Hmm lol, only issue with looking at scale lengths is that it starts you thinking..
A strat is a 25.5" scale length.. the guitar I'm designing is 27" .. but now I'm considering ~28.5" given that for standard tuning that results in a better wavelength (and harmonic) calculation where an open string is either a whole, half or quarter. It also assists in further drop tuning (down side is more string tension).
Here's a 28.5" scale 6 string..
Gawd damn lol..
Edit: explaination of the thinking..
1. Without a string Sine waves (sound) are a simple beast - they only sit at the frequency (fundamental) or divisions of 2, such as 1/2, 1/4 where the side crosses the line. Therefore your sine wave and the frequency are tied as 1/frequency = length of the full wave.
2. Complex waves are made up of adding a number of sine waves together, this includes the overtones (harmonic). The more asymmetrical the sine wave the more even harmonics (warmer sound) but the more symetrical the distortion of the sine wave.
3. The frequency of the 7 string B string is 61.74Hz so 1/61.74 = 0.0161969 meters wave length or 16.196mm or multiple of.. drop A would be 55Hz or 18.181mm.
4. Scale length can therefore be aligned to this - if you look at the 27" scale this leaves a lot of multiples that have odd fractions, however if you take that 181.181 and multiply that at 4.. you get what is basically 727.72mm which is basically 28 5/8th inch scale length... now if you wonder why people go for that precise scale length then that's the reason.. Now when you look at the other frequencies of the other strings at 727.72/wave length they are either very very close to a full wave length division, 1/2 a division or a 1/4 division.. which can be fine tuned by the bridge and nut intonation. In short this works out quite a nice scale length for a nice sounding guitar.. with harmonic content making the guitar sound better, cleaner sound.. also next up strings...
5. As strings vibrate, the higher the tension, the more sideways force is applied to the mass of the string the faster it vibrates. String tension is mathematically linked to frequency too, f=1/(2L)*sqrt(T/µ), which basically means the the string tension goes up squared the length.. so the longer it is the higher the tension. A slacker thicker string required on a shorter length for the same frequency has less clarity, fatter sound and less attack. A thinner string, with less mass to move, vibrates faster/cleaner leading to a cleaner, clearer, but leaner with more attack sound for the same frequency.
You'll note that they're linked via tension but sound itself will not follow the same tension orientated maths, thus you will end up with a complex harmonic overtone sound. The higher the harmonics that are created, the less pleasing the guitar sounds, even with distortion etc.
So this had got me thinking hard.. I could make a 272.72 scale guitar and easily update the design at this stage. Sure it would have more tension on the strings compared to the 25.5" scale strat but I don't really shred for shred's sake that much and the usual modern tricks of harmonics etc are as easy on a higher tension anyway. With a fixed bridge I don't have the need to worry about trems and a longer scale length for lower tuning is more stable and has less intonation issues.
I deliberately oversized the case length I've made.. so this is very very tempting..
Next up is the pickup positions
If you want to see the maths:
https://till.com/articles/PickupResponse/
