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 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]]. | ||
== Temperaments == | == Temperaments == | ||
The nanisma is tempered out in such notable | 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. | ||
=== Nanic === | |||
See [[Very high accuracy temperaments #Nanic]]. | |||
=== Nanismic === | === Nanismic === | ||
| Line 21: | Line 24: | ||
: sval mapping generators: ~2, ~3, ~5 | : sval mapping generators: ~2, ~3, ~5 | ||
[[Optimal tuning]] ([[CTE]]): ~2 = | [[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~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 }} | {{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]]: 6.09 × 10<sup>-3</sup> | ||
== Etymology == | == 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>. | 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>. | ||
== External links == | == External links == | ||
Latest revision as of 15:53, 16 March 2025
| Interval information |
reduced subharmonic
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 is considered as a 3=7 xenharmonic bridge. It also describes the difference between [108 -68⟩ (a stack of four 17-commas) and the septimal minor third of ratio 7/6, and also the difference between [-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.
Temperaments
The nanisma is tempered out in such notable edos as 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.
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]]
- sval mapping generators: ~2, ~3, ~5
Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9578, ~5/4 = 386.3137
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: 6.09 × 10-3
Etymology
This comma was named by Margo Schulter in 2002[1].