Negri extensions

Negri temperament has various extensions to the 11 limit.

Tuning spectra

Negri

Gencom: [2 15/14; 45/44 49/48 56/55 78/77]

Gencom mapping: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]

ET generator	eigenmonzo (unchanged-interval)	supersecor (¢)	comments
	16/15	111.731
	8/7	115.587
	11/9	115.803
	15/14	119.443
	16/13	119.824
1\10		120.000
	7/5	123.498
	15/13	123.871
3\29		124.138
	13/10	124.298
	4/3	124.511	7 and 9 limit minimax
5\48		125.000
	30517578125/26795786661	125.469	7 limit least squares
	[0 63 -26 -1⟩	125.579	9 limit least squares
	10/9	125.673
	11337408/9765625	126.238	5 limit least squares
2\19		126.316
	6/5	126.337	5 limit minimax
	[0 79 -40 -5 16 2⟩	126.445	13 limit least squares
	[0 34 -17 -2 7⟩	126.511	11 limit least squares
	[0 73 -46 -4 20 4⟩	126.619	15 limit least squares
	18/13	127.324
	9/7	127.486	11, 13 and 15 limit minimax
5\47		127.660
	14/13	128.298
3\28		128.571
	5/4	128.771
	11/10	129.374
	11/8	129.736
	7/6	133.435
	15/11	134.238
	13/12	138.573
	14/11	139.169
	13/11	144.605
	12/11	150.637

Negril

Gencom: [2 15/14; 49/48 65/64 91/90 875/858]

Gencom mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]

ET generator	eigenmonzo (unchanged-interval)	supersecor (¢)	comments
	16/15	111.731
	8/7	115.587
	15/14	119.443
	16/13	119.824
1\10		120.000
	7/5	123.498
	15/13	123.871
	14/11	123.906
	11/10	124.091
3\29		124.138
	13/11	124.164
	15/11	124.203
	13/10	124.298
	4/3	124.511	7, 9, 11, 13 and 15 limit minimax
	[0 -149 8 -15 113 -23⟩	124.700	15 limit least squares
	[0 -136 21 -14 98 -21⟩	124.764	13 limit least squares
	[0 -125 15 -15 81⟩	124.854	11 limit least squares
	11/9	124.882
	12/11	124.965
5\48		125.000
	11/8	125.094
	30517578125/26795786661	125.469	7 limit least squares
	[0 63 -26 -1⟩	125.579	9 limit least squares
	10/9	125.673
	11337408/9765625	126.238	5 limit least squares
2\19		126.316
	6/5	126.337	5 limit minimax
	18/13	127.324
	9/7	127.486
5\47		127.660
	14/13	128.298
3\28		128.571
	5/4	128.771
	7/6	133.435
	13/12	138.573

Negric

Gencom: [2 15/14; 33/32 49/48 65/64 91/90]

Gencom mapping: [⟨1 2 2 3 3 4], ⟨0 -4 3 -2 4 -3]]

ET generator	eigenmonzo (unchanged-interval)	supersecor (¢)	comments
	16/15	111.731
	8/7	115.587
	15/14	119.443
	16/13	119.824
1\10		120.000
	7/5	123.498
	15/13	123.871
3\29		124.138
	13/10	124.298
	4/3	124.511	7 and 9 limit minimax
5\48		125.000
	30517578125/26795786661	125.469	7 limit least squares
	[0 63 -26 -1⟩	125.579	9 limit least squares
	10/9	125.673
	11337408/9765625	126.238	5 limit least squares
2\19		126.316
	6/5	126.337	5 limit minimax
	18/13	127.324
	9/7	127.486
	[0 106 -31 4 -38 11⟩	127.602	13 limit least squares
5\47		127.660
	[0 -95 25 -5 31⟩	127.706	11 limit least squares
	[0 109 -28 5 -43 13⟩	127.718	15 limit least squares
	14/13	128.298
3\28		128.571
	5/4	128.771
	11/9	128.951	11, 13 and 15 limit minimax
	13/11	130.113
	14/11	130.415
	12/11	131.170
	15/11	132.610
	7/6	133.435
	11/8	137.829
	13/12	138.573
	11/10	165.004

Negroni

Gencom: [2 15/14; 49/48 55/54 65/64 91/90]

Gencom mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]

ET generator	eigenmonzo (unchanged-interval)	supersecor (¢)	comments
	16/15	111.731
	8/7	115.587
	15/14	119.443
	16/13	119.824
1\10		120.000
	11/9	121.799	11, 13 and 15 limit minimax
	12/11	122.785
	11/8	123.245
	7/5	123.498
	15/13	123.871
	15/11	124.068
	13/11	124.101
3\29		124.138
	11/10	124.166
	[0 19 -22 -7 32⟩	124.180	11 limit least squares
	[0 33 -66 -14 90 -6⟩	124.186	15 limit least squares
	[0 49 -50 -15 76 -8⟩	124.215	13 limit least squares
	13/10	124.298
	14/11	124.424
	4/3	124.511	7 and 9 limit minimax
5\48		125.000
	30517578125/26795786661	125.469	7 limit least squares
	[0 63 -26 -1⟩	125.579	9 limit least squares
	10/9	125.673
	11337408/9765625	126.238	5 limit least squares
	6/5	126.337	5 limit minimax
	18/13	127.324
	9/7	127.486
5\47		127.660
	14/13	128.298
3\28		128.571
	5/4	128.771
	7/6	133.435
	13/12	138.573