Monzo: Difference between revisions

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{{interwiki

| de = Monzo-Notation

| en = ~~Monzos~~

| en = Monzo

| es = Monzo

| ja = モンゾ

}}

This page gives a pragmatic introduction to '''monzos'''. For the formal mathematical definition of visit the page [[Monzos_and_Interval_Space|Monzos and Interval Space]].

~~== Etymology ==~~

~~Monzos are named in honor of [[Joe Monzo]].~~

== Definition ==

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]].

A '''monzo''', or in descriptive but longer terms, '''harmonic space coordinates''', 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]].

For a more mathematical discussion, see also [[Monzos and Interval Space]].

== Etymology ==

Monzos are named in honor of [[Joe Monzo]].

"Harmonic space coordinates" is seen used by Plainsound Music Edition as of 2020<ref>https://www.plainsound.org/HEJI/</ref>.

== Examples ==

@@ Line 1: / Line 1: @@
 {{interwiki
 | de = Monzo-Notation
-| en = Monzos
+| en = Monzo
 | es = Monzo
 | ja = モンゾ
 }}
 This page gives a pragmatic introduction to '''monzos'''. For the formal mathematical definition of visit the page [[Monzos_and_Interval_Space|Monzos and Interval Space]].
-== Etymology ==
-Monzos are named in honor of [[Joe Monzo]].
 == Definition ==
-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]].
+A '''monzo''', or in descriptive but longer terms, '''harmonic space coordinates''', 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]].
 For a more mathematical discussion, see also [[Monzos and Interval Space]].
+== Etymology ==
+Monzos are named in honor of [[Joe Monzo]].
+"Harmonic space coordinates" is seen used by Plainsound Music Edition as of 2020<ref>https://www.plainsound.org/HEJI/</ref>.
 == Examples ==