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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}} (a stack of four [[17-comma|17-3-comma]]) 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]]. Tempering out the monzisma slices the interval of fourth [[4/3]] in two.
* [[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]]

Latest revision as of 09:32, 18 January 2026

Interval information
Factorization 2109 × 3-67 × 7-1
Monzo [109 -67 0 -1⟩
Size in cents 0.1890355¢
Name nanisma
Color name s10r7, quinbisaru 7th
FJS name [math]\displaystyle{ \text{9d7}_{7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 218
Weil norm (log2 max(n, d)) 218
Wilson norm (sopfr(nd)) 426
Comma size unnoticeable
Open this interval in xen-calc

The nanisma (monzo: [109 -67 0 -1⟩) is an unnoticeable 7-limit (also 2.3.7-subgroup) comma measuring about 0.189 cents. It is the tiny interval between the pythagorean ratio [107 -67⟩ and the harmonic minor seventh of ratio 7/4.

The nanisma also describes the difference between [108 -68⟩ (a stack of four 17-commas) and the septimal minor third of ratio 7/6, and the difference between [-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 edos as 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

See Very high accuracy temperaments #Nanic.

Nanismic

Subgroup: 2.3.5.7

Comma list: [109 -67 0 -1⟩

Mapping: [⟨1 0 0 109], ⟨0 1 0 -67], ⟨0 0 1 0]]

mapping generators: ~2, ~3, ~5

Optimal tunings:

  • WE: ~2 = 1199.999111 ¢, ~3/2 = 701.957264 ¢, ~5/4 = 386.315493 ¢
error map: ⟨-0.0009 +0.0014 -0.0000 +0.0001]
  • CWE: ~2 = 1200.000000 ¢, ~3/2 = 701.957796 ¢, ~5/4 = 386.315103 ¢
error map: ⟨0.0000 +0.0028 +0.0014 +0.0018]

Optimal ET sequence: 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 (Sintel): TBD

Etymology

This comma was named by Margo Schulter in 2002[1].

External links

Notes

  1. ↑ Yahoo! Tuning Group | Proposal: a high-order septimal schisma
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