Essential tempering comma: Difference between revisions

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For various odd limit diamonds, we get the following essential tempering commas using the derivation above:

* 5-odd-limit (complete): 128/125.

; 5-odd-limit (complete)

* 7-odd-limit (complete): 126/125, 64/63.

: 128/125.

* 9-odd-limit (complete): 225/224, 126/125, 245/243.

* 11-odd-limit (complete): 540/539, 441/440, 385/384, 243/242, 225/224, 896/891, 176/175, 126/125, 245/243.

* 13-odd-limit (complete): 1001/1000, 2200/2197, 729/728, 540/539, 441/440, 847/845, 385/384, 364/363, 352/351, 351/350, 325/324, 1573/1568, 243/242, 1188/1183, 225/224, 640/637, 196/195, 1287/1280, 896/891, 176/175.

* 15-odd-limit (complete): 1001/1000, 1575/1573, 2200/2197, 729/728, 676/675, 540/539, 441/440, 847/845, 385/384, 364/363, 352/351, 351/350, 325/324, 1573/1568, 3388/3375, 243/242, 1188/1183.

* 17-odd-limit (complete): 2601/2600, 2431/2430, 1275/1274, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 936/935, 833/832, 1575/1573, 2200/2197, 729/728, 715/714, 676/675, 595/594, 561/560, 540/539, 442/441, 441/440, 847/845, 2880/2873, 2028/2023, 385/384, 375/374, 364/363, 352/351, 351/350, 4928/4913, 2295/2288, 325/324, 1573/1568

* 19-odd-limit (complete): 4200/4199, 3136/3135, 2926/2925, 2601/2600, 2432/2431, 2431/2430, 5491/5488, 1729/1728, 1540/1539, 1521/1520, 1445/1444, 6864/6859, 1331/1330, 1275/1274, 1216/1215, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 969/968, 936/935, 2720/2717, 6144/6137, 833/832, 1575/1573, 5415/5408, 3762/3757, 2200/2197, 729/728, 715/714, 676/675, 1862/1859, 595/594, 2912/2907, 2299/2295, 3978/3971, 561/560, 540/539, 513/512, 495/494, 476/475, 2304/2299, 456/455, 442/441, 441/440, 4704/4693, 847/845, 1235/1232, 2880/2873, 2057/2052, 2028/2023, 400/399, 385/384, 375/374, 364/363.

* 21-odd-limit (complete): 5985/5984, 4914/4913, 4200/4199, 4096/4095, 3136/3135, 2926/2925, 2601/2600, 2432/2431, 2431/2430, 2080/2079, 2058/2057, 3971/3969, 5491/5488, 1729/1728, 1701/1700, 3213/3211, 1540/1539, 1521/1520, 1445/1444, 6864/6859, 1331/1330, 1275/1274, 1216/1215, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 969/968, 936/935, 2720/2717, 3553/3549, 4394/4389, 6144/6137, 833/832, 1617/1615, 1575/1573, 5415/5408, 3762/3757, 2200/2197, 729/728, 715/714, 9261/9248, 676/675, 1862/1859, 595/594, 2912/2907, 2299/2295, 3978/3971, 561/560, 6080/6069, 540/539, 513/512, 495/494, 476/475, 2304/2299, 456/455.

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

; 7-odd-limit (complete)

: 64/63, 126/125.

; 9-odd-limit (complete)

: 126/125, 225/224, 245/243.

; 11-odd-limit (complete)

: 126/125, 176/175, 225/224, 243/242, 245/243, 385/384, 441/440, 540/539, 896/891.

; 13-odd-limit (complete)

: 176/175, 196/195, 225/224, 243/242, 325/324, 351/350, 352/351, 364/363, 385/384, 441/440, 540/539, 640/637, 729/728, 847/845, 896/891, 1001/1000, 1188/1183, 1287/1280, 1573/1568, 2200/2197.

; 15-odd-limit (complete)

: 243/242, 325/324, 351/350, 352/351, 364/363, 385/384, 441/440, 540/539, 676/675, 729/728, 847/845, 1001/1000, 1188/1183, 1573/1568, 1575/1573, 2200/2197, 3388/3375.

; 17-odd-limit (complete)

: 325/324, 351/350, 352/351, 364/363, 375/374, 385/384, 441/440, 442/441, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 847/845, 936/935, 1001/1000, 1089/1088, 1156/1155, 1275/1274, 1573/1568, 1575/1573, 2025/2023, 2028/2023, 2200/2197, 2295/2288, 2431/2430, 2601/2600, 2880/2873, 4928/4913.

; 19-odd-limit (complete)

: 364/363, 375/374, 385/384, 400/399, 441/440, 442/441, 456/455, 476/475, 495/494, 513/512, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 847/845, 936/935, 969/968, 1001/1000, 1089/1088, 1156/1155, 1216/1215, 1235/1232, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539, 1575/1573, 1729/1728, 1862/1859, 2025/2023, 2028/2023, 2057/2052, 2200/2197, 2299/2295, 2304/2299, 2431/2430, 2432/2431, 2601/2600, 2720/2717, 2880/2873, 2912/2907, 2926/2925, 3136/3135, 3762/3757, 3978/3971, 4200/4199, 4704/4693, 5415/5408, 5491/5488, 6144/6137, 6864/6859.

; 21-odd-limit (complete)

: 456/455, 476/475, 495/494, 513/512, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 936/935, 969/968, 1001/1000, 1089/1088, 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1862/1859, 2025/2023, 2058/2057, 2080/2079, 2200/2197, 2299/2295, 2304/2299, 2431/2430, 2432/2431, 2601/2600, 2720/2717, 2912/2907, 2926/2925, 3136/3135, 3213/3211, 3553/3549, 3762/3757, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4914/4913, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248.

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.

== See also ==

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 For various odd limit diamonds, we get the following essential tempering commas using the derivation above:
-* 5-odd-limit (complete): 128/125.
+; 5-odd-limit (complete)
-* 7-odd-limit (complete): 126/125, 64/63.
+: 128/125.
-* 9-odd-limit (complete): 225/224, 126/125, 245/243.
-* 11-odd-limit (complete): 540/539, 441/440, 385/384, 243/242, 225/224, 896/891, 176/175, 126/125, 245/243.
-* 13-odd-limit (complete): 1001/1000, 2200/2197, 729/728, 540/539, 441/440, 847/845, 385/384, 364/363, 352/351, 351/350, 325/324, 1573/1568, 243/242, 1188/1183, 225/224, 640/637, 196/195, 1287/1280, 896/891, 176/175.
-* 15-odd-limit (complete): 1001/1000, 1575/1573, 2200/2197, 729/728, 676/675, 540/539, 441/440, 847/845, 385/384, 364/363, 352/351, 351/350, 325/324, 1573/1568, 3388/3375, 243/242, 1188/1183.
-* 17-odd-limit (complete): 2601/2600, 2431/2430, 1275/1274, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 936/935, 833/832, 1575/1573, 2200/2197, 729/728, 715/714, 676/675, 595/594, 561/560, 540/539, 442/441, 441/440, 847/845, 2880/2873, 2028/2023, 385/384, 375/374, 364/363, 352/351, 351/350, 4928/4913, 2295/2288, 325/324, 1573/1568
-* 19-odd-limit (complete): 4200/4199, 3136/3135, 2926/2925, 2601/2600, 2432/2431, 2431/2430, 5491/5488, 1729/1728, 1540/1539, 1521/1520, 1445/1444, 6864/6859, 1331/1330, 1275/1274, 1216/1215, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 969/968, 936/935, 2720/2717, 6144/6137, 833/832, 1575/1573, 5415/5408, 3762/3757, 2200/2197, 729/728, 715/714, 676/675, 1862/1859, 595/594, 2912/2907, 2299/2295, 3978/3971, 561/560, 540/539, 513/512, 495/494, 476/475, 2304/2299, 456/455, 442/441, 441/440, 4704/4693, 847/845, 1235/1232, 2880/2873, 2057/2052, 2028/2023, 400/399, 385/384, 375/374, 364/363.
-* 21-odd-limit (complete): 5985/5984, 4914/4913, 4200/4199, 4096/4095, 3136/3135, 2926/2925, 2601/2600, 2432/2431, 2431/2430, 2080/2079, 2058/2057, 3971/3969, 5491/5488, 1729/1728, 1701/1700, 3213/3211, 1540/1539, 1521/1520, 1445/1444, 6864/6859, 1331/1330, 1275/1274, 1216/1215, 1156/1155, 1089/1088, 2025/2023, 1001/1000, 969/968, 936/935, 2720/2717, 3553/3549, 4394/4389, 6144/6137, 833/832, 1617/1615, 1575/1573, 5415/5408, 3762/3757, 2200/2197, 729/728, 715/714, 9261/9248, 676/675, 1862/1859, 595/594, 2912/2907, 2299/2295, 3978/3971, 561/560, 6080/6069, 540/539, 513/512, 495/494, 476/475, 2304/2299, 456/455.
-It is not necessary to use the full ''q''-odd-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 540/539, 441/440, 385/384, 3388/3375, 243/242.
+; 7-odd-limit (complete)
+: 64/63, 126/125.
+; 9-odd-limit (complete)
+: 126/125, 225/224, 245/243.
+; 11-odd-limit (complete)
+: 126/125, 176/175, 225/224, 243/242, 245/243, 385/384, 441/440, 540/539, 896/891.
+; 13-odd-limit (complete)
+: 176/175, 196/195, 225/224, 243/242, 325/324, 351/350, 352/351, 364/363, 385/384, 441/440, 540/539, 640/637, 729/728, 847/845, 896/891, 1001/1000, 1188/1183, 1287/1280, 1573/1568, 2200/2197.
+; 15-odd-limit (complete)
+: 243/242, 325/324, 351/350, 352/351, 364/363, 385/384, 441/440, 540/539, 676/675, 729/728, 847/845, 1001/1000, 1188/1183, 1573/1568, 1575/1573, 2200/2197, 3388/3375.
+; 17-odd-limit (complete)
+: 325/324, 351/350, 352/351, 364/363, 375/374, 385/384, 441/440, 442/441, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 847/845, 936/935, 1001/1000, 1089/1088, 1156/1155, 1275/1274, 1573/1568, 1575/1573, 2025/2023, 2028/2023, 2200/2197, 2295/2288, 2431/2430, 2601/2600, 2880/2873, 4928/4913.
+; 19-odd-limit (complete)
+: 364/363, 375/374, 385/384, 400/399, 441/440, 442/441, 456/455, 476/475, 495/494, 513/512, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 847/845, 936/935, 969/968, 1001/1000, 1089/1088, 1156/1155, 1216/1215, 1235/1232, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539, 1575/1573, 1729/1728, 1862/1859, 2025/2023, 2028/2023, 2057/2052, 2200/2197, 2299/2295, 2304/2299, 2431/2430, 2432/2431, 2601/2600, 2720/2717, 2880/2873, 2912/2907, 2926/2925, 3136/3135, 3762/3757, 3978/3971, 4200/4199, 4704/4693, 5415/5408, 5491/5488, 6144/6137, 6864/6859.
+; 21-odd-limit (complete)
+: 456/455, 476/475, 495/494, 513/512, 540/539, 561/560, 595/594, 676/675, 715/714, 729/728, 833/832, 936/935, 969/968, 1001/1000, 1089/1088, 1156/1155, 1216/1215, 1275/1274, 1331/1330, 1445/1444, 1521/1520, 1540/1539, 1575/1573, 1617/1615, 1701/1700, 1729/1728, 1862/1859, 2025/2023, 2058/2057, 2080/2079, 2200/2197, 2299/2295, 2304/2299, 2431/2430, 2432/2431, 2601/2600, 2720/2717, 2912/2907, 2926/2925, 3136/3135, 3213/3211, 3553/3549, 3762/3757, 3971/3969, 3978/3971, 4096/4095, 4200/4199, 4394/4389, 4914/4913, 5415/5408, 5491/5488, 5985/5984, 6080/6069, 6144/6137, 6864/6859, 9261/9248.
+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.
 == See also ==