User:DisasterBlaster/Sandbox

1153470752371588581/1152921504606846976, [-60 29 0 5>, Pentarchisma. Tempering this out equates five Archytas fifths (32/21) to three octaves and two Pythagorean commas. Notably also the difference between five archytasmas (64/63) to the 19-comma, five aberschismas to the magic comma, and thus splits the tritave into 5 intervals, each equated to 5103/4096.

2359010787328/2353579470675, [30 -23 -2 0 0 3>, Americomma. Named for the thirteen (13-limit) colonies, I first equated three differences between the classic grave fifth and the tridecimal superfifth to two semitones (16/15) and then lowered it by a Pythagorean comma. It is also the difference between three fairytale commas (1001/1000) and the Alpharabian comma, so if I had discovered it that way, I probably would have called it the 'golden age comma'.

2227754207823337509102134573095845373483021732054960903603121346630505452738612005129840239901060253798165190221481644194672219102234100585084307285020612396607419274589973120157653414182912/2225162600151951363007033152993599624222548002301240820607412498364688251174265176004917913113524094823669968964896751311917308619080538805575749308555359790062766478513367474079132080078125, [629 -328 -47>, Reckless comma. Difference between the schisma and four atoms or 43 Pythagorean commas and 47 syntonic commas.

23763/23762, [-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -2>, Averfifthsma. Taking the averiant between the common minor third and the common major third gives us 109/89, much closer to a neutral third than 11/9 that is tempered by the rastma (243/242), and squaring it gives the Averfifthsma as its difference to the fifth

80623115361291412000794652124944906491201/80000000000000000000000000000000000000000, [-43 20 -40 0 0 0 0 0 0 0 0 20>, Pitching comma. 1.8 semitones approximate 111/100 so well that comparing a stack of thirty to the eighth harmonic gives only ~13.43 cents of error. 111/100 is to this comma as 27/25, which produces Bug, is to the ennealimma.

204840021458546589812482594366668142542429986589197318528619143395036962199099876801/204800000000000000000000000000000000000000000000000000000000000000000000000000000000, [-91 0 -80 0 80>, Octacontalimma. In the same vein as the previously-mentioned pitching comma and ennealimma; equates 1.65 semitones to 11/10. Is a 7.272727...th-octave temperament.