Essential tempering comma: Difference between revisions

Line 45:

; 25-odd-limit (incomplete)

: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 8625/8624, 9261/9248, 10626/10625, 12168/12167.

: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.

; 27-odd-limit (incomplete)

: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 8625/8624, 10626/10625, 12168/12167.

: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 10626/10625, 12168/12167.

; 29-odd-limit (incomplete)

: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 7425/7424, 8625/8624, 10626/10625, 12168/12167.

: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7425/7424, 8625/8624, 10626/10625, 10935/10933, 12168/12167.

; 31-odd-limit (incomplete)

: 969/968, 1001/1000, 1024/1023, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6175/6174, 6864/6859, 7425/7424, 8625/8624, 10626/10625, 12168/12167, 15625/15624, 17577/17576, 29792/29791.

: 969/968, 1001/1000, 1024/1023, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6175/6174, 6864/6859, 6877/6875, 7425/7424, 8625/8624, 10626/10625, 10935/10933, 12168/12167, 15625/15624, 17577/17576, 29792/29791.

It is not necessary to use the full ''q''-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.

@@ Line 45: / Line 45: @@
 ; 25-odd-limit (incomplete)
-: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 8625/8624, 9261/9248, 10626/10625, 12168/12167.
+: 676/675, 715/714, 729/728, 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 9261/9248, 10626/10625, 12168/12167.
 ; 27-odd-limit (incomplete)
-: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 8625/8624, 10626/10625, 12168/12167.
+: 736/735, 760/759, 833/832, 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2200/2197, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3762/3757, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4914/4913, 5083/5082, 5415/5408, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 8625/8624, 10626/10625, 12168/12167.
 ; 29-odd-limit (incomplete)
-: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 7425/7424, 8625/8624, 10626/10625, 12168/12167.
+: 875/874, 897/896, 936/935, 969/968, 1001/1000, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2720/2717, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3553/3549, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4394/4389, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6144/6137, 6175/6174, 6864/6859, 6877/6875, 7425/7424, 8625/8624, 10626/10625, 10935/10933, 12168/12167.
 ; 31-odd-limit (incomplete)
-: 969/968, 1001/1000, 1024/1023, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6175/6174, 6864/6859, 7425/7424, 8625/8624, 10626/10625, 12168/12167, 15625/15624, 17577/17576, 29792/29791.
+: 969/968, 1001/1000, 1024/1023, 1089/1088, 1105/1104, 1156/1155, 1197/1196, 1216/1215, 1225/1224, 1275/1274, 1288/1287, 1331/1330, 1445/1444, 1496/1495, 1521/1520, 1540/1539, 1701/1700, 1729/1728, 1863/1862, 2024/2023, 2025/2023, 2025/2024, 2058/2057, 2080/2079, 2185/2184, 2300/2299, 2376/2375, 2431/2430, 2432/2431, 2500/2499, 2601/2600, 2646/2645, 2737/2736, 2926/2925, 3025/3024, 3060/3059, 3136/3135, 3213/3211, 3250/3249, 3381/3380, 3520/3519, 3888/3887, 3971/3969, 4096/4095, 4200/4199, 4225/4224, 4375/4374, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 5083/5082, 5491/5488, 5776/5775, 5985/5984, 6175/6174, 6864/6859, 6877/6875, 7425/7424, 8625/8624, 10626/10625, 10935/10933, 12168/12167, 15625/15624, 17577/17576, 29792/29791.
 It is not necessary to use the full ''q''-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 243/242, 385/384, 441/440, 540/539, 3388/3375.