2058/2057: Difference between revisions

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| Comma = Yes

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'''2058/2057''', the '''xenisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.7.11.17 [[subgroup]]) [[comma]] measuring about 0.84 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]], or equivalently the amount by which 49/44 (2.7.11 minor tone) * 14/11 exceeds [[17/12]]

'''2058/2057''', the '''xenisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.7.11.17-[[subgroup]]) [[comma]] measuring about 0.841 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]], or equivalently the amount by which a stack consisting of [[49/44]] and 14/11 exceeds [[17/12]].

== Commatic relations ==

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== Temperaments ==

Tempering out this comma in the 17-limit results in the rank-6 '''xenismic ~~temperament~~''', or in the 2.3.7.11.17 subgroup, the rank-4 '''xenic ~~temperament~~'''. In either case it enables [[xenismic chords]].

[[Tempering out]] this comma in the 17-limit results in the rank-6 '''xenismic''' temperament, or in the 2.3.7.11.17 subgroup, the rank-4 '''xenic''' temperament. In either case it enables [[xenismic chords]].

=== Xenic ===

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{{Mapping|legend=2| 1 0 0 0 1 | 0 1 0 0 1 | 0 0 1 0 3 | 0 0 0 1 -2 }}

: mapping generators: ~2, ~3, ~7, ~11

: ~~sval mapping generators~~: ~2, ~3, ~7, ~11

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9939{{c}}, ~3/2 = 701.9458{{c}}, ~7/4 = 968.6949{{c}}, ~11/8 = 551.4810{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9446{{c}}, ~7/4 = 968.6908{{c}}, ~11/8 = 551.4738{{c}}

[[Optimal ~~tuning]]s:~~

{{Optimal ET sequence|legend=1| 31, 41g, 46, 58, 63, 72, 89, 118, 135, 207, 342, 400, 535, 742, 1395, 1930, 2672 }}

* [[CTE]]: ~2 = 1\1, ~~~3/2 = 701.9397~~, ~~~7/4 = 968.6818~~, ~~~11/8 = 551.4639~~

* [[CWE]]: ~2 = 1\1, ~~~3/2 = 701.9446~~, ~~~7/4 = 968.6908~~, ~~~11/8 = 551.4738~~

~~{{Optimal ET sequence|legend=1| 46, 58, 63, 72, 89, 118, 135, 207, 342, 400, 535, 742, 1395, 1930, 2672 }}~~

[[Badness]] (Sintel): 0.0963

=== Xenismic ===

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[[Optimal tuning]]s:

* [[~~CTE~~]]: ~2 = ~~1\1~~, ~3/2 = 701.~~9397~~, ~5/4 = 386.~~3137~~, ~7/4 = 968.~~6818~~, ~11/8 = 551.~~4639~~, ~13/8 = 840.~~5277~~

* [[WE]]: ~2 = 1199.9939{{c}}, ~3/2 = 701.9458{{c}}, ~5/4 = 386.3258{{c}}, ~7/4 = 968.6949{{c}}, ~11/8 = 551.4810{{c}}, ~13/8 = 840.5458{{c}}

* [[CWE]]: ~2 = ~~1\1~~, ~3/2 = 701.~~9445~~, ~5/4 = 386.3208, ~7/4 = 968.6908, ~11/8 = 551.4738, ~13/8 = 840.5389

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9446{{c}}, ~5/4 = 386.3208{{c}}, ~7/4 = 968.6908{{c}}, ~11/8 = 551.4738{{c}}, ~13/8 = 840.5389{{c}}

{{Optimal ET sequence|legend=1| 43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg }}*

{{Optimal ET sequence|legend=1| 31, 41g, 43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg }}*

<nowiki>*</nowiki> [[optimal patent val]]: [[3756edo|3756]]

[[Badness]] (Sintel): 1.32

== Etymology ==

~~The xenisma~~ was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>.

This comma was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>. Its name comes from the Ancient Greek word [[wiktionary: ξένος #Ancient Greek|''xénos'']] ("strange"), which may suggest the strange and wonderful qualities in a [[neogothic]] setting of supraminor and submajor thirds.

== ~~Notes~~ ==

== References ==

[[Category:Xenismic]]

[[Category:Commas ~~with unknown etymology~~]]

[[Category:Commas named by translating something into another language]]

@@ Line 4: / Line 4: @@
 | Comma = Yes
 }}
-'''2058/2057''', the '''xenisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.7.11.17 [[subgroup]]) [[comma]] measuring about 0.84 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]], or equivalently the amount by which 49/44 (2.7.11 minor tone) * 14/11 exceeds [[17/12]]
+'''2058/2057''', the '''xenisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.7.11.17-[[subgroup]]) [[comma]] measuring about 0.841 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s exceed [[34/21]], or equivalently the amount by which a stack consisting of [[49/44]] and 14/11 exceeds [[17/12]].
 == Commatic relations ==
@@ Line 23: / Line 23: @@
 == Temperaments ==
-Tempering out this comma in the 17-limit results in the rank-6 '''xenismic temperament''', or in the 2.3.7.11.17 subgroup, the rank-4 '''xenic temperament'''. In either case it enables [[xenismic chords]].
+[[Tempering out]] this comma in the 17-limit results in the rank-6 '''xenismic''' temperament, or in the 2.3.7.11.17 subgroup, the rank-4 '''xenic''' temperament. In either case it enables [[xenismic chords]].
 === Xenic ===
@@ Line 31: / Line 31: @@
 {{Mapping|legend=2| 1 0 0 0 1 | 0 1 0 0 1 | 0 0 1 0 3 | 0 0 0 1 -2 }}
+: mapping generators: ~2, ~3, ~7, ~11
-: sval mapping generators: ~2, ~3, ~7, ~11
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9939{{c}}, ~3/2 = 701.9458{{c}}, ~7/4 = 968.6949{{c}}, ~11/8 = 551.4810{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9446{{c}}, ~7/4 = 968.6908{{c}}, ~11/8 = 551.4738{{c}}
-[[Optimal tuning]]s:
+{{Optimal ET sequence|legend=1| 31, 41g, 46, 58, 63, 72, 89, 118, 135, 207, 342, 400, 535, 742, 1395, 1930, 2672 }}
-* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9397, ~7/4 = 968.6818, ~11/8 = 551.4639
-* [[CWE]]: ~2 = 1\1, ~3/2 = 701.9446, ~7/4 = 968.6908, ~11/8 = 551.4738
-{{Optimal ET sequence|legend=1| 46, 58, 63, 72, 89, 118, 135, 207, 342, 400, 535, 742, 1395, 1930, 2672 }}
+[[Badness]] (Sintel): 0.0963
 === Xenismic ===
@@ Line 63: / Line 64: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9397, ~5/4 = 386.3137, ~7/4 = 968.6818, ~11/8 = 551.4639, ~13/8 = 840.5277
+* [[WE]]: ~2 = 1199.9939{{c}}, ~3/2 = 701.9458{{c}}, ~5/4 = 386.3258{{c}}, ~7/4 = 968.6949{{c}}, ~11/8 = 551.4810{{c}}, ~13/8 = 840.5458{{c}}
-* [[CWE]]: ~2 = 1\1, ~3/2 = 701.9445, ~5/4 = 386.3208, ~7/4 = 968.6908, ~11/8 = 551.4738, ~13/8 = 840.5389
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9446{{c}}, ~5/4 = 386.3208{{c}}, ~7/4 = 968.6908{{c}}, ~11/8 = 551.4738{{c}}, ~13/8 = 840.5389{{c}}
-{{Optimal ET sequence|legend=1| 43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg }}*
+{{Optimal ET sequence|legend=1| 31, 41g, 43, 46, 58, 72, 103, 121, 149, 161, 190g, 224, 270, 311, 354, 400, 460, 581, 742, 814, 935, 1084, 1323, 1395, 2137, 3072e, 3342eg, 4156eg }}*
 <nowiki>*</nowiki> [[optimal patent val]]: [[3756edo|3756]]
+[[Badness]] (Sintel): 1.32
 == Etymology ==
-The xenisma was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>.
+This comma was named by [[Margo Schulter]] in 2000<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_12989.html Yahoo! Tuning Group | ''Re: Kalisma/xenisma (new names?) -- JI tuning and Scala file'']</ref>. Its name comes from the Ancient Greek word [[wiktionary: ξένος #Ancient Greek|''xénos'']] ("strange"), which may suggest the strange and wonderful qualities in a [[neogothic]] setting of supraminor and submajor thirds.
-== Notes ==
+== References ==
 [[Category:Xenismic]]
-[[Category:Commas with unknown etymology]]
+[[Category:Commas named by translating something into another language]]