The Fugue, an outline of the substantials of a fugue

<BODY BGCOLOR="#FFFFFF"><HR> <P ALIGN=CENTER><FONT SIZE=5> <A HREF="http://www.geocities.com/nap7079/index.html" TARGET="_BLANK">Home</A><BR><HR><BR> <P ALIGN=CENTER><A HREF="http://www.mp3.com/clavier" TARGET="_BLANK">Listen</A> to my recordings on <A HREF="http://www.mp3.com/clavier" TARGET="_BLANK">MP3</A>: <P>Beethoven's famous Pathetique Sonata, Mozart's Fantasy in c minor, Purcell's Suite in a minor, Brahms's Variations on an Hungarian Song, Fractal Music, and more... <BR><BR> </FONT> <HR> <BR> <P ALIGN=CENTER><FONT SIZE=8><B>THE FUGUE</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=4> Following is an outline of Hugo Norden's "Foundation Studies in Fugue." During the Spring 2000 semester at <A HREF="http://www.mwsc.edu" TARGET="_BLANK">Missouri Western State College</A>, I studied counterpoint in my composition class. The next step for me was to study the fugue, a musical form in which counterpoint is used in its most pure way. I wrote this outline first, to get a more intensive reading out of Norden's book, and second, to have a quick reference about the structure of fugues in the future. Hopefully this outline will help you getting interested in fugues and having a good reference source. This outline will not prevent you from reading the book, since it is much more in detail with many music examples. If you like this outline (or don't like it), you can <A HREF="mailto:cpb7079@griffon.mwsc.edu">e-mail</A> me and give me some feedback! </FONT SIZE> </P> <HR> <TABLE width="100%" border="0" cellspacing="0" cellpadding="10"> <TR> <TD ALIGN=CENTER><A HREF="fuge.html#1">Chapter I</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#2">Chapter II</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#3">Chapter III</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#4">Chapter VI</A><TD> </TR> <TR> <TD ALIGN=CENTER><A HREF="fuge.html#5">Chapter V</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#6">Chapter VI</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#7">Chapter VII</A><TD> <TD ALIGN=CENTER><A HREF="fuge.html#8">Chapter VIII</A><TD> </TR> </TABLE> <HR> <P ALIGN=CENTER><FONT SIZE=6><B>THE FUGUE</B></FONT></P> <P ALIGN=CENTER>Based on Hugo Norden's <I>Foundation Studies in Fugue</I></P> <P ALIGN=CENTER><A NAME=1><FONT SIZE=5><B>Chapter I</B></FONT></A></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Subject</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-A fugue consists of the statement and development of a single subject (the main idea). It usually is </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>stated at the beginning of the fugue by a single voice.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-The subject usually has following three characteristics:</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ it is usually brief, but represents a complete musical idea</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ it is easy recognizable in contrapuntual texture</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ it is easy to manipulate (harmonic, melodic, and contrapuntual) and to exploit</FONT></P></DD></DL> <P ALIGN=LEFT> <FONT SIZE=3>-The opening of a subject ('head' of the subject or 'La tęte du sujet') should be strong and easy to </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>recognize.</FONT></P> </DL> <P ALIGN=CENTER><A NAME=2><FONT SIZE=5><B>Chapter II</B></FONT></A></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Answer</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-In the simplest case, the answer is the subject (dux) transposed to the dominant key (5<SUP>th</SUP> higher or </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>4<SUP>th</SUP> lower).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-If a subject in the major key contains a leading tone, the answer (comes) requires an accidental for </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>its leading tone.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-If a subject is in the minor key, the answer requires accidentals for both the II and VII notes of the </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>dominant key.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-If the subject contains additional accidentals, these too must be reflected in the answer.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-An answer that is a literal transposition (every note is transposed exactly a perfect 5<SUP>th</SUP> up or a </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>perfect 4<SUP>th</SUP> down) of the subject to the dominant key is identified as a REAL answer.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-When notes in the subject are in the dominant key andare answered in the tonic key in contrast to </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>the rest of the subject, the resulting answer is said to be TONAL.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=4><B>Subjects That Require a Real Answer</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Those subjects will begin and end on the I or III notes, and</FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-They will not contain a leap from the I or III notes to the V or VII notes at or near the beginning.</FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>Subjects That Require a Tonal Answer</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Group I</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ Subjects of this kind will begin with one or more notes in the dominant key and complete </FONT> </P></DD><DL> <DD><P> the subject in the tonic key. The parts that are in the dominant key will be answered in </P> <DD><P ALIGN=LEFT><FONT SIZE=3>the tonic key, and vice versa.</FONT></P></DD></DL> </DL> <P ALIGN=LEFT> <FONT SIZE=3>-Group II</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ Subjects of this kind start in the tonic key and end in the dominant key, while their answers </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>do exactly the opposite.</FONT></P></DD></DL> </DL> <P ALIGN=LEFT> <FONT SIZE=3>-Group III</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ Subjects of this kind start in the dominant key, have a middle section in the tonic key, and </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>end in the dominant key. </FONT> </P></DD></DL> </DL> <P ALIGN=LEFT> <FONT SIZE=3>-Group IV</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ The subject contains a leap from the I or II to the V or VII notes at or near the beginning, </FONT></P></DD> <DL><DD><P ALIGN=LEFT>or</P></DD></DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>~ The entire subject is answered in its subdominant key. Subjects answered this way usually </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>begin on V or VII notes.</FONT></P></DD></DL> </DL> <P ALIGN=LEFT> <FONT SIZE=4><B>Modulating Effects to the Dominant Key</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-In order for a subject to end on V or VII, a modulation from the tonic key (either the opening or </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>the middle section of the subject) has to take place. Following thematic devices serve this </FONT></P><DD></DL> <DL><DD><P ALIGN=LEFT>purpose:</P></DD></DL> <DL><DD><P ALIGN=LEFT><FONT SIZE=3>~ The modulation takes place at an ascending major 2<SUP>nd</SUP> from accented to unaccented notes </FONT> </P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ It takes place between repeated notes from accented to unaccented notes</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ In a conspicious leap, usually (but not necessarily) from unaccented to accented notes</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ After a tied or dotted note or rest, provided it does not damage a suspension</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ In a descending minor 2<SUP>nd</SUP> , often from accented to unaccented notes</FONT></P></DD></DL> <P ALIGN=CENTER><A NAME=3> <FONT SIZE=5><B>Chapter III</B></FONT></A></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Countersubject</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Countersubject means countermelody, counterpoint (punctus contra punctum). In a fugue it is the </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>counterpoint to the subject appearing simultaneously with the comes.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-The countersubject must be so constructed that it will function equally well both above and below </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>the subject and the answer (invertible counterpoint).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3><B><FONT SIZE=4>Process for Composing a Countersubject</FONT></B> </FONT> </P> <P ALIGN=LEFT><FONT SIZE=3><I>1.) All of the subject is in the tonic key:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Those subjects require a real answer (literal transposition). But, these in turn subdivide into two </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>classes of contrapuntual construction:</FONT></P> <DD><P ALIGN=LEFT><FONT SIZE=3>~ those without tied notes, and</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ those with tied notes</FONT></P></DD></DL> <P ALIGN=LEFT> <FONT SIZE=3>-Subjects without tied notes:</FONT></P> <DL> <DD><P>~ the longer note, whether in the subject or in the countersubject, will serve as Cantus </P></DD> <DL> <DD><P>Firmus; the part with faster <FONT SIZE=3>notes will act as counterpoint</FONT></P></DD></DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>~ when the countersubject is transposed to its dominant key, it automatically provides the </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>countersubject for the </FONT>answer</P></DD> </DL> </DL> <P>-Subjects with tied notes:</P> <DL> <DD><P>~ the suspensions and retardations in the subject should be treated first</P></DD> <DD><P>~ then all the suspension opportunities against the subject should be treated</P></DD> <DD><P>~ finally, the remainder of the countersubject should be composed and the suspensions </P></DD> <DL> <DD><P>embellished if desired</P></DD> </DL> </DL> <P><I>2.) Most of the subject is in the tonic key:</I></P> <P ALIGN=LEFT>-Set up a three-stave Double Counterpoint format with the subject on the top line, and on the </P> <DL> <DD><P ALIGN=LEFT>bottom line the answer transposed to its subdominant key.</P></DD></DL> <P ALIGN=LEFT>-Fill in the countersubject on the middle line so that it will produce correct counterpoint </P> <DD><P ALIGN=LEFT>against both subject and answer.</P> </DL> <P ALIGN=LEFT>-Copy out the countersubject in Double Counterpoint against both subject and answer (transposed </P> <DL> <DD><P ALIGN=LEFT>back to its original key). The countersubject, too, must be transposed to match the </P> <DD><P ALIGN=LEFT>key of the answer.</P> </DL> <P ALIGN=LEFT>-Although the countersubject is the same melodically for both subject and answer, its contrapuntual </P> <DL> <DD><P ALIGN=LEFT>operation is different.</P></DD> </DL> <P ALIGN=LEFT>-If the subject begins on a dominant note, the countersubject should begin before the subject </P> <DL> <DD><P ALIGN=LEFT>in order to make a suitable approach to the limited contrapuntual resources that are </P></DD> <DD><P ALIGN=LEFT>available in Double Counterpoint at the 9<SUP>th</SUP> (The answer transposed to its </P></DD> <DD><P ALIGN=LEFT>subdominant key and the subject form a 9<SUP>th</SUP> in Double Counterpoint format, in </P></DD> <DD><P ALIGN=LEFT>between which the countersubject must be added).</P></DD> </DL> <P ALIGN=LEFT><I>3.) Most of the subject is in the dominant key:</I></P> <P ALIGN=LEFT>-Set up a three-stave Double Counterpoint format with the subject on the bottom line, and the </P> <DL> <DD><P ALIGN=LEFT>answer transposed to its dominant on the top-line. The dominant portion of the </P> <DD><P ALIGN=LEFT>subject thus will relate in Double Counterpoint at the 8<SUP>th</SUP> ve while the notes in the tonic </P> <DD><P ALIGN=LEFT>key relate at the 9<SUP>th</SUP>.</P> </DL> <P ALIGN=LEFT>-Fill in the countersubject on the middle line so that it will provide suitable counterpoint against both </P> <DL> <DD><P ALIGN=LEFT>subject and answer.</P> </DL> <P ALIGN=LEFT>-Copy out the countersubject in Double Counterpoint against both subject and answer (both </P> <DL> <DD><P ALIGN=LEFT>countersubject and answer transposed to its original key).</P> </DL> <P ALIGN=CENTER><A NAME=4><FONT SIZE=5><B>Chapter IV</B></FONT></A></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Stretto</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Stretto is the contrapuntual device wherein the subject or answer is played against itself </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>canonically, or when the subject and answer are made to overlap.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-It is most necessary in a stretto formation that all entries of the subject or answer be stated with all </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>intervals being used literally. The themes can be modified intervallically or used only </FONT></P> </DL> <DL><DD><P>partially.</P></DD></DL> <P ALIGN=LEFT><FONT SIZE=3><I>1.) Literal Stretto:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The subject is treated canonically, the answer does not appear. </FONT> </P> <P ALIGN=LEFT><FONT SIZE=3>-It can be structured as a canon at the 8ve, in Double Counterpoint at the 15<SUP>th</SUP>. This process will </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>automatically produce one canon at the 8ve above, and another canon at the 8ve </FONT></P> </DL><DL><DD><P>below.</P></DD></DL> <P ALIGN=LEFT><FONT SIZE=3><I>2.) Stretto by contrary motion:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-This kind of a stretto can be constructed by exact intervallic imitation in contrary motion (an </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>ascending minor 2<SUP>nd</SUP> can just be imitated by a descending minor 2<SUP>nd</SUP>) or by inexact </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>imitation (an ascending minor 2<SUP>nd</SUP> can be imitated either by a descending minor 2<SUP>nd</SUP> </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>or a descending major 2<SUP>nd</SUP>).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3><I>3.) Retrograde Stretto:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>- The subject or answer is played backwards against itself (Crab Canon or Cancrizans Motion).</FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Three reasons why this kind of stretto is impractical:</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ it cannot be recognized audibly, </FONT> </P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ many rhythms become disjointed and ineffective when heard backwards, and</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ it is likely to set up awkard harmonic situations.</FONT></P></DD></DL> <P ALIGN=LEFT> <FONT SIZE=3><I>4.) Stretto by Augmentation:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The subject is played against the subject in augmentation (the note values are doubled, tripled, </FONT></P><DL><DD><P>etc.).</P></DD></DL> <P ALIGN=LEFT><FONT SIZE=3><I>5.) Stretto by Diminution:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The subject is played against the subject in diminution (smaller note values).</FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>6.) Stretto in Contrary Motion and Retrograde:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-This kind of stretto entails a crab canon in contrary motion.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>7.) Stretto in Contrary Motion and Augmentation:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-This kind of stretto entails an augmentation in contrary motion.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>8.) Stretto in Contrary Motion and Diminution:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>9.) Stretto in Retrograde and Augmentation:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>10.) Stretto in Retrograde and Diminution:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>11.) Stretto in Contrary Motion, Retrograde, and Augmentation.</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>12.) Stretto in Contrary Motion, Retrograde, and Diminution.</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>Solving the Stretto Problem</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Constructing Strettos to a given subject, as in a fugue examination, and</FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Constructing an original subject to yield pre-planned stretto combinations.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>1.) Constructing strettos to a given subject:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Fit the beginning of the subject against the end of the subject in as many ways as possible.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3><I>2.) Composing a subject with pre-established stretto requirements:</I></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Formulate the problem (for example compose a subject of type real in the key of D-major, 2/4 </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>rhythm, 3 measures long, to yield a stretto at the 8ve above after 1 measure).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Set up the canon problem so that the first and last notes will conform to the terminal specifications </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>stated before.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Complete the canon.</FONT></P> <P ALIGN=CENTER><FONT SIZE=5><A NAME=5><B>Chapter V</B></A></FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Codetta and Episode</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The terms codetta and episode both refer to connecting passages that are generally composed of </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>free material that may be either similar to or different from motives in the subject or </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>countersubject. The codetta is used to lead to a new entrance of the subject or </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>answer in the exposition, while the episode is designed to link entries of the subject or </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>answer after the exposition is completed.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=4><B>Codetta</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The first codetta appears at the end of the initial statement of the subject when there is a time lag </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>between the end of the subject and the beginning of the answer.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-The codetta between the second and third entries is usually longer and more substantive than the </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>one between the first and second entries.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-In a four-voice fugue there can also be a codetta between the third and fourth entries.</FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>Episode</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The episode differs from the codetta chiefly in its location in the fugue, which is after the exposition </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>(all voices have come in with the subject and answer for the first time).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=4><B>Process for the Writing of an Episode</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The harmonies at the two ends of the episode must be clearly defined (those two ends are the </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>ending of one subject and the beginning of the other subject).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Decide on a contrapuntual or harmonic device to direct the contrapuntual texture from the </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>beginning to the end of the episode (for example a canon in contrary motion derived </FONT> </P> <DD><P ALIGN=LEFT><FONT SIZE=3>from the opening motive of the countersubject).</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Connect the episode artistically at both ends so that there are no 'seams' or 'rough edges'.</FONT></P> <P ALIGN=CENTER><FONT SIZE=5><A NAME=6><B>Chapter VI</B></A></FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Pedal-Point and Cadenza</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Pedal-Point:</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ The purpose of a pedal-point is to reestablish the tonality of the composition after it </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>has become clouded by the numerous modulations and disgressions along </FONT> </P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>the way within the middle entries of the subject and answer and in the </FONT></P></DD></DL> </DL><DL><DD><P>connecting episodes.</P></DD></DL> <P ALIGN=LEFT> <FONT SIZE=3>-Cadenza:</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ The purpose of the cadenza is to halt the contrapuntual flow of the fugue, and to </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>bring the composition to a satisfactory close.</FONT></P></DD></DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>~ The cadenza is generally made up of new material that does not appear in the </FONT> </P></DD><DL> <DD><P ALIGN=LEFT> <FONT SIZE=3>subject (other than the episode and the pedal-point)</FONT></P></DD></DL> </DL> <P ALIGN=CENTER> <FONT SIZE=5><A NAME=7><B>Chapter VII</B></A></FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>The Exposition</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The opening section of the fugue wherein each voice is brought in singly, alternating between </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>subject and answer.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Following is one example of a possible exposition in a four-part fugue: </FONT> </P> <PRE> S subject countersubject A answer countersubject free part T subject countersubject free part free part B answer </PRE> <P ALIGN=LEFT> <FONT SIZE=4><B>The Process of Writing an Exposition</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Write the correct answer to a subject and compose a suitable countersubject.</FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-Decide on an entrance arrangement, and write in the subject, answer, and countersubject where </FONT> </P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>desired.</FONT></P> </DL> <P ALIGN=LEFT><FONT SIZE=3>-Complete the exposition by supplying the necessary codetta and free parts.</FONT></P> <P ALIGN=CENTER><FONT SIZE=5><A NAME=8><B>Chapter VIII</B></A></FONT></P> <P ALIGN=LEFT><FONT SIZE=4><B>Harmony</B></FONT></P> <P ALIGN=LEFT><FONT SIZE=3>-The fugal harmony must be considered on three levels:</FONT></P> <DL> <DD><P ALIGN=LEFT><FONT SIZE=3>~ the key scheme of the composition as a whole</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ the underlying chordal structure</FONT></P></DD><DD><P ALIGN=LEFT> <FONT SIZE=3>~ the vertical relationship between the several voices</FONT></P></DD></DL> <P ALIGN=LEFT> <FONT SIZE=3>-In order to see the underlying chordal structure, it is necessary to remove all embellishing </FONT></P> <DL><DD><P>materials.</P></DD></DL> <P ALIGN=LEFT><BR><BR> </P><HR> <P ALIGN=CENTER>  <a href="http://usa.nedstatbasic.net/cgi-bin/viewstat?name=fugue"><img src="http://usa.nedstatbasic.net/cgi-bin/nedstat.gif?name=fugue" border=0 alt="" nosave width=22 height=22></a>   <script type="text/javascript" language="JavaScript">  </script>  </P> </BODY> </HTML>