Nanisma: Difference between revisions

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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 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and ~~also~~ the difference between {{monzo| -109 69 }} and the wide septimal major third of ratio [[9/7]]. ~~It can also be thought~~ of as the difference between [[Mercator's comma]] and the [[garischisma]].

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]].

== Temperaments ==

The nanisma is tempered out in such notable [[edo]]s 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.

=== Nanic ===

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

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

[[Optimal tuning]]s:

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

[[~~Optimal tuning~~]] ([[~~CTE~~]]): ~2 = 1200.~~0000~~, ~3/2 = 701.~~9578~~, ~5/4 = 386.~~3137~~

: [[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 }}

{{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 }}

[[Badness]]: ~~6.09 × 10<sup>-3</sup>~~

[[Badness]] (Sintel): TBD

== Etymology ==

@@ Line 7: / Line 7: @@
 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 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[garischisma]].
+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]].
 == Temperaments ==
-The nanisma is tempered out in such notable [[edo]]s 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.
 === Nanic ===
@@ Line 21: / Line 21: @@
 {{Mapping|legend=1| 1 0 0 109 | 0 1 0 -67 | 0 0 1 0 }}
+: mapping generators: ~2, ~3, ~5
-: sval mapping generators: ~2, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}, ~5/4 = 386.315493{{c}}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9578, ~5/4 = 386.3137
+: [[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 }}
 {{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 }}
-[[Badness]]: 6.09 × 10<sup>-3</sup>
+[[Badness]] (Sintel): TBD
 == Etymology ==