User:DisasterBlaster/Sandbox: Difference between revisions
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1153470752371588581/1152921504606846976, [-60 29 0 5> Pentarchisma. Tempering this out equates five [[32/21|Archytas fifths]] (32/21) to three octaves and two [[Pythagorean comma|Pythagorean commas]]. Notably also the difference between five [[64/63|archytasmas]] (64/63) to the [[19-comma]], five [[Aberschisma|aberschismas]] to the [[magic comma]], and thus splits the [[tritave]] into 5 intervals, each equated to 5103/4096. | 1153470752371588581/1152921504606846976, [-60 29 0 5>, Pentarchisma. Tempering this out equates five [[32/21|Archytas fifths]] (32/21) to three octaves and two [[Pythagorean comma|Pythagorean commas]]. Notably also the difference between five [[64/63|archytasmas]] (64/63) to the [[19-comma]], five [[Aberschisma|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 [[40/27|classic grave fifth]] and the [[20/13|tridecimal superfifth]] to two semitones (16/15) and then lowered it by a [[Pythagorean comma]]. It is also the difference between three [[Fairytale comma|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'. | |||
Latest revision as of 10:00, 3 August 2026
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'.