From Harmonic Structure to HCF to Sample Value, Part 5: Focusing on Pitch Specification and Alteration

Up to this point I've treated the Anchor (and Base Frequency, possibly not mentioned here since 2010) as more-or-less integral aspects of a Harmonic Structure, but really the Anchor only exists to provide a couple of services.

First, and most obviously, the Anchor is a point of reference for specifying the pitches of the fundamentals of the harmonic series composing the structure, and also of the HCF (Highest Common Fundamental). For this purpose it is enough that the Anchor's own frequency be unambiguous. Tuning would simply involve incremental alterations to that frequency.

The other service the Anchor provides is the ability to move a harmonic structure up/down-scale as a unit, by integer-ratio factors. This is what I previously referred to as "Consonant Transposition" on the theory that such a change is likely to be more consonant than using an irrational factor.

There could be other ways to provide these services, of course, including the option of separating the scalar component of the definition of the Anchor's frequency from the integer-ratio component, by bringing back the concept of a Base Frequency.

The Base Frequency would be specified simply using a Double (double precision floating point value), which you could think of as a multiplication factor that is always applied to 1.0 Hertz.

The Anchor would then be specified as an integer-ratio multiple of the Base Frequency.

Tuning would be accomplished by altering the factor relating the Base Frequency to 1.0 Hz, and consonant transposition would be accomplished by altering the ratio relating the Anchor to the Base Frequency.

This seems a little cleaner to me than combining a Double and an integer ratio into a 'dual-component' type, but your mileage may very.

In any case, these details need not be exposed to the user! What matters is that the pitches of the fundamentals of the series composing the harmonic structure are tunable as a unit and editable by integer-ratio factors, collectively as well as individually, and that those pitches as well as that of the HCF are clearly specified.