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Most tuners are set to 440hz which is the frequency of the A string and when in an orchestra setting, an A will be played generally from the oboe for everyone to tune to. The A on an oboe is actually at 443hz.
In answer to your question though, ask your teacher why he or she wants you to tune the D first? Your teacher may have a very valid reason for wanting you to do it that way.
I've alway's heard to start with the A string first too. Tuning the A to 440 hz then tuning down to the D and G in perfect fifth's, to be tuned in pair's. Myself, I still can't do that, I have to use some sort of tuning device. My thought's before were maybe starting more to the center of the bridge for equal pressure, I dunno.
I have found that not tuning in order A, D, G, E causes the tuned strings to go out of tune when you get around to the A string. In my own experience, tuning G first then A causes the G to go out of tune. I believe its the pressure on the bridge exerted at certain points. Im sure theres a physics explanation regarding the best order of tuning. However, I dont know it.
"Please play some wrong notes, so that we know that you are human" - said to Jascha Heifetz.
This doesn't exactly answer the question, but is related.
During tuning I hit the side edges of the bridge with little fillips to stabilize things. My idea is that that will cause the bridge to reach a stable position on the belly and cause the strings to be stable in their notches. Also sometimes I press down equally on the lengths and afterlengths of each string.
Does it do any good? How would I know?
I guess if you do the G string first you are lifting the bridge at the E string. Only an infinitesimal amount but it will move .
So by the time you tune the E string, the pressure is equalised so the G string will be out of tune again.
I guess if you have a 5 string instrument, starting with the middle string will equalise the pressure across the bridge from the start.
Just my 2p worth, as I have no sense, sorry cents......
I am amazed at how old people of my age are.....
When I pick up the fiddle, I try to tell---or should I say guess---by ear alone whether any are out of tune. Then I use the electronic tuner and play all four strings in a row, noting which ones are out of tune and approximately how much. If any are out of tune, I turn all the fine tuners of the out-of-tune strings the estimated amounts needed---without playing any strings---and give the bridge a little whack from each side with my middle fingernail as mentioned in my post above. Then I start again---playing all four again to know whether they are all in tune yet.
So in a sense I tune them all at the same time, not in a sequence.
If i have PC on - i check strings with FiddlerMan's tuner and can start to tune from any string i wish. If the PC is off - i use a pipe whistling tuner - this one is E, or i can use camerton A and start from A. Didn't notice any difference. Whatever i start with - i check it again after i tune them all, and then double check =) It's much quickier than it sounds, lmao =)
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