Feb. 26, 2017
(con't from Part XX)
There are times when the voice movement of 2 notes in the same octave or in different octaves may lead to a momentary collision at the interval of what amounts to a semitone, or minor 2nd.
A minor 2nd "near miss" interval like this is considered dissonant, but when it's only momentary it can be quite agreeable and lend a little sparkle, a little spice and color to the writing without sounding disagreeable at all.
An example of this may be found in the exposition of the the D Major Op. 28 Fugue, where the 1st countersubject makes a momentary minor 2nd with the answer, an effect which is maintained right side up or inverted throughout the rest of the Fugue with each entry in a major key.
The terms "consonant/dissonant" require a bit of comment ...
In Western harmony intervals made up of notes that sound pleasing together are called "consonant;" chords built only of consonant intervals sound pleasant and stable; we can listen to a consonant chord for what seems like a long time without feeling the need that it should change to a different chord.
Intervals that are "dissonant" can sound harsh or unpleasant or may feel unstable; when we hear a chord with a dissonance in it, we may feel the music pulling us toward the chord that resolves the dissonance.
Certain dissonances also give music color and spice and keep it from sounding boring, page after page.
This is what makes dissonances important -- perhaps more important even than consonances.
Obviously, what sounds pleasant or unpleasant is partly a matter of opinion; of course, if some or all of the notes of the instrument are out of tune, then no intervals will sound pleasant, but this is not what consonance and dissonance, in harmonic terms, is all about.
The choice of temperament or tuning system will greatly affect which intervals sound consonant and which sound dissonant [See blog, Temperaments and Tuning, Parts I, II, III, IV, V].
Consonance and dissonance refer to intervals and chords; an interval is measured between 2 notes; when there are more than 2 notes sounding at the same time, we have a chord.
The minor 2nd "near miss" interval, which consists of 2 adjacent half steps on the piano keyboard, its inversion (Major 7th), or its compound (minor 9th), tend to be unsettling but are not strictly forbidden in 4 part writing.
A very famous example of this -- of an agreeable minor 2nd -- with which organ scholars soon become familiar is found in the final cadence of the great F Major organ Toccata of J.S. Bach, where we find a Bb in the moving pedal line in the bottom octave of the pedals at the same time we hear a big F Major chord for both hands in spread harmony above it.
We derive the minor 9th interval not by inverting the minor 2nd (which creates a Major 7th) but by transposing the highest note of the minor 2nd interval to the next highest octave (or by transposing the lowest note of the minor 2nd to the next lowest octave, same difference); in either case we arrive at a compound interval, meaning larger than the octave.
Dissonance is an interesting concept in music; for the longest time, classical music has operated under the header of consonance, that whatever was easy on the ear was considered "good."
The name of our intervals in Western music reflects that fact; the octave, 5th, and 4th are given the title "perfect" for their inherently consonant sounds.
The 2nd and 7th are relegated to merely being Major or minor, their dissonant quality betraying them; only through the work of the modern genre has there been a paradigm shift in regard to dissonance and the means in which music applies it.
The 2nd has an uneasy quality about it from the get go; it's just too close to the root; the minor 2nd in particular doesn't sound all that good unless held only momentarily, in which case it adds a little unexpected sparkle that tickles the ear.
The 3rd on the other hand starts to get better and sounds "sweet," the Major 3rd being a particularly strong and consonant interval.
The minor 3rd also has a different quality but can work very well in certain context; the quality the 3rd gives to the chord forms the main character and, harmonically, is the most important part of the chord.
The 4th is a bit awkward; while it bears the title of "perfect" it sometimes sits awkwardly between the 3rd and the 5th.
The 5th along with the 3rds are the 2 intervals which form the consonant basis on which chords and triadic harmony can be built.
The "tritone" or 3 whole steps (represented on the page by an augmented 4th or diminished 5th), having been dubbed "diabola in musica" or "the devil's interval" centuries ago due to it's tonal ambiguity, has a hauntingly beautiful character.
For a fair number of years this interval was considered to have an evil character and was only used in composition when the devil or things that were considered evil were the subject of the work.
The Major 6th and minor 6th are important intervals which, like the 3rds, sound "sweet."
The 7th is important in the way in which it works with the tonic to provide the finality on which music can end.
The Major 7th is the inversion of the minor 2nd, and the minor 7th which forms part of the dominant 7th chord was the most important harmonic development of the Baroque era and has been the basis of most music the West has produced for the last 5 centuries.
During his lifetime J.S. Bach was widely known throughout Europe for his virtuoso abilities as an organist and improvisor, but his true abilities and sheer mastery as a composer did not become widely known until nearly a century after his death.
Respected for their intellectual depth, technical command, and artistic beauty, all the works of J.S. Bach show a robust contrapuntal technique and an unrivaled control of harmonic and motivic organization.
Most likely begun in the early 1740's or earlier, Bach copied in 1745 a 1st edition of 12 fugues and 2 canons all based upon the same theme.
This manuscript has a slightly different title, added afterwards by Bach's sons: "Die Kunst der Fuga" (The Art of Fugue).
A 2nd edition was published in 1751, a year after his death, which contains 4 canons and 14 fugues, one of which is unfinished.
Each of the 14 fugues, save for the unfinished one, use the same deceptively simple little theme in d minor.
Manuscript copies as well as the first printed editions use open scoring, where each voice is written on its own staff [See blog, Open Score, Parts I, II].
This has led to the assumption that this collection was created as an intellectual exercise meant to be studied and not heard.
Musicologists today, however, agree that it was probably intended to be played on a keyboard instrument.
When we look at the 1st fugue, called Contrapunctus I, on the 55th bar we find a held F4 and E4 in the right hand as the left hand line rises from C#4 to resolve on D4, which has all 3 voices colliding on the tonic, supertonic, and mediant notes (1st, 2nd, and 3rd scale degrees) in the same octave, on the same beat.
Here the E4 and F4 meet on a minor 2nd interval at the same moment that the leading tone C#4 resolves upward to D4.
In music this represents a "near miss" (photo).
But under Bach's hand, these 3 voices weave in and out with such mastery here, and this near miss is approached with such skill and woven so cunningly into the surrounding musical fabric that the ear accepts these 3 tones as a consonant chord!
Bach must have reasoned that anyone who could slither into and out of such a difficulty and get away with it would have trouble hiding his identity ... and the fact that this happened on the 55th bar of the 1st fugue in the series could have been no accident [See blog/archive subpage, The Art of Fugue].
Did this give old Bach a chuckle or two? ... it is likely.
With everything else he was able to soar playfully above every technical challenge.
He must have laughed at this one.
So we have it on authority of the strongest fugue writer in history that when 2 melodic lines approach each other so closely that they momentarily form an interval of a minor 2nd with each other at some point, they don't have to be rewritten to eliminate the "near miss."
On the contrary, if for no other reason than to honor the greatest man of all [See blog, Bach Photo Album], we should keep these little near misses in the score and laugh about them, too, just as old Bach must have.
Hundreds of examples of a dissonant harmony formed by adjacent notes at a minor 2nd "near miss" interval apart (or where 2 voices line up vertically at a Major 7th or minor 9th) may be found in the compositions posted on this web site.
One more reason for us to thoroughly enjoy what we're writing and how we're writing it.
(con't in Part XXII)