a list of presumably all the possible 33,624 thirteen note "melody lines" (or "collection of notes" - if you will allow) produced
by graph walking the set of the 12 intervals (major & minor: 2nds, 3rds, 6ths, 7ths; perfect 4ths & 5th; augmented 4th or diminished 5th, and the octave),
within an - and inclusive of the - octave, starting from C (or solfege "Do"), constrained by:
1. not being allowed to visit a next note having an already "seen" interval. A note may be re-visited - but through a different interval path.
2. not leaving the octave
3. and then ending on either C, or the C an octave above.
You can find these by:
1. downloading the pdf in the title above and searching below for a particular index number;
2. clicking on a path group to the right to populate the search below; edit it and press ENTER;
3. using the search below - which uses either a simple numeric lookup (indexed by the pdf) or a simple string match on the path.
Upon pressing ENTER from the input area - the search, for instance, "CAGC"
will find all melody lines that match "Do La Sol Do" somewhere in the path of the melody line.
Using AND will sub-select each AND group - so: "CAGC and GEC" will sub-select "GEC" melodies from the melodies matching the prior "CAGC".
Use a space between terms to get multiple matches;
use "number + limit" to get a range of items between the most adjacent numbers.
More than 101 melodies will not be displayed; you must filter further.
Click on the found melody to hear a
pretty "setPeriodicWave" wave-pattern-y AudioContext version of it.
Many thanks to Dr. Evan Fein at Juilliard for coming up with
a wider version of this exercise (he absents constraints #2 & 3), and
Paul Rosen and Gregory Dyke for the notation rendering with abcjs.
Of course, if you find errors, please do let me know.