Temperament addition: Difference between revisions

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Revision as of 00:03, 1 January 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits →4. Linear independence between temperaments by only one basis vector (i.e. addability) ← Older edit		Revision as of 01:18, 1 January 2022 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,171 edits m →Introductory examples: fix more no-spaces equal signs, annoying Newer edit →
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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]].		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}}.