Is there a term for melodic improvisation where only specific intervals are taken into consideration?

As an example, Beginning on C, the player then has the option of moving either up or down, (Or repeating the same note) but only in the intervals of:

Min 2nd (C#/Db), Min 3rd (D#/Eb), Aug 4th/Dim 5th (F#/Gb), Min 6th (G#/Ab), Min 7th (A#/Bb), and into the next octave. (Min 2nd + Octave). Once the player decides on an interval, and plays it, he or she then selects the next interval from the same set.

If the second notes were F#/Gb, the available notes would then be: G, A, C, D, and E.

Below is a short passage composed under the stipulations above, as an illustration. enter image description here

No key was applied, because I don't have the knowledge of which key would clean up the notation most efficiently.

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    Did you see this technique described somewhere/by someone? Or maybe there was a related idea that triggered this concept in your mind? I'm not familiar with it but find it interesting. Do you have any examples of a melody/improvisation that's based on this technique? – jdcode Apr 29 '18 at 1:00
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    No jdjazz, I do not. I have spent the last two years listening almost exclusively to the music of Robert Fripp. His guitar playing from 1994 - 2004 included many harsh, dissonant sounding sections, particularly in his improvisations with King Crimson's Double Duo formation. I don't know what he was thinking, or what method he was drawing on as he improvised, but I thought that the method outlined in this question would make it easier to formulate a general feel (motif) in improvised music: in my case try to mimic his. (Check this example of Fripp's soloing: youtu.be/tHAJncjlQHM?t=564 ) – user47327 Apr 29 '18 at 2:38
  • I just tried to notate something in Musescore using this technique of composing. I can't think of any way of making it look less messy. It contains many accidental's making for difficult reading, at least for me, though my reading is very poor. – user47327 Apr 29 '18 at 3:13
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    @Erik What you're talking about sounds like what I'm looking for, and I think your answer is correct. I've removed my response to your answer from the posted question. – user47327 Apr 29 '18 at 19:17
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    @DaleyCodyYakoweshen That's great! To expand on your question the concept of interval inversions might interest you too. – Erik Apr 29 '18 at 19:30

To me this looks like scale transposition. Every played note becomes the new root note for the scale consisting of the stated intervals.

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