The passage below is quoted from the paper, "Seven Steps to Heaven--A Species Approach to Twentieth Century Analysis and Composition" by Henry Martin.

It should be emphasized that the ic-0 and ic-5 relationships presented so far have various potentials for consonance and dissonance. The realization in Example 12 is particularly dissonant because cross-relations are conspicuous. An ic 5 counterpoint could also be written to the same C. F. to minimize potential dissonance. Another measure of potential dissonance in an exercise is the interval between the modal tonics.

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"Potential" appeared three times in this passage. Does the first time mean the possibility of the two modal scale can form many consonance and dissonance intervals? What do "potential dissonance" or "potential consonance" mean? Does potential here have another meaning?


My understanding of the explanation in the text, given the example below it, is that from one position there is the potential for dissonance with respect to subsequent notes, i.e. in a "horizontal" manner, as opposed to the more typical "vertical" one. For instance, F#-F is clearly a dissonant interval. When it occurs "vertically" (or, harmonically) the dissonance is very obvious. But when it occurs "horizontally" (i.e. melodically) as in the manner shown above, it is still dissonant (i.e. unpleasant), but the effect is not as pronounced (in terms of unpleasantness), and therefore more subtle / harder to analyse, unless one is looking for "horizontal" dissonant patterns specifically.

The dissonance in the given example is even more subtle, since the dissonance does not occur along the same melodic line; in other words, neither the soprano nor the tenor melodic lines contain dissonant intervals by themselves in isolation, but when the two are put together harmonically, you have a dissonant interval formed by the F# from the soprano line 'leading' to an F in the tenor line (what the author refers to here as "cross-relations").

Contrary to harmonic dissonance, when dealing with melodic dissonance, clearly, until we've heard the next note in the series, we can only talk about the "potential" for dissonance, since we do not know if the resulting melodic interval is dissonant or not until the next note in the series has actually occured.

The implication in this passage is, however, that there are certain chords or harmonic intervals, that simply due to their position or configuration they have a higher potential for melodic dissonance, in the sense that there is presumably a higher number of subsequent patterns from that position that would lead to dissonance. Therefore it is not only important to find the right subsequent notes that do not lead to dissonance, but it is also important to pick chords / configurations that give you more flexibility in the first place, such that you have a larger variety of subsequent patterns to chose from later that will not be dissonant.

PS. Not strictly related to this, but you might find this video interesting, offering a more mathematical interpretation of what it means for harmonies or melodies to be "dissonant", and the physical basis of their unpleasantness. Or this one if you're feeling a bit more hardcore!

  • wow!Thank you very much!You really helped me,but I have another question now:what is “cross-relation”? Does it mean half-step or half-tone? – Lee Jul 11 '17 at 7:48
  • @Lee I mention that in the second paragraph. I think the author means relations that cross melodic lines, like in this example where the dissonant relation "crosses" from the soprano to the tenor line and back again (and is thus more "conspicuous" according to the author). – Tasos Papastylianou Jul 11 '17 at 12:19
  • @jdjazz (is that true? I would've thought it's generally possible to choose a different answer on the stackexchange platform if a better answer one comes up) – Tasos Papastylianou Jul 12 '17 at 22:31
  • @Lee, if this is the answer you were looking for, I encourage you to click the check icon next to Tasos's post. At the top of his answer, you'll see an upvote button (an up arrow), a downvote button (a down arrow), and a check. The check indicates that a particular response answers your question. If someone else later posts a different answer that you prefer, you can then change your decision and choose to check the later answer. So giving the check now isn't binding. – jdjazz Jul 12 '17 at 22:34

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