Whenever you play two notes at the same time, the difference in pitches is called an interval. Because of how pitch perception works, generally we care about the ratio of frequencies, rather than the ...
Just intonation favours expressing intervals across the entire keyboard as ratios of small numbers:
(Perfect) octave - 2:1
Perfect fifth - 3:2
Perfect fourth - 4:3
Major third - 5:4
Minor third - 6:5
Before 12tet came about, some instruments - such as harpsichords - whch are tuned specifically, would be tuned so that their notes sounded best in certain keys. Just Intonation and other temperaments ...
The core questions are:
1. At what tempo should the second movement of Beethoven's Fifth begin?
2. How should it be counted?
About Beethoven and tempo indications
At the time Beethoven composed the ...