I was terribly shocked yesterday, when my composition teacher told me, that the dominant does in fact means the triad of the 5th step in the welltemperated system. And not the triad of the 2nd overtone, as it is close to.
I have always thought that theory of harmony was only overcoming the problems of the weird tone system by using a primitive language. But it does never say, what the words really means. Take the dominant - it´s explained as both the triad of the 5th step in the welltempered system and as the triad of the 2nd overtone, now that is not the same and there are no ways, that it can be the compared.
Then there are two possible means of a dominant:
1. the dominant is the triad on 5th step of our tonesystem, a triad that comes close to the triad of the 2nd overtone.
2. the triad of the 5th step of our tonesystem is a triad that comes close to the dominant, the triad of the 2nd overtone.
Can it really be true, that example 1 is the correct? I just think it is stupid not to have a name for the fundamental functions, the ones, that the major/minor-tonality theory are trying to be like.
Couldn´t I just get this confirmed? 1 or 2? ???
It depends on your tuning system. In modern tuning, the dominant obviously refers to the triad build on the 5th scale degree, since our tuning system divides the octave into equal intervals (equal-temperament). Of course, if you pluck a dominant "harmonic" on a string, you will actually be hearing a "just" dominant. They are very close (off by 0.11%). The answer to your question is that it depends on the tuning system. In modern tuning, it's the 5th scale degree.
thank you very much for the information! But still, when you call this "just" dominant a dominant, it wouldn´t be the same? My teacher claimed, that I could not call the harmony produced by a clean fifth a dominant.
If I recall my college theory right, the tonal sequence goes like this:
VII: Subtonic
VI: Submediant
V: Dominant
IV: Subdominant
III: Mediant
II: Supertonic
I: Tonic
"Tonic" refers to the home chord, but I can't remember exactly why V is "dominant. It makes musical sense, though; the V chord is the most common chord after I in nearly all tonal music. "Subdominant" refers to the IV chord being a 5th lower than the tonic, just as the V chord is a 5th higher. "Mediant" refers to III's position halfway between tonic and dominant, while "submediant" is halfway between subdominant and tonic. "Supertonic" and "subtonic" are obvious enough.
Here's a good place to repeat a musical theorist's joke:
Q: What do you get when you mix a Picardy third and a Beethoven fifth?
A: A supertonic. ;)
Quote from: mikkeljs on April 13, 2007, 08:05:51 AM
I was terribly shocked yesterday, when my composition teacher told me, that the dominant does in fact means the triad of the 5th step in the welltemperated system. And not the triad of the 2nd overtone, as it is close to.
I have always thought that theory of harmony was only overcoming the problems of the weird tone system by using a primitive language. But it does never say, what the words really means. Take the dominant - it´s explained as both the triad of the 5th step in the welltempered system and as the triad of the 2nd overtone, now that is not the same and there are no ways, that it can be the compared.
Then there are two possible means of a dominant:
1. the dominant is the triad on 5th step of our tonesystem, a triad that comes close to the triad of the 2nd overtone.
2. the triad of the 5th step of our tonesystem is a triad that comes close to the dominant, the triad of the 2nd overtone.
Can it really be true, that example 1 is the correct? I just think it is stupid not to have a name for the fundamental functions, the ones, that the major/minor-tonality theory are trying to be like.
Yes, example 1 is correct; the dominant is the triad on step 5 of the key. Period. You are thinking in terms of acoustics and not functional harmony. The issue is further complicated in the minor mode, where literally (say in A minor) the dominant triad would be E minor in the natural mode, but functionally the dominant triad is always major, with the G sharped in this case.
I spoke with my composition teacher again today. So he just confirmed it again. And that the functions, we speak of, doesn´t make academically sence if they should prove their theories, but that they serve, as well as choral harmonization, as a help on a abstract and alternative level only.
I just got completely confused and couldn´t beleived it, when I got told, that it was 1 and not 2.
As I understand it, "dominant" is the most important function next to tonic, for several reasons. Key of C: As an interval, G is related to C ideally as a fifth, or ideally 2:3. This is the closest related ratio to tonic (1:1). F to C is a fourth, 4:5, and so on. all the other ratios are larger than 2:3. So 2:3 is the most related, or "dominant" relation. As an overtone, the fifth is very prominent, after the octave.
Its not really helpful to try to fall back on acoustics. In common practice tonality there are only two primary relationships to the tonic: dominant and subdominant. Chords on other scale degrees : ii, iii, vi, and viio are subsitutes for the sd,t,t and d, respectively. Not because of acoustics, but due to the shared notes between the subsitutions and the t,sd or d (i.e. The ii chord shares two notes with the IV chord)