I'd advice to check Bass Tuner BT1 into your phone. It's free. It's a tuner that shows development of pitch over time.
The harmonics are only going to get the bass kind of in tune, especially if you’re playing with keyboard or fretted instruments: the 3rd partial (“7th fret harmonic”) is just a hair sharper than the 4th partial of the lower adjacent string when compared to 12-TET, which means that if your A is in tune the D and G strings will be slightly flat (with the G flatter than the D) and the E will be slightly sharp when tuned using harmonics. It’s not by a lot and I doubt it’s something most listeners will notice, but it’s something to be aware of when tuning to harmonics/pure intervals.When tuning with pizz, I play as softly as a tuner can detect, to minimize the effect of pulling and releasing the string.
When tuning arco, I double check with harmonics of adjacent strings.
Too much weight with too little bow speed will make the string sound flat in my experience.Those are two very different questions.
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I don't know about the string, bow weight can make the string sharper, but I'm not sure what would make it flatter.
The harmonics are only going to get the bass kind of in tune, especially if you’re playing with keyboard or fretted instruments: the 3rd partial (“7th fret harmonic”) is just a hair sharper than the 4th partial of the lower adjacent string when compared to 12-TET, which means that if your A is in tune the D and G strings will be slightly flat (with the G flatter than the D) and the E will be slightly sharp when tuned using harmonics. It’s not by a lot and I doubt it’s something most listeners will notice, but it’s something to be aware of when tuning to harmonics/pure intervals.
Too much weight with too little bow speed will make the string sound flat in my experience.
Inharmonicity is kind of inherent with any stringed instrument, and from what I understand thicker and shorter strings will be more inharmonic than thinner and longer strings (but please don't quote me on this). I've definitely noticed over the past few years that the 3rd partial ("7th/19th fret" harmonic) of my E strings (usually the Spirocore weich extension string, sometimes I use the medium) tends to be significantly sharper when the E string is "in tune" to 12-TET compared to the top 3 strings' 3rd partials.To the first point, I have a pet theory that certain strings are worse than others for tuning harmonics. Unfortunately, the strings that I distrust the harmonics most, I prefer virtually everything else about them.
To the second point, my teacher was recently telling me that slow bow speed made pitches go flat. I was dubious but tried it and he/you are absolutely right.