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

Stuff

Orwell as 9-form

(Note that 13/10 and 20/13 are mapped via tridecimal orwell)

Degree	0-step	1-step	2-step	3-step	4-step	5-step	6-step	7-step	8-step	9-step
Cents	43	200	314	471	586	743	857	1014	1129
Ratios	36/35~33/32	9/8	6/5	21/16	7/5	(20/13)	18/11	9/5	27/14~48/25
Cents	0	157	271	429	543	700	814	971	1086
Ratios	1/1	11/10~12/11	7/6	9/7~14/11	11/8~15/11	3/2	8/5	7/4	15/8~28/15
Cents		114	229	386	500	657	771	929	1043	1200
Ratios		15/14~16/15	8/7	5/4	4/3	16/11~22/15	11/7~14/9	12/7	11/6~20/11	2/1
Cents		71	186	343	457	614	729	886	1000	1157
Ratios		25/24~28/27	10/9	11/9	(13/10)	10/7	32/21	5/3	16/9	35/18~64/33