I was practicing counterpoint (2nd species) and decided to experiment with ending on a perfect 5th except the top line was a C and the bottom an F. I know this isn't technically allowed in 2nd species, but I just wanted to see how it would sound.... What I noticed is it didn't sound very resolved. My question is why does is a perfect 5th with a C on top not able to resolve a melody that is in C? Do our ears favor the bottom note of an interval? I'm guessing it has something to do with the harmonic series, but does anyone else have any insight into this?
I'm guessing it has something to do with the harmonic series, but does anyone else have any insight into this?
Your assumptions are correct!
The bass layer as fundament has the strongest overtones which produces the most interferences with the tenor or soprano voices.
For this R. Breithaupt writes in his book natural piano technic about the use of the pedal:
I. the bass range of the instrument is the most outstanding, dynamic absolutely dominant, 2. the treble range is the absolutely weakest. This results in the following conditions: 1. If the bass layer is mixed with the lower tenor, any bass, even if the tenor is mitigated. 2. The same applies to the mixture: bass position tenor position, bass position, low tenor position and tenor old position it is melodic, compared to the high treble, low tenor position old position, low tenor position treble. high tenor treble, - 3. The greatest attention demands the mixture of the two outermost layers: low bass position high treble position.
More cannot be said "theoretically" about it. We only want to add that for finely organized natures the three layers and their mixtures are represented as three color complexes, which in their differenciations can also correspond to the deeper emotions of a musical spirit. This belongs in the area of the "psychological attack". It can be taken for granted that the dynamics of the positions are also of considerable influence in the art of polyphonic playing.
The participation, or the strength, of the overtones is fundamental for the development of the “Klang” (sound).
Find more info here:
Natural piano-technic (Breithaupt)
This answer above was concerning your headline
"Is the bottom note favored?"
When we write - as you say in C - we are in a certain tonic and this means: we are here "at home" in C major. You can develop a cantus firmus using the whole scale but the bass tone at the ende should be a C.
If you end now on F (bass) and C (upper voice) you don't have the "home feeling" and this is producing your impression of "not resolving." (Unless your tune is modulating to F introducing a some Bb in the melody.
An additional point: The perfect fifth was usual in early music as finalis, later the octave was preferred, until the ending of the 3rd and 5th became popular in modern music (pop etc.)
C-F is P4. F-C is P5. P5 always sounds far more settled to me. Probably because in F-C, there is a harmonic which (particularly with low notes) is audible. That F note has a harmonic of note C, so it's more solid.
In C-F, the low C has a harmonic - but it's a G note. That hardly blends with the higher F, so it doesn't sound so settled.
By the way, C-F is not the same interval as F-C! C-F is P4, F-C is P5. They may well be the same two note names, but the way they interact - as you have found out - is different. And indeed, they're named differently.
...but my question is why.... An interval of C1-F1 sounds resolved while an interval of F1-C2 does not sound resolved even though it is the same interval (perfect 5th)...
Your question is confusing, because
F1 is a perfect fourth and
C2 is perfect fifth.
You are calling them the same interval, but they are not. The difference is very important regarding harmony generally, and specifically cadences.
Octave 1 and 2 are very low so I've raised them two octaves...
The basic harmony and cadence concept is inverted chords are unstable and don't create a sense of resolution. A final cadence goes to a root position chord.
...why does is a perfect 5th with a C on top not able to resolve a melody that is in C? Do our ears favor the bottom note of an interval?
This adds to the confusion, because a perfect fifth with a
C on top means that the lower tone is an
You doing species counterpoint.
C is the final of the mode, then the final chord of the cadence needs to be a root position chord on
...Do our ears favor the bottom note of an interval?
The bottom note is the bass. Within harmony the bass most definitely plays a special role. I wouldn't call it "favored", but it is critical in defining chords.
The reason the passage won't sound resolved in
C major is because
F is not the final of the mode. The bass needs to play
C - the final of
C major - to get the resolution of a cadence.
Something like this would be normal...
If the ending is harmonize with a perfect fourth, it creates the sound of a suspension that needs to be resolved...
I don't know what your experiments were, but these are melodies in
C ending on a
F with a
C above. Both will feel like a move from tonic to subdominant and that will not give a feel of final resolution for an ending.
...I'm guessing it has something to do with the harmonic series
The harmonic series outlines a root position triad in the first several harmonics. Many people feel this is the acoustical explanation about why a root position triad has a feeling of stability.
That provides an explanation but only in part. The overtone series explains why an inverted chord does not have the sense of stability for cadences. But it does not explain why a root position chord in
C does not have a feeling of resolution. That non-resolved feeling has nothing to do with the overtone series.
The special status the tonic chord holds as the final chord comes from the scale tones
TI a half step below the tonic degree and
FA a perfect fourth above the tonic scale degree. Only the tonic chord has that special relationship.