chord voicing with arpeggiations and inversions
This question is in two parts.
A) Assume the rules of 4-part harmony. Should the first note of an arpeggio be the one that is included in the chord for best sonority? For example, we are told, with regard to doublings, to double the root first. In that case, would the following situation not be ideal (please see below)?
Or, because the listener must only wait one quarter note (see arpeggio in tenor) is this acceptable? In other words, technically speaking, should the arpeggio start with the most ideal chord tone (double the root first, then the fifth next. Try not to double the third)?
B) Regarding the voicing of chords in inversion, is the "root," third," and "fifth" the same as those if the chord were in root position? If a C major chord is in first position, when we are voicing the chord do we call the C the root? Or, because we've inverted the chord, is the E the root? Any information/tips on the voicing of chords in inversion is appreciated.
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If this question is just one of practice there would be 2 rules to consider:
sustaining the common tone of 2 chords = keeping in the same voice: e.g. the third in the soprano
the rule about doubling priority (root, 5th, 3rd)
So if this is not an exam task you can just ignore the point of doubling or like you say:
because the listener must only wait one quarter note (see arpeggio in tenor) is this acceptable?
yes, it is
(Even in a test situation you can ignore it - but you should point this out to to tell them that you are aware of it. You can double the 5th aswell as the root and the third in the octave will be ok too.)
And if the soprano is not given you can handle it to fulfill the rules.)
Your second question concerning the root: yes the root note is the note on which the thirds are built and that gives the name to the chord.
That’s why the other chord positions are called inversions: then the root tone isn‘t the bass note. As the third is in the bass it’s a sixth chord (I6) because of the interval of 6th between bass tone and root (= 1. inversion). Look up: chord inversions.
Should the first note of an arpeggio be the one that is included in the chord for best sonority?
Your wording - "the one that is included in the chord" - is confusing to me. I sounds like you are asking about non-chord tones like a suspension, but I don't think that is your intent. I think you mean something like "should it be a tone that will complete the full voicing of all chord tones?"
The first beat of a bar is most important. I would say you want the chords on the first beat to be the essential harmony notes fulfilling good harmony.
With chord tones C E E given in the other voices the G is missing from a complete chord, it seems the question is "should the missing voice (which will sing the arpeggiated chord) start on G to provide the missing chord tone on the first beat and then the other arpeggiated tones can fall on less essential beats?"
If you want nice balance chord with full, sonorous chords: I think yes.
C would seem to be the next best starting choice - not ideal because then the chord will be incomplete on the first beat.
E would be a bad starting choice, because the chord will be poorly balanced with too much emphasis on the chord third.
Regarding the voicing of chords in inversion, is the "root," third," and "fifth" the same as those if the chord were in root position?
Yes.
Those chord tone identities are relative to the root as pitch classes above the root in closed position.
Pitch class just means all C's like C3, C4, C5... are members of pitch class C.
That's kind of a wordy description. Basically, if you take all the given tones, rearrange them by octave transposition to be stacked up in thirds, the first tone is the root with 35d, 5th, etc above the root:
C E G = C root, E third, G fifth
...rearrange the tones to another inversion and spacing like E C G and it maintains the same chord tone identities...
E C G = E third, C root, G fifth
A) Should the first note of an arpeggio be the one that is included in the chord for best sonority?
How you voice a chord is essentially up to your taste (unless your professor demands otherwise). If you are following a set of voice-leading rules/counterpoint/etc, then default to those as your guidelines. With regard to doublings, plenty of rules exist depending on the context (counterpoint, block chords, orchestration, etc). However in your specific example, doubling root between the bass and tenor is (in my estimation) more an issue of clarity. If you had put the 3rd of the chord (here, E) in the tenor's lower register, it could be considered a bit of a muddy voicing as it would be close to the bass's C in the lower register. Choosing the voicing that effectively outlines the harmony (or voice leading) you want for a specific passage is part of the craft. If you're writing an exercise, try to follow the rules. If you're writing your own music, try follow your ears, and always remember to listen carefully.
B) Regarding the voicing of chords in inversion, is the "root," third," and "fifth" the same as those if the chord were in root position?
Yes. A C major triad will always contain the notes C, E, and G, precisely because that it is how it is (essentially) defined[*]. What you mean to look for is the bass note, which is simply the lowest sounding note in the chord/sonority. So if you had (from bottom to top) the notes G E C E, it would still be a C major triad (because it contains the pitch classes C, E, and G and nothing else) but in second inversion (because the bass note is its fifth, G). In fact, both chords spelled G E C and G C E (spelling bottom to top) are in second inversion precisely because they have the G (again, C's fifth) in the bass. (An E in the bass is first inversion, meaning its third is in the bass). The spelling beyond that is a question of voicing as opposed to inversion.
[*] A major triad is, from root up, a major third to the next note followed by a minor third to the final note. Starting on C, this yields the notes C, E, and G together.
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