Melodies are still there. However for the last 10 or 15 years almost everything I hear on radio a songs with fairly long introductions that are quite melodic and musically very well done followed by a segue into a cha-cha with disco drums added. Not really enough variety for dancing.
So I went through the chapter again. I actually found an example of octave leaps on all the active tones. On page 18 par. 28:
However I think it's important to into account par.6 in page 6.
So while it is possible to leap an octave whenever (so long as you haven't recently made a wide skip), the tendency and urgency of the active tones should be ...
I'm not familiar with arabic music, but in western terms he is playing something close to the dorian b2 scale (2nd mode of melodic minor). As well as phrygian, as you say. The #4 you refer to I hear more as a temporary b5, making it locrian instead of phrygian for a brief moment.
You're mixing up a key signature with a key or tonic of a mode.
A key signature of no sharps and flats is C major...
...or A minor...
...or D Dorian, or E Phrygian, etc. etc.
Basically, all tones except the B could be a possible tonic.
In classical music harmony, specially cadences, define the tonic. Other means, mostly rhythmic, can define the tonic. ...
Here's what we know about your melodies:
uses C Major scale
uses D, E, F, G, A
starts on D
"didn't feel resolved ending on C ... [on] a D it sounded resolved"
Your melodies are either in D Dorian or D Aeolian (minor), not C Major.
D dorian is the second mode of C Major so it's understandable that you have confused them with one another. Likewise, they ...
If you read a book about good melodies and rules for good melodies you will certainly find some advice or rules developed of the cantus firmus era.
Music (and of course the composer) is always working with expectations and surprisings! Why should this not be in a melody?
I remember children songs we sang in the primary school playing with this effect. ...
I think he's suggesting that the melodic leap of an octave behaves much like a repeated tone (octave equivalence). By the way, I recommend book highly. It's a bit old-fashioned (not so much as Geotschius's other books) but one can adapt as necessary.