User:Overthink/Sandbox

Interval information

Factorization	2-702 × 3400 × 7-99 × 11100
Monzo	[-702 400 0 -99 100⟩
Size in cents	0.02984219¢
Name(s)	missing ?
Special properties	reduced
Tenney norm (log2 nd)	1959.86
Weil norm (log2 max(n, d))	1959.86
Wilson norm (sopfr(nd))	4397
Audio demonstration
Open this interval in xen-calc

The difference between 100 896/891's and 7/4

Rank-3 tuning spectrum

9-odd-limit: 1/1, 10/9, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 7/5, and complements

Single tunings fully defined by eigenmonzos (+ the octave):

{10/9, 9/8, 6/5, 5/4, 4/3}, {10/9, 8/7}, {10/9, 7/6}, {10/9, 9/7, 7/5}, {9/8, 8/7, 7/6, 9/7, 4/3}, {9/8, 4/3, 7/5}, {8/7, 6/5}, {8/7, 5/4, 7/5}, {7/6, 6/5, 7/5}, {7/6, 5/4}, {6/5, 9/7}, {5/4, 9/7}

Marvel

{10/9, 9/8, 6/5, 5/4, 4/3}:

~3/2: 701.955 ¢, ~5/4: 386.314 ¢

{10/9, 8/7}:

~3/2: 700.670 ¢, ~5/4: 383.743 ¢

{10/9, 7/6}:

~3/2: 700.413 ¢, ~5/4: 383.229  ¢

{10/9, 9/7, 7/5}:

~3/2: 700.027 ¢, ~5/4: 382.458 ¢

{9/8, 8/7, 7/6, 9/7, 4/3}:

~3/2: 701.955 ¢, ~5/4: 382.458 ¢

{9/8, 4/3, 7/5}:

~3/2: 701.955 ¢, ~5/4: 378.602 ¢

{8/7, 6/5}:

~3/2: 700.027 ¢, ~5/4: 384.386 ¢

{8/7, 5/4, 7/5}:

~3/2: 698.099 ¢, ~5/4: 386.314 ¢

{7/6, 6/5, 7/5}:

~3/2: 699.384 ¢, ~5/4: 383.743 ¢

{7/6, 5/4}:

~3/2: 694.243 ¢, ~5/4: 386.314 ¢

{6/5, 9/7}:

~3/2: 698.099 ¢, ~5/4: 382.458 ¢

{5/4, 9/7} (impossible)

Additional eigenmonzo tunings up to 21-odd-limit (new intervals: 21/20, 16/15, 15/14, 21/16)

{21/20, 16/15}

{21/20, 5/4}

{21/20, 9/7}

{16/15, 8/7} (impossible)

{16/15, 7/6}

{16/15, 9/7}

{16/15, 7/5}

{15/14, Incomplete

Gene- rator	~3/2
~5/4	EDO tuning					11\19	18\31			7\12				31\53		24\41	1\22
	(↓↓↓)	Eigenmonzo			112/75			25/14	25/21		63/50	189/100	567/400		3/2
		(↓↓↓)	Size (¢)		694.243	694.737	696.774	698.099	699.384	700.000	700.027	700.413	700.670	701.887	701.955	702.439	709.091
		56/45	378.692												{3/2, 7/5}
	6\19		378.947			19edo
	13\41		380.488													41edo
	7\22		381.818														22edo
		9/7	382.458					{5/3, 9/7}			{7/5, 9/5}				{3/2, 7/4}
		245/162	383.229									{7/6, 9/5}
	23\72		383.333							72edo
		36/35	383.743						{5/3, 7/6}				{7/4, 9/5}
		175/144	384.386								{5/3, 7/4}
	17\53		384.906											53edo
		5/4	386.314		{5/4, 7/6}			{5/4, 7/4}							{3/2, 5/4}
	10\31		387.097				31edo
	4\12		400.000							12edo

11-odd-limit adds 12/11, 11/10, 11/9, 14/11, 11/8

15-odd-limit: 16/15, 15/14, 15/11

21-odd-limit: 22/21, 21/20, 21/16

Test

Approximation of odd harmonics in 562edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.536	+0.163	+0.569	-1.063	-0.428	+0.753	+0.699	-0.329	-0.716	-1.030	-0.516
	Relative (%)	+25.1	+7.6	+26.7	-49.8	-20.1	+35.3	+32.7	-15.4	-33.5	-48.2	-24.2
Steps (reduced)		891 (329)	1305 (181)	1578 (454)	1781 (95)	1944 (258)	2080 (394)	2196 (510)	2297 (49)	2387 (139)	2468 (220)	2542 (294)

Approximation of odd harmonics in 509edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.60	+0.33	+0.13	-1.16	+0.35	+1.12	+0.93	+1.13	-0.46	+0.73	-1.16
	Relative (%)	+25.4	+13.9	+5.6	-49.2	+14.9	+47.6	+39.3	+48.1	-19.5	+31.0	-49.3
Steps (reduced)		807 (298)	1182 (164)	1429 (411)	1613 (86)	1761 (234)	1884 (357)	1989 (462)	2081 (45)	2162 (126)	2236 (200)	2302 (266)