Extended Just Intonation
Just intonation refers to a musical tuning idea which couldn't be simpler. The intervals between musical notes- all musical notes, in any tuning system- are defined in terms of ratio of frequency. So traditional music education teaches us a convenient trick that is insidiously misleading: that we add intervals to get other intervals. In physical terms, the frequencies are being multiplied, not added.
If a fly next to your left ear beats its wings 50 times a second, and another fly next to your right ear beats its wings 100 times a second, you will hear the interval known as an octave. But the difference of 50 wingbeats means nothing; if the left fly got excited and started to beat its wings 75 times a second, and the right fly heard the other and got excited enough to beat its wings 125 times a second, you would no longer hear an octave (you'd hear a major sixth). The octave is represented by the x2, not by the +50.
A lot of my university colleagues were bewildered and amazed when I talked about this, but if I could only have found the right way to explain it, it would have made sense to anyone who could pass 4th grade.
Harry Partch's contribution to this line of thought was to bring in higher prime numbers to multiply frequencies by. Our well-known 12-note system has notes that approximate frequency ratios up to multiples of 5: a minor sixth is close to an 8:5 ratio, a minor third is close to a 6:5 ratio. Partch used multiples of 7 and 11, which indeed can sound very beautiful in certain harmonies. These higher prime numbers in the frequency ratios are the reason for the word "extended" being added on to "just intonation". Some of those who have followed him have taken this even further, using harmonies based on multiples of 13, 17, 19, and on and on.