Consummating a dream sequence incites the orientation of metaphysical apparitions
somnambulistically sauntering weaving the silken lace through an everlasting labyrinth.
Elusively meandering through pages of a mysterious manuscript we ascertain a disquisition
reciting verses of equanimity redeeming the virtue of steadfastness through the apocalypse.
Approximating the rebirth of philosophical thought processes we direct our passions
to an eclectic pallet of coloristic viewpoints electrifying our stimuli to engender coalitions.
Indelible dedication will persevere while the hideous impostors disappear into their ashes
elevating the plausibility of circumstance reiterating the authenticity of interrelationships.
An irreproachable voice resounds acclamations connoting a provocation of enthusiasm
rendering speechlessness and spawning hopefulness as we beseech our bounteous creator.
The rhythm of cosmic dances stimulates the choreograph to depict movements of contour
to ornament the panorama with figures of rapture imprinting an insinuative allusion.
Promenades of pilgrims are progressing modestly as fairies flutter encircling with lyricism
the atmospheric phosphorescence bestowing blessings as a common denominator.
Divulging the common belief that halcyon retribution is our wondrous reward
we appease throngs of bystanders exhilarating perspicacity and personal introspection.
Translucent illustrations assist the perceptivity of reflections as they glimmer toward
the twilight’s amorous nuances undertoning the tranquil environment in recollection.
Silently stalk the shadows as dusk departs the daylight and Venus then appears upward
against the firmament arranging the celestial canvas evoking an imaginative exoticism.
Commemorating the boundless congeniality we entrust humanity to collaborate in unison
blending our aptitudes and uniqueness to design a reality as buoyant as we all envision.
Optimizing our particular tendencies will embolden the trepid and liberate the innovator
as he flourishes his notions alleviating misery and proclaiming the need for celebration.
Instinctive sentiments annunciate the palpability of a new-fangled conclusion
eradicating negativity and ushering in a golden era of refinement and differentiation.

Earlier in my first blog (UNDERSTANDING BASIC HARMONY) I presented all the twelve keys in major and in minor. We will first look at the key of “C” major and “A” minor once again.  In C major the other related keys must as well have the note C within their scale. In A minor the related minor keys must as well have the note “C” within them. Now I will list all the keys and their scales and darken the “C” in all of the related keys.

C   major scale   C-D-E-F-G-A-B-C                 A minor scale    A-B-C-D-E-F-G-A

Db major scale  Db-Eb-F-Gb-Ab-Bb-C-Db    Bb minor scale    Bb-C-Db-Eb-F-Gb-Ab-Bb

D   major scale   D-E-F#-G-A#-B-C#-D          B minor scale    B-C#-D-E-F#-G-A#-B

Eb major scale  Eb-F-G-Ab-Bb-C-D-Eb           C minor scale    C-D-Eb -F-G-Ab-Bb-C

E   major scale   E-F#-G#-A-B-C#-D#-E          C# minor scale  C#-D#-E-F#-G#-A-B

F  major scale    F-G-A-Bb-C-D-E-F                 D minor scale     D-E-F-G-A-Bb-C-E-F

F# major scale   F#-G#-A#-B-C#-D#-E#(f)      D# minor scale   D#-E#(f)-F#-G#-A#-B-C#-D#

G  major scale   G-A-B-C-D-E-F#                     E minor scale     E-F#-G-A-B-C-D-E

Ab major scale  Ab-Bb-C-Db-Eb-F-G-Ab          F minor scale      F-G-Ab-Bb-C-Db-Eb-F

A   major scale   A-B-C#-D-E-F#-G#-A             F# minor scale   F#-G#-A-B-C#-D#-E

Bb major scale  Bb-C-D-Eb-F-G-A-Bb              G minor scale     G-A-Bb-C-D-Eb-F-G

B   major scale B-C#-D#-E-F#-G#-A#-B           G# minor scale    G#-A#-B-C#-D#-E-F#-G#

If we wish to find the related keys to any other key, say “E” we use the same idea and all the keys that have an “E” in their structures are the related keys. This applies as well to C# minor.

E   major scale   E-F#-G#-A-B-C#-D#-E          C# minor scale  C#-D#-E-F#-G#-A-B

F  major scale    F-G-A-Bb-C-D-E-F                 D minor scale     D-E-F-G-A-Bb-C-E-F

F# major scale   F#-G#-A#-B-C#-D#-E#(f)      D# minor scale   D#-E#(f)-F#-G#-A#-B-C#-D#

G  major scale   G-A-B-C-D-E-F#                     E minor scale     E-F#-G-A-B-C-D-E

Ab major scale  Ab-Bb-C-Db-Eb-F-G-Ab         F minor scale     F-G-Ab-Bb-C-Db-Eb-F

A   major scale   A-B-C#-D-E-F#-G#-A             F# minor scale   F#-G#-A-B-C#-D#-E

Bb major scale  Bb-C-D-Eb-F-G-A-Bb              G minor scale     G-A-Bb-C-D-Eb-F-G

B   major scale B-C#-D#-E-F#-G#-A#-B           G# minor scale    G#-A#-B-C#-D#-E-F#-G#

C   major scale   C-D-E-F-G-A-B-C                    A minor scale    A-B-C-D-E-F-G-A

Db major scale  Db-Eb-F-Gb-Ab-Bb-C-Db    Bb minor scale    Bb-C-Db-Eb-F-Gb-Ab-Bb

D   major scale   D-E-F#-G-A#-B-C#-D           B minor scale    B-C#-D-E-F#-G-A#-B

Eb major scale  Eb-F-G-Ab-Bb-C-D-Eb           C minor scale    C-D-Eb -F-G-Ab-Bb-C

The Beatles’ “She’s Leaving Home” is in the key of “E” and utilizes this idea of related keys. We will look at the chord progression E-Bm-F#m-C#m-F#-B. We see the usage of chords from two different related keys. Firstly the B minor comes from the key of “A” then later the F# major comes from B major.  The B minor is chord on the second step of A major. The F# major is on the fifth step in the key of B. Both the key of “A” and the key of “B” have an “E” in the structure and sound harmonious with the original key of ”E”.

At this point I will present various chord progressions using the principle of the “seven related keys.” The next progression, once again in “E” major, comes from “Hey Joe” from Jimi Hendrix. C-G-D-A-E. We can see the C major and G major could come from the key of “C” which has the note “E” on the third step of the scale and D major and A major could come from the key of “D” which has the note E as its second step.

Another example could be in A minor Am-F-Cm-Gm-Bbm-Fm-Ab-Eb-D-G. C minor to G minor can be analyzed (iv-i) in G minor which has a “C” as its fourth step. The same analysis is true for Bb minor to F minor being the movement (iv-i) in F minor with “C” this time on the fifth step of the F minor scale. The next two chords are this movement (vi-iii) in the key of C minor which has of course “C” as its first step. Lastly the movement from D major to G major is from E minor and is the movement (vii-iii) and the note “C” can be found on the as well on the 6th step of the E minor scale.

A final example will show once again the principle in “C” major with the usage of all of the other six related keys. C-F-Em-Eb-Gm-D-Bm-Bb-Dm-Db-Fm-C-Eb-Ab-Bb-F-C. The first three chords are from C major (I-IV-III). The next two Eb major to G minor are from Eb major which has a “C” as its sixth step and this movement in Eb major is (I-III). The next two chords are D major and B minor and are from the key of G major and move as such (V-III). Then we have Bb major moving to Dm  from the key of Bb major giving us the movement of (I-III). Bb major has a “C” as its second step. Then we duplicate this movement in Db major which has a “C” on its seventh step. Db major to F minor in the key of “Db” move also (I-III). Then I return to the chord C major. Thereafter we have Eb major to Ab major which is the (V-I) movement in the key of “Ab”.  The key of Ab major has a “C” on its third step. Then we have Bb major to F major coming from F major with the movement (IV-I). F major has a “C” on its fifth step and then we return to C major.

In my second blog we ventured into the usage of the dominant seventh chord. Each one of the chords derived from this technique can take on a secondary dominant on the fifth step above it. An embellished version of our last chord progression can look like this.

C-C7-F-B7-Em-Bb7-Eb-D7-Gm-A7-D-F#7-Bm-F7-Bb-A7-Dm-Ab7-Db-C7-Fm-G7-C-Bb7-Eb-Eb7-Ab-F7-Bb-C7-F-G7-C.

Of course we needn’t use a dominant seventh chord before each chord but for study purposes I have shown all of these possible resolutions.

Lastly we can use the cadence we learned later in the blog and bring it also into play with all chords derived from this technique. Once again all of the cadences needn’t come into play.

C-Gm-C7-F-;F#dim-B7-Em;-Fm-Bb7-Eb;-Adim-D7-Gm;-Em-A7-D-;C#dim-F#7-Bm;Cm-F7-Bb;-Edim-A7-Dm-;Ebm-Ab7-Db-;Gdim-C7-Fm-;Dm-G7-C-;Fm-Bb7-Eb-;Bbm-Eb7-Ab-;Cm-F7-Bb-;Gm-C7-F-;Dm-G7-C.

In the following blog we will begin to expand our usage of the Roman Numeral formula and as well adventure into more four-note chords. Also we will learn some newer elements found in traditional harmony.

3. Voice-Leading from chord to chord

The basic principle of “voice-leading” is to blend one chord to another without a radical spring. This gives a wished effect especially for accompanying because a melody should come forward and the chords should move smoothly and support the melody.

In the first blog (UNDERSTANDING BASIC HARMONY) I presented all of the three-note chords (triads) in each of their three positions. The basic three-note chords (triads) in C major or A minor look as such. C major is (C-E-G or E-G-C or G-C-E) D minor is (D-F-A or F-A-D or A-D-F) E minor is (E-G-B or G-B-E or B-E-G) F major is (F-A-C or A-C-F or C-F-A) G major is (G-B-D or B-D-G or D-G-B) A minor is (A-C-E or C-E-A or E-A-C) B diminished is (B-D-F or D-F-B or F-B-D). We call the first position the root position; (C major example C-E-G). The next position is the first inversion; (C major example E-G-C) The third position is the second inversion; (C major example G-C-E).

Now I will show how we use these various positions to bring about good “voice-leading”. Say we have our first chord progression from the first paper (C-G-Am-F). Using our three different chord positions we can obtain a smooth movement. Say we begin with the root position (C-E-G). We then look at the chord G and search for the position that best blends with (C-E-G). G major has these three positions (G-B-D or B-D-G or D-G-B). If we look at the second position of G major we see that G is also at the top of the chord. This is perfect in that (C-E-G), the root position of C major, has the G also at the top. Therefore the movement will look like this (C-E-G to B-D-G). This is much better than jumping to the root position of G major. So if it is possible to have a common note, in this case G, we mostly try to join the chords with this common note. This is the general practice for practical “voice-leading”.

We will now look at the two other positions of C major and connect them to the following chord G major. From the first inversion (E-G-C) we see the common note G in the middle of this position. Therefore we look for the G major with G as the middle note.The result is (E-G-C to D-G-B).The last position from C major is (G-C-E). We see here that G is the beginning note so the root position of G major will follow resulting in this movement (G-C-E to G-B-D).

The next movement in the chord progression is G major to A minor. When we look at these chords we will notice immediately that there are no common notes. We then simply move each note to the following note in the scale. For example (G-B-D to A-C-E) or (B-D-G to C-E-A) or (D-G-B to E-A-C). In classical music the movement from (G-B-D to A-C-E) was not used. Therefore the other possibility (G-B-D to E-A-C).

Now I will connect the three chords with this technique of voice-leading. Firstly starting with the root position of C major (C-E-G to B-D-G to C-E-A). Next starting from the first inversion of C major (E-G-C to D-G-B to E-A-C). Then starting from the second inversion of C major (G-C-E to G-B-D to A-C-E) or the classical variant (G-C-E to G-B-D to E-A-C).

Lastly we will connect the chord A minor to F major. As we look at these two chords we see that they actually have two common notes to help us move smoothly. We will start with the root position of A minor (A-C-E). Both the notes A and C are found in F major. The voice-leading from the root position of A minor to the chord F major will appear like this (A–C-E to A–C-F). Then from the first inversion we move as such (C-E-A to C-F-A) and from the second inversion we have (E-A–C to F-A–C).

The entire chord progression in all three variations stands so. From the root position of C major (C-E-G to B-D-G to C-E-A to C-F-A). From the first inversion of C major (E-G-C to D-G-B to E-A–C to F-A–C). Then from the second inversion of C major (G-C-E to G-B-D to A–C-E to A–C-F). With the classical variant we have (G-C-E to G-B-D to E-A–C to F-A–C).

We have now gone through the basic principles of voice-leading with three-note chords. Of course with the addition of the four-note chord we have even more possibilities. In the next blog I will be presenting the seven related keys in music. This will greatly expand our harmonic knowledge. An analysis of a Beatle song will also be there.

In the previous blog (Understanding Basic Harmony) we worked with three-note chords (triads). Now we will venture into the world of four-note chords. However in this blog we will start with the fifth (V) step of each scale. In C major our fifth step is G. The chord is G major (G-B-D) and when it receives the note F on top it becomes a dominant seventh chord. The symbol receives a 7 next to the capital letter, therefore G7.

One way to easily learn all dominant seventh chords is to look at all the major chords and add on the fourth note which is exactly two half steps lower than the first note. Whole steps are the distance of two adjacent notes and a half step is only the distance of an adjacent note. With C major we can look at the octave C and going two adjacent notes lower we receive Bb.

Therefore C7 looks like this (C-E-G-Bb).

In traditional music the dominant seventh chord moves from the fifth step to the chord on the first step. Therefore the chord movement we all know very well, G7-C. In the age of the Baroque this chord relationship went through a transformation bringing the secondary dominant into existence.

In the first paper we learned of the seven steps and the three-note chords that appear on each step. The baroque began using “borrowed” dominants to resolve to each step of the major or minor scale. These are the dominant seventh chords we call secondary dominants. Without any further ado I will now give the row of secondary dominants as they appear in C major and A minor.

As I have explained the normal relationship is G7-C. In Roman Numerals this stands as such (V7-I). As we can decipher the dominant is built on the fifth step of the major scale. Therefore G dominant 7th moves to C major. Now we will place a dominant 7th before every step of the scale and resolve it to the three-note chord found there. Therefore always a dominant seventh chord built five scale tones higher than the coming chord.
G7(V7/I)-C(I) ; A7(V7/II)-Dm(II) ; B7(V7/III)-Em(III) ; C7(V7/IV)-F(IV) ; D7(V7/V)-G(V) ; E7(V7/VI)-Am(VI); F#7(V7/VII)-B dim(VII)     In minor the same relationships exist but they are simply analyzed differently.
E7(V7/i)-Am(i) ;F#7(V7/ii)-B dim(ii) ; G7(V7/iii)-C(iii) ; A7(V7/iv)-Dm(iv) ; B7(V7/v)-Em(v) ; C7(V7/vi)-F(vi) ; D7(V7/vii)-G(vii)

The word cadence is perhaps new for some of us but it simply means a progression of at least three chords that resolve after a dominant. Therefore the placement of another chord before the dominant. An example could be Dm(II)-G7(V7/I)-C(I). This relationship is found often especially in jazz standards. I have added the minor chord that begins on the second step. This cadence we can use with the destination being a major chord. For example Gm(II/IV)-C7(V7/IV)-F(IV) or Am(II/V)-D7(V7/V)-G(V).
Looking at the second chord of the minor we see we have the diminished chord. This will be the (II) chord for this cadence with the destination being a minor chord. This looks as such: B dim(II/VI)-E7(V7/VI)-Am(VI).

Now I will write the cadence as it resolves to the other minor chords on step (II) and step (III). Edim(II/II)-A7(V7/II)-Dm(II) ; F#dim (II/III)-B7 (V7/III)-Em (III). All of these cadences can be used in either C major or A minor. An example in the literature is Ray Charles’ refrain to “Let’s Go Get Stoned.”     C(I)-Bdim(II/VI)-E7(V7/VI)-Am(VI) ;Gm(II/IV)-C7(V7/IV)-F ; Dm(II)-G7(V7)-C(I).
When we follow the Roman Numerals we can begin to transpose this knowledge into other keys. Now I will guide us through a transpositional process. G7(V7/I)-C(I) ; A7(V7/II)-Dm(II) ; B7(V7/III)-Em(III) ; C7(V7/IV)-F(IV) ; D7(V7/V)-G(V) ; E7(V7/VI)-Am(VI) ;F#7(V7/VII)-B dim(VII) was our original row of secondary dominants.

We will use the Roman Numerals to help us find each new chord say in the Key of F. The basic dominant 7th chord going to the (I) chord in “C” is G7(V7)-C(I). C7(V7/I)-F(I) is the transposition in that C is the fifth step of F major and F being the first step. This is how a formula in Roman Numerals translates into a transposition. G is the second step in F major and G minor is the chord on the second step. As I stated before, five notes higher from the “G” , in this case, is where the secondary dominant will be built. Therefore the V7 of the (II) step (G-A-Bb-C-D) is D7. One further example is A as the third step of the F major scale and A minor is the (III) chord. Once again, five notes higher from “A ” is where the secondary dominant will be built. Therefore the V7 of the (III) step (A-Bb-C-D-E) is E7.

Finally I will move the chord progression of Ray Charles to the key of “A”. C(I)-Bdim(II/VI)-E7(V7/VI)-Am(VI) ;Gm(II/IV)-C7(V7/IV)-F ; Dm(II)-G7(V7)-C(I) was the example of cadences using the addition of the (II) chord before the (V7 ) and then resolving to a destination chord. In the key of “A “we start with the (I) chord A. Then we must look at the end of the cadence. All cadences are separated by a colon. Our first cadence ends on Am in “C”. This chord is the (VI) chord and the (VI) chord in A is F# minor.

Now we will look at the formula of the cadence. The (II) chord of the (VI) chord (A minor) in “C” is B diminished. The (II) chord of the (VI) chord in “A” is one step higher than F# therefore G# diminished. Then exactly like earlier, we count five notes higher from F# and land on C# and C#7 is our secondary dominant. Therefore the first four chords can be transposed as such A(I)G#dim(II/VI)-C#7(V7/VI)-F#m(VI).

Next we have the cadence in the key of “C”which ends on F major. F major is the (IV) chord in C major. The (IV) chord in “A” is D major. Again we will look at the formula of the cadence. The (II) chord of the (IV) chord (F major) in the key of “C” is G minor. The (II) chord of the (IV) chord in the key of “A” is one step higher than D therefore E minor.

Then exactly like earlier, we count five notes higher than D and land on A and A7 is our secondary dominant. Therefore the next three chords appear as such Em(II/IV)A7(V7/IV)D(IV). Lastly the cadence back home II-V7-I. In “A” this is Bm(II)E7(V7)A(I). Our entire transposition is
A(I)-G#dim(II/VI)-C#7(V7/VI)-F#m(VI) ;Em(II/IV)-A7(V7/IV)-D ; Bm(II)-E7(V7)-A(I). The next blog we will learn about “voice leading” to insure  smooth movements from chord to chord.

1.  UNDERSTANDING BASIC HARMONY (Playing by ear)

One very clear idea is to take a look at any keyboard. We have the white keys and the black keys. The white keys represent a collection of tones which we call diatonic. These pitches came to be through the playing of music stretching back to ancient Greece. We have seven tones and each can be the first tone of a given scale. The note left of the two black notes is “C”. From the note C the white notes are named C,D,E,F,G,A, and B. Each of the possible scales has traditionally carried the name of a Greek tribe.

When we play C to C we discover our major scale and it also carries the name Ionian. When we play from A to A we discover our minor scale which is also called the Aeolian. Out of these two scales we can build chords that are found in many songs we know and cherish. A capital letter means a major chord and a capital letter followed by a small “m” means a minor chord. Guitar players can learn chords by studying tablature and the keyboardist must learn the combinations of separate pitches that construct a chord. A chord is the combination of three notes or more.

1a. Playing Piano by Ear

The basic three-note chords (triads) in C major or A minor look as such. C major is (C-E-G or E-G-C or G-C-E) D minor is (D-F-A- or F-A-D or A-D-F) E minor is (E-G-B or G-B-E or B-E-G) F major is (F-A-C or A-C-F or C-F-A) G major is (G-B-D or B-D-G or D-G-B) A minor is (A-C-E or C-E-A or E-A-C) B diminished is (B-D-F or D-F-B or F-B-D).

I will now write tabs representing various chordal movements.

C-G-Am-F ;  C-Em-Am-G ; Am-F-C-G ; Am-Dm-F-C ; F-C-G-Am ; C-Em-Am-Dm ;

Dm-G-F-C ; Am-F-Em-G ; Em-F-G-C ; Dm-Am-G-C ; F-G-Am-Em ; F-Am-G-C

These are all built with only four chords but of course we can expand our chord progression to encompass as many chords as we wish.

C-G-Am-F-Dm-G-Em-Am-F-C-G-Dm-Am-Em-F-C

We can also play the four chords more than once. C-G-Am-F-C-G-Am-F etc.

We have worked till now in what we call the “key” of C or the “key” of A minor. Each step of the scale will now receive a number. In C major C is “1” D is “2” E is “3” F is “4” G is “5” A is “6” and B is “7”. Often these numbers will be represented in Roman Numerals. C is “I” D is “II” E is “III” F is “IV” G is “V” A is ”VI” and B is “VII”.

Our chord progressions can be described with these Roman Numerals. C major (C) is “I” , D minor (Dm) is “II”, E minor (Em) is “III”, F major (F) is “IV” , G major is “V” A minor is “VI” and the weird chord B diminished (Bdim) is ”VII”.

The minor keys begin with the Roman Numerals in the lower case. For example A minor (i) B diminished (ii) C major (iii) D minor (iv) E minor (v) F major (vi) G major (vii). Therefore our chord movements can look like this when we use our Roman Numerals.

C-G-Am-F (I-V-VI-IV) C-Em-Am-G (I-III-VI-V) Am-F-C-G (i-vi-iii-vii) Am-Dm-F-C (i-iv-vi-iii) F-C-G-Am (vi-iii-vii-i) Dm-G-F-C (II-V-IV-I) Am-F-Em-G (i-vi-v-vii) Em-F-G-C (III-IV-V-I) Dm-Am-G-C (II-VI-V-I) F-G-Am-Em (vi-vii-i-v) F-Am-G-C (IV-VI-V-I) There are twelve keys, which begin on all tones from C-Db-D-Eb-E-F-F#-G-Ab-A-Bb-or B. Or for the minor keys A,Bb,B,C,C#,D,D#,E,F,F#,G,G#.

A guitarist can either capo or bar his chords and reposition the strings to ring in all keys. Playing in C we can capo or bar the strings from the first fret and we shall receive the key of D flat. Moving the capo or barring from the second fret brings the key of D. Another example is playing in E Major and barring or using the capo from the first fret resulting in the key of F Major.

The keyboardist has a bit more work. It is wonderful that the white notes give us the key of C and the key of Am but each piano method goes very painstakingly through the learning of each new key. However there only a dozen in total and the pianist can work with the graphics of the keyboard and can find his way through all 12 keys. All the other keys use at least one of the black notes. The note left of the two black notes once again is “C”. Therefore we have our orientation.

A black note has two possible names. The movement from a white note to the right carries the name of the white note with a “sharp” sign added to it. For example from D to the black note to the right is D sharp, which has the symbol as such, D#. Or when we move to the left of the white note E it receives the name E flat, which has the symbol Eb. When we look at the keyboard we see always the same pattern. Two black notes separated by two white notes and three black notes separated by two white notes.For facility I will give the interested reader the letters of all 12 keys, major and minor.

C major scale C(I)D(II)E(III)F(IV)G(V)A(VI)B(VII)C

A minor scale A(i)B(ii)C(iii)D(iv)E(v)F(vi)G(vii)A

Db major scale Db(I)Eb(II)F(III)Gb(IV)Ab(V)Bb(VI)C(VII)Db

Bb minor scale Bb(i)C(ii)Db(iii)Eb(iv)F(v)Gb(vi)Ab(vii)Bb

D major scale D(I)E(II)F#(III)G(IV)A(V)B(VI)C#(VII)D

B minor scale B(i)C#(ii)D(iii)E(iv)F#(v)G(vi)A(vii)B

Eb major scale Eb(I)F(II)G(III)Ab(IV)Bb(V)C(VI)D(VII)Eb

C minor scale C(i)D(ii)Eb(iii)F(iv)G(v)Ab(vi)Bb(vii)C

E major scale E(I)F#(II)G#(III)A(IV)B(V)C#(VI)D#(VII)E

C# minor scale C#(i)D#(ii)E(iii)F#(iv)G#(v)A(vi)B(vii)C#

F major scale F(I)G(II)A(III)Bb(IV)C(V)D(VI)E(VII)F

D minor scale D(i)E(ii)F(iii)G(iv)A(v)Bb(vi)C(vii)D

F# major scale F#(I)G#(II)A#(III)B(IV)C#(V)D#VI)E#(f)(VII)F#

D# minor scale D#(i)E#(f)(ii)F#(iii)G#(iv)A#(v)B(vi)C#(vii)D#

G major scale G(I)A(II)B(III)C(IV)D(V)E(VI)F#(VII)G

E minor scale E(i)F#(ii)G(iii)A(iv)B(v)C(vi)D(vii)E

Ab major scale Ab(I)Bb(II)C(III)Db(IV)Eb(V)F(VI)G(VII)Ab

F minor scale F(i)G(ii)Ab(iii)Bb(iv)C(v)Db(vi)Eb(vii)F

A major scale A(I)B(II)C#(III)D(IV)E(V)F#(VI)G#(VII)A

F# minor scale F#(i)G#(ii)A(iii)B(iv)C#(v)D(vi)E(vii)F#

Bb major scale Bb(I)C(II)D(III)Eb(IV)F(V)G(VI)A(VII)Bb

G minor scale G(i)A(ii)Bb(iii)C(iv)D(v)Eb(vi)F(vii)G

B major scale B(I)C#(II)D#(III)E(IV)F#(V)G#(VI)A#(VII)B

G# minor scale G#(i)A#(ii)B(iii)C#(iv)D#(v)E(vi)F#(vii)G#

To facilitate transposition we will now analyze the members of each chord. Earlier I assigned a Roman Numeral to each step of the scale. Therefore I will offer an analysis of each chord from C major or A minor. C major the first chord (I) or in minor (iii) is (I-III-V).  D minor the second chord (II) or in minor (iv) is (II-IV-VI).  E minor the third chord (III) or in minor (v) is (III-V-VII) F major the fourth chord (IV) or in minor (vi) is (IV-VI-I) G major the fifth chord (V) or in minor (vii) is (V-VII-II) A minor the sixth chord (VI) or in minor (i) is (VI-I-III) and B diminished the seventh chord (VII) or in minor (ii) is (VII-II-IV).

Now we will take our formula with the Roman Numerals representing a given chord movement and transpose it from C or A minor to any other key we want and then translate it into the same chord movement in a new key. For example our first example C-G-Am-F (I-V-VI-IV) in E major is E-B-C#m-A (I-V-VI-IV) or F-Am-G-C (IV-VI-V-I) in Ab major is (Db-Fm-Eb-Ab). Taking a look at our E major scale we will use the Roman Numerals to figure out for example B major. B major in the key of E is the fifth chord. Its formula is (V-VII-II). Looking at our E major scale above we see the notes will be (B-D#-F#).  Our sixth chord has the formula (VI-I-III). The sixth chord in E is C# minor. Therefore the sixth step C# the first step E and the third step G# result in C# minor. With the help of this small tutorial we can begin a wonderful journey to a full understanding of harmony coming in the next blogs.

It is always refreshing to witness the growth of a young musician and how exciting it is and rewarding as a teacher to see their personal students reach fruition. Of course openness to the student is imperative for the freedom of a given student’s expression. Like all the other arts, literature, painting, acting, dance and poetry, it is essential to have the proper tools to excel.

I am as a Juilliard graduate highly thankful to have been given these tools and I was inventive enough to formulate newer ideas which were only possible with this education. I am often highly distraught and disheartened to see, during my lifetime, the absolute disintegration of the opportunities for young people to learn and participate in musical projects. Of course the wonderful jam sessions in my cellar as a teenager were just as important. Education can begin by sharing with fellow young musicians and putting a band together and simply learning from each other.

However these beginnings can be taken to higher levels by having our chance to perhaps study the chorales of Johannes Sebastian Bach and analyze his chord progressions. We could thereafter try to write brand new melodies to his highly interesting chord progressions and write a tab that many guitarists and pianists could read.

If a musician doesn’t read music he can mastermind with a friend that does. We will discover that this German composer actually still has an influence on many pieces that have been written in the last 100 years. In the Afro-American tradition is Bach’s harmony the basis for many pieces and especially in the Gospel church music. The harmonies can be tastefully “bluesified” and take on a totally different character but the original resource remains the same.

With George Gershwin and Duke Ellington the mix of modal coloring of a tonal progression also came to be. Therefore in all facets of today’s music I would say it is worth our time to educate ourselves learning the structural harmony that began some 400 years ago.

In my future blogs I will be giving tips on educational processes that could spur on the world of music. I hope I can inspire not just the young but people of all ages to open up the wonderful possibilities that a furthered musical education can give us.

THE PATTERNING OF MUSICAL SYMMETRIES
Through my explorations into the harmony at the beginning of the 20th Century and my passion for the hard-bop modern jazz from 1955 to the present, I have formulated a new concept as an alternative to the “equal importance” of notes, as found in dodecaphony.
Through the observance of musical symmetries I began to pattern tritones following typical serial methods. For Example C-F#, E-A#, Eb-A, Bb-E, Ab-D A-D#. This I will utilize for the building of the first row. Then one can, like a twelve-tone row, invert the row. This results in seven new tritones which are structurally related. *C-F#, Ab-D, A-D#, D-G#, E-A#, Eb-A. At this point I distribute pitches around the tritones and develop modes for a melodical and harmonical resource. In other words each modal resource will be built with the tritone as a nucleus. One can think of it like a solar system where the tritone is the sun and the other chosen notes are planets.
I will now give a written example of some modal structures which are held together by their relationships through the tritone. One also needn’t be irritated if more than one tritone appears in a scale. Only the ordered tritones build this structuring.
• C-Db-E-F#-G-Ab-Bb This mode belongs to tritone C-F#.
• E-F#-G-A#-B-D-D# This mode belongs to tritone E-A#.
• Eb-F#-G-A-Bb-C-Db This mode belongs to tritone Eb-A.
• Bb-Cb-D-E-F-Gb-Ab This mode belongs to tritone Bb-E.
• Ab-B-C-D-Eb-F-Gb This mode belongs to tritone Ab-D.
• A-B-C-D#-E-G-G# This mode belongs to tritone A-D#.
• The Scheme in Inversion
• C-Db-E-F#-G-Ab-Bb This mode belongs to tritone C-F#.
• Ab-Bb-Cb-D-Eb-F#-G This mode belongs to tritone Ab-D.
• A-B#-C#-D#-E-F#-G This mode belongs to tritone A-D#.
• D-Eb-F#-G#-A-Bb-C This mode belongs to tritone D-G#.
• E-G-G#-A#-B-C#-D This mode belongs to tritone E-A#.
• Eb-F-Gb-A-Bb-C#-D This mode belongs to tritone Eb-A.
I personally stay with three various modes and their transpositions per piece or movement. This is highly helpful for melodic and harmonic homogeny. For my scheme above I have twelve modes which are all related to each other through the patterning of the tritone. The choice of notes around a given symmetry is personal. If you wish to write mostly darker intervals, fine. If you wish to be diatonic, fine.
The point of the concept is to move modes with structured symmetries instead of the equality of pitches utilized in dodecaphony. One can freely choose his harmonic palette by arranging the wished pitches around a given symmetry. When utilizing this method one will hear, as each chosen symmetry moves one to another, a clear and logical harmonic movement.

In general, as well, I personally utilize a matrix for my transpositional schematics. This matrix is in itself symmetrical. It looks as such: I-II-#II-III-#IV-#V-VI-bVII. This is also not the only possibility for logical transpositions. We can as well develop inverted forms or otherwise related schemes. An example could be I-bII-III-#II-bVI-V.
The tritone is not the only symmetry in a twelve-note well-tempered environment. We have as well the augmented triad (C-E-G#). This triad can be used to control chromatics exactly in the same manner as I have already shown with the tritone.
If one wishes to move from a mode with the tritone as the existing center, an augmented fourth or a major third or augmented fifth with the augmented triad as the central symmetry, then one must consider the distribution of notes around the given central symmetry. This is in a diatonic example completely clear.
From C Lydian to F# Lydian we see that each structure has seven notes. In C we have D and E above C and G, A and B over F#. If we reverse the distribution over C and F# we will hear the harmonic movement of an augmented fourth. In other words then three notes over C and two over F#.