Nanisma: Difference between revisions

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'''~~Nanisma~~''' is ~~a no~~-~~five~~ [[7-~~limit~~]] [[~~unnoticeable~~ comma]]. It is the tiny interval between the pythagorean ratio {{monzo|107 -67}} and the harmonic minor~~-7th~~ of ratio [[7/4]]~~; {{monzo|109 -67 0 -1}} in [[monzo]] and 0.18903555 [[cent]]s in size~~.

{{Infobox Interval

| Monzo = 109 -67 0 -1

| Name = nanisma

| Color name = s<sup>10</sup>r7, quinbisaru 7th

| Comma = yes

}}

The '''nanisma''' ({{monzo|legend=1| 109 -67 0 -1 }}) is an [[unnoticeable comma|unnoticeable]] [[7-limit]] (also [[2.3.7 subgroup|2.3.7-subgroup]]) [[comma]] measuring about 0.189 [[cent]]s. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor seventh of ratio [[7/4]].

The nanisma ~~is considered as a 3=7 xenharmonic-bridge. It~~ also describes the difference between {{monzo|108 -68}} and the septimal minor~~-3rd~~ of ratio [[7/6]], and ~~also~~ the difference between {{monzo|-109 69}} and the wide septimal major~~-3rd~~ of ratio [[9/7]].

The nanisma also describes the difference between {{monzo| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and the difference between {{monzo| -109 69 }} and the wide septimal major third of ratio [[9/7]]. In terms of commas, it is the difference between [[Mercator's comma]] and the [[garischisma]].

== ~~Temperament~~ ==

== Temperaments ==

The nanisma is tempered out in such notable ~~EDOs~~ as {{EDOs| 306~~, 612~~, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

The nanisma is tempered out in such notable [[edo]]s as {{EDOs| 306, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

=== ~~No-five nanismic (1277&2860)~~ ===

=== Nanic ===

~~Comma list: {{monzo|109 -67 0 -1}}~~

See [[Very high accuracy temperaments #Nanic]].

~~Mapping~~: ~~[<1~~ 2 ~~-25|, <0 -1 67|]~~

=== Nanismic ===

[[Subgroup]]: 2.3.5.7

~~POTE generator~~: ~~~3/2 = 701.9578~~

[[Comma list]]: {{monzo| 109 -67 0 -1 }}

~~Vals:~~ {{~~Val list~~| ~~53, 200, 253~~, ~~306~~, ~~665, 971, 1277, 4137, 5414, 6691, 7968 }}~~

: mapping generators: ~2, ~3, ~5

=== ~~7-limit Monzism (53&612) ===~~

[[Optimal tuning]]s:

~~The ''monzism'' temperament (53&612, named by~~ [[~~User~~:~~Xenllium~~|~~Xenllium]]) is a rank~~-~~two temperament which tempers out the~~ [[~~monzisma~~]], {{~~monzo|54 -37 2~~}}, ~~as well as the ragisma, [[4375~~/~~4374]]~~.

* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}, ~5/4 = 386.315493{{c}}

: [[error map]]: {{val| -0.0009 +0.0014 -0.0000 +0.0001 }}

* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957796{{c}}, ~5/4 = 386.315103{{c}}

: error map: {{val| 0.0000 +0.0028 +0.0014 +0.0018 }}

~~Comma list: 4375/4374,~~ {{~~monzo~~|~~-55 30 2~~ 1}}

{{Optimal ET sequence|legend=1| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}

~~Mapping:~~ [~~<1 2 10 -25|, <0 -2 -37 134|~~]

[[Badness]] (Sintel): TBD

~~POTE generator~~: ~~~310078125~~/~~268435456 = 249~~.~~0207~~

== Etymology ==

This comma was named by [[Margo Schulter]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38852.html#38854 Yahoo! Tuning Group | ''Proposal: a high-order septimal schisma'']</ref>.

~~Vals~~: ~~{{Val list~~| ~~53, 559, 612, 1277, 1889 }}~~

== External links ==

* [http://tonalsoft.com/enc/n/nanisma.aspx Tonalsoft Encyclopedia| ''Nanisma'']

~~Badness: 0.046569~~

== Notes ==

~~=== 11-limit Monzism (53&612) ===~~

[[Category:Nanismic]]

~~Comma list: 4375/4374, 41503/41472, 184549376/184528125~~

[[Category:Commas with unknown etymology]]

~~Mapping: [<1 2 10 -25 46|, <0 -2 -37 134 -205|]~~

~~POTE generator: ~231/200 = 249.0193~~

~~Vals: {{Val list| 53, 559, 612 }}~~

~~Badness: 0.057083~~

~~== See also ==~~

* [[Unnoticeable comma]]

[[Category:~~7-limit~~]]

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

@@ Line 1: / Line 1: @@
-'''Nanisma''' is a no-five [[7-limit]] [[unnoticeable comma]]. It is the tiny interval between the pythagorean ratio {{monzo|107 -67}} and the harmonic minor-7th of ratio [[7/4]]; {{monzo|109 -67 0 -1}} in [[monzo]] and 0.18903555 [[cent]]s in size.
+{{Infobox Interval
+| Monzo = 109 -67 0 -1
+| Name = nanisma
+| Color name = s<sup>10</sup>r7, quinbisaru 7th
+| Comma = yes
+}}
+The '''nanisma''' ({{monzo|legend=1| 109 -67 0 -1 }}) is an [[unnoticeable comma|unnoticeable]] [[7-limit]] (also [[2.3.7 subgroup|2.3.7-subgroup]]) [[comma]] measuring about 0.189 [[cent]]s. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor seventh of ratio [[7/4]].
-The nanisma is considered as a 3=7 xenharmonic-bridge. It also describes the difference between {{monzo|108 -68}} and the septimal minor-3rd of ratio [[7/6]], and also the difference between {{monzo|-109 69}} and the wide septimal major-3rd of ratio [[9/7]].
+The nanisma also describes the difference between {{monzo| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and the difference between {{monzo| -109 69 }} and the wide septimal major third of ratio [[9/7]]. In terms of commas, it is the difference between [[Mercator's comma]] and the [[garischisma]].
-== Temperament ==
+== Temperaments ==
-The nanisma is tempered out in such notable EDOs as {{EDOs| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.
+The nanisma is tempered out in such notable [[edo]]s as {{EDOs| 306, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.
-=== No-five nanismic (1277&amp;2860) ===
+=== Nanic ===
-Comma list: {{monzo|109 -67 0 -1}}
+See [[Very high accuracy temperaments #Nanic]].
-Mapping: [&lt;1 2 -25|, &lt;0 -1 67|]
+=== Nanismic ===
+[[Subgroup]]: 2.3.5.7
-POTE generator: ~3/2 = 701.9578
+[[Comma list]]: {{monzo| 109 -67 0 -1 }}
-Vals: {{Val list| 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968 }}
+{{Mapping|legend=1| 1 0 0 109 | 0 1 0 -67 | 0 0 1 0 }}
+: mapping generators: ~2, ~3, ~5
-=== 7-limit Monzism (53&amp;612) ===
+[[Optimal tuning]]s:
-The ''monzism'' temperament (53&amp;612, named by [[User:Xenllium|Xenllium]]) is a rank-two temperament which tempers out the [[monzisma]], {{monzo|54 -37 2}}, as well as the ragisma, [[4375/4374]].
+* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}, ~5/4 = 386.315493{{c}}
+: [[error map]]: {{val| -0.0009 +0.0014 -0.0000 +0.0001 }}
+* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957796{{c}}, ~5/4 = 386.315103{{c}}
+: error map: {{val| 0.0000 +0.0028 +0.0014 +0.0018 }}
-Comma list: 4375/4374, {{monzo|-55 30 2 1}}
+{{Optimal ET sequence|legend=1| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}
-Mapping: [&lt;1 2 10 -25|, &lt;0 -2 -37 134|]
+[[Badness]] (Sintel): TBD
-POTE generator: ~310078125/268435456 = 249.0207
+== Etymology ==
+This comma was named by [[Margo Schulter]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38852.html#38854 Yahoo! Tuning Group | ''Proposal: a high-order septimal schisma'']</ref>.
-Vals: {{Val list| 53, 559, 612, 1277, 1889 }}
+== External links ==
+* [http://tonalsoft.com/enc/n/nanisma.aspx Tonalsoft Encyclopedia| ''Nanisma'']
-Badness: 0.046569
+== Notes ==
-=== 11-limit Monzism (53&amp;612) ===
+[[Category:Nanismic]]
-Comma list: 4375/4374, 41503/41472, 184549376/184528125
+[[Category:Commas with unknown etymology]]
-Mapping: [&lt;1 2 10 -25 46|, &lt;0 -2 -37 134 -205|]
-POTE generator: ~231/200 = 249.0193
-Vals: {{Val list| 53, 559, 612 }}
-Badness: 0.057083
-== See also ==
-* [[Unnoticeable comma]]
-[[Category:7-limit]]
-[[Category:Unnoticeable comma]]