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OM-AIS (All-Interval Series): New library for Openmusic

Hi everyone!
This is the pre-release of the OM-AIS (All-Interval Series) Library for Openmusic.
It was created to deal with calculations and manipulations of AIS. There is 3856 possible normal form AIS, 1928 prime form AIS and some invariant AIS (R-invariants and QI invariants).The operations available are:

  • retrogradation (R )
  • inversion (I)
  • retrograde inversion (RI)
  • operation Q (Q)
  • multiplication (M)
  • inversion multiplication (IM)
  • retrograde Q (QR)
  • operation 0 - (0)

References
PWGL Book, p.142, by Mikael Laurson and Mika Kuuskankare
PWConstraints, by Mikael Laurson.
The Structure of All-Interval Series by Robert Morris and Daniel Starr
On Eleven-Interval Twelve-Tone Rows, by Stefan Bauer-Mengelberg and Melvin Ferentz
The Composition of Elliott Carter’s Night Fantasies, by John F. Link
Harmony Book, by Elliott Carter

Updated:jan 7/2021 - Minor corrections in tutorial patches and a new patch for calculating AIS (require the OMCS library). Thanks to Fabio De Sanctis De Benedictis and to Karin Haddad for testing the library.

I intend to review some of the calculations in a near future, but if you have any problems, questions or suggestions, please let me know.

Best Regards,
Paulo Henrique Raposo.

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