Say i want to harmonize a melody by a major 3rd. do i just stack a note 4 semitones higher on top of each note of the melody? what if the harmony note disagrees with the key i'm in?

singing question: how do you sing a harmony to someone elses singing without the aid of a musical instrument?

1. Yes
1a. You play it that way anyway or move the note down a semitone so it fits the key. This is called harmonizing in diatonic (fitting the key) thirds
2. It's hard and requires a lot of practice. Your best bet it to ask this in the vocals thread.
just count 3 notes in the scale from the note you want to harmonize... should end up with a major and a minor melody playing in harmony. for singing you just do it
Learn the difference between major 3rds and minor 3rds.

Harmonize major thirds on I, IV, V notes. Minor Thirds on ii, ii, vi notes.

For example, the C major scale, then the thirds:

1 2 3 4 5 6 7


No matter what, when you harmonize in thirds, notes should be on the same scale.

if you try and harmonize every note in the melody by a major third, you'll end up with out of key notes. Which may or may not sound good. you'll just have to listen to it and find out (but it probably won't sound good).

You going to have to use some minor thirds along with the major 3rds.

for example, if you melody goes C E D A F, harmonizing every note by a M3 will get you an E, G#, F#, C#, and A. Those three notes with a sharp are out of the C major scale. If you want to stay in key, E D and A will need to be harmonized by a minor third.

When you harmonize a melody, take the note you want to add to ( for example, an E) and examine where it falls in the scale. In the case of an E in C major, it is a iii chord (third scale degree, which is a minor triad). Then, rather than paying attention to the quality of the interval you wish to harmonize it with, choose the quantity. In this case you chose a third. A 3rd from E is G, and in this scale it is a minor third. The qualities of the interval will take care of themselves.
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