676/675: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = island comma, parizekma

~~| Ratio = 676/675~~

| Color name = 3oogg2, bithogu 2nd,<br>Bithogu comma

~~| Monzo = 2 -3 -2 0 2~~

| Comma = yes

~~| Cents = 2.5628~~

| Name = ~~Island Comma~~

| Color name = Bithogu

| ~~FJS name =~~

~~| Sound~~ =

}}

'''676/675''' is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth. ~~It is tempered~~ out ~~in any edo where~~ the perfect fourth ~~can be divided~~ into two equal halves, making [[~~The_Archipelago|~~island chords]] possible.

'''676/675''', otherwise known as the '''island comma''', or the '''parizekma''', is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth (from which its S-expression of [[169/168|S13]]/[[225/224|S15]] = (16/12)/(15/13)<sup>2</sup> is derived), and also between [[26/25]] and [[27/26]] (from which its [[S-expression]] of S26 is derived). Tempering this comma out divides the perfect fourth into two equal halves, making [[island chords]] possible.

[[~~Category~~:13-~~limit~~]]

== Temperaments ==

[[Category:~~Unnoticeable comma~~]]

See [[The Archipelago]] for the "rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments" associated with tempering out this comma, and [[Island chords]] for chords making use of the resulting structure.

[[Category:~~Interseptimal~~]]

== Etymology ==

The name ''island comma'' was given by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95448.html#95608 Yahoo! Tuning Group | ''Parizekmic temperament?'']</ref>.

The 9-note MOS sounds like you're on some kind of tropical island off the coast of Barbados playing jubilant sun-music with the natives or something. More specifically, I feel like it takes the "island" feel of 5-equal and expands it out into diatonic and chromatic versions.

</blockquote>

—Mike Battaglia

== See also ==

* [[Semifourth]]

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

== Notes ==

[[Category:Island]]

[[Category:Commas named for their regular temperament properties]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = island comma, parizekma
-| Ratio = 676/675
+| Color name = 3oogg2, bithogu 2nd,<br>Bithogu comma
-| Monzo = 2 -3 -2 0 2
+| Comma = yes
-| Cents = 2.5628
-| Name = Island Comma
-| Color name = Bithogu
-| FJS name =
-| Sound =
 }}
-'''676/675''' is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth. It is tempered out in any edo where the perfect fourth can be divided into two equal halves, making [[The_Archipelago|island chords]] possible.
+'''676/675''', otherwise known as the '''island comma''', or the '''parizekma''', is the difference between two [[15/13]]'s and a [[4/3]] perfect fourth (from which its S-expression of [[169/168|S13]]/[[225/224|S15]] = (16/12)/(15/13)<sup>2</sup> is derived), and also between [[26/25]] and [[27/26]] (from which its [[S-expression]] of S26 is derived). Tempering this comma out divides the perfect fourth into two equal halves, making [[island chords]] possible.
-[[Category:13-limit]]
+== Temperaments ==
-[[Category:Unnoticeable comma]]
+See [[The Archipelago]] for the "rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments" associated with tempering out this comma, and [[Island chords]] for chords making use of the resulting structure.
-[[Category:Interseptimal]]
+== Etymology ==
+The name ''island comma'' was given by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_95448.html#95608 Yahoo! Tuning Group | ''Parizekmic temperament?'']</ref>.
+<blockquote>
+The 9-note MOS sounds like you're on some kind of tropical island off the coast of Barbados playing jubilant sun-music with the natives or something. More specifically, I feel like it takes the "island" feel of 5-equal and expands it out into diatonic and chromatic versions.
+</blockquote>
+—Mike Battaglia
+== See also ==
+* [[Semifourth]]
+* [[Unnoticeable comma]]
+* [[List of superparticular intervals]]
+== Notes ==
+[[Category:Island]]
+[[Category:Commas named for their regular temperament properties]]