Keyboards so that the notes were evenly spaced (like the frequencies given in the table presented above). In the early 20th century, it was decided to tune There were actually several different tuning systems in use during Bach's time, including meantone (which aimed to make major 3rds sound good, but was not as concerned about the quality of major 5ths, with the effect that some keys were not usable), and Werckmeister's 1691 tuning which allowed composers to create music in any key (with the effect that the various keys had a different tonal quality). Sounded great in those keys, but pretty awful in other unrelated Instruments, especially strings, sounded 'right' in those keys.
Tuned for a particular group of keys, so that all the Playing the same note will play E `= 659.26\ 'Hz'` [just a littleĪround 400 years ago, keyboards (usually harpsichords and organs) were But notice (from the frequency table above) that a piano This is possible, and we can play a beautiful, perfect E at `440 ×ġ.5 = 660\ 'Hz'`. On a violin (or viola or any fretless stringed instrument) To get a 'perfect 5th' (the interval between AĪnd the E above, say), we need to play a note which has `1.5` times An interesting problem has faced musical instrument makers for
