Bonus+Units


 * __SECONDARY DOMINANTS:__**


 * //"Make a chord sound like a Tonic chord by putting its' dominant in front of it!"// **

Secondary dominant **(also** applied dominant**) is a specific type of harmonic device. It refers to a chord that has a dominant-like function built on a scale degree other than the 5th of the prevailing key.**
 * The V7/V, the dominant of the dominant is the most common. The chord to which a secondary dominant progresses can be thought of as a briefly tonicized chord or pitch (tonicizations longer than a phrase are modulations).**




 * The secondary dominant will contain an altered tone in the chord structure. Notice the A major chord above. It contains a C# which is not in the original key of C. It turns the chord into a dominant chord resolving to d minor. The A chord is a V of d minor.**

**SUMMARY** We have seen that we can take the three naturally-occuring minor chords from a major key - the ii-chord, iii-chord, and vi-chord- and create //secondary dominant chords// by simply making them major. We can do the same changes in chords from a minor key. Our ear hears them as behaving like dominant chords because we hear the raised third degree that wants to move to the root of the chord a 4th higher or fifth lower, just like dominant chords do. When we change the structure of a chord in this manner, the name of the chord must change. To call something a ii-chord means that the root of the chord is based on the second degree of the scale **//and//** that it is minor. By making it major, it cannot be a ii-chord anymore. Some people are tempted to simply call it a II -chord (i.e., they use upper-case for the number) but this is not correct. It must be renamed in the manner shown in this lesson.

[]

**Modulation** is most commonly the act or process of __changing from one key to another__. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest. of a chord as the tonic for less than a phrase is considered tonicization.
 * __MODULATION:__**

Modulation should most often occur to keys that are **closely related**. A closely related key is one that shares one accidental more or less with the original key. For Example: The Key of G has one sharp - Closely related keys would have one sharp less (C Major) or One Sharp More (D Major). You can also use the relative minors of all of these keys A minor, E minor, and B minor.

Another way to look at it is this: Original Key is G Major...
 * Think of the quality of each chord built off of G major.
 * Use the key of the scale degree in G with the quality that is implied by the chord structure.
 * G Major, a minor, b minor, C major, D Major, e minor, (Do not use the 7th!)


 * TYPES**

====Common chord modulation **(also known as diatonic pivot chord modulation) moves from the original key to the destination key (usually a closely related key) by way of a chord both keys share. For example, G major and D major share 4 chords in common: G, Bm, D, Em. This can be easily determined by a chart similar to the one below, which compares chord qualities. The I chord in G Major—a G major chord—is also the IV chord in D major, so I in G major and IV in D major are aligned on the chart.** ====



A **chromatic modulation** is so named because it occurs at the point of a chromatic progression, one which involves the chromatic inflection of one or more notes whose letter name, thus, remains the same though altered through an accidental. Chromatic modulations are often between keys which are //not// closely related. A secondary dominant or other chromatically altered chord may be used to lead one voice chromatically up or down on the way to the new key. (In standard four-part chorale-style writing, this chromatic line will most often be in one voice.)

In this case, the V chord in FM (C major) would be spelled C-E-G, the V in dm (A major) would be spelled A-C♯ -E. Thus the chromaticism, C-C♯ -D, which is here split between voices but may often easily be part-written so that all three notes occur in one voice.

**Phrase (also called direct or abrupt) modulation** is a modulation in which one phrase ends with a cadence in the original key, and begins the next phrase in the destination key without any transition material linking the two keys. This type of modulation is frequently done to a closely related key -- particularly the dominant or the relative major/minor key.

**Sequential Modulation:** Even though a sequence does not have to modulate, it is also possible to modulate by way of a sequence. A sequential modulation is also called rosalia. The sequential passage will begin in the home key, and may move either diatonically or chromatically. Harmonic function is generally disregarded in a sequence, or, at least, it is far less important than the sequential motion. For this reason, a sequence may end at a point that suggests a different tonality than the home key, and the composition may continue naturally in that key.

A **parallel key modulation** is a change of mode, but maintains the same tonal center. For example, one section of a composition may be in the key of E major and then modulate to E minor. This can be done directly or facilitated by the various modulation techniques described above. Depending on the length of the modulation and whether or not it returns to the original key, it may or may not be designated by a change of key signature.

= PHRASE AND PERIOD STRUCTURE =

function). Phrase 1--- H.C. (or I.A.C) Phrase 2 -- A.C (or P.A.C.)
 * Phrase** – a musical sentence or complete thought that ends with a cadence.
 * Period** – a logical grouping of phrases that give an impression of closure (Expository


 * ANTECEDENT** (weak or open) **CONSEQUENT** (stronger or closed)

cadence is expected. (overlap or dovetail). material not heard in the original phrase. Phrase 1 ---I.A.C. Phrase 2 H.C. Phrase 3 --I.A.C. Phrase 4 ---P.A.C.
 * Asymmetrical** – a period in which the phrases differ in length.
 * Symmetrical** - a period in which the phrases are the same length.
 * Parallel** – a period in which the musical material is almost exactly the same.
 * Contrasting** – a period in which the phrases have differing musical material.
 * Modulating** – a period in which the Consequent phrase modulates.
 * Cadential extension** – the addition of musical material beyond the point at which a
 * Elision** – the cadence point of one phrase becomes the beginning of the next phrase
 * Interpolation** – the repetition of a phrase becomes longer by the insertion of new
 * Double Period** – phrase 1 and 3 are often identical or very similar.

H.C. or I.A.C (Transitional and Developmental functions),
 * Phrase group** – NOT a period structure. Groups of phrases that end with weak cadences

P.A.C. (Cadential function).
 * Cadential Phrase Group** (or Closing section) - groups of phrases that end primarily with

Form links [|Basic Assumptions concerning form]  [|Binary form]  [|Ternary form]  [|Rounded binary form]  [|Sonata form] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;"> [|Rondo form] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;"> [|Theme and variation] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"> [|Ostinato] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"> [|Theme and Variations] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"> [|Suite] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"> [|Fugue]

<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"> [|Composers' Rules of Enagement]

<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">Wiki on Form

<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">PRINCIPLES OF COUNTERPOINT:

<span style="color: #333333; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">Counterpoint is the art of shaping two or more melodies to sound together.


 * **Single Melody** ||
 * Our study is primarily of vocal melody. Similar principles apply to instrumental melody, but an instrumental style is harder to define precisely. Instruments are able to leap, for example, with far more agility and speed than a singer, and so can perform melodies that wouldn't work at all when sung. Still, however, it will be good practice to imagine that you are writing for a singer, even if you are not. Famous melodies are often ones we can sing, even if written for the violin.

Therefore the first principle will always be this: can you sing your melody? If you cannot, try to make it easier to sing. Here are some ways to accomplish that:

1. Make the melodic motion mostly stepwise, with some small leaps (a leap being any interval larger than a whole step).

2. Keep the melody within a limited range, generally within a single octave or perhaps an octave and a half at the most.

3. Avoid [|augmented or diminished] leaps.

4. Compensate any large leaps by moving in the opposite direction immediately afterward.

5. If you make two successive leaps of any size, see that they are part of the same triadic chord.

With regard to rhythm:

6. Keep the rhythmic values large enough that a singer could easily perform them. Avoid very small note values (32nd notes and less) unless the tempo is very slow.

7. Avoid Lombardic (short-long dotted) rhythms in your ideally vocal melody.

8. Include at least two different note lengths, for variety. || <span style="color: #333333; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; line-height: normal;">**Combining Melodies**

1. Melodies in all voices should follow the principles for single melodies described [|earlier]. 2. A voice should not leap to a [|dissonance], outside of certain exceptions to be described later. 3. Dissonances formed between voices should be //resolved// by stepwise movement to a //consonant// interval. 4. Voices should try to move in opposite directions as much as possible and generally give an impression of independence. 5. If two voices form a [|perfect interval] they should not move directly to another perfect interval, especially in the same direction.


 * First Species Counterpoint:**

<span style="color: #333333; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 12px; line-height: normal;">In First Species exercises you'll write note-to-note polyphony: the notes all move together. The voices are rhythmically identical, but aim for independence in their melodic lines. Traditionally these exercises are performed using whole notes, like this exercise in two parts:


 * **How to Write in First Species** ||
 * Below are the style "rules" that Counterpointer will enforce when you are writing in First Species. At first it may be difficult to meet all these requirements when writing note-against-note! With practice you'll find it gets easier and when it does you'll be ready to move on to Second Species.

The subject of dissonance might need a little discussion: Dissonance is not permitted in 2-part First Species writing, and some authorities would forbid all dissonance even in 3 or more parts. But Fux allows certain dissonances between the upper voices when writing in 3 or more parts. With regard to an example in which his student has written what we would call a first inversion diminished triad he says one should avoid that diminished fifth between upper voices "if possible," but that the no-dissonance rule "is not very strictly applied in composition of several parts." We will follow Fux and allow diminished fifths or augmented fourths natural to the scale if they do not involve the bass voice.

<span class="V14" style="color: #333333; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Melodic movement__:

No voice should make a leap larger than a fifth, except for the octave and the ascending minor sixth.

Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.

Leaps greater than a fifth should be compensated by movement in the opposite direction. If the leap is ascending make sure the compensation is stepwise.



A leap of an octave should be balanced: preceded and followed by notes within the octave.



No voice should move by a chromatic interval (any augmented or diminished interval).



Avoid repeating a pitch when possible, especially in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.

Keep each voice confined to a singable range for the part, preferably not exceeding a tenth from its highest to its lowest pitch.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Rhythm__:

Voices all move together in the same rhythm as the [|cantus firmus]. For traditional exercises all notes are whole notes.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Independence of voices__:

Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).



Avoid writing //direct fifths or octaves// (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct fifths in the outer voices will be accepted if the upper voice moves by step.

Do not let two voices leap to a perfect interval unless one of them is an inner part.

Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (that is, parallel 1st-inversion triads are OK).



Avoid writing more than three of the same interval in a row in any two parts (e.g. four consecutive thirds or four consecutive sixths).



Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice).



Do not move to an octave with leaping motion in either voice unless the movement is oblique (one voice remaining on the same pitch).

One perfect interval can follow another in the same voices only if one of the voices moves stepwise.

Avoid the unison except at the beginning or end. Authorities disagree: [|Fux] forbids unisons except at terminals (though he occasionally shows on in his examples). Jeppeson is much more free with unisons. But since these exercises are mostly based on the Fux method we'll keep his objection to unisons.

In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Dissonance handling__:

In first species there is no dissonance, so the only harmonic intervals allowed are the thirds, sixths, fifth, and octave (and, when in 3 parts or more, the fourth if its lower tone is not the bass). The diminished fifth and augmented fourth will be considered consonant if they are not formed with the bass. Note also Fux's admonition that full triads should be used whenever possible, and when that is not possible use thirds and sixths in preference to "empty" fifths.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Harmony__:

If in two parts the music must begin and end with perfect consonances (octaves, fifths, or unisons). Octaves or unisons are preferrred at the end, and Jeppeson says that an octave or unison is the only choice if the cantus firmus is above the counterpoint. Counterpointer will allow a fifth. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. [|Fux] advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third. However, a concluding major triad was common practice and is acceptable here.

The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.

Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).

In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).

In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Non-modal tones may be introduced, however, if they accord with [|conventional principles for altered tones]. ||


 * **Second Species Counterpoint** ||
 * In Second Species counterpoint one part moves in rhythmic values that are half those of the [|cantus firmus], assuming the meter is binary (divisible by two). In a triple meter the moving voice will have three notes to one of the cantus firmus. If there are more than two voices, one voice has the shorter note values while the others move together as in [|First Species] : ||


 * **How to Write in Second Species** ||
 * You'll begin as before with 2-part writing, with the whole-note cantus firmus either below or above the added part. Remember to begin with a half rest; it's characteristic of Second Species. But when writing in 3 parts, two will actually be in First Species; only one voice will be in the shorter notes.

The big change in Second Species (aside from the quicker movement) is that you can now introduce dissonances formed with the bass, and they can be any kind of dissonance, including 2nds, 7ths, etc. But these can come only on the second note of each pair within a measure, and must be approached and left by step and otherwise follow the below style rules.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Melodic movement__:

(As in [|first species] ) No voice should make a leap larger than a fifth, except for the octave and the ascending minor sixth.

(As in first species) Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.

(As in first species) Leaps greater than a fifth should be compensated by stepwise movement in the opposite direction.

(As in first species) No voice should move by a chromatic interval (any augmented or diminished interval).

(As in first species) Avoid repeating a pitch in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.

(As in first species) Keep each voice confined to a singable range for the part, preferably not exceeding a 10th from its highest to its lowest pitch.

//(New)// Avoid writing the same melodic interval twice on the same pitches. For example:

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Rhythm__:

//(New)// In binary meter one voice has two notes to each note of the [|cantus firmus] ; in ternary meter the faster part moves 3 to 1. If there are additional voices, they move with the cantus firmus as in first species.

//(New)// In both binary and ternary meter you may occasionally substitute a rest for the first note of each group (that is, the one that coincides with the cantus firmus).

//(New)// The faster voice should begin after the cantus firmus, following a rest. The parts will still end together and can use the same note value for the final sonority. In three or more parts only one voice will be moving faster than the others; the others can still enter together.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Independence of voices__:

(As in [|first species] ) Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).

(As in first species) Avoid writing direct fifths or octaves (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct 5ths in the outer voices will be accepted if the upper voice moves by step.

//(New)// Avoid writing parallel octaves or fifths between two adjacent downbeat notes (beginnings of measures) unless the intervening accompaniment note leaps by more than a third. In the second of these parallels between downbeats the leap of a fourth is thought to mask the effect of the parallel.



(As in first species) Do not let two voices leap to a perfect interval unless one of them is an inner part.

(As in first species) One perfect interval can follow another in the same voice only if one of the voices moves stepwise.

(As in first species) Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (that is, parallel 1st-inversion triads are OK). Fourths can also be allowed if one of the tones is nonessential.

(As in first species) Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice).

(As in first species) Avoid the unison except at the beginning or end. Authorities disagree: Fux forbids unisons except at terminals (though he occasionally shows on in his examples). Jeppeson is much more free with unisons. But since these exercises are mostly based on the Fux method we'll keep his objection to unisons.

(As in first species) In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Dissonance handling__:

//(New)// The second (unaccented) note of each pair in the fast voice can be either consonant or dissonant. The accented notes must be consonant. In triple meter either the second or third note of each group can be dissonant, but not both.

//(New)// Any dissonant note must be approached and left by step.

<span class="V14b" style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">__Harmony__:

(As in [|first species] ) If in two parts the music must begin with perfect consonances (octaves, fifths, or unisons) and end with octaves or unisons. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. Fux advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third.

(As in first species) Avoid doubling a seventh.

(As in first species) The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice, be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.

(As in first species) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).

(As in first species) In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).

(As in first species) In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Nonmodal tones may be introduced, however, if they accord with [|conventional principles for altered tones]. ||