1. Terms: Scale Degrees

   1 Tonic
   2. Supertonic
   3. Mediant
   4. Subdominant
   5. Dominant
   6. Submediant
   7. Leading Tone
   8. Octave

1. Major Keys #

a. Construct: Begin with F# and continue up in 5ths: F#, C#, G#, D#, A#, E#, B#

b. Identify: The last sharp in the key signature is 1/2 step lower than the Major key. (ie 3#'s (F#, C#, G#) = A Major)

1. Major Keys b

a. Construct: Begin with Bb and continue down in 5ths: Bb, Eb, Ab, Db, Gb, Cb, Fb

b. Identify: The penultimate b in the keysignature is the Major Key (ie 4bs (Bb, Eb, Ab, Db) =Ab Major (1b=F)

1. Terms:
   1 Passing Tone
   2. Neighbor Tone
   3. Incomplete Neighbor
   4. Double Neighbor
   

1. Natural Minor Keys #

a. Construct: Begin with F# and continue up in 5ths: F#, C#, G#, D#, A#, E#, B#

b. Identify: The last sharp in the key signature is a whole step higher than the natural minor key. (ie 3#'s (F#, C#, G#) = F# Natural Minor)

2. Natural Minor Keys b

a. Construct: Begin with Bb and continue down in 5ths: Bb, Eb, Ab, Db, Gb, Cb, Fb

b. Identify: The penultimate b in the keysignature is the minor 3rd of the natural minor Key (ie 4bs (Bb, Eb, Ab, Db) where Ab is the minor 3rd of F minor

Note: The Natural Minor is the only form of minor that is represtented by a keysignature and will always be a minor 3rd below its corresponding or "Relative" Major Key

Rules to Construct and identify Harmonic and Melodic Minor key signatures

3. Harmonic Minor

a. We already saw that the 1/2 steps in Major have a strong gravitational pull. Of particular importance was the pull from the leading tone to the tonic (octave). In order to preserve that critical gravitational pull we often raise the 7th scale degree of the Natural minor one half step thereby transforming it to Harmonic minor.

4. Melodic Minor

a. By raising the 7th scale degree in Harmonic Minor, we get an awkward interval between 6 and 7 which sounded foreign to 18th century ears. Hence, to avoid such an interval, a melody that rises to the leading tone of Harmonic minor can avoid that awkward interval by also raising the 6th scale degree. When both the 6th and 7th scale degrees of the natural minor key are raised a half step, it is considered melodic minor.

Group 1) Unison, 4th, 5th & 8va

Group 1 qualitive identifier: If the upper tone of an interval is in the major key of the lower tone, the interval is Perfect. If it is a half step higher it is Augmented. If it is a half step lower, the interval is Diminished

Major <-> Minor
Augmented <-> Diminished
Perfect <-> Perfect

Group 2) 2nds, 3rds, 6ths, 7ths

Group 2 qualitive identifier: If the upper tone of an interval is in the major key of the lower tone, the interval is Major. If it is a half step higher it is Augmented. If it is a half step lower, the interval is Minor. If it is a whole step lower, the interval is Diminished.

So whats up with the P4? Can it be both Consonant and Dissonant? Indeed it can.

1st Species Counterpoint Rules Summary:

1. More stepwise motion than leaps
2. dont repeat notes
3. leap of 1,3,5,m6(up), 8va only.
4. Leaps of 5th or greater must be counterbalanced.
4a. No more than 3 consecutive leaps

5. Parallel, Similar, Oblique and Contrary Motion
6. All harmony must be perfect or imperfect consonances
7. No voice crossing, no overlaps
8. 1st interval must be perfect.

9. No Parallel perfect intervals
10. Avoid hidden (direct) perfect intervals
(leaping to perfect intervals in similar motion
11 Avoid open perfect intervals
(leaping from one perfect interval to another in contrary motions)

Summary of General Rules for 4 part writing.

1. No Parallel Perfect Intervals
2. Parallel perfect 4th OK in upper voices
3. P5 to dim5 OK
4. dim5 to P5 Bad
5. Avoid parallel 5ths in contrary motion (going from close position to open or vice versa)
5. Avoid parallel 8vas in contrary motion (going from close position to open or vice versa)
6. Avoid Overlaps
7. Avoid Hidden P5ths and P8vas

8.  Leading Tones (^7 in Major and +^7 in minor)  Resolve up to the tonic
9.  Dissonance with the bass tends to resolve down
10.  Chordal 7ths are considered dissonant within the chord and tend to resolve down (even if consonant with the bass)

1.  Authentic Cadence:
When the cadence ends on I i.e. V-I

1. Perfect Authentic Cadence: Soprano ends on Tonic
2. Imperfect Authentic Cadence: Soprano ends on 3rd or 5th scale degree

2. Semi-Cadence:
When the cadence ends on V i.e. I-V

1. Doubling
a.  OK to double any tone of the I chord
b.  Never double the L.T. of the V chord.
c. Never Omit the 3rd. It identifies the quality.

2. I-V-I in minor
a.  When a progression creates an expectation of V-I, the 7th scale degree must be a leading tone and thus, in minor, must be raised.

8. Expaning I and V in 4 parts
a. When expanding i and V in 4 parts, you can have inner voices move in contrary motion as well as similar and oblique. Remember, you can omit the 5th of any chord but never double the leading tone and never omit the 3rd.

I6 and V6

1.  New Possibilities for the Bass
a. The primary function of the I6 and V6 is to expand upon the 1 and V respectively
b. By using less stable bass tones, the I6 and V6 soften the cadential effect.
c. By using the 6-3 position of the I & V chords, we enrich the harmonic capacity of the progression without losing the critical relationship between the tonic and dominant structures. As well, since the bass line can now fall on the 1st and 3rd scale degress for the I chord and the 5th and 7th scale degrees for the V chord, the bass line begins to take on a melodic character of its own.

Make sure you can write correct 4 part harmony for the below examples following all the above rules: Make sure you can handle doing this if you were given just the melody or just the bass with or without figuration.

1. Descending Resolution of 4 (7th above the root)
a.    Just as the Vii6 chord contained a tritone in the upper voices between the 4th and 7th scale degrees that had to resolve (most ofter 4 to 3 and 7 to 8), so too does the V7 chord contain the 4th and 7th scale degrees and so too must these scale degrees resolve. As with the Vii6, the most common resolution is 4 to 3 and 7 to 8.

2.  V6-5
a. Like the V6 chord, the V6-5 has the leading tone as its bass. However since the 7th of the chord is now present it forms a tritone against the bass and therefore the bass of the V6-5 must resolve upwards to the 1st scale degree. (the exception is when the V6-5 is part of a larger expansion of V)

4.  V4-3
a. If we eliminate the root of the V4-3 chord we are left with a Vii6 chord. The V4-3 and Vii6 are very similar in their function and contrapuntal voice leading. Just as we saw that the 2nd scale degree bass of the Vii6 was more stable than the active leading tone bass of the V6 and therefore could move easily to either the 1st scale degree or the 3rd scale degree, so too may the same be said for the bass of the V4-3.

b. Similarly we saw that Vii6 served as a very effective expansion of I since the dissonance of the diminished chord made the chord very active. The same tritone dissonance exists in the V4-3 and a similar resolution will occur

1. The 7th of the V4-3 chord is now consonant against the bass so like the Vii6 chord, when the V4-3 ascends to a I6, the 4th scale degree may resolve upwards.

2. When the V4-3 chord moves as a neighbor to 15 or passes from 16 to 15 the 4th scale degree will resolve down as expected.

5.  V4-2
a. With the V4-2 chord we now add a new tone available to our bass: the 4th scale degree. Since that bass tone will always form a dissonance with the leading tone, the bass of a V4-2 will always resolve down.

b. The main function of the V4-2 is as a passing chord from V5 to 16 and
c. As a upper neighbor (complete or incomplete) to 16
d. As an intermediary allowing V7 to fall to 16 via V4-2 (remember V7-16 should be avoided as it results in hidden octaves

Connecting I and V by stepwise bass
a. With the addition of the 4th scale degree that does not represent a dissonance and can rise (remember V4-2 will have a 4th scale degree that falls to I6) we can now harmonize an ascending bass line. Note that V43 or Vii6 can be used to bridge I and I6

a. With the addition of II, II6 and IV, we can now harmonize the melodic motion ^5,^6,^7,^8. When harmonizing the leading tone^7, avoid the V or V7 chord as they will tend to lead to parallelisms. Instead use Vii6, V43 or V42 (note V6 and V65 would result in doubled leading tones)

15 Chord Progressions and Rhythm
a. Dont repeat a chord from a weak beat to a strong one
b. Dont repeat a bass note from a weak beat to a strong one (ie IV-II6) except when the bass functions as a suspension (ie II6 to V42)

16 Subordinate Progressions
a. Since we now can expand 1-V with intermediary harmonies, the aggregate expansion can itself be throught of as a smaller, more localized representation of I or V which can, in turn be expanded. This will become a critical element in the study of musical form. If the localized expansion sounds too cadential, avoid root position I and V.

Moving to V7 & Doubling.
a. Since the Cad64 is an integral part of the dominant harmony, it moves most naturally to V7 with the ^1 (4th above the bass) resolving down to the leading tone and the ^3 (6th above the bass) resolving down to the ^2 (5th above bass of V7) Sometimes, we will see the ^3 resolve up to the ^4 to create the 7th of the V7. When the ^3 is doubled it is obviously best to have one lead to the ^2 and the other lead to the ^4 to avoid parallelisms. In four part writing, it is best to double the bass (most stable) then the 6th above (consonant). Try to avoid the 4th (dissonant) unless it appears in free or complex textures.

Rhythm
a. Like the suspension of the ^4 in a II/II6/IV - V7 (inv) progression, the suspensions in the Cad64 should occur on a metrically relatively strong beat and resolve on the following weak beat. (or in the case of slow progressions the resolution may occur on the next strong beat)

Moving to V7
a. IV II and II6 all move well to V7. In fact they all share the 4th scale degree. When this 4th scale degree is present in the same voice in the IV, or II or II6 chord AND in the V7, the dissonance in the V7 is said to be "prepared", Throughout our study of harmony, we will see many benefits to preparing dissonances. When the preparation of the dissonance occurs on a strong beat the preparation is called a "suspension". The strength of the prepared 7th is significant and, at times can warrant its doubling.

If the Cad64 were to be preceded by a chord containing the leading tone (variations of V or Vii6) we would spoil the harmonic party created by the delayed resolution to ^7 of the Cad64. Therefore, we will say that the Cad64 is approached only from intermediate harmonies or a tonic chord