Good day stack family,
So in the harmonic series, we have a fundamental (pitch/note) and a succession of harmonics that stem from the fundamental which also hold other pitches within themselves.
My question is, let's say we have a ratio of 3:2 which is a 5th in a scale pertaining to the fundamental. Where does first of all 3 and 2 stem from exactly, what do those numbers represent?
My second question is why does the third harmonic (3) get put in a ratio with the second harmonic (2) aka 3:2 instead of the 3rd harmonic being put in a ratio with the fundamental which would be 3:1?
I see this pattern a lot where ratios will be created from a harmonics previous harmonic like for e.g. 5:4,3:2 and so on, instead of the ratio being created with a harmonic and the fundamental each time which only exists in unison 1:1 and an octave 2:1.
My last question is, I've seen ratios that are something ridiculous like 54:72 like a tritone I believe, how do these massive jumps in ratio come about?
EDIT: Based on the Plomp and Levelt curve for musical tones, here is a list of an octave in chronological order of the interval with most consonance, straight down to the interval of most dissonance (in order of consonance to dissonance) using the key of C..
- Unison - C to C - 1/1
- Octave - C to C1 - 2/1
- Perfect Fifth - C to G - 3/2
- Perfect Fourth - C to F - 4/3
- Major Third - C to E - 5/4
- Major Sixth - C to A - 5/3
- Minor Third - C to Eb - 6/5
- Minor Sixth - C to Ab - 8/5
- Tritone - C to F# - 7/5
- Minor Seventh - C to Bb - 9/5
- Whole Tone - C to D - 9/8
- Major Seventh - C to B - 15/8
- Semitone - C to C# - 16/15
Is this statement and list correct in its order of consonance to dissonance? If not could you correct the order of the intervals please and rectify the statement as this would finalise my query?