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Is there a name for a chord where the root note is played twice?
For example, if I play a C major chord and hit the C one octave above as well:
C-E-G-C
Note: I'm not talking about inverted chords, in this example I mean a normal C major with an additional C one octave above the root C played simultaneously.
Is there a name for a chord like this? Or is it simply called a C major as well since the second C doesn't add another tone?
To take your naming idea further, there's root position, first and second inversions. This much you know. However, taking it further, add just an extra C on top... but don't stop there, because there's a plethora of other ways to voice those three notes, especially on a piano, or using an orchestra. In fact, so many varieties of that C-E-G combination - C at the bottom of the piano, a G in the middle, an E,G,C at the top is just another...I can't work out how many different combinations of 4,5,6 or more notes, but it's going to be more than lots! The problem is/would be, that they would all need special names, so the operation would get unwieldly, to say the least!
So, sorry, no, there are no particular names for voicings such as you suggest, so if you need to transmit a particular one to others, it could be done by writing out the dots for them to read, showing them on whatever instrument, or merely showing what voicing you need.
chord qualities don't spec octaves. only the halfsteps involved.
arrange it however you like, but it's still the C major chord if you've got C,E,G in any (or even ALL) octaves.
an 2nd, 3rd inversion (etc, etc) are just a small subset of possible arrangements. use as many octaves as you like and whichever octaves you like.
If you need to spell out octaves, etc you just use ole standard notation and write which arrangement you mean.
Chord symbols are designed to indicate harmonic function, whereas the specific "way" in which you play a chord (i.e. the order you put the notes in and which notes get doubled) is called the chord's voicing.
Therefore, your chord is simply called C major, and if you asked me to describe its voicing, I would say it has a doubled root.
The exception to this would be if you change the bass note, in which case a "slash chord" indicates the bass note, e.g. C/E is a C major chord with E as the lowest note. If the new bass note was a part of the original chord, then we have an inversion.
As far as I know, there are no names for different voicings of chords, only inversions.
Something worth noting though, is that when describing cadences, there are two kinds of authentic cadences: perfect and imperfect. An authentic cadence is when a dominant (V/viio) resolves into the tonic. In order for a cadence to be perfect authentic both chords must be in root position, and relevant to your question: the tonic must also be the highest voice in the chord.
For example (notes in ascending order):
G-B-D(V) -> C-E-G-C(I) is a perfect authentic cadence.
G-B-D(V) -> C-E-G(I) is an imperfect authentic cadence.
G-B-D-G(V) -> C-E-G-C-E(I) is an imperfect authentic cadence.
Yes, it is's just a C major triad.
It's in root position, but you already know about chord inversions.
I would say there are two related ideas/terms to be aware of:
It may seem obvious that it's four-part harmony, but the important thing is in common practice harmony - where chords are primarily triadic with seventh chords less prevalent - the difference between four-part harmony and fewer voices is significant. Either the chords are complete seventh chords or some number of chord tones are doubled. Good part writing is picky about how doubled parts are handled. There's no need to go into the details here - things like: don't double a tendency tone - just be aware of it and look up part writing for more info.
There aren't specific names/terms for particular doublings - CEGC, CEGE, CEGG, CCEG etc. would all be just root position C major chords in four-part harmony. You can just name the doubled tones, like C major with the root doubled or C major in first inversion with the fifth doubled, etc.
You might also consider...
Adding octave numbers will be helpful...
C4 E4 G4 C5 is closed voicing where all the tones fit within the smallest range. There is only one form for each inversion of a chord in closed voicing.
E3 C4 G4 C5 or C4 G4 E5 C6 would be examples of open voicings. There are lots of possible open voicings, but usually only one or two tones are skipped. Also, it's common for the bass to be much lower than upper voices like C3 E4 G4 C5. Technically an open voicing, because of the large interval between bass and tenor, but all three upper voices are in closed voicing relative to each other.
You can have combinations of doublings, partial chords, and open voicing like: a four-part, first inversion, open voicing, G dominant seventh chord with the chord's fifth omitted and the root doubled. A mouthful to say, but perfectly descriptive. The actual chord could be B2 G3 G3 F4 or B2 G3 F4 G4 etc. Actually, other than the inversion specifying which tone is in the bass the various possible distribution of the other voices into different octaves doesn't matter that much. In terms of good part writing the harmony will be handled more or less the same regardless in which octave the parts are placed.
The main descriptors:
There is no chord name specifically for a chord with the root in two octaves. It would just be called C Major.
This is because chord symbols (i.e., names) contain only a certain subset of the information needed to play a chord. They tell you the notes, but not the octave, order (~inversion) or quantity of each.
When a performer plays off a chord chart, they have to fill in that missing information. On piano, it's very common to play the root of the chord in your left hand, and also in your right (in a different octave). If you play the root too low, the bass player may come and slap you, but that's another story.
If you want to name a chord, remove any duplicate notes prior to looking for the name. They are a performance detail that is not captured by chord symbols. If you need that detail, use a different notation technique.
