Radical interval: Difference between revisions

Line 1:

<span style="display: block; text-align: right;">[[:de:Nichtganzzahlige_Intervallvektoren Deutsch]]</span>

<span style="display: block; text-align: right;">[[:de:Nichtganzzahlige_Intervallvektoren|Deutsch]]</span>

A ''fractional monzo'' is like an ordinary [[Monzos_and_Interval_Space|monzo]] except that coefficients have been extended to allow them to be rational numbers. If |e2 e3 ... ep> is a fractional monzo, then it represents 2^e2 3^e3 ... p^ep just as with an ordinary monzo. Hence, for instance, |1/13 -1/13 7/26> represents the interval 2^(1/13) 3^(-1/13) 5^(7/26). By taking the [[Least_common_multiple|least common multiple]] of the denominators, intervals represented by a fractional monzo can always be written as an nth root of a positive rational number; for instance from our example, (312500/9)^(1/26). By taking a dot product with <cents(2) cents(3) ... cents(p)| the value in cents of a monzo or fractional monzo may be obtained. For instance, in the above example (1/13)*1200.0 - (1/13)*cents(3) + (7/26)*cents(5) = 696.1648 cents.

Revision as of 00:00, 17 July 2018 view source Wikispaces>FREEZE No edit summary ← Older edit		Revision as of 00:09, 17 September 2018 view source Mike Battaglia (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, emailconfirmed, Interface administrators, Sysops 1,399 edits m Text replacement - "(\[\[\:(dev\|es\|purdal\|de\|en):[^[:space:]\\|]) (.])" to "$1\|$3" Newer edit →
Line 1:		Line 1:
	<span style="display: block; text-align: right;">[[:de:Nichtganzzahlige_Intervallvektoren Deutsch]]</span>		<span style="display: block; text-align: right;">[[:de:Nichtganzzahlige_Intervallvektoren\|Deutsch]]</span>

	A ''fractional monzo'' is like an ordinary [[Monzos_and_Interval_Space\|monzo]] except that coefficients have been extended to allow them to be rational numbers. If \|e2 e3 ... ep> is a fractional monzo, then it represents 2^e2 3^e3 ... p^ep just as with an ordinary monzo. Hence, for instance, \|1/13 -1/13 7/26> represents the interval 2^(1/13) 3^(-1/13) 5^(7/26). By taking the [[Least_common_multiple\|least common multiple]] of the denominators, intervals represented by a fractional monzo can always be written as an nth root of a positive rational number; for instance from our example, (312500/9)^(1/26). By taking a dot product with <cents(2) cents(3) ... cents(p)\| the value in cents of a monzo or fractional monzo may be obtained. For instance, in the above example (1/13)1200.0 - (1/13)cents(3) + (7/26)*cents(5) = 696.1648 cents.		A ''fractional monzo'' is like an ordinary [[Monzos_and_Interval_Space\|monzo]] except that coefficients have been extended to allow them to be rational numbers. If \|e2 e3 ... ep> is a fractional monzo, then it represents 2^e2 3^e3 ... p^ep just as with an ordinary monzo. Hence, for instance, \|1/13 -1/13 7/26> represents the interval 2^(1/13) 3^(-1/13) 5^(7/26). By taking the [[Least_common_multiple\|least common multiple]] of the denominators, intervals represented by a fractional monzo can always be written as an nth root of a positive rational number; for instance from our example, (312500/9)^(1/26). By taking a dot product with <cents(2) cents(3) ... cents(p)\| the value in cents of a monzo or fractional monzo may be obtained. For instance, in the above example (1/13)1200.0 - (1/13)cents(3) + (7/26)*cents(5) = 696.1648 cents.