My mother, a non-professional music teacher of Indian-classic (North indian) Vocal-music and Nazrul's songs. She is good in her stream (in my opinion), she had a strong interest for indian classic; and was selected to get private-lessons to Sipra Bose (passed away on 2008), a notoriously weird genius of North-indian classics.
But surprisingly; she cannot 'copy' a simple musical sequence. So she can't sing correctly the simplest school-songs, Tagore's songs, popular film-songs, band-songs, and any other forms that requires a 'correct copying'. She usually never try them in presence of others because people indeed start laughs or jokes or badly bullies or assaults.
I've tried analyzing how she's dealing the music in mind. If I play a note on the harmonium, she can quite effortlessly identify it (though not quantitatively like an absolute pitch) and sing it. She can quite effortlessly identify the common-notes of 2 different songs. But if I sing a small (say 4- or 5- or 6-note) sequence from a song; she can't memorize it, and certainly distorts it. She often seeks my help if some of her students requests for teaching a song such as a Tagore's song. But She tells that she is most effortless at the Vistaar (=expansion) portion, one of the portion of a North-Indian classic performance which requires least-degree of copy-capacity, and solely dependent on the artist's creativity.
I, never in true-sense, learned music. I couldn't improve on the lessons my mother tried to give me. But I often sang in small-programs of college and university; where people (including teachers) started to gives beats; clapped a lot after performance; and it was considered as good as well as emotional.
Surprisingly, at singing; indeed I didn't had any slightest emotions. They were actually ditto-copy of some old-day film songs ... just like a tape-recorder. I can, quite effortlessly recall (better to tell 'hear') and repeat a song in mind, in ditto.
When I tried to analyze my-way of thinking music; When I play a single note on the harmonium; it seems quite impossible to memorize. But when I play more-than-one reed in a particular sequence and speed and rhythm; memorization becomes easier; and very surprisingly; with increasing of sequence length upto a certain level; the ease increases. (Just like we can't hold a coin in one finger... the more figer is allowed, the more easy it is to pick up the coin) for say; if it is a 10 or 20 note - long sequence; it is rather difficult to forget. I can "hear" it mentally; in ditto I listened.
I can, like my mother, synthesize new music in mind... but not as much like my mother. When I hum a tune in my mind; usually I sing the same sequence in repetition.
But as its disadvantage; when I mentally sing a song; the "the upcoming note" (what is next of current-note) become so 'loud' that I couldn't remember any-other note at that time. So I have a rather poor 'analysis' ability on music.
Now; my question is; Is there any terms for these 2 opposite traits? Seemingly it is not about absolute vs relative pitch. It is about the ability to recall the notes in sequence or not. Maybe it is some concept associated to semantic or episodic memory?