Auxiliary Notes and Linear ProgressionsIf we take examples of counterpoint where one voice moves at four times the rate of theother,weget newpossibilitiesinvoiceleadingpatterns, aswenowhavemorerhythmicindependence. This is sometimes referred to as Third Species counterpoint. This results intwo new types of elaboration: the Auxiliary ote and the !inear "rogression.In this kind of counterpoint, one voice moves through four notes whilst the other voicestays on the same note. As in second species, the first beat of the four beats must be aconsonant interval but dissonancescanoccuronother beats, asindicatedintheaboveexamples. This creates two new possible voice leading patterns, the auxiliary note and thelinear progression.The auxiliary notes are indicated by #A# in the examples. In a$ the consonant intervalof a %th rises to the dissonant interval of the &th. This returns immediately to the consonant%thonthe'rdbeat. Thisexamplealsocontainsapassingnoteontheweak(thbeat,marked #"#, passing from the consonant interval of a %th to the consonant interval of a 'rd.In b$ the interval of a )th falls to the dissonant (th and immediately returns to the consonant)th.This movement awayfromaharmonynotetoanad*acent note+consonant ordissonant$ followed by a subse,uent return is referred to as an auxiliary note. The auxiliarynote may be above or below the consonant note and may be separated from the consonantnote by a tone or a semitone. The auxiliary note normally +but not always$ occurs on theweek second beat.Another possibility, inthirdspecies, is thelinear progression. Inc$ andd$ theconsonant intervals onthefirst beats of thebars areinterspersedwithstepby stepmovements. These are like a succession of passing notes and conse,uently the dissonanceheremayoccur either onthesecondor thirdbeat. Inc$ thedissonanceoccursonthesecond +weak$ beat but in d$ the dissonance occurs on the strong 'rd beat of the bar. Thepoint about the linear progression is that one or more parts move by successive contiguoussteps whilst one or more voices stay stationary. !inear progression may ascend or descend.Theseauxiliary notes andlinear progressionsarevoiceleadingelaborationoftheunderlying consonant one to one movement. If we strip away this surface voice leading weare left with the following one to one movement:!ike other voice leading patterns, linear progressions and auxiliary notes can occur invarious combinations when writing in more than two parts. These patterns are developed inlater musictoformdifferent waysof elaboratingunderlyingstructural chords. Thelinearprogression can move upwards or downwards and can occur in any voice: the melody, thebasspart oranymiddlevoice. Inthefollowingexampletwolinearprogressionsmoveinparallel -.ths:!inear progressions may create new chords on the way but these are in reality voiceleading movements that decorate the underlying chord progression. In the above example,this is chord I/ to / +assuming we are in a tonalkey of 0 ma*or$. The following exampleshows a linear progression combined with an auxiliary note pattern:The linear progression and auxiliary note patterns move in correct counterpoint witheach other and are combined with arpeggiation in the middle voices. The voice leading herecreatesacadential patternandtheunderlyingprogressionisfromchordII toI, whenexpressed in terms of tonal functional harmony. 1e should remember that in -%th centurypolyphonytheydidnot thinkinsuchterms.At that time, thecadencewastheresult ofcounterpoint rather than harmony.