@oid Have even dumber version - 6 instead of 9 object - 1/3 enhancement in brutalist/ minimalist matrix.]]
Interpolation-scale.pd

@oid: Thnx for patch.
Yea, u have to be right - Slider is more imprecise cause it is px based - and it is same in MAX, Pd, Plugdata,
I often use number box instead of slider to make more exact out.

Have a good one.

Hi,
how can one do ratio approximation -- fraction from number? (need it for - well tempered - scale, that should also be used on time and modulation).
Some starting patch would be great, cause I did not find anything on web.

It was once provided by Omar Misa on FB, but it got deleted.. it was small patch using prepend and based on simple logic, that u consequently setting numerator w 1-9 denominator, until it match/ is close .. cool was, that u can also set/ show deviation.. and ultimately set what deviation is acceptable or set it some categories..

Imo for musical purposes, u often don't need complex object/ object-patch/ open object (that is hard to follow without Ph.D. or having Pd as almost only instrument and not just one of sometimes over hundred plugins), but rather a simpler patch w/ explanation of logic behind it/ context (like on U-he, D16groups manuals).. so u can alter it to suit your needs.
Just my opinion.
..................................

As a tribute to Omar I've shared patch - in patch section - using his interpolation technique and update it for 3 values.

Happy patching.

Edit: Ok, I am digging to it from scratch - I am now sure, that it will be one of the least eloquent patch on the planet heavily relying on brute force....

EDIT: As I ve said *- least eloquent patch is done..CounterFin.pd

Patch simply rise denominator,. When its fraction ratio is below numeric ratio, it increases numerator +1 and start rising denom. from 1 again...
Increment/Decrements - allow set +/- 1 manually in different part, giving some overview for ratios - specily those that are close by, helping build your scale or its function(s), can serve as modulation etc.

It allows also easy set of deviation parameters, cause chances to find clear fraction from large ratio are pretty slim,

Hi.
this patch is rather for Plugdata, since Pd imo does not have gate, tough u can use else/router, which is the same.

As a tribute to Omar I've shared a patch using his interpolation technique and update it on 3 values.
There was discussion on this topic on FB too (also deleted, tough) and consensus was, that value offset created when adding nother interpolation is caused by imprecision of slider. I found it is not EDIT "completely" true,
Slider in Plugdata is pretty precise.
It is - obviously - cause by leaving the smallest step value in previous approximation, which distorts the final result.
Solution is to send "0" to not used part, when interpolating other value..
EDIT: *Tough as mentioned, despite 6 digits are pretty fine (enough for DIY fine-tuning in DAW, without noticeable side-fxs. W/out this there was offset even 1/3 of step - 0.02-4 cca, now it is in 0.5 Hz range - beyond vst synth resolution), but this is definitely not the best suited approach for 12 decimals scala-like Pro fine-tuning etc.. that wont fly

BTW there should be probably even more elaborate solution, for more values - like using append+scale... if someone would like to beat the efficiency (make it dumber)) contest..

Happy patching.

Scale version is - obviously - in comments sesction..

https://www.dropbox.com/scl/fi/s1wncx9eytc50sukzwris/Interpolation.pd?rlkey=utcp4cd7dder4jpuduggkomji&dl=0