I do not understand the difference between a chord and a triad. Are they the same thing or do they have differences? (i.e. Cmaj. chord v.s. Cmaj. triad)
The basic accepted definition of a chord is minimum three separate notes.Some would be happy saying two. Thus a triad is a chord. However, chords can have more than three separate (named) notes. So, triads are chords, but chords may not be triads.
The most used triads are 1,3 and 5. Translating in key C to C, E, and G. There are four different types of triads - major, minor, diminished and augmented. Majors have (consecutive) intervals of M3 and m3. Minors have m3 and M3. Diminisheds have m3 and m3, while augmenteds have M3 and M3.
Since triads have three and only three notes played, those can be voiced close or open. Close has all three notes as near as possible to each other, giving for example, C E G, or E G C, or G C E as the options - root, 1st and 2nd inversions, in that order.
Open triads use the same notes (here in key C) but they could be anywhere on the instrument (obviously an instrument which can play all simultaneously), and those inversions are dictated by the lowest note.
It stands to reason that any or all of those three notes could be played in multiple octaves, and often are. Then, they still constitute only C major, but then it's played as a chord - triads having only three notes.
Chord is the broad category and triad is a specific kind of chord.
The simultaneous sounding of multiple tones makes chords. Here is a quote from Elie Siegmeister's Harmony and Melody...
Harmony had its roots in the chord - a group of tones sounded simultaneously.
Even more importantly chords are conceptual, you need to analyze music to determine which tones combine to make chords. In many cases it can be ambiguous which tones constitute the tones of a chord.
Triads are chords of three tones, a third and a fifth above a root tone. Usually the implication is the tones are stacked up thirds, but to be technically clear, such chords built of thirds are called tertian chords.
Going back to Rameau and the concept of the perfect chord common practice harmony is triadic. Many harmony texts define a chord as three tones which makes sense, because triadic harmony is the topic of those texts. Other texts, like Siegmeister's define chord as simultaneous sounding of any number of tones. There really isn't a conflict between those differing definitions. It's just a matter of whether the focus is on triadic harmony or the broad sense of harmony as the vertical combination of tones.
In your example...
i.e. Cmaj. chord v.s. Cmaj. triad
The general understanding would be those terms are synonymous. But, as "chord" is a broad concept, it should be understood that a "C major chord" could refer to an incomplete chord of, for example, the root and third. "C major triad" is more specific and you would expect it means all three chord tones are actually present.
These terms apply regardless of instrumentation. They would be used the same for piano, guitar, chorus, etc. etc.
All triads are chords. Not all chords are triads. Triads are 3 note chords generally constructed by taking every other note of a scale, such as C,E,G or D,F,A. The notes in a triad do not have to be played in any particular order. For example from low to high it can be C,G,E.
A chord can have as few as 2 or many more than 3 notes in it. There are many different ways of constructing chords. They can be stacks like a triad but with more notes or can be triads with added notes or any combination of 2 or more notes.
A triad can also have more than 3 notes but if it does it uses one or more of the same 3 notes repeated in different octaves. An example from low to high is: C,G,E,G,C.
a chord is kind of a logic, or a universal; it's an endless series because the chromatic nature of notes is 'regular' it will repeat ad infinum by doubling the frequencies of its parts whatever they are. i found CmM11b5b9 !!
any unique chord combines only enough intervals from only 1 chromatic bass note & the notation used for a chord contains the bass position + implies a unique triad using the fewest possible marks.
I.the roman numeral indicates the bass of the chord according to a key signature that may not be immediately clear , but , since it's just a capital , a major chord , and nothing else is indicated lets just create the harmonic space from the bass note of C natural . that 1 mark implies 1 bass note and 2 up intervals:
1 interval has 2x full steps, the 3rd degree &
1 interval 1x full + 1x half step; for a fifth degree.
the bass triad is C E G and on the Staff it looks great ••• .the triad expresses the chord
I, as written
G, - , -- , -- , -- , - C--E,--G,.-,.-- ,-- ,-- ,
a triad musical-izes the chords in a piece, so the chord progression survives for generations of future performance and interpretations of "1=C, , no! can 1=E my bassoon is big as a balloon ?" .
projecting a harmonic space through a piece is the gravity of the triads the 3 notes ringing out on time so they basically express the drama of the chord progression
the triad multiplies the options so that music is enriched with harmony that is relieving of passing tones & selective against too much flub. , with 3 notes there is now just enough elements to juggle , to create suspense & bring something to life musically ! . the 3 pitches, notes uniquely projecting in triad the chord, assert two more choices of 'lowest' sounding notes in place of the tonic bass note & share harmonic space . . further, multiple intervals from each of the 3 notes in the triad enchant the named chord with tonal tricks and illusions - melody .
a progression of chords , navigated by the ensemble , on time, uncovers the triads by landing on the bass position , , which may be inverted !! still, with the same pair of intervals above and below! the fundamental bass of the triad , enter harmony
G,.-,.-- ,-- ,-- ,-
E--G,.-,.-- ,-- ,-- ,-C,--E,
can't really think of a better resource to actually do your question some justice than this article & hope i wasn't too confusing or boring . anyway they use the word "triad" here often to refer to a single specific spooky set of intervals that are a triad; they aren't referring to 'all triads' always ok just keep that in mind o