Essential tempering comma: Difference between revisions

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The '''essential tempering commas''' are commas that induce [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered triads]].

Note the definition is about ''triads''. There are commas that induce essentially tempered chords whose basic forms are ''tetrads'', and these may not satisfy the definition given below. For example, 81/80 induces an essentially tempered tetrad (→ [[didymic chords]]), despite that any three of the components are essentially just.

== Definition ==

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21: 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

~~We don't need~~ to use the full q-limit diamond; from ~~Diamond~~([1,3,5,7,9,11,15]) we get: 540/539, 441/440, 385/384, 3388/3375, 243/242

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

== See also ==

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 The '''essential tempering commas''' are commas that induce [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered triads]].
+Note the definition is about ''triads''. There are commas that induce essentially tempered chords whose basic forms are ''tetrads'', and these may not satisfy the definition given below. For example, 81/80 induces an essentially tempered tetrad (→ [[didymic chords]]), despite that any three of the components are essentially just.
 == Definition ==
@@ Line 28: / Line 30: @@
 : 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
-We don't need to use the full q-limit diamond; from Diamond([1,3,5,7,9,11,15]) we get: 540/539, 441/440, 385/384, 3388/3375, 243/242
+It is not necessary to use the full ''q''-limit diamond; from diamond ([1, 3, 5, 7, 9, 11, 15]) we get: 540/539, 441/440, 385/384, 3388/3375, 243/242
 == See also ==