Equal temperment was invented before pianos were invented.
Even before piano-fortes. Sixteenth century. J.S.Bach wrote a book of exercises in all keys to promote the use of equal temperment. The well tempered clavier.
Scale development, ie the the diameter of piano strings, length of strings, and weight/unit length of strings, has developed over the years. Where the hammer hits the string matters, too. Major advancement occurred in ~1880 with the Steinway grand, and for consoles the 1939 Steinway 40. Different price points have different "scales" which affect the overtones available. IMHO. I have heard radio broadcasts performed on piano-fortes from Beethoven's era, and they sound like a 1920's 48" upright, one of the quality American Piano Supply line. Not the 1920 Steinway, which sounds modern, if A=427.
There are a lot of pianos sold with *****y overtone ensembles, just to save money. A cheaper piano sells better, except to the expert listener. 99.9% of pianos are sold by appearance, especially appearance of the salesman. Listen to a solo on the top octave. 95% of consoles will sound like "plick plick plick pick", not "ping ping ping ping" with a defined pitch. Most American males have destroyed their hearing so they can't hear the difference.
For mean tone tunings or other obsolete tunings, one has to go back to pre-1700 pipe organs, virginals, and harpsichords. Mean tone survivors sound horrid in keys with lots of sharps or flats.
An education is available without travel these days, on youtube etc. Get a good pair of headphones, do some educational listening.
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Back to the tuning thing.
C at 256 Hz was a commonly referred standard in the oldest books in my great Uncle's bookshelf. I read 'em. Then in the 1930s or 1940s, 440 Hz for the A came into broad acceptance; Steinway lead the way with their concert and studio grands; Mason and Hamlin, Chickering, Knabe and a wide waltz of others also started tuning similarly.
The harder instruments are the brass and woodwinds. The lengths of their speaking tubes (i.e. most of the instrument) is critically related not just to an open fundamental pitch, but also on the harmonics imparted as a function of the taper of the tube. Which depends on the open pitch.
So, while all brass and woodwind instruments (with a near-exclusion of the oboe) have a way to adjust the pitch of the device a few dozen ¢ (hundredths of a half note), in the end, with pitch changes comes timbre changes. And not necessarily very nice ones.
When one assembles a whole orchestra of musicians, it is darned helpful if all the instruments are correctly voiced for some pitch-in-common between them. Then the orchestra sounds best, at least in theory.
Hence why 440 Hz for the A is now THE standard.
All the 432 Hz aficionados notwithstanding.
⋅-⋅-⋅ Just saying, ⋅-⋅-⋅
⋅-=≡ GoatGuy ✓ ≡=-⋅
C at 256 Hz was a commonly referred standard in the oldest books in my great Uncle's bookshelf. I read 'em. Then in the 1930s or 1940s, 440 Hz for the A came into broad acceptance; Steinway lead the way with their concert and studio grands; Mason and Hamlin, Chickering, Knabe and a wide waltz of others also started tuning similarly.
The harder instruments are the brass and woodwinds. The lengths of their speaking tubes (i.e. most of the instrument) is critically related not just to an open fundamental pitch, but also on the harmonics imparted as a function of the taper of the tube. Which depends on the open pitch.
So, while all brass and woodwind instruments (with a near-exclusion of the oboe) have a way to adjust the pitch of the device a few dozen ¢ (hundredths of a half note), in the end, with pitch changes comes timbre changes. And not necessarily very nice ones.
When one assembles a whole orchestra of musicians, it is darned helpful if all the instruments are correctly voiced for some pitch-in-common between them. Then the orchestra sounds best, at least in theory.
Hence why 440 Hz for the A is now THE standard.
All the 432 Hz aficionados notwithstanding.
⋅-⋅-⋅ Just saying, ⋅-⋅-⋅
⋅-=≡ GoatGuy ✓ ≡=-⋅
I live with a professional sackbut (baroque trombone) player, who greatly prefers A=466 since that was the standard that the original instruments were made to, and her instruments are copies of those. Most modern “authentic instrument” ensembles will use historical pitch and temperament, particularly variants of meantone tuning, in their concerts and recordings. The only reasons they might choose A=440 is if there is an instrument (a big organ) that can’t be retuned, or if they have a particularly old fashioned or ignorant conductor. Otherwise it’s generally 466 or 415. Woodwinds also have a preference for 392. Harpsichords are frequently tuned in meantone, making some keys off limits, but making the keys it can play sound better.
Tuning and temperament are separable. You can have equal temperament at 466, or meantone at 440. Most vocal ensembles, unaccompanied by instruments, will instinctively adapt their singing to blend the pitches, meaning they have somewhat flexible temperament, making purer harmonies even if they are nominally in equal temperament. The same goes with tunable instruments, like the trombone or violin: good players will pitch up or down to blend the notes, making broader or narrower gaps as they play. It’s only the more mechanical or fixed pitch instruments, like pianos, that make this difficult.
I should also note that a 466 trombone can play at 440, simply by transposing down. So if A=440 then G=392, Ab=415, and A#=466. So to play an A=440 on an A=466 instrument, you play an Ab.
Tuning and temperament are separable. You can have equal temperament at 466, or meantone at 440. Most vocal ensembles, unaccompanied by instruments, will instinctively adapt their singing to blend the pitches, meaning they have somewhat flexible temperament, making purer harmonies even if they are nominally in equal temperament. The same goes with tunable instruments, like the trombone or violin: good players will pitch up or down to blend the notes, making broader or narrower gaps as they play. It’s only the more mechanical or fixed pitch instruments, like pianos, that make this difficult.
I should also note that a 466 trombone can play at 440, simply by transposing down. So if A=440 then G=392, Ab=415, and A#=466. So to play an A=440 on an A=466 instrument, you play an Ab.
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One thing's for sure - if you've never looked into music theory you're in for a big surprise! It's a whole discipline probably as complex as all of electronics. I found this out recently when I dipped my toes into looking at the difference between equally tempered instruments and just intonation. Like standing before a precipice!
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