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| The '''starscape comma''' is a [[7-limit]] [[unnoticeable comma]], with a ratio of 645700815/645657712, a monzo of [-4 17 1 -9⟩, and a size of 0.11557 cents. It is tempered out in temperaments such as [[Minortonic family|domain]] and [[supermajor]]. | | {{Infobox Interval |
| | | Ratio = 645700815/645657712 |
| | | Name = starscape comma |
| | | Color name = Lr<sup>9</sup>y-6, latritriru-ayo negative 6th |
| | | Comma = yes |
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| | The '''starscape comma''' is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]], with a [[ratio]] of 645700815/645657712, a [[monzo]] of {{monzo| -4 17 1 -9 }}, and a size of 0.11557 [[cent]]s. It is the difference between a stack of nine [[9/7|septimal major thirds]] [[octave reduction|octave reduced]] and a [[6/5|classical minor third]]. |
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| == Temperament == | | == Temperament == |
| Tempering this comma out gives starscape temperament. | | Tempering out this comma gives the starscape temperament (→ [[Very high accuracy temperaments #Starscape or Latritriru-ayo]]). It is tempered out in rank-2 temperaments such as [[domain (temperament)|domain]] and [[supermajor]]. |
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| === Starscape (2019 & 171 & 3125) ===
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| Subgroup: 2.3.5.7
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| [[Comma list|Commas]]: 645700815/645657712 | |
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| [[Mapping]]: [⟨1 0 4 0], ⟨0 1 1 2], ⟨0 0 -9 -1]]
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| [[POTE generator|POTE generators]]: ~3 = 1901.9509, ~9/7 = 435.0709
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| [[Vals]]: [[171edo|171]], [[342edo|342]], [[1848edo|1848]], [[2019edo|2019]], [[2783edo|2783]], [[2954edo|2954]], [[3125edo|3125]], [[3296edo|3296]], [[4973edo|4973]], [[5144edo|5144]]
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| [[Badness]]: 0.000545
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| Temperament finder: http://x31eq.com/cgi-bin/uv.cgi?uvs=%5B-4%2C17%2C1%2C-9%3E&page=2&limit=7
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| === Domain ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 250047/250000, 645700815/645657712 | |
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| [[Mapping]]: [⟨3 -3 -9 -8], ⟨0 17 35 36]]
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| [[Wedgie]]: ⟨⟨51 105 108 48 28 -44]]
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| [[POTE generator]]: ~10/9 = 182.467
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| [[Optimal GPV sequence]]: [[171edo|171]], [[1164edo|1164]], [[1335edo|1335]], [[1506edo|1506]], [[1677edo|1677]], [[1848edo|1848]], [[2019edo|2019]], [[2190edo|2190]], [[11943edo|11943]], [[13962edo|13962]], [[15981edo|15981]], [[18000edo|18000]], [[20019edo|20019]], [[22038edo|22038]]
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| [[Badness]]: 0.013979
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| === Supermajor ===
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| Subgroup: 2.3.5.7
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| [[Comma list]]: 4375/4374, 52734375/52706752
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| [[Mapping]]: [⟨1 15 19 30], ⟨0 -37 -46 -75]]
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| [[Wedgie]]: ⟨⟨37 46 75 -13 15 45]]
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| [[POTE generator]]: ~9/7 = 435.082
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| [[Optimal GPV sequence]]: [[11edo|11]], [[80edo|80]], [[171edo|171]], [[764edo|764]], [[1106edo|1106]], [[1277edo|1277]], [[3660edo|3660]], [[4937edo|4937]], [[6214edo|6214]]
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| [[Badness]]: 0.010836 | |
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| == See also == | | == See also == |
| | * [[Unnoticeable comma]] |
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| * [[Unnoticeable comma]]
| | [[Category:Commas with unknown etymology]] |
| Ratio
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645700815/645657712
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| Factorization
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2-4 × 317 × 5 × 7-9
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| Monzo
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[-4 17 1 -9⟩
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| Size in cents
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0.1155704¢
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| Name
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starscape comma
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| Color name
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Lr9y-6, latritriru-ayo negative 6th
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| FJS name
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[math]\displaystyle{ \text{5d}{-6}^{5}_{7,7,7,7,7,7,7,7,7} }[/math]
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| Special properties
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reduced
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| Tenney height (log2 nd)
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58.5325
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| Weil height (log2 max(n, d))
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58.5326
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| Wilson height (sopfr(nd))
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127
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| Comma size
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unnoticeable
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| Open this interval in xen-calc
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The starscape comma is an unnoticeable 7-limit comma, with a ratio of 645700815/645657712, a monzo of [-4 17 1 -9⟩, and a size of 0.11557 cents. It is the difference between a stack of nine septimal major thirds octave reduced and a classical minor third.
Temperament
Tempering out this comma gives the starscape temperament (→ Very high accuracy temperaments #Starscape or Latritriru-ayo). It is tempered out in rank-2 temperaments such as domain and supermajor.
See also