Nanisma: Difference between revisions

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| Comma = yes

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'''Nanisma''' (~~[[monzo]]:~~ {{monzo| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].

'''Nanisma''' ({{monzo|legend=1| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor-7th 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]].

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]].

== Temperament ==

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.

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

=== Nanismic ===

[[Subgroup]]: 2.3.5.7

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

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

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137

{{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>

=== Nanic ===

[[Subgroup]]: 2.3.7

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

~~[[Sval]] [[mapping]]: [~~{{~~val~~| 1 ~~2 -25 }}, {{val~~| 0 -1 67 }}]

: sval mapping generators: ~2, ~3

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578

[[Optimal ~~tuning]] ([[POTE]]): ~3/2~~ = ~~701.9578~~

{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}

~~{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968 }}~~

[[Badness]]: 0.0138

== See also ==

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
-'''Nanisma''' ([[monzo]]: {{monzo| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].
+'''Nanisma''' ({{monzo|legend=1| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo| 107 -67 }} and the harmonic minor-7th 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]].
+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]].
 == Temperament ==
 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.
-=== No-five nanismic (1277&amp;2860) ===
+=== Nanismic ===
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: {{monzo| 109 -67 0 -1 }}
+{{Mapping|legend=1| 1 0 0 109 | 0 -1 0  67 | 0 0 1 0 }}
+: sval mapping generators: ~2, ~3, ~5
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137
+{{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>
+=== Nanic ===
 [[Subgroup]]: 2.3.7
 [[Comma list]]: {{monzo| 109 -67 -1 }}
-[[Sval]] [[mapping]]: [{{val| 1 2 -25 }}, {{val| 0 -1 67 }}]
+{{Mapping|legend=2| 1 0 109 | 0 -1 67 }}
+: sval mapping generators: ~2, ~3
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.9578
+{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
-{{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968 }}
+[[Badness]]: 0.0138
 == See also ==