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You can tune any instrument to any arbitrary frequency for center-c and as long as all the notes are of the same relative difference between them the melodies will generally work and harmonize. As long as all the instruments are synced it will sound ok in a band too.
In modern day we have a definition of what frequency center C is. But I have to wonder, how do we know the modern day frequency for middle-C is anywhere near the frequency used historically. In fact, when even was the idea solidified at all?
@freemo
You can't tune any instrument for any arbitrary frequency.
That's why the tuning sequence of an orchestra starts with the oboe.
Historic woodwind instruments preserve their pitch and make it available to contemporary precision frequency meters even though measurement instrumentation to determine absolute frequency wasn't available when they were built.
@tatzelbrumm Huh? I dont follow how you got to the consequent from that antecedent.
@freemo
How can you determine absolute pitch of musical ensembles from times before precise frequency measurement devices were available?
You examine instruments that cannot really be tuned, but whose pitch is based solely on their geometry and physical constants that don't change over time.
> How can you determine absolute pitch of musical ensembles from times before precise frequency measurement devices were available?
You cant, thats was the whole point of my post. Today we tune to specific frequencies as a base line. In the past it was arbitrary. How far back in the past determines how arbitrary it is.
Thats the whole point, a song that may have survived a long time may have been intended for a very different pitch than it is in modern times. Unless they had some standard way to get an approximate baseline pitch (such as defining a standard for the size of a tuning fork)
@freemo
There are (wind) instruments whose pitch only depends on physical dimension and speed of sound, cf.
https://www.oboefiles.com/why-does-the-oboe-tune-the-orchestra-and-how-to-do-it-right/
If the physical dimension and speed of sound didn't change since the instruments were build, you can reconstruct absolute pitch from the past.
@tatzelbrumm Right, and such a windinstrument **if** the dimensions are preceisly standardized would be a frequency reference itself. I agree at that point you have a somewhat standardized middle C.
But when did wind instruments become universally standardized in their dimensions? Moreover when did such a standard become closely aligned with a specific musical note.
@freemo @tatzelbrumm of your instrument didn't sound like your peers, you'd tune the odd one out to match. Factor in traveling musicians and it settles to a standard.
Right, id expect there to be local syncing and even somewhat of a natural local standard that would form naturally... The question is more about when did people try to quantify and define those standards against an actual frequency that is some how referenced.
"Scientific pitch was originally proposed in 1713 by French physicist Joseph Sauveur and based on the numerically convenient frequency of 256 Hz for middle C,"
@freemo It probably went like this:
Person 1: Your talk of counting vibrations of a twine is witchcraft.
Person 2: No, it makes a difference. Watch: (vibrates string at 261.63 Hz) Seeee?
Person 1: C? That is absurd! Graphemes are for scribes, not bards.
Person 2: And judgment is for judges, not peasants.
Person 1: ...Tell me more about your black magic.
@freemo We can say with certainty that concert pitch (actually set by A4 being standardized at 440hz today) was higher in the past - as high as A = 401hz. Not every instrument is tunable. Bells and some double reed instruments will never change pitch over their life times. By looking at bells from the 15th and 16th c we can tell that music was in general pitched somewhat higher then today.
The big innovation in modern tuning is equal temperament. All modern digital tuning has an precisely equal ratio between each half step. (about 1.059 to 1) This makes music work like you describe. Start on any pitch and the music will sound the same if the relative intervals are followed.
However much more than absolute pitch, relative pitch is hard without modern measurement methods, Prior to the 1700s the most common tuning was to tune in pure 5ths where every 5th was tuned by ear to a 2/3 ratio. It works pretty well until you get to the point where you go from the end of the circle of fifths back to what should be the note you started on. You find you are off by a scotch less than a quarter tone. This terrible sounding interval is a "wolf fifth" because it howls.
In pure fifths each key had its own flavor and so it was important to play a piece in the key it was written in. The major thirds that define the modern major chords are the most effected by these variations which explains why many pieced before JS Back and company are dominated by 4ths and 5ths that are safer in a pure-fifths tuning.
Bach's innovation which caught on across western music was to "fudge the thirds" to make them all sound similar - giving us the last common tuning the so called well-tempered tuning.
@antares The bell approach makes a **lot** of sense. that said bells can presumably be tuned by grinding,and i assume that is how they are fine tuned after the initial casting. But yea your point that once tuned they tend to remain fixed and cant be tuned without modifying the instrument makes a lot of sense.
Thanks for a wonderful response, lots of good info here.
"perfect fifths" are not a problem for fretless stringed instuments, winds and vocals. they just keep exact harmonics. only piano and fretted instruments have this problem and they're not really "classical" instruments. they rarely play grand concerts, operas, etc. but yes, the false notes are heard on piano pretty well. this is frustrating so I prefer fretless stringed instruments as more perfect ones.
@freemo en.m.wikipedia.org/wiki/History_of_pitch_standards_in_Western_music