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Does anyone know where I can get a list of all possible 2-note, 3-note etc melodic sequences? I could use a script to generate them myself, but if someone else has already done the work this would save me a lot of trouble.

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    By the time you add timing into the equation, there are hundreds of thousands - the main reason why there are so many different melodies! A possible task, but then what happens to the data? – Tim Jun 13 at 12:01
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There was an attempt of "Copyrighting all the melodies to avoid accidental infringement", see this TED-talk:

The numbers are huge!

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Such list will make lot of sense, because when you have this catalogue you can decipher and recognize written music much faster (sight reading! (like reading entire words than spelling the letters like a 6 years old child that starts reading.) That's is like a kind of meta or makro reading.

You can make your list yourself: It will also be a good ear-training, if you try to imagine with your inner ear the sound by singing and playing them (solfege). You can write a matrix with letters or numbers and also using the abbreviations of minor (m) Major (M) dim. and aug. naming the standard intervals - just to have the inventary - but much better is you notate them in sheet music!

2 tones:

There are 12 intervals up and 12 intervals down = about 48 intervals

3 tones:

After each interval you can add an other one of this 24 intervals, so you'll have 24 steps for 2 tones and 24X24 for 3 tone melodic motifs. (about 600 combinations).

If you ignore the rhythmic motifs you will have a list of about 600 combinations. Many of this motifs you can ignore because they are rarely used in music. (theory and practice ;). Finally it would be interesting to have a statistic of the most applied motifs.

I haven't made such a list but I can always represent it in my mind.

I'm very interested in your solution, as I am looking for something similar, as I want to name them by their shape and figure like the neumes in Gregorian chant have been characterized or the ornaments like trills, mordent and praller. But there will be longer motifs than only 3 tones.

Maybe this idea will help us making such a list:

Describing them - as changing notes, - passing tones, - chord tones, (harmonic reduction to the chords from which this motifs come from, - than scales - typical head motifs of songs or compositions.

On my way to find such figurations I came to the theme of musica poetica and have found the book of Dietrich Bartel with all the terms of music motifs and right now I 've found this book by A. Beyschlag Die Ornamentik der Musik

as I have found out that the elements and figures I am looking for to characterize and label them are a part of the ornaments in music.

Look up ornaments in wiki and also figuration.

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