memorize the diminished chords in the first column. In fact, you really only need to memorize Cdim. If you know that one chord, you can just move all the notes up a half-step each and get C#dim. Move those notes up another half-step each and you'll get Ddim.  See how simple that was! Instead of memorizing twelve chords, you just memorize one, along with a simple trick used in chord analysis.

The Circle of Fifths:  how the melody moves

Piano music is composed of three independent dimensions:  tone, duration, and loudness. These three characteristics can be used to create an astounding variety of music with every mood and emotion known to the human race (a trait well utilized by the motion picture industry). If you have watched and heard people play classical, popular, jazz, country, Latin, etc. on the very same piano, then you probably share my amazement about what can be done with a mere 88 tones. But does all this variety have anything in common? What makes harmony? What makes a melody? Why is music so pleasant?

I can only give one little piece of insight on this complex subject. It relates to chords. A melody can be viewed as a progression of chord notes played separately, or as a progression of chords themselves. In this section, I will focus on the latter.

Chord progressions are most clearly illustrated with the so-called Circle of Fifths. The Circle is drawn like a clock with 12 positions which represent the 12 major scales. Each scale or chord is denoted by its root key. C is placed at the 12 o'clock position. You can derive the rest of the root notes with the following procedure:
CircleOfFifths.gif (5800 bytes)

1. At the piano, place your thumb on middle C. Then find the 5th in the C scale. It will be G. Then write "G" at the 11 o'clock position.

2. G becomes the next root key. Place your thumb on middle G. Then find the 5th in the G scale. It will be D. Then write "D" at the 10 o'clock position.

3. Keep doing this, proceeding counterclockwise, until all 12 positions are filled. Your diagram should look like the one shown.

The Circle of Fifths also has another interesting property that is useful to know. As you proceed counterclockwise from C, the number of black keys in the scales denoted by the root letter first increases and then decreases as you move around the circle. The C scale (at 12 o'clock) has no black keys, but the A scale (at 9 o'clock) has 3 black keys (sharps), the Gb scale (at 6 o'clock) has 6 black keys, and the Eb scale (at 3 o'clock) has 3 black keys (flats). Hence, you will often see the Circle of Fifths drawn with the number of sharps and flats given alongside the root key. Note that the number of sharps increase going down the left side, and that the number of flats increase going down the right side:


C5SharpFlats.gif (4007 bytes)

Another concept you need to understand is the so-called "key signature." You will find it at the beginning of every piece of music between the clef sign and the time signature. For our purposes it serves two main functions:

1. It tells which notes in the music are to be automatically sharped or flatted.  In the key of Eb, for instance, the notes E, B, and A are automatically flatted unless local notation indicates to do otherwise.

2. It designates a "home base" on the Circle of Fifths for chord progressions:

Some examples of key signatures (the sharps and flats after the clef sign) are shown below:

 KeySignature.gif (9527 bytes)

Chords progress in four basic patterns depending on the type of music:

1. Elementary Classical: In this pattern the chords progress back and forth around home base, never moving more than one letter away from it.  Bach's Minuet in G uses G as its home base. It starts out on G, then progresses back and forth to C, G, D, G, D, G, and D, revisting the home base before going to the next chord. Other elementary classical music may use a slightly different pattern. The progression will either visit home base on each move, or jump across (skip) home base and move  directly to an adjacent chord, before finally returning home.

The Elementary Classical pattern is found in folk songs, children's songs, patriotic songs, hymns, and many of our revered, traditional classics.

2. Classical: The pattern for Classical starts at home base, jumps counterclockwise 1, 2, or more letters, and then progresses back to home. The pattern may repeat, often with variations in the length of the counterclockwise jump.

ClassicalProgression.gif (4815 bytes)

To check your understanding of this concept, draw a similar diagram for Bach's Prelude No. 1 from The Well-Tempered Clavichord in the key of C. The chord progressions are C, Dm7, G7, C, Am, D7, G, Cmaj7. Remember that you only diagram the root key from the chord, regards of whether the chord is minor, major, diminished, seventh, or whatever. Such diagrams also help you see the "pull" of home base.

There are variations on this general pattern. The music might not start out on home base, but goes to home from some initial location on the circle, and then follows the Classical pattern afterwards. Also, the trip back to home might not be direct but may have some "detours" or surprises built into it.

Of course, all sorts of chords can be used. One that shows up very frequently is the dominant seventh. Recall that when you used tetrachords to construct the Cmaj scale, there were no black keys in the scale anywhere. Cmaj7 was C, E, G,and B. However, the C dominant seventh is (from the table) C, E, G, and Bb. Note that the Bb is really not part of the C scale. That is why it is often called a flatted seventh. This note, however, is in the next scale (F) named clockwise on the Circle of Fifths. The same reasoning applies to the other chords as well. A dominant F7 includes an Eb which is actually a member of the Bb scale (the next letter clockwise on the circle). Inclusion of the dominant seventh therefore tends to "pull" the melody clockwise towards home base.

Progressions homeward might not always appear to be clockwise. If this seems to be the case, note whether or not a diminished chord is used. Remember that these chords can be named after any note in them: a Cdim can also be an Ebdim, Gbdim, or an Adim. (See Diminished Chords above.) The same is true of augmented chords. Hence, you may still be able to find a root key that fits either the Elementary Classical or Classical pattern despite the initial appearances

3. Romantic: Romantic chord progressions include the patterns for Elementary Classical and Classical, but include an additional twist:  two home bases are used instead of one.

To illustrate this concept, draw a circle diagram (like that above) for the first two bars of Chopin's Prelude (Op. 28, No. 20). In case you don't have the sheet music handy, the chord progression is Cm, Fm, G7, Cm, Ab, Db, Eb7, Ab.  And again, remember that you only diagram the root note, regardless of whether or not the chord is minor, seventh, diminished, etc.  So Cm diagrams as C, Eb7 diagrams as Eb,  and Ab of course diagrams as Ab.  Refer to the Circle of Fifths, and then draw out all 8 circles showing only the root keys actually used.  You will see clearly that there are two home bases and that each home base (in this particular example) uses the Elementary Classical pattern.

If you were to play the first two bars of the melody of this piece, you would find the sounds to be very similar, almost like an echo or a repetition, but around a different home base.

The distinctive characteristics of the Romantic chord progressions are:

1. The melody around the second home base is either the same or very similar to the melody around the first home base.

2. The second home base is usually clockwise ahead of the first home base. In the example, the first home base is at 12 o'clock and the second is at 4 o'clock.  You will not confuse this with a Classical progression because Classical starts at a home base and jumps backwards (counter clockwise) first and then moves clockwise.

3. A Romantic progression is usually very obvious. For that to be true, the two progressions must be close togethernot more than four bars, and usually only one or two. If this is not the case, the melody is more likely to have been transposed into a different key.

Most popular music does not use Romantic progressions, but may seem to have something like it. Popular music commonly uses the AABA melody pattern; sometimes there is a key signature change going from the first melody A to the second melody A  (e.g.: Tea for Two) and that might sound like a Romantic progression. But it does not meet criteria #2 or #3 and is really a change of key, not a Romantic progression. Likewise, the change from melody A to melody B is not a Romantic progression, because two different melodies are in use, and therefore criteria #1 is not satisfied.

4. Impressionist and Modern:   Both of these patterns have a home base (i.e., a key signature).   Impressionist may follow the Classical pattern, but with a larger jump away from home and a longer progression back to home. The progression might even involve the whole circle. This typically requires many measures of music and long chord progressions, but they are still short enough for you to hear the pattern. 

The Modern progression is more extreme.   The progressions are too long and too wide-ranging for the ear to discern a pattern, but they can probably be seen on a graph.  If you are playing for your own enjoyment at home, you won't have any use for Modern.

For many more details see: How to play the piano despite years of lessons, Ward Cannel and Fred Marx, 1976, pages 138-166,  (ISBN 0-385-14263-3)


A Short List of Musical Terms

( See list)


Essential Dictionary of Music Notation, Tom Gerou, Linda Lusk, 1996 (ISBN 0-88284-730-9)

Pocket Music Dictionary, HAL Leonard Publishing Corporation, 1993 (ISBN 0-7935-1654-4)

How to play the piano despite years of lessons, Ward Cannel and Fred Marx, 1976 (ISBN 0-385-14263-3)


Chord Finders:

Music reference:

Free Piano Lessons  tutorials, quizzes, illustrations, sound

Highly Effective K12 Education

"High Performance in High Poverty Schools: 90/90/90 and Beyond", by Douglas B. Reeves

"They have overcome:   high-poverty, high-performing schools in California" by Lance T. Izumi with K. Gwynne Coburn and Matt  Cox, September, 2002

"Inside the Black Box of High-Performing High-Poverty Schools" (A report from the Prichard Committee for Academic Excellence, Lexington, Kentucky) by Patricia J. Kannapel and Stephen K. Clements With Diana Taylor and Terry Hibpshman,  February 2005  

"No excuses: Lessons from 21 high-performing,. high-poverty schools", Heritage Foundation, Washington, DC,  S. C. Carter, (2000).

"Reaching New Heights with High-Performing, High-Poverty  Schools", Melanie L. Byrd, Esq., Senior Program Associate, February 2006

"Why do Finland's schools get the best results?", April 2010,

Discovery Learning Project (and others)

"The Discovery Learning Project promotes the development and use of discovery or inquiry-based methods in teaching and learning. The University of Texas at Austin has an illustrious history of innovation in this style of teaching and learning. "

"Challenging the myths of modern schooling",
The Underground History of American Education, John Taylor Gatto, 2003,  






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