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

Header test

11-limit

R a n d o m

11-limit 2

R a n d o m

11-limit

R a n d o m

11-limit 3

R a n d o m

Filler characters

| class="wikitable center-all"

! Gene-
rator

! colspan=17 | ~3/2

|-

! rowspan=17 | ~5/4

! colspan=3 | EDO tuning

! rowspan=3 |

|

| 11\19

| 18\31

|

|

| 7\12

|

|

|

| 31\53

|

| 24\41

| 1\22

|-

! rowspan=2 | (↓↓↓)

! colspan=2 | 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