Cello tuning by harmonics Just intonation vs ET

1. Is just intonation the harmonic series?
2. Why does just intonation sound better?
3. Is Pythagorean tuning just intonation?

Is just intonation the harmonic series?

Just intonation frequencies are based on the harmonic series. A fundamental tone is picked and then all of its harmonics are transposed within one octave (that is, in the range of the first two harmonics). The first N harmonics account for 12 different notes in that range.

Why does just intonation sound better?

Our brains tell us that the first interval is more consonant, simply because it requires less effort to process than the second one. Of course, in the real world, things are rarely absolutely perfect and two tones in the ratio of 40001:50001 will be heard as "near enough" to 4:5.

Is Pythagorean tuning just intonation?

Applying the first part of this concept, some scholars refer to Pythagorean tuning as "3-limit just intonation," since all intervals are derived either from fifths (3:2) or octaves (2:1), ratios involving 3 as the largest prime.