Are melodic intervals in relation to key or simply the last played notes?

Question

Is the concept of 'intervals' in this sense any note in relation to the tonic note of the key, (whether that tonic note is being played at the time or not), or are melodic intervals just the immediate notes preceding the current note, regardless of key or other context?

So for example, in the key of C major...

if you play an F note, then a G note... does that mean this interval is the perfect second in between these two notes?

Or are these notes intervallic in relation to the tonic note of C?

In other words, is this F to G in the key of C a major second interval, or is this a perfect fourth, then a perfect fifth (C-F C-G)?

Answer 1

An interval is the distance between any two named pitches, regardless of context. So, F and G are a major second apart from each other no matter what context they appear in.

In a melodic interval the notes sound consecutively.

In a harmonic interval the notes sound simultaneously.

In terms of their relationship to a tonic pitch, that is thought of less in terms of interval or more in terms of the functional relationship. For example, B in the key of C major is called the "leading tone", because its function "leads" upward to the tonic. On the other hand, B in the key of D major is the "submediant", one role of which is as the tonic of the relative minor scale.

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Examples

X:0
T:F and G in the key of C
T:F and G are a major second apart
K:C
M:C
L:1/4
C"_P4"xF"_M2"xG"_P5"xC

X:0
T:F and G in the key of A
T:F and G are still a major second apart
K:A
M:C
L:1/4
C"_d4"x=F"_M2"x=G"_d5"xC

X:0
T:F and G as a melodic interval
K:C
M:C
L:1/4
C"_P4"xF"_M2"xG"_P5"xC

X:0
T:F and G as a harmonic interval
K:C
M:C
L:1/4
C"_M2"[FG]2C

Answer 2

Your question: are the tones F and G referred to C an interval called the 4th respectively the 5th or can they also be related to each other?

The answer is: yes!

Interval means the difference - or better: the distance - to the root of the scale, but also to the root of the chord and even the distance between any two or more tones, sounding together as “Klang” or as sequence of tones in a melody.

You are correct: F is the 4th and G the 5th regarding the distance (=interval) to C and and there is a major second between F and G.

Answer 3

Intervals are note specific. And not even pitch specific!

Obviously an interval is the 'space' between two notes - but those two notes could be found in different keys, so can't be key specific. Example: (yours) F>G is M2. Both F and G are in key C, and key F.

However, the key specific bit could be that certain notes are not in a particular key, or are usually sharp/flat in a particular key. But that's somewhat irrelevant, as an interval is that between two named notes.

You seem confused about inversions. The difference between P4 and P5 is always M2 - there's no need to reference your F and G in key C - or any other key.

For simplicity's sake, intervals are found by counting (up works better). Any letter name to any other letter name (higher) provides the number of that interval. So, C>A. C D E F G A. 6 letter names = a sixth - of some sort.

Then we need to qualify what sort of 6th. Maybe that's over answering the question as it stands?

EDIT: one can use the root of a key to determine certain intervals, but not all. For example, in key C major, C>D=M2, C>E=M3, C>F=P4, C>G=P5, C>A=M6, C>B=M7. However, all those intervals will be called what they're called when found in any key. Confusing? A little.