Patent gap

A patent gap is a notable gap between patent tunings of an interval. This may be applied in the context of all edos, or in the context of those supporting a specific regular temperament, often containing a specific tuning optimum or structurally significant tuning. They usually represent mild exotemperings and occur often in temperaments with very few patent vals. They are one of the main motivations for using non-patent tunings.

A notable general patent gap is that between 714.3 and 720 cents for the perfect fifth 3/2, containing the tuning of half-comma archy. Another is the gap between 666.7 and 675c, also for 3/2, locking out approximate golden and eigenmonzo-5/4 tunings of mavila temperament from being supported by edos (however 25edo supports the similar structure trismegistus).

A notable temperament-specific patent gap is between 700 and 709 cents for the pajara 3/2 generator, making xenharmonic flat pajara tunings (including most calculated tuning optima) completely inaccessible from a patent val perspective.

Additionally, there is a gap in the tunings of 8/7 between 39edo's tuning (about 246 cents) and 5edo's tuning (about 240 cents); this is notable as large numbers of tunings cluster sharp of the gap (specifically the tunings of semaphore) despite the most accurate tuning of 8/7 being flat of it. This renders tunings of 8/7 at about 242c (such as optimized semaphore tunings or flat septimal meantone tunings) inaccessible if using patent vals.