dissonant filter

The dissonant filter automatically labels the function of non-harmonic notes in contrapuntal textures. All harmonic seconds and sevenths are considered dissonant as well as fourths above the lowest sounding voice.

Each input **kern spine is expected to be monophonic and have no subspine branching. If there are chords in the music, only the first note of the chord is used, and secondary subspines will be ignored.

Below is an example of the dissonant filter in action using an excerpt from Josquin’s chanson Ce povre mendiant/Pauper sum ego. To apply the filter to a file, include the line !!!filter: dissonant anywhere in the file. The dissonant function labels for each voice will be inserted in spines immediately to the right of each **kern spine. In the following display the labels are shown above the notes to which they apply. P means a rising passing tone and p means a lower passing tone. See the complete list of label abbreviations further below.

Try editing the above Humdrum score to generate various types of dissonances. Removing the first line (!!!filter: dissonant) will turn of the dissonance analysis, and adding -u to !!!filter: dissonant -u will merge subcategories into a single main category for the dissonant types.

Another interesting variation is to use the following filter:

!!!filter: dissonant --colorize | extract -i kern

The --colorize option will color dissonances based on metric position: red for semibreve and higher levels, green for the minim level, and blue for the semi-minim level. The following extract tool removes the text labels.

Dissonant function labels

Dissonant notes are marked with single-letter label abbreviations in the notation as well as in the Humdrum score. The first table below gives the detailed default label categories used in the dissonance analysis, while the second table gives more generalized categories that do not distinguish melodic directions.

The -u option (meaning undifferentiated) collapses up/down subcategorizations into a single label designated by an uppercase letter:

Examples of each dissonant type are given below. Note that the musical examples are generated dynamically using verovio within the page, and the dissonant tool labels notes as the webpage is loaded.

Passing notes (P, p)

A passing tone is approached by step and left by step in the same direction. The preceding note must be metrically stronger than the dissonant note, and the note the passing tone is dissonant against must begin before the passing tone and must sustain at least through the end of the passing tone. These are labeled with uppercase P and lowercase p for ascending and descending passing tones respectively.

Neighbor notes (N, n)

Neighbor tones have similar requirements as passing tones, except instead of being approached and left by step in the same direction, neighbor tones are approached and left by step in opposite directions. N and n are used to label upper and lower neighbors respectively.

Double neighbors (D, d)

In a double neighbor figure, a primary note is ornamented by both an upper and lower neighbor before returning to the primary note. Both dissonant notes are given the same label based on which type of dissonant neighbor comes first, D if the figure begins with an upper neighbor, and d if it begins with a lower neighbor. While the first dissonance must be relatively weak metrically compared to the primary note, the second of the two double neighbors can be accented, such as in this excerpt from the chanson attributed to Josquin Mala se nea.

Échappée notes (E, e)

An échappée (also called an escape tone) is approached by step and left by leap in the opposite direction. The dissonant note must be metrically weaker than the note that precedes it and a note in another voice must start before the Échappée and sustain at least until the end of the Échappée.

Cambiatas notes (C, c, K, k)

A nota cambiata is approaced by step and left by a leap of a third in the same direction. It must be metrically weaker than the note that preceded it. If after leaping a third, the melody moves a step in the opposite direction (thus filling in the note that was skipped over) the dissonance gets a K or k label for the long-form cambiata. If this change of direction does not occur then a C or c label is used.

As with most other dissonance labels (with the exception of suspension and agent labels), a lowercase letter means it was approached by step down, as in the example above, and an uppercase letter means the dissonance was approached by step up, as in the example below.

Anticipations (A, a)

As demonstrated in the example below, anticipations that are approached by a step up are labeled with A; otherwise, they are labeled with a when approached by a step down, and then repeated in place. An anticipation is metrically weaker than the notes before and after it.

Reverse nota cambiatas (I, i)

A “reverse” nota cambiata is a weak dissonance approached by leap and resolved down by step in the same direction. It is labeled with an I or an i for its ascending and descending versions respectively. These are relatively rare in the Renaissance. This example from the Gloria Ockeghem’s Missa Fors seulement includes an incomplete anterior lower neighbor, labeled with an i.

Reverse échappées (J, j)

The “reverse” échappée is a weak dissonance that is approached by leap and then resolved by step in the opposite direction. It is labeled J when that initial leap is up, and j when it is down, similar to neighbor tones. This often occurs as an ornament of a suspension. While only dissonant suspensions are labeled, consonant suspensions also receive this same type of ornamentation. The example below taken from the Sanctus of the Missa Sub tuum presidium contains two parallel reverse échappées, one decorating a consonant suspension in the Altus, and the other ornamenting a consonant suspension (unlabeled) in the Superius.

Suspensions (S, s, G, g)

A suspension consists of a voice that becomes dissonant either by sustaining or restriking a note before resolving the dissonance down by step. This sustained voice was referred to as the patient by Artusi, and it gets an S or s label at the moment of the dissonance. Another voice strikes a note that is dissonant against the suspended note, and this voice gets a G or g label for agent. It is common to have more than one agent per suspension such as in m. 37 in the example below.

This example, taken from Obrecht’s motet Mille quingentis, features both a binary and a ternary suspension. The first suspension (in m. 34) is binary, because the dissonance phase of the suspension lasts a unit of time (in this case a minim, or half note) that groups in twos in the given mensuration. The second suspension above (in m. 37), its dissonant phase lasts a semibreve, or whole note, (when ornamentation is disregarded) so this suspension is ternary and receives uppercase S and G labels. If you prefer not to distinguish between binary and ternary suspensions, use the -u option and all suspensions and agents will be labeled with uppercase letters.

Consonant suspensions are ignored by the dissonant tool.

Rearticulated suspension (r)

The most common type of suspension ornamentation in the Renaissance is to leap down a third from the suspened dissonance before resolving both dissonances with a step up. This type of ornament falls under the larger category of reverse échappées (see above). Another type of ornamentation consists of a simple rearticulation of the suspended note before it resolves down by step. The reartuclated note is generally a semi-minim (quarter note) and is labeled in the analyses with an r. While this figuration (shown below) does occur in tonal music, there are almost no occurrences of this in the entire JRP database of scores. This demonstrates how dissonance analysis can be used to inform the study of style change over time.

Fake Suspensions (F, f)

Sometimes the preparation of a suspension is itself dissonant like in the example below from the Kyrie in Mouton’s Missa Da pacem. This is often referred to as a fake suspension though would more accurately be called a fake preparation to an otherwise normal suspension. It is usually approached by step up or down and remains in place or is restruck to become the dissonant portion of a suspension. Since we know the suspension will resolve down by step, we use an uppercase F or lowercase f to convey whether the dissonance was approached by leap or by step respectfully. Because this happens over a pedal, and an agent is also needed for the suspension, this is generally only found in three or more voices, though could happen in two voices if the pedal tone were rearticulated at the moment it serves as the agent of the suspension.

Occasionally a fake suspension is preceded by an anticipation and these are detected as well, such as in the example below taken from the same Mouton Kyrie.

Occasionally a fake suspension is preceded by an anticipation as in the example above taken from the same Mouton Kyrie. In this case the fake suspension label takes the same case as that of the anticipation.

Suspensions with missing agents (M, m)

In some cases a suspension seems to be missing an attacked agent. This figure consists of a voice moving up or down by step, then sustaining over the following beat, and then resolving down by step all over a pedal tone. This dissonance is labeled M or m based on whether the dissonant note is approached by leap or by step respectively. The example below is taken from Obrecht’s motet Factor Orbis.

Chanson idiom (h)

A chanson idiom functions as an ornamented anticipation to the agent of a suspension and is labeled with an h. It usually occurs in the placement of a weak minim, (half-note) and consists of a quarter note that is dissonant against the preparation to the suspension and is approached by step down. This dissonance is also left by step down to another quarter note that is then followed by the agent of the suspension a step up (on the same pitch as the chanson idiom). The example below is taken from the contra and tenor parts of the chanson Cela sans plus attributed to Josquin des Prez:

Dissonant 3rd quarter passing tone (Q, q)

A dissonant third quarter passing tone, a regular passing tone. It corresponds to a dissonance in the metric position of a weak minim that lasts only a quarter note. It is approached and left by step in the same direction and must be preceded by a note with a duration of at least a minim (half-note). If it descends, it gets the q label as in the following example.

A dissonant third quarter passing tone, labeled q in the example below, is similar to a descending passing tone. It corresponds to a dissonance in the metric position of a weak minim that lasts only a quarter note. It is approached and left by a step down and must be preceded by a note with a duration of at least a minim (half note). There is no ascending form for this dissonance type.

Though it is less common, when the same figure happens in its ascending form, it gets labeled with a Q as in the following example taken from the Superius and the Altus of the Credo in Josquin’s Missa De beata virgine.

Dissonant third quarter neighbor (B, b)

This dissonance is the neighbor-tone version of the dissonant third quarter passing tone. The example below is taken from the altus and bassus parts from the Credo of Josquin’s Missa La belle se siet (NJE 13.3).

The dissonance type consists of a neighbor tone in the metric position of a weak minim (half-note) that lasts only a quarter note in duration. Although we detect both upper- and lower-neighbor varieties of this dissonance type, like regular neighbor tones, the dissonant third quarter lower neighbor is by far more common than the upper-neighbor version. The upper- and lower-neighbor versions of this dissonance type are labeled with a B and a b repsectfully.

Appoggiaturas (T, t)

An appoggiatura is a dissonance that is relatively accented with respect to the notes before and after it. It is approached by leap and resolved down by step. It is labeled with a T when the leap is up and t when the leap is down. This label is only assigned if the requirements are met and the note would otherwise be unexplainable. This excerpt from the Sanctus of Josquin’s Missa Hercules dux Ferrarie features an appoggiatura approached from below.

Accented passing tones (V, v)

Accented passing tones are metrically strong with respect to the notes before and after them, and last no longer than the following note. They are approached and left by step in the same direction and labeled V when those steps are up, and v when those steps are down. They will get detected even if they are decorated with an anticipation immediately before. This dissonance definition could correspond to dissonant third quarter passing tones, and also the chanson idiom dissonance type. An accented passing tone will only get labeled as such if it does not meet the stricter requirements for any other dissonance type. In the Sanctus of Missa Cum iocunditate attributed to Josquin, accented passing tones are found in certain contrapuntal dispositions where a primary motive is set against itself in multiple voices, such as in the excerpt below.

Accented neighbor tones (W, w)

Accented neighbor tones are metrically strong with respect to the notes before and after them, and last no longer than the following note. They are approached and left by step in opposite directions and labeled W when approached by step up, and w when approached by step down. They will get detected even if they are decorated with an anticipation immediately before. This dissonance definition also matches that of dissonant third quarter neighbor tones, and potentially the L and Y types. An accented neighbor tone will only get labeled as such if it does not meet the stricter requirements for any other dissonance type. The excerpt below taken from the motet Benedicite, omnia opera attributed to Josquin contains an accented upper neighbor in the Altus.

Resolution against suspension dissonance (X, x)

When a voice sounds the note of resolution of a suspension in a descending line against the dissonant portion of the suspension in another voice, it is labeled with an x. There is no ascending form of this dissonance so an uppercase X is only used if the -u setting is invoked. This dissonance necessarily only occurs when three or more voices are present, because in addition to the dissonance itself, two other voices must form a suspension. It often occurs in even thicker textures though, such the excerpt below taken from the motet Victime paschali laudes by Brunet.

Parallel accompaniment (L, l)

If a dissonance does not correspond to any identifiable categories (and would normally receive a Z label), and moves in parallel motion by another voice that is an idenfiable dissonance, this parallel accompaniment is given an L if it is approached by step up, or an l if it is approached by step down. This type of dissonance often occurs in tandem with a chanson idiom such as in the example below taken from Lannoy’s Cela sans plus. While the voices are still analyzed in a pairwise fashion, since this dissonance type requires a second voice to be in an identifiable dissonance condition with a third voice, this type is only identified in pieces with three or more voices.

Only against known dissonance (Y, y)

When a note is only dissonant against known dissonance types, it receives a Y or y label depending on whether it was approached from below or from above respectively. This sort of scenario often occurs in thicker textures, such as in the example below with both a Y and a y taken from the Sanctus of the Missa Pro defunctus attributed to Josquin.

Unknown dissonances (Z, z)

Dissonances not assignable to one of the above categories are given a Z label to indicate their function is unknown. A capital Z means that the interval of the dissonance is a 2nd or 7th. A lower-case z means that the dissonance is a 4th against the lowest sounding note in the sonority. In the example below taken from the Sanctus of Josquin’s Missa Hercules dux Ferrarie what appears at first to be a suspension in the Altus is not resolved properly, resulting in the Bassus and Superius voices receiving Z and z labels respectively.

URL filtering of repertories

The dissonant tool can be used with available VHV repertories by adding the filter to the URL for the works, such as with the Tasso in Music Project:

     http://verovio.humdrum.org/?k=ey&file=tmp&filter=dissonant

To remove lyric text from analysis results, use the filter: extract -i kern | dissonant:

     http://verovio.humdrum.org/?k=ey&file=tmp&filter=extract%20-ikern%7cdissonant

The filter extract -i kern extracts only **kern spines and filters out non-kern spines.

JRP dissonant tool

Work pages on the Josquin Research Project website have links for the given work to view the dissonant labeling analysis in VHV. For example the page:

     http://josquin.stanford.edu/work/?id=Jos2801

contains a button labeled Dissonant on the bottom left side of the page. Clicking on that button will load the score for the current page into VHV and do an online analysis of the dissonant labels:

Dissonance summaries

These are more useful for the command-line version of the tool, but can be viewed in VHV by typing command-c when the option is used.

The -c option displays a count of the different types of dissonances and total dissonances within a work:

humcat jrp://Jos2721 | dissonant -c

**dis	**sum	**v1	**v2	**v3
P	31	17	6	8
p	13	9	1	3
N	2	0	0	2
n	21	5	3	13
E	1	0	0	1
e	1	0	1	0
Q	1	0	1	0
s	6	1	2	3
G	11	5	4	2
h	1	0	0	1
Z2	1	1	0	0
Z7	1	0	0	1
*-	*-	*-	*-	*-
!!total_dissonances:	90

The -u option can also be used with the -c option to count dissonances without subgrouping them by direction:

humcat jrp://Jos2721 | dissonant -cu

**disu	**sum	**v1	**v2	**v3
P	44	26	7	11
N	23	5	3	15
E	2	0	1	1
Q	1	0	1	0
S	6	1	2	3
G	11	5	4	2
H	1	0	0	1
Z	2	1	0	1
*-	*-	*-	*-	*-
!!total_dissonances:	90

In this case the first spine data type is labeled as **disu to indicate the undifferentiated directions for each category.

References

Antila, Christopher, Alexander Morgan, et al. VIS Framework (version 3.0.3). Python. Montreal: McGill University, 2016.

Bent, Margaret. “Grammar of Early Music: Preconditions for Analysis.” In Tonal Structures in Early Music, edited by Cristle Collins Judd, 15-59. London: Garland Publishing, 1998.

Burmeister, Joachim. Musical Poetics. Translation by Benito Rivera. New Haven: Yale University Press, 1993. Originally published 1606.

Cohen, David. “Metaphysics, Ideology, Discipline: Consonance, Dissonance, and the Foundations of Western Polyphony.” Theoria 7: 1–86.

DeFord, Ruth. Tactus Mensuration, and Rhythm in Renaissance Music. Cambridge: Cambridge University Press, 2015.

Fuller, Sarah. “Contrapunctus Theory, Dissonance Regulation, and French Polyphony of the Fourteenth Century.” In Medieval Music in Practice: Studies in Honor of Richard Crocker, edited by Judith Peraino, 113–52. Middleton, Wisconsin: American Institute of Musicology, 2013.

———. “Organum – discantus – contrapunctus in the Middle Ages.” In The Cambridge History of Western Music Theory, edited by Thomas Christensen, 477–502. Cambridge: Cambridge University Press, 2002.

Jeppesen, Knud. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. Translated by Glen Haydon. New York: Dover Publications, 1992 (original Danish edition published by Wilhelm Hansen, in Copenhagen, 1931).

Melin, William Eugene. “The Music of Johannes Tinctoris: A Comparative Study of Theory and Practice.” PhD diss., Ohio State University, 1973.

Moll, Kevin. Counterpoint and Compositional Process in the Time of Dufay: Perspectives from German Musicology. Edited and translated by Kevin Moll. New York: Garland Publishing Inc., 1997.

Morgan, Alexander. “Renaissance Interval-Succession Theory: Treatises and Analysis.” PhD diss., McGill University, 2017.

Morris, R. O. Contrapuntal Technique. Oxford: Oxford University Press, 1922.

Patrick, P. H. & Strickler, K. (1978) “A Computer-Assisted Study of Dissonance in the Masses of Josquin Desprez.” Computers and the Humanities. 12 (4), 341–364.

Pontio, Pietro. Ragionamento di musica. Compiled by Suzanne Clercx. Kassel: Bärenreiter, 1959. Originally published Parma: 1588.

———. Ragionamento di musica. Electronic version published by Dupraz, Christophe. Traités Musicaux Romans, 2013. Accessed August 14, 2016.

Rothfarb, Lee. “Tinctoris vs. Tinctoris: Theory and Practice of Dissonance in Counterpoint.” In Theory Only 9.2–3 (1986): 3–31.

Sachs, Klaus-Jürgen. “Counterpoint.” Grove Music Online. (accessed July 12, 2016).

———. Der Contrapunctus im 14. und 15. Jahrhundert: Untersuchungen zum Terminus, zur Lehre und zu den Quellen. Wiesbaden: Steiner, 1974.

Schubert, Peter. Modal Counterpoint, Renaissance Style, 2nd ed. New York: Oxford University Press, 2008.

Siegler, Andie, and Jon Wild. “Schematizing the Treatment of Dissonance in 16th-century Counterpoint.” In Proceedings of the International Society for Music Information Retrieval (2015): 645–650.

Tinctoris, Johannes. Liber de arte contrapuncti. In Johannes Tinctoris Opera Theoretica. Compiled by Albert Seay. n.p.: American Institute of Musicology, 1975. Originally written 1477.

———. Liber de arte contrapuncti. Translated by Albert Seay. Rome: American Institute of Musicology, 1961. Originally written c. 1477.

———. Liber de arte contrapuncti. Translated by Jeffrey Dean. Last accessed November 16, 2015. Originally written 1477.

Trachier, Olivier. Contrepoint du XVIe siècle. Paris: Durand, 1999.

Vicentino, Nicola. Ancient music adapted to modern practice (L’antica musica ridotta alla moderna prattica). Translated by Maria Rika Maniates and edited by Claude Palisca. New Haven, Yale University Press 1996. Originally published 1555.

Zarlino, Gioseffo. Art of Counterpoint. Translated by Guy Marco and Claude Palisca, edited by Claude Palisca. New Haven and London: Yale University Press, 1968. Originally published: 1558.