Temperament addition: Difference between revisions

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=Introductory examples=

For example, the sum of [[12-ET]] and [[7-ET]] is [[19-ET]] because {{map|12 19 28}} + {{map|7 11 16}}={{map|(12+7) (19+11) (28+16)}}={{map|19 30 44}}, and the difference of 12-ET and 7-ET is 5-ET because {{map|12 19 28}} - {{map|7 11 16}}={{map|(12-7) (8-11) (12-16)}}={{map|5 8 12}}.

For example, the sum of [[12-ET]] and [[7-ET]] is [[19-ET]] because {{map|12 19 28}} + {{map|7 11 16}} = {{map|(12+7) (19+11) (28+16)}}={{map|19 30 44}}, and the difference of 12-ET and 7-ET is 5-ET because {{map|12 19 28}} - {{map|7 11 16}} = {{map|(12-7) (8-11) (12-16)}}={{map|5 8 12}}.

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We can write these using [[wart notation]] as 12p + 7p=19p and 12p - 7p=5p, respectively. The similarity in these temperaments can be seen in how, like both 12-ET and 7-ET, 19-ET (their sum) and 5-ET (their difference) both also support [[meantone temperament]].

Temperament sums and differences can also be found using commas; for example meantone + porcupine=tetracot because {{vector|4 -4 1}} + {{vector|1 -5 3}}={{vector|(4+1) (-4+-5) (1+3)}}={{vector|5 -9 4}} and meantone - porcupine=dicot because {{vector|4 -4 1}} - {{vector|1 -5 3}}={{vector|(4-1) (-4--5) (1-3)}}={{vector|3 1 -2}}.

Temperament sums and differences can also be found using commas; for example meantone + porcupine=tetracot because {{vector|4 -4 1}} + {{vector|1 -5 3}} = {{vector|(4+1) (-4+-5) (1+3)}} = {{vector|5 -9 4}} and meantone - porcupine = dicot because {{vector|4 -4 1}} - {{vector|1 -5 3}} = {{vector|(4-1) (-4--5) (1-3)}} = {{vector|3 1 -2}}.

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 =Introductory examples=
-For example, the sum of [[12-ET]] and [[7-ET]] is [[19-ET]] because {{map|12 19 28}} + {{map|7 11 16}}={{map|(12+7) (19+11) (28+16)}}={{map|19 30 44}}, and the difference of 12-ET and 7-ET is 5-ET because {{map|12 19 28}} - {{map|7 11 16}}={{map|(12-7) (8-11) (12-16)}}={{map|5 8 12}}.
+For example, the sum of [[12-ET]] and [[7-ET]] is [[19-ET]] because {{map|12 19 28}} + {{map|7 11 16}} = {{map|(12+7) (19+11) (28+16)}}={{map|19 30 44}}, and the difference of 12-ET and 7-ET is 5-ET because {{map|12 19 28}} - {{map|7 11 16}} = {{map|(12-7) (8-11) (12-16)}}={{map|5 8 12}}.
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 We can write these using [[wart notation]] as 12p + 7p=19p and 12p - 7p=5p, respectively. The similarity in these temperaments can be seen in how, like both 12-ET and 7-ET, 19-ET (their sum) and 5-ET (their difference) both also support [[meantone temperament]].
-Temperament sums and differences can also be found using commas; for example meantone + porcupine=tetracot because {{vector|4 -4 1}} + {{vector|1 -5 3}}={{vector|(4+1) (-4+-5) (1+3)}}={{vector|5 -9 4}} and meantone - porcupine=dicot because {{vector|4 -4 1}} - {{vector|1 -5 3}}={{vector|(4-1) (-4--5) (1-3)}}={{vector|3 1 -2}}.
+Temperament sums and differences can also be found using commas; for example meantone + porcupine=tetracot because {{vector|4 -4 1}} + {{vector|1 -5 3}} = {{vector|(4+1) (-4+-5) (1+3)}} = {{vector|5 -9 4}} and meantone - porcupine = dicot because {{vector|4 -4 1}} - {{vector|1 -5 3}} = {{vector|(4-1) (-4--5) (1-3)}} = {{vector|3 1 -2}}.