Muggles

Muggles is the rank-2 temperament tempering out 126/125, the starling comma, and 525/512, Avicenna's enharmonic diesis. It is an alternative 7-limit extension to magic. 11-limit extension of the Muggles include:

• Muggles (3e&16 or 16&19) - tempering out 45/44 and 385/384
• Muggloid (3&16 or 16&19e) - tempering out 33/32 and 176/175

See Magic family #Muggles for more technical data.

Tuning spectra

Muggles

Gencom: [2 5/4; 45/44 65/64 78/77 126/125]

Gencom mapping: [⟨1 0 2 5 0 4], ⟨0 5 1 -7 11 -1]]

ET generator	eigenmonzo (unchanged-interval)	generator (¢)	comments
	11/9	347.408
	16/13	359.472
	15/11	372.610
	13/10	372.893
	12/11	374.894
5\16		375.000
	8/7	375.882
	13/11	375.899
	11/10	376.500
	14/11	376.805
	13/12	376.905
11\35		377.143
	7/5	377.186
	11/8	377.393	11-, 13- and 15-odd-limit minimax
	[0 113 -12 -68 58 -26⟩	377.630	13-odd-limit least squares
	[0 -21 -5 27⟩	377.640	7-odd-limit least squares
	[0 134 9 -81 63 -33⟩	377.718	15-odd-limit least squares
	[0 85 -14 -62 46⟩	377.758	11-odd-limit least squares
	7/6	377.761	7-odd-limit minimax
	15/13	378.249
	15/14	378.419
	18/13	378.489
	9/7	378.534	9-odd-limit minimax
	[0 93 -4 -44⟩	378.554	9-odd-limit least squares
	14/13	378.617
	6/5	378.910
6\19		378.947
	10/9	379.733
	27/20	379.968	5-odd-limit least squares
	4/3	380.391	5-odd-limit minimax
	16/15	381.378
7\22		381.818
	5/4	386.314

Muggloid

Gencom: [2 5/4; 33/32 65/64 105/104 126/125]

Gencom mapping: [⟨1 0 2 5 5 4], ⟨0 5 1 -7 -5 -1]]

ET generator	eigenmonzo (unchanged-interval)	generator (¢)	comments
	16/13	359.472
	11/8	369.736
	13/11	372.302
	11/10	372.499
	13/10	372.893
5\16		375.000
	12/11	375.064
	8/7	375.882
	15/11	376.086
	11/9	376.839	11-, 13- and 15-odd-limit minimax
	13/12	376.905
11\35		377.143
	7/5	377.186
	7/6	377.761	7-odd-limit minimax
	15/13	378.249
	15/14	378.419
	18/13	378.489
	9/7	378.534	9-odd-limit minimax
	14/13	378.617
	6/5	378.910
6\19		378.947
	10/9	379.733
	4/3	380.391	5-odd-limit minimax
	16/15	381.378
7\22		381.818
	5/4	386.314
	14/11	391.246