I’m studying first species counterpoint and trying to wrap my head around why we try not to use unisons, octaves and perfect 5ths outside of the beginning and end. I understand that unisons, octaves and perfect 5ths create a sense of stand still (especially octaves and unisons) because when I add them into practice exercises I can hear how they kind of cause a stump in a counterpoint that’s mostly 3rds and 6ths. I can also hear how more dissonant intervals like 3rds or 6ths make the piece sound like it wants to keep moving. When I listen to more dissonant intervals, the more dissonant it is (in terms of frequency), the more it sounds more like two notes rubbing against each other compared to consonant intervals that sound more harmonious. When I practice writing counterpoint it’s easy for me to implement these principles, but it bugs me that I don’t know why theoretically. Does anyone have any insight or a better explanation for what I’m trying to describe? Hopefully this all makes sense...
3 Answers
Yes.
I think you understand and describe it perfectly clearly!
It might help you to know that the way people try to objectively qualify the consonance/dissonance of an interval is the frequency ratio of the two tones. That's frequency in regard to the vibrations, like A440 Hz. The octave above would be 880 Hz, double. As a ratio it's 2:1, a simple ratio. As you move across the spectrum of intervals the ratios become more complex and our perception of them is increasing dissonance. The perfect fifth is 3:2, the major third is 5:4, but if we jump ahead to the dissonant minor second the ratio is 16:15. Sorry for the long digression...
What you intuitively called dissonant notes "rubbing against each other" is probably just your perception of those increasingly dissonant interval ratios.
In music theory the "stability" is the term used in connection with those interval ratios and related harmonic concepts. The very simple octave is stable. The dissonant minor second is unstable. Root position chords are stable, inverted chords are unstable. Extend that idea with stable is un-moving and unstable is moving. We now have the link between a dissonance and the notion of forward movement. Unstable dissonances generate movement forward until a stable consonance provides a stable resting point.
A lot of this is just a theoretical model. You could have a passage in all thirds which are sort of the middle of the consonance/dissonance model rhythmically moving and stopping for reasons that cannot be explained by the simplicity of a ratio. Apply the principle with some flexibility. Applied in broad strokes: cadences emphasis stable perfect fifths and octaves, while the interior motion of phrases abounds with comparatively less stable thirds and sixth. Applied to momentary detail: dissonant non-chord-tones like suspensions and passing tones create exciting forward impulses in what otherwise might be bland consonances.
A related idea you might add is variety of interval types. Contrapuntal music prizes interval variety. It's right in Fux! I think the rule is to not use a interval type more than three times consecutively. The concern for variety goes a long way in explaining why parallel perfect fifths, which are more consonant that thirds, are forbidden, but the parallel thirds are OK. Parallel fifths are monotonously the sample - perfect, perfect, perfect... - but thirds change quality - minor, major, minor... There is nothing inherently wrong with parallel fifths. The style just regards then as too much of the same.
So, ratios maps to stability which equates to movement, and emphasize variety. I think those are the deep underpinnings of movement in counterpoint.
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Awesome response! ThanksSo yea this makes sense. Consonant intervals (in terms of frequency) sound more stable than dissonant ones. Do you think this is because consonant intervals sound more like one note than dissonant ones? For example, if you end a counterpoint on a minor second or some other dissonant interval, it doesn't sound like we ended on the tonic note of the key even if that tonic note is in the bass of the counterpoint My guess is that's because the interval we're playing is so dissonant that it becomes too far removed from the tonic note and becomes a different note completely. Commented May 9, 2020 at 19:40
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What I don't understand is how this applies to movement/stability. Why does an interval that sounds like one note seem more still/stable than an interval where it's less clear what note is being produced? Commented May 9, 2020 at 19:41
There's lots of literature on the subject. (Google, Google Scholar, etc.) The question is why some combinations seem to "require" motion and some seem not to. To some extent, it's cultural; to some extent, even within culture, it's stylistic; to some extent there seems to be some acoustic reason.
Wiki: https://en.wikipedia.org/wiki/Consonance_and_dissonance
In Western music, the intervals may be ranked from consonant (octave, fifth) through dissonances (not all "authorities" are in agreement with this list) semi-consonant (major and minor sixths and thirds) semi-dissonant (minor sevenths, major seconds), and really dissonant (major sevenths and minor seconds, tritones); the perfect fourth is weird. In two part harmony it's dissonant; in chords, it's dissonant against the bass but consonant in upper parts: 64 vs 63 chords for example). The treatment of the fourth doesn't match acoustics; the idea of "beats" is part of the theory but apparently not all.
Some styles have different approaches. In blues, the chords are I7, IV7, V7 (for the most part) but cadences are generated by the 5-1 root movement rather than by resolving the tritone from V7-I (or one could say the the V-I tritone is resolved an the b7 in I7 is just for "color"; both analyses give the same results.
Ending on a IM7 chord (like C-E-G-B) doesn't always seem dissonant.
The book by Ludmila Ulehla's book: "Contemporary Harmony" does indicate some dissonant treatments used by composers in different styles.
Historical view:
Gregorian chant allowed only songs in unison, prime and octave, later the perfect fifth and Fourth. (Organum). The purpose of this rule was the auditive intelligibility of the word of God.
Aside this aspect it seems to be a fact that dissonant chords are stressing the ear and disturbing the concentration - even the 3rd and the 6th have been considered as dissonant.
(In a later era the 6th 3rd became consonant but not perfect.)
The psychological impression of tension and desire of resolution can be explained by the psychophysical impression and experience of dissonant intervals but other theories claim that this experience is cultural acquired.
So we can come to the conclusion that not the tones want to go somewhere (leading tone resolution) but the composer wants the tones to go somewhere.
The development in harmony and treating the tensions goes from avoiding to accept and tolerate dissonances to search and welcome them and avoiding consonances from early Renaissance, common practice period to the music of the 20th century with total decay of tonality and dissolution of harmony.
So you always have to be conscious on which rules of which c.p. of which era you are referring.
A useful introduction and resume may be found here:
https://www.uvic.ca/finearts/music/assets/docs/Counterpoint%20online.pdf
