According to a certain "logic," I feel compelled to say that the C-F interval can obviously be given in inversion, forming a perfect 4th in the first case and, in the second case, a
perfect 5th (with the interval given in an inverted state), but one could say the same thing (and all the more so) for the interval between C-G, since the latter is a more "stable" interval.
That would be too simple and practically wouldn't make sense, so I await responses from others, as it seems clear to me that there is
something that goes far beyond the simple interval and its inversion.
I do not believe there is a difference, from the point of view of the tonic of the interval, whether the notes are played consecutively or simultaneously because the physical qualities of the individual notes constituting the interval are constant regardless of consonance and dissonance.
Instead, it could change in the sense that a chord alone says little or nothing in a tonal context; in reality, even just 2 notes say little, but at least they are 2 elements and not one.
Tonalitity is made of relationships, a relationship that can exist between at least 2 elements, therefore:
C and F melodically can be understood as:
V of F major or F minor
I IV of C major or minor
III and VI of A minor
etc.
C-F harmonically is a dyad found in a lot of harmonies.
In the tonal system, a dyad does not establish clear relationships. If the do-fa dyad is found in a piece where all the other dyads you mentioned are present, however, it clearly identifies the tonic function for do and the subdominant function for fa.
As they say, when you press "let's consider the C ionian scale," you are actually already giving the answer. And it is so obvious and banal that it embarrasses me to say it...
Crystal clear, having read it only once quickly before the "incident" I hadn't dwelled on "the C Ionian scale: C-D-E-F-G-A-B"
What I wrote remains valid, because as I was saying 2 notes or a dyad are too little and we don't know at what point of the musical discussion we are... therefore any modulations that may be necessary
Excuse me Modale: since when does an interval have a tonic?
It is true that the interval of a fourth makes one feel more dominant-tonic than the reverse (but it is the context in which it is inserted that ultimately makes the difference).
But it is also true that a modulation to the fourth degree makes this feel exactly like a fourth and not like a tonic, at least until I negate the old tonic and the new one is strongly confirmed (if I play C C7 F, then the first choice is G7 C, not Bb C7 F).
Of course an interval possesses a tonic; if we play C, the overtones that arise from C are many, as we all know, and between C and the overtones, the tonic is C.
But between C and F, perhaps the same rule does not apply! What do you think?.
I invite everyone to conduct research in the literature.
Ok, you meant harmonics... since Frank had used this term and you were talking about overtones, I thought there was something else implied.
I don't think harmonics are used to establish a key within an interval, also because for example to establish a key, a characteristic degree is needed, whether tonal or modal, and a well-defined scalar structure.
The concept of the tonic has nothing to do with harmonics, not even in a scale and not even in tonal harmony; otherwise, inversions would change the function of the chord, which only happens in rare, historical cases, and by convention (see the second inversion of the tonic chord).
Of course an interval possesses a tonic; if we play C, the overtones that arise from C are many, as we all know, and between C and the overtones, the tonic is C.
do we want to define the word "interval" or do we want to give everyone a different meaning for words? Intervals are calculated between REAL sounds, not between harmonics. To say that a C is the tonic of its own harmonic series is simply saying a complete STUPIDITY. I am sorry to be so heavy-handed, but many of modale's interventions seem placed as if they were enigmatic revelations, while they are often full of "linguistic metaphors". In acoustics, the mere use of the term "Do" or "C" (I imagine Anglo-Saxon notation looks cool, I don't know) is an imprecision, because in the harmonic series there is no equality of octaves. That is, there are MANY Cs. But the harmonic series IS NOT a scale and therefore the term "tonic" has no reason to be used when talking about the harmonic series. Furthermore, if we talk about intervals and harmonic sounds (that is, consonances and dissonances, not harmonies), I would be truly curious to understand why in the C-A interval the "tonic" (or, just throwing it out there, the sound that expresses the most consonant and therefore most stable harmonic series) is C, when it is known that A appears as the TWENTY-FIFTH harmonic of C while C appears as the nineteenth harmonic of A. Same issue for the C-D interval: the second (Pythagorean) appears AFTER the minor seventh (septimal) in the harmonic series; therefore, according to our DIY harmonic theory, between C and D it is D that expresses the most consonant and stable harmonic spectrum.
The reality is that all harmonic functions and criteria are "inspired" by acoustic processes, but adapted to artistic needs. To produce the 'dove's egg' (the perfect solution) of this discussion—namely, that tonic harmonies can function as the dominant of the subdominant—there is no need to involve harmonics; one only needs to look at the history of music...
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Eagle
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Reply 20 by Eagle
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thallo wrote:
To give birth to the dove's egg of this discussion, namely that tonic harmonies can function as the dominant of the subdominant, there is no need to bother with harmonics; one only needs to look at music history...