A scientific way of looking at a scale is that it is 12 ratios, all related to a reference audio frequency. We call the ratios "intervals" in music. So if you start with the A note and apply the 12 intervals or ratios you get a set of 12 notes in a chromatic scale. The set of ratios or intervals is also called a "Temperament" in music. The ratios have been calculated so that music theory works when you play the notes: for example they are calculated so that when you stack the root, 3rd and 5th, the audio frequencies actually work together to make a nice harmonious chord.
The standard used for design and construction is to use A as the reference note and to set it to 440Hz. 440Hz is not a prison which players are forced to stick to. It is just a design number in the middle of a range so that dimensions can be calculated in the design stage. The player has the freedom to select A = 430Hz to 450Hz to get the sound they want, in general. When they tune the A note, the musical instrument is made to apply the 12 intervals or ratios to create the other notes. A higher frequency for A will make all the notes higher, and a lower frequency for A will make all the other notes lower.
Going back to the Snark Hz-1 Guitar and Bass Tuner. It is sold as a Guitar and Bass tuner. The user manual shows frequencies which are generated by the interval ratios when A = 440Hz. If you want to use another A note pitch, you need to recalculate all the pitches, there are tables on the internet. I have no idea how the HF-1 detects the audio frequency, but I suspect it may require more sustain or energy than you can get on a ukulele, so it just wont work on a ukulele which is why the Snark company sell it as a Guitar and Bass tuner. Its a cheap lesson to learn that tuners are just tuners, there are some which wont work on a trumpet or violin or ukulele.
Confirming that the HF-1 does not work for a ukulele is probably a useful public service because some of the advertising is not clear on it being for guitar and bass. It would be interesting to see if it does work when you plug into an amp and cad get more sustain and a hight sound energy level.
