Monzo: Difference between revisions

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~~This page gives a pragmatic introduction to~~ '''~~monzos~~'''. ~~For~~ the ~~formal mathematical definition~~, ~~visit~~ the ~~page~~ [[~~Monzos and interval space~~]].

A '''monzo''' is a way of notating a [[JI]] [[interval]] that allows us to express directly how any "composite" interval is represented in terms of those simpler prime intervals. They are typically written using the notation {{monzo| a b c d e f … }}, where the columns represent how the primes 2, 3, 5, 7, 11, 13, etc, in that order, contribute to the interval's prime factorization, up to some [[Harmonic Limit|prime limit]].

~~== Definition ==~~

Monzos can be thought of as counterparts to [[vals]]. Like vals, they also only permit integers as their entries (unless otherwise specified).

~~A '''monzo''' is a way~~ of ~~notating a JI interval that allows us~~ to express directly how any "composite" interval is represented in terms of those simpler prime intervals. They are typically written using the notation {{monzo| a b c d e f … }}, where the columns represent how the primes 2, 3, 5, 7, 11, 13, etc, in that order, contribute to the interval's prime factorization, up to some [[~~Harmonic Limit|prime limit~~]].

~~Monzos can be thought of as counterparts to~~ [[~~vals~~]]~~. Like vals, they also only permit integers as their entries (unless otherwise specified)~~.

For the formal mathematical definition, visit the page [[Monzos and interval space]].

== History and terminology ==

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 | ja = モンゾ
 }}
-This page gives a pragmatic introduction to '''monzos'''. For the formal mathematical definition, visit the page [[Monzos and interval space]].
+A '''monzo''' is a way of notating a [[JI]] [[interval]] that allows us to express directly how any "composite" interval is represented in terms of those simpler prime intervals. They are typically written using the notation {{monzo| a b c d e f … }}, where the columns represent how the primes 2, 3, 5, 7, 11, 13, etc, in that order, contribute to the interval's prime factorization, up to some [[Harmonic Limit|prime limit]].
-== Definition ==
+Monzos can be thought of as counterparts to [[vals]]. Like vals, they also only permit integers as their entries (unless otherwise specified).
-A '''monzo''' is a way of notating a JI interval that allows us to express directly how any "composite" interval is represented in terms of those simpler prime intervals. They are typically written using the notation {{monzo| a b c d e f … }}, where the columns represent how the primes 2, 3, 5, 7, 11, 13, etc, in that order, contribute to the interval's prime factorization, up to some [[Harmonic Limit|prime limit]].
-Monzos can be thought of as counterparts to [[vals]]. Like vals, they also only permit integers as their entries (unless otherwise specified).
+For the formal mathematical definition, visit the page [[Monzos and interval space]].
 == History and terminology ==