User:2^67-1/Sandbox

Testing

The blackwood-dicot-semaphore equivalence continuum is a continuum of 7-limit rank-3 temperaments describing the set of all 7-limit rank-3 temperaments supported by 10edo. Any rank-2 temperament supported by 10edo can thus be represented by a line between two points in this continuum.

All temperaments in the continuum satisfy (25/24)^p(49/48)^q ~ 256/243, equating a stack of dicot commas (25/24) and semaphore commas (49/48) with the blackwood comma (256/243).

The blackwood comma is the characteristic 3-limit comma tempered out in 10edo.

Selected temperaments with integer p and q

p	q	Temperament	Comma
			Ratio	Monzo
0	0	Blackwood	256/243	[8 -5 0 0⟩
0	1	Archytas (squared)	4096/3969	[12 -4 0 -2⟩
0	2	Buzzard	65536/64827	[16 -3 0 -4⟩
0	3	Slendric (squared)	1058841/1048576	[-20 2 0 6⟩
0	∞	Semaphore	49/48	[-4 -1 0 2⟩
1	0	Srutal	2048/2025	[11 -4 -2 0⟩
1	1	Mirwomo	33075/32768	[15 -3 -2 -2⟩
1	∞	Jubilic	50/49	[1 0 2 -2⟩
2	0	Negri	16875/16384	[-14 3 4 0⟩
∞	0	Dicot	25/24	[-3 -1 2 0⟩
∞	1	Jubilic	50/49	[1 0 2 -2⟩
∞	2	Breedsmic	2401/2400	[-5 -1 -2 4⟩