I am trying to learn more about the neurological basis of harmony perception. However, I am having a bit of trouble understanding the musical technical terminology being used by the authors in a chapter of a book entitled "Neurobiology of Harmony Perception" by Tramo et al. in The Cognitive Neuroscience of Music.

In particular, they say

In this paper, we present neurophysiological, neurological, and psychoacoustic evidence to support our contentions that (1) pitch relationships among tones in the vertical dimension influence consonance perception and (2) consonance cannot be explained solely by the absence of roughness. (pg 130)

This claim seemed hard to interpret for me without defining the ideas of "pitch relationships" and "vertical dimension."

Here, I think they define "vertical dimension"

We restrict our consideration of harmony to basic tenets articulated by Piston,2 among others. Harmony has a vertical dimension and a horizontal dimension. The vertical dimension encompasses the relationships among simultaneous notes. By convention, note refers to a pitch in the musical scale, and harmonic interval refers to two notes sounded simultaneously. (pg 128).

By "pitch relationships", I think this paragraphs clarifies what it means

In summary, the temporal fine structure of the perfect fifth and fourth contains representations of the two notes constituting the interval, plus harmonically related bass notes that are implied by the interval. In music, these bass notes support the deep structure of harmony. Parncutt demonstrated experimentally that listeners associate major triads with pitches that are harmonically related to note F₀s, including the fundamental bass, plus the pitches of note F₀s actually in the stimulus. These pitches cannot be accounted for simply on the basis of combination tones. Houtsma and Goldstein showed that musicians can use missing F₀ pitches to identify melodic intervals (major and minor seconds and thirds), even when two upper harmonics are presented separately (dichotically) to each ear. (134-135)

Also this may be of help for interpreting

We interpret our findings and the results of previous psychoacoustic experiments as evidence in favour of the hypothesis that harmony in the vertical dimension, like harmony in the horizontal dimension, is principally a function of the pitch relationships among tones, with roughness playing a secondary role. In light of these observations, and in view of the likelihood that cognitive representations of pitch hierarchies influence harmony perception in the vertical dimension, we urge that the terms sensory consonance and sensory dissonance be reconsidered. (pg 147)

Thus, if I am interpreting their claim accurately, I think they mean the following

a chord’s consonance depends on both (1) the ratios between the notes and (2) the absence of roughness


Am I interpreting their claim correctly? What do the terms "vertical dimension" and "pitch relationship" signify in this context?


Regarding the term roughness, the following passage may help define it:

Figure 9.6C shows Plomp and Levelt’s idealized plot of the relationship between consonance and critical bandwidth (the latter is defined here by loudness summation). Note that the curve reaches an asymptote near the end of the x axis, at about one critical bandwidth. Thus a critical band account of consonance as the absence of roughness cannot apply to pure-tone intervals that are wider than a minor third or so. (pg 142).

So I assume they mean "roughness" in the sense of Plomp and Levelt. See this answer for more information about newer versions related to their models.

  • 1
    In all the terminology, what does the term 'roughness' actually mean?
    – Tim
    Sep 9, 2015 at 6:21
  • @Tim I updated it. At the bottom. See if that makes sense. Sep 9, 2015 at 7:04
  • @StanShunpike Really interesting question here...I plan to put an answer down when I have some time to sit down and type it out! For now, have you read much about musical semiotics? Sep 10, 2015 at 1:50
  • Not at all! fill me in. What are musical semiotics? Sep 10, 2015 at 3:20

2 Answers 2


The "vertical" and "horizontal" dimensions are an analogy with conventional western music notation. "Vertical" means the relationship between the different notes of a chord, considered in isolation. "Horizontal" (or "temporal") means the relationship between a chord and the preceding and/or following chords.

I'm struggling to understand your difficulty understanding the term "pitch relationships". It just means "the relationships between different pitches". Of course that interpretation only makes sense if the words are describing something that is actually perceived as a thing - and "semiotics" is the general term for debates about that type of question. (See https://en.wikipedia.org/wiki/Semiotics)

I think you answered your own question about "roughness".


Am I interpreting their claim correctly?

I think they mean the following: "a chord’s consonance depends on both (1) the ratios between the notes and (2) the absence of roughness."

Almost. Their claim is more along the lines of:

A chord's consonance depends on (1) the ratios between the notes; (2) the absence of roughness; and (3) some other yet-to-be identified factor or factors.

Put another way, conditions (1) and (2) are necessary, but not sufficient.

What does the term "vertical dimension" signify in this context?

"Vertical dimension" here means "the ratio of the vibrational rates of the fundamental frequencies of one or more given pitches".

"Verticality" in music is used in two ways: one specific, one more general. It's often used as a synonym for "simultaneities"; that is, pitches sounding at the same moment. However, it can also be used more broadly to refer to the relationship (vibrational ratio) of any two pitches, regardless of when they occur in time. Pitches occurring one after the other still have a "vertical" relationship.

What does the term "pitch relationship" signify in this context?

"Pitch relationship" here refers to the ratios of the vibratory rates of the fundamental frequencies of two (or more) pitches. In the context quoted above they seem to be saying that their findings do not consider the relationship in time between the pitches; that they only use simultaneous pitches in their study; or that time does not affect their results.

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