Scale of the Day: A Pythagorean Octotonic-1 - Lydian Mode

The A Pythagorean Octotonic-1 - Lydian Mode - Scale. It's a Pythagorean tuning because the largest prime factor for these frequency ratios is 3. It's an Octotonic-1 scale because it's an 8-note scale of alternating whole/half steps. And it's in "Lydian Mode" because the largest prime factor (3) is always found in the numerator - making each note either the tonic or an otonal interval relative to the tonic. This otonality leads to the odd spellings such as the C double-sharp augmented third - as the D-natural perfect fourth would be the utonal 4/3 - or the B-Sharp augmented second - instead of the also utonal C-natural minor third (32/27). Which highlights the fact that the Pythagorean augmented third does not equal the Pythagorean perfect fourth - something that is lost in equal temperament.