RULES ... ?! ... What's this about rules ... ? Well, let's think about it for a minute ... Rules are there to serve us [See blog, The Rule Book]. Put very simply, there's stuff that we should avoid doing ... stuff that could take us in the wrong direction without having a good reason and purpose in mind [See blog, Getting Started With Writing, Part XXVIII]. For example, when we're camping, the rule is, we don't pitch our tent in the middle of the only single lane dirt road leading in and out. Why? ... because if we pitch our tent on main street we can expect to get run down by a bus. If we're spending the night in the woods, the rule is, we don't pitch our tent on the southeast slope of a mountain. Why? ... because that's the part of the landscape that receives the sun's warmest rays in the morning, and cold blooded animals like venemous snakes prefer to make their dens nearby so they can sun themselves in the morning to get warm -- we camp for recreation, not to become victims of venemous snake bites. When we're camping, the rule is, we don't barbeque on a charcoal stove barefoot or in our flip-flops. Why? ... because it means a 3rd degree burn if one of those red hot coals drops off the stove and lands on bare toes. Another rule about camping: during the summer months we don't wear purple (violet), blue, blue-green, or yellow clothing in the woods. Why? ... because purple (violet), blue-green, and blue are the only colors that bees, wasps, and hornets can see; their eyes also see something called "bee's purple," which is a combination of yellow and ultra-violet, something that human eyes can't see; everything else to them looks black, white, and gray; these insects are most likely to be attracted to something purple (violet), blue, blue-green, or yellow in color. So, the rule is, when we're in the woods in the summer, we don't wear a yellow or purple shirt. There are many, many other examples, but they all illustrate a point: Theorists have distilled from the many inspired composers of earlier centuries, notably J.S. Bach, a set of "rules" based upon what works best under ordinary circumstances. An organist needs to become familiar with and learn these rules so that their own writing or improvising sounds equally smooth and beautiful. This series of blog postings describes many of these part-writing rules in the course of discussion ... stuff not to do, and stuff we can do occasionally ... and this posting will serve as a quick reference summary. This does not take in every possible rule but rather several of the more important things to remember when writing and editing our own compositions for the organ; for those who wish to explore this is closer detail, reference works such as Marcel Dupre's "Methode d'Orgue" may be consulted (by codifying these laws and rules in Part II of this work Dupre provides the means to get through a whole set of difficulties encountered at every step in playing organ pieces, all based on examples drawn from the organ works of Bach). Once we've written a work, we need to go back and edit it, to see if we can find anything that needs "fixing;" included here are such things as eliminating unprepared dissonances in fugal answers, avoiding consecutives (5ths, octaves, and unisons), augmented intervals, and the leading of all 4 voices in similar motion either up or down, making sure the voices stay within their normal ranges and do not cross (unless it's to teach some aspect of technique or maybe, as Bach demonstrated in some of his settings of the Chorales, to avoid consecutive perfect 5ths or octaves between the inner voices), making sure the soprano and bass lines move in contrary motion whenever possible, making sure that 7th scale degrees always rise a half step when they function as leading tones, making sure that upward scalar passages in the minor key have the 7th AND 6th scale degrees raised a half step (following the melodic minor scale), and making sure that unnecessary double bars and uneven spacing of bar lines, if present in the electronic score, are eliminated or otherwise fixed. A leap of a 7th up or down should be avoided in the soprano and middle voices but is less objectionable when confined to the bass (examples of this may be found in the scores of the c minor Op. 11 Prelude & Fugue and the Op. 31 and Op. 32 Postludes); when thinking instrumentally the leap of a 7th in the bass is permissible in an ascending or descending scalar passage if it will prevent similar motion in all 4 parts or to keep the scale from traveling too high or low in the bass. For examples of how this works with an ascending diatonic scale in the bass, see Communion in E Major Op. 17, 1st section, and Praeludium from Op. 10, 1st fugal section and 2nd free section. For an example of how this works with a descending diatonic scale in the bass, see the Fugue from Op. 26. For examples of how this works with a descending diatonic scale in the bass, see Lied in B Major Op. 15, trio section, Pastorale in Ab Major Op. 12, 3rd section, and Choral from Op. 18, final section. Another rule is, when we're harmonizing a melody at a cadence, we never follow the dominant chord with the subdominant chord; there is always the rare exception, but generally the best suggestion is, after the dominant chord we just resolve it to the tonic chord. Usually these kinds of things are an easy fix, but very often they can escape our notice when we're in the middle of doing our writing and can slip through our attention until we go back and do some editing another time with fresh eyes. In general, when we're writing polyphonically in 4 parts, each of the parts should stay within an octave of the adjacent part(s) and within their own voice ranges, generally never crossing; when it's a tight squeeze they may share a unison provided it leads to better voice leading, and the bass may descend all the way to the bottom of the manual bass octave, i.e. to low 8-foot C2. The general limits of range of the voices used in 4 part spread harmony may be accepted as: 1) SOPRANO (middle C4 to A5), 2) ALTO (tenor F3 to C5), 3) TENOR (tenor C3 to middle G4), and 4) BASS (D2 to middle E4). It should be emphasized that these are GENERAL limits of range and these values may be listed slightly differently elsewhere. At times it's permissible to extend the upward range of the soprano line one more semitone to Bb5 if it creates better voice leading and can be approached by step; the score for Fugue in g minor Op. 23 has an example of this. As for the octave registers, they're named after what's found on the standard 88-key piano keyboard with the lowest C (16-foot C) on the piano being "C1." In this system, numbering upward, the low bass C key on the manual (8-foot C) is then notated "C2," tenor C would be "C3," middle C would be C4," altissimo C above that would be "C5," and the high C key would be "C6." As was said, we should endeavor to write pitches which stay always within the ranges of the individual voices and never outside the range of a given voice (the bass line in organ music may be written very low, all the way to the bottom, if desired). This means keeping the soprano and alto lines generally within an octave of each other, and also the alto and tenor generally within an octave's distance (the bass is permitted to descend well past an octave below the tenor, if desired). There are exceptions to this, of course; for example, at the conclusion of a fugue, the alto may be written low and the soprano high where more than an octave's distance separates these 2 voices on the final chord, as in Bach's "Little" Fugue in g minor [See also Fugue in g minor Op. 23]. When we're writing our fugues we need to pay close attention to the boundaries of the 2 inner voices, keeping in mind that the alto should not descend below tenor F3 and the tenor never higher than alto A4. The alto may rise as high as soprano C5 and the tenor may descend as low as tenor C2, but these are the extreme limits. It helps to visualize these notes on the staff as the goal posts and foul lines of the playing field on which the 4 voices of our music will play out. In any system of tonal triadic harmony as we have it today, where the 3 functional primary chords of a key (tonic, dominant, subdominant) are composed of 3 notes each, it will be necessary to double one of these notes to create a 4 part texture. When a triad is in root position, we generally double the root; when it's in 1st inversion, we generally double the soprano note; when it's in 2nd inversion, we generally double the bass note. There are exceptions: With minor triads (root or 3rd in the bass), the 3rd is often doubled, particular if the 3rd is the tonic, dominant, or subdominant note of the key. With diminished triads (usually in 1st inversion), we double the 3rd; when the 5th is in the soprano, we double the 5th. WIth augmented triads, we double the bass note. In a 7th chord, usually all 4 voices are present; in the major-minor 7th chord with the root in the bass, the root is sometimes doubled and the 5th is omitted. In any altered triad, we avoid doubling the altered tone unless it's the root; otherwise, it's treated as non-altered triads. As for chord connection, we should try to move each voice the shortest distance possible, with the soprano and bass moving in contrary motion wherever possible. In contrary motion, voices move in opposite directions; when one moves upward, another moves downward. In oblique motion, a voice moves upward or downward while another remains stationary. In similar motion, voices move upward or downward together. In 4 part writing we do not double the leading tone, any altered tone (including the 6th and 7th scale degrees in minor), any nonharmonic tone, or the 7th of any chord. The 7th of a dominant 7th chord is considered such a charged tone that it should never be doubled in 4-part writing. Consecutive (similar) motion in perfect consonances (unisons, perfect 5ths, octaves) between any 2 parts is strictly forbidden in species counterpoint instruction, and during the common practice period of the 17th-18th centuries it was strongly discouraged in order to maintain the relative independence of the individual parts. So-called "consecutive perfect 5ths" or "parallel 5ths" are progressions in which the interval of a perfect 5th is immediately followed by a different perfect 5th between the same 2 musical parts, or voices. Consecutive perfect 4ths are allowed -- BUT, be advised -- when they occur between 2 voices in fugue writing and the same 2 moving lines reappear in subsequent entries one has to be on guard, because consecutive perfect 5ths result when consecutive perfect 4ths are inverted. It's a beginner's mistake that can come back and have us shaking our heads later, about why we didn't catch it sooner -- but, that's perfectly okay, because that's how we learn. TIP: If we've written fugues, especially with 2 or 3 countersubjects which reappear in subsequent entries, we should check the exposition for consecutive 4ths that may have escaped our attention and eliminate them, then go back and get the subsequent entries congruent with it. Perfect 5ths and octaves sound "pure" to the ear; this has the psychoacoustic effect momentarily of "fusing" the separate voices and weaking their harmonic independence, thus, voices moving in parallel perfect intervals tend to lose their harmonic autonomy for a moment.
Thus, it's important harmonically to observe a few rules of counterpoint, one of which is to use as many imperfect consonances (major or minor 3rds or 6ths) as possible because these will help outline the horizontal chordal movement.
Because perfect intervals like a 5th or an octave don't have "quality" -- meaning that they can't be major or minor -- as a result they don't give us that sense of the chord and tend to ruin the strength of a harmonic progression.
So, the golden rule therefore is: never use octaves of 5ths in succession -- instead it's better to follow each with an imperfect consonance like a 3rd or a 6th. In the 19th century the writing of consecutive perfect 5ths became more common however, arising out of new textures and new conceptions of propriety in voice leading generally; they even became a stylistic feature in the work of some composers, notably Chopin, and with the early 20th century and the breakdown of common practice norms the prohibition became less and less relevant (a notable example is the score for "Berceuse" from Twenty Four Pieces in Free Style, Op. 31, by Louis Vierne). We're very apt to run into consecutive octaves and perfect 5ths (and their inversions, perfect 4ths) when we're writing countersubjects for fugues and other passages having imitations or canons and therefore these should be carefully scrutinized. When we find consecutive octaves or perfect 5ths we may succeed in combing them out by creating a suspension, i.e., by simply dotting the rhythm of one of the lines, which preserves the original shape of the melodic line without changing any of the notes themselves, or maybe holding a note longer by tying it to the next one. Sometimes a solution to consecutive 5ths can be found by inserting a brief rest. If none of this works, we next think to change one or more notes to the closest note(s) that preserves the prevailing harmony and the overall shape of the moving line. Sometimes the direction of the line itself, up or down, begs to be changed, and this may turn out to be the best way to handle it. J.S. Bach, believe it or not, in some 413 four-part settings of the Lutheran hymns of his day, sometimes permitted voice lines to cross (apparently to avoid consecutive 5ths and octaves) but in other place included successive 5ths and octaves in some of these settings! The ear, of course, has to be listening to everything when we're making any such adjustments; they should in every case be the least change in the shape of the line that we can get away with; the result should be undetectable to most listeners and for those with a particularly keen ear more like a minor little variation inserted deliberately to keep things from sounding monotonous [for examples of how this is done, the scores for Chorale in d minor Op. 9, Pastorale in Ab Major Op. 12, and Choral and Fugue in D Major Op. 18 may be checked]. When writing polyphonically each part should be singable; this means avoiding melodic leaps of an augmented 2nd, augmented 4th (tritone), or of compound (greater than an octave) intervals because these are all awkward to sing. A leap of a diminished 5th up or down is considered permissible [examples of this type of leap may be found in the subject from the Op. 26 Fugue (upward leap of diminished 5th) and the 2nd countersubject from the the Op. 24 Fugue (downward leap of a diminished 5th)]. It's also best, generally, to avoid leaps of a 7th, save for the exceptions mentioned above. We generally avoid having 2 adjacent voices approach each other momentarily at the interval of a minor 2nd, but, if it creates better voice leading and there's no acceptable alternative, the minor 2nd "near miss" interval made by the 2 voices is not strictly forbidden [See blog, Getting Started With Writing, Part XXI]. When 2 voices move upwards or downwards in similar motion, the lower voice is usually not allowed to move to a position higher than that just left by the upper voice; this will avoid any ambiguity to the ear which might follow an apparent melodic progression between the 2 voices. Triad positions should be changed when necessary to keep voices in correct pitch range or to avoid large leaps in an inner voice. In 4 part triadic harmony one of the notes must be doubled, which is usually the root of the chord; at a cadence, the root of the final triad also may be tripled, omitting the 5th of the chord. The 7th of a 7th chord is expected to resolve downward by step to the 3rd of the next major or minor chord; less commonly it may be found resolving upward by step, as in the final cadence of the Op. 26 Fugue. All 4 notes of a dominant 7th chord are usually present, but for smoothness and voice leading, the 5th may be omitted and the root doubled. As for things we can occasionally do, we generally and rather sternly avoid voice crossings in 4-part (SATB) texture; when in fugue writing the exact duplication of the melodic outline of a voice line would impose a voice crossing with an adjacent voice, it's generally better to transpose one or more adjacent notes in that melodic line an octave higher or lower; this does not apply to the subject however -- the melodic outline of a fugue subject is considered inviolate, and to change its melodic outline in any subsequent entries would do violence to it and alter its character. Using Bach as authority, crossing of voices is justified however if it improves voice leading or teaches some aspect of technique; this might apply to certain studies (etudes) with high Pedal parts, for example, deliberately written this way for the purpose of teaching, as in Trio in Eb Op. 14; Bach himself used crossings of the inner voices many times in his 4 part harmonizations of the Lutheran Chorales. A diminished 5th preceded or followed by a perfect 5th is generally permissible, although some prefer to avoid this type of motion altogether; some writers avoid only motion one way (diminished 5th to perfect 5th, or perfect 5th to diminished 5th) or maybe if only the bass is involved; here again, Bach employed this freely in his Chorales. Two adjacent voices may form a unison (share the same tone momentarily) when there is no other acceptable alternative, provided the unison is within the normal range of both voices. The 7th scale degree in a major key, or the raised 7th scale degree in a minor key, when it functions as a leading tone, should progress upward to the tonic note when in an outer voice (soprano or bass); exceptions to this are rare. We should keep in mind however that not every note a half step below the tonic functions as a leading tone and therefore would not require the same resolution [See blog, Getting Started With Writing, Part XIX]. A leading tone found in a moving bass line below the harmony of a tonic chord, for example, is not functioning as a leading tone and does not require a resolution to the next note above it. The leading tone, as was stated before, is such a charged note that it should never be doubled; when it functions as a leading note in a dominant harmony and it's trying to "get somewhere," it resolves upward a half step to the tonic note. If it does not, it's called a "frustrated leading tone," and should never appear in an outer voice (soprano or bass) where it's most noticeable; frustrated leading tones in an inner voice (alto or tenor) are permissible but are commonly avoided [See blog, Getting Started With Writing, Part II]. The settings of the Chorales written by Bach contain many instances of a frustrated leading tone in an inner voice resolving at a cadence on the 5th below instead of rising a half step. At a final cadence the rule is, the leading tone is never allowed in the bass, but composers have occasionally found reason to ignore this; Louis Vierne, for example, broke it with abandon in the coda of the Fugue from his First Symphony for organ. NOTE: This Symphony is in 6 large movements with the Fugue appearing as the second movement; the entire Symphony is dedicated to his dear friend Alexandre Guilmant, who was a master fugue writer and a stickler for clarity and for following the rules of voice leading to the letter; knowing this, and how strict Guilmant was about this in his teaching, Vierne approaches the final cadence of this Fugue (after a passage which is already heavy handed enough) with slow spread chords for both hands holding doubled minor second intervals at a fff dynamic; what follows is a leading tone written into the bass, and, if that wasn't enough to jar the dedicatee's sensitivities, Vierne doubled this leading tone in octaves using both feet -- salt, pepper, and vinegar -- quite a combination for old Guilmant's digestion to handle ... but Vierne wrote it this way to grab the older man's attention; it was a prank, pure and simple; old Guilmant evidently took the joke well because he not only appreciated the dedication but learned the whole Symphony note for note and traveled around the world performing it with pride. Life improves dramatically when someone breaks a rule and finds beauty where they were told, or understood, that there was none. Pastorale in Ab Major Op. 12 also contains an example of a leading tone rising a half step in the bass at a final perfect cadence. The tritone (3 whole steps) is resolved inward if it's a diminished 5th and outward if it's an augmented 4th, whenever possible; this so-called "diatonic tritone" is the basis of all Western music, a very unstable interval, and wants to resolve to the dominant chord [See blog, Modal Harmony, Part III]. These are the main rules that help keep our part writing out of any serious trouble, but the bottom line is, once you get beyond these basic rules, an artist uses them as his/her most obedient humble servants and is free to write as (s)he wants. Some contemporary new music written in the neo-style breaks just about every rule of voice leading there is, and, in certain situations, it creates interesting effects. It's important to remember: music first, theory second ... it's up to us to turn the latter into the former. In addition, there are also certain general practices in force in fugue writing which come under the heading of "rules": It matters, for example, on which note of the scale the subject begins and whether or not it leaps; we need to know this in order to arrive at a correct answer; this is because the beginning and ending pitch of the subject is important in determining whether the answer will be tonal or real. There are 2 types of answers in fugue writing: tonal and real. A tonal answer typically (but not always) stays in the same key as the subject where some linear intervals may be altered to stay in the tonic key; it also usually has the dominant note (scale degree 5) on the 1st or 2nd beat. With a real answer all intervals are transposed a 5th up or a 4th down, as an exact replica of the subject intervals, but in a new key; it will either modulate to the dominant or imply a dominant harmony. If the subject begins on the octave or 1st degree of the key, then the answer (the transposition by which the subject is repeated in similar manner) generally follows on the 5th degree of the key (i.e., the answer is in the upper 5th, or dominant); if the subject begins instead on the 5th degree of the key, then the answer should follow on the 1st degree of the key (i.e., the answer is in the upper 4th, or subdominant); this could take the form of a real answer in the subdominant key OR a tonal answer in the dominant key. The answer, if it's an exact transposition of the subject, note for note, creates a "real fugue"; if one or two of the answer's beginning notes must be adjusted tonally to stay in consonant tonic harmony when the answer begins, then we have a "tonal fugue." If the subject starts on the tonic (1st degree) and leaps to the dominant (5th degree), and if the answer will be in the dominant key, then the answer must leap from the dominant to the tonic; this is because a tonal answer is required; if the answer were real, the result would be too sudden a change to be acceptable because the music would arrive in a new tonic on the 2nd degree. The only exception to this is when the tail (last few notes) of the subject outlines the dominant scale or otherwise points strongly to the dominant key; in this situation we can have a real answer in the dominant. By the same reasoning, if the subject leaps from dominant to tonic, and the answer is to be in the dominant key, then it would be answered by tonic to dominant. Tonal answers are very common in Bach's keyboard fugues; 28 of the "48" (Well-Tempered Clavier, Vols I and II), for example, have tonal answers; all the rest have real answers; so we see that in the majority of cases in this collection the melody is slightly changed when the answer appears. Intervals of a subject that ranges at its beginning in the lower part of the scale (scale degrees 1-5) will appear contracted in the answer (in the range of scale degrees 5-8) -- for example, leap of a 5th in the subject will contract to leap of a 4th in the answer, a 3rd to a 2nd, a 2nd to a unison. Conversely, intervals of a subject that ranges at its beginning in the upper part of the scale (scale degrees 5-8) will appear expanded in the answer (in the range of scale degrees 1-5) -- for example, a leap of a 4th in the subject expands to a 5th in the answer, a unison to a 2nd, a 2nd to a 3rd. These intervallic contractions and expansions are accommodations to the hold of tonic harmony, which generally prevails at the close of the subject, as the answer starts ... UNLESS the tail of the subject points strongly to the dominant. The contractions and expansions in the tonal answer last only until the prevailing tonic harmony shifts toward the dominant; as that shift occurs, the intervals of the subject are duplicated in the answer such that the answer is an exact transposition of the subject a 5th higher. A subject beginning on the 2nd degree of the scale is generally answered by the 6th degree, and vice versa; the 3rd degree is generally answered by the 7th degree, and vice versa; and the 4th degree, like the 5th degree, is answered by the 1st degree, and vice versa. Exceptions to these "rules" are encountered at times for reasons which may make it necessary, when the subject starts on the 1st degree of the key, for it to be answered on the 4th degree of the key ... or when it starts on the 5th degree for it to be answered on the 2nd degree. Many theorists teach that fugue subjects DO NOT begin on scale degree 3 --the reason being that this would force the answer to begin on an unprepared dissonance -- a diminished triad on scale degree 7; this does not take into consideration subjects which have a tail which either outlines part of the scale of the dominant key or modulates, pointing strongly to the dominant key. In such a case, the answer needs to be tonal but it's certainly within the realm of easy possibility. We might therefore create a personal "rule" for our own selves: a fugue subject may begin on the 3rd scale degree provided that its tail either outlines a segment of the dominant scale or points strongly to the dominant and is supplied with a tonal answer [See blog, Getting Started With Writing, Parts XVIII, XXXIII, XXXVI]. The same applies to the (1st) countersubject; if its last note or two points to the dominant key, then a chromatic inflection will be needed in this last note or two to allow a smooth return to the tonic key for the 3rd entry and keep the music from escaping to the dominant of the dominant this early in the fugue. Rules have come into existence by examining the habits of composers over a long period of time, then determining what they did and did not do in order for the music to sound smooth and satisfying. A bit of advice about editing: we're human; we have to expect that occasionally a minor error may creep into our writing while we're seized with inspiration and our "pen" is flying ... something we know better not to do but we just didn't see it on the first draft. Before we take our pieces to a printing company and pay to have them bound in a personal working booklet with laminated front and back covers we should therefore pay heed to 3 things: Firstly, and this is very important ... we need to conduct a very careful, slow, painstaking, thorough review to edit every score, measure by measure, to check for errors; having to take it back to the printer to replace defective pages once the booklet is already bound adds to the cost and may succeed in damaging something, as this is typically done by machine. While this review is taking place we should also consider assembling a cover page, table of contents, and suggestions for performance to be included in the master copy. Secondly, once we're certain that no further corrections will be needed in the master copy and all the information is there, it's very helpful to convert the scores to PDF files which can be printed front and back to minimize the number of pages; fewer pages mean fewer page turnings when reading from the booklet. Thirdly, and this seems obvious, we should request that the booklet be bound in a plastic comb or coil binding so it will lay flat on the rack. There's one more thing: Before any budding composer gets disgusted with themselves for printing their work only to find a spot with consecutive 5ths or octaves in it after the fact, they would be interested to know that J.S. Bach (whose genius for part writing has never been equalled, and to whom all composers who come after him look for the absolute model, and rightfully so) actually wrote consecutive perfect 5ths and octaves into his settings of the Lutheran Chorales. You mean to say, Bach ... JOHANN SEBASTIAN BACH ... broke this "First Commandment of part writing?" The short answer is, yes indeed, he certainly did! There are at the very least 46 instances of consecutives in his settings of the Chorales; of these, only 10 involve octaves, thus the majority of consecutives are 5ths ("J.S. Bach: 413 Chorales" published by Christopher Czarnecki, in this author's opinion, is the best edition of the Bach Chorales from which to practice sight reading or study voice leading). Bach evidently felt that consecutive 5ths are far less objectionable than consecutive octaves, and those involving inner voices (alto and tenor) are far less objectionable than soprano-bass consecutives; in the Bach Chorales we find a complete lack of outer voice consecutives. The question as to why Bach wrote the consecutives that he did is difficult to answer; some have suggested that since he quickly tossed off his cantata-ending Chorales at the end of the week prior to Sunday services in Leipzig, he simply overlooked these consecutives; if he did, then these are truly oversights. Others have suggested that he simply became tolerant of such "forbidden successions." It's hard to imagine any consecutives evading this great composer's eye and ear, but, on the other hand, it may tell us something about the kinds of consecutives he considered allowable; both points of view could be right to some degree, i.e., some consecutives may have been intentionally allowed and others simply escaped his attention. The point is, Bach included consecutives in his writing, whether or not they were intentional or mistakes made in haste; and so, if one or two consecutives happen to creep into our own writing and manage to elude our own eye or ear even after editing, we can count ourselves in very good company. As was stated above, the settings which Bach wrote for the Lutheran Chorales also contain frequent voice crossings (tenor with bass, alto with tenor), and, in one 5-part setting, he writes 4 of the 5 moving lines in similar motion; there are also many instances where the stretch for one hand or both hands simultaneously is a 10th which the player's hands must be able to accommodate or the setting, as written, is unplayable. In addition, at final cadences, when he writes scale degree 7 (the leading tone) in the tenor voice, quite often it doesn't resolve upward to the tonic note; instead we find it falling to the 5th scale degree (the dominant), a clear indication that he placed great importance on having all 3 pitches represented in the final chord. All of this suggests another important lesson: If we take someone important from history and write them off just because they made a mistake or did something that offends our sensibilities today, then we're going to be forgetting about a lot of important people. One last thought: when we're writing a passage of polyphonic music in a minor key, we need to know whether scale degrees 6 + 7 should be raised with an accidental or not ... Answer: we are taught that the melodic form of a minor scale is raised 6 + 7 ascending and natural form (i.e. following the key signature of the passage) when descending; within practice this statement is only half correct ... The correct explanation is that the 6 + 7 is only raised when dominant harmony (with major quality) or if a diminished chord is present or implied, regardless whether the melody is ascending or descending; if dominant harmony or a diminished chord is not present, 6 + 7 will be in natural form. An illustrated example of this may be found in the score of the f minor Postlude Op. 32, in the coda at measure 78; here dominant harmony prevails on the first beat, switches to subdominant harmony on the 2nd beat, and returns for the 3rd and 4th beats; because halfway through the 2nd beat the top line begins its climb to the tonic with a raised 6, the bass also takes a raised 6 upon leaving a natural 7 to avoid creating a dissonant minor 2nd with the top line. Dominant harmony however does not always have to be of major quality; the idea of dominant harmony that always has to be of major quality is for most music written between the 17th to 19th centuries. A possible answer to why 6 + 7 are raised ascending within a melodic scale played on its own is because the mind fills in the harmony and assumes dominant harmony once the 5th note is heard. NOTE: Introduction and Fugue in G Major Op. 20 illustrates an important point -- the Fugue subject incorporates an ascending scalar pattern having a high point on the 6th scale degree; at the same moment that this note is reached, the 1st countersubject outlines the dominant tetrachord ascending which also includes the 6th scale degree; when in subsequent entries this subject appears in the minor mode with that 1st countersubject, in order not to do violence to the subject the 6th scale degree in the 1st countersubject would NOT be chromatically raised as expected; in other words, it must take the harmonic minor form rather than the melodic minor form in order achieve consonant harmony with the subject, the lesson being that the subject always governs the form or shape that the countersubject(s) must take to achieve consonant harmony; interestingly enough, one of the notes in the 2nd countersubject which sounds at that same moment on the 6th scale degree is also bent downward from the melodic form, i.e., without chromatically inflection, in order to sound in consonant harmony with the other 2 lines; the observant student will also note in the score how parallel perfect 5ths were avoided between the subject and both of these countersubjects at the moment when all 3 moving lines arrive at the 6th scale degree -- in one case a perfect 5th between the subject and 1st countersubject merely follows a diminished 5th, and in the other case the 6th scale degree of the 2nd countersubject is preceded and followed by a brief rest, thus interrupting the melodic lines. (con't in Part XXI)