Dual-n
A dual-n tuning is a tuning where two separate mappings are provided for a basis element, turning the one basis element into two basis elements.
The most common type of dual-n tuning is dual-fifth tuning, aka dual-3 tuning, where the subgroup 2.3 is replaced by 2.3+.3−.
However it is also possible to do this for any other basis element. You could have a dual-2 tuning, dual-5 tuning, dual-7 tuning, etc.
Use cases
One situation in which it might make sense to use a dual-n tuning is for use with an equal-step tuning that has low relative error on all primes except one (call it n).
But the tuning’s step size is small enough that one can't avoid hearing prime n, so a no-ns tuning doesn’t make sense.
One could use a dual-n tuning where n is that prime in order to make the equal-step tuning workable.
"Small enough"
How small is "small enough" is subjective and up to an individual composer's taste.
Some would say a step size of 30 cents is small enough, meaning that prime n must be within 15 cents.
Some would say a step size of 20 cents is small enough, meaning that prime n must be within 10 cents.
Some would say a step size of 10 cents is small enough, meaning that prime n must be within 5 cents.
Some would choose some other step size, while some would say the whole dual-n concept isn’t for them and they would rather use no-n no matter the step size.
It’s not a science and is up to a composer's discretion.
Scales with dual-n interpretations
- Many large ed4s (dual-2)
- Many medium or large local anti-zeta edos [idiosyncratic term ]
- Many of the sooty fox scales [idiosyncratic term ]
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Todo: complete list, add examples |