Beginner Why are the perfect fourth and perfect fifth named as such?

5
Forest of Dean UK
Level
Beginner
I have heard one explanation as follows.

Before we all started using 12 Tone Equal Temperament, all the frequencies were mathematically correct. Nice simple ratios of the frequencies. But there were other problems in that to play in another key you would have to retune the piano. So a compromise was made in using 12 Tone Equal Temperament. So you could now play in any key without retuning your instrument. But of the nice simple ratios of the various intervals, most are now not accurate (with the exception of the octave), but you would have a job to hear the error. The only other intervals that are still accurate are the fourth and the fifth, so they are referred to as perfect.

Is this explanation true or is there another reason?
 
Solution
2nds, 3rds, 6ths and 7ths have a major and minor version. There is no major or minor version of the 4th, 5th or octave. Hence the name "perfect".

Perfect and minor intervals can be reduced 1/2 step, in which case they are "diminished". Perfect and major intervals can be increased 1/2 step, these are "augmented".
The only other intervals that are still accurate are the fourth and the fifth, so they are referred to as perfect.

This may come from confusing perfect with pure.

Just intonation is sometimes called pure. Although 4ths and 5ths in ET are not the same as in Just, as mentioned above. Close but no cigar as Pythagoras is famous for saying.
 
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