FloraC at 13:29, 18 September 2025

2025-09-18T13:29:03Z

← Older revision		Revision as of 13:29, 18 September 2025
Line 596:		Line 596:

	[[Category:Lists of intervals]]		[[Category:Lists of intervals]]
	[[Category:Superparticular ratios]]		[[Category:Superparticular ratios\|*]]

FloraC at 13:26, 18 September 2025

2025-09-18T13:26:04Z

← Older revision		Revision as of 13:26, 18 September 2025
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			{{Breadcrumb}}

	== 41-limit (incomplete) ==		== 41-limit (incomplete) ==
	{\| class="wikitable center-6" style="width:100%"		{\| class="wikitable center-6" style="width:100%"

FloraC: Created page with "== 41-limit (incomplete) == {| class="wikitable center-6" style="width:100%" ! width="10%" | Ratio ! width="10%" | Cents ! width="15%" | Factorization ! width="15%" | Monzo ! width="45%" | Name(s) ! width="5%" | MetaDenoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See square superparticular for details. |- | 41/40 | 42.749 | 41/(2³×5) | 2.5.41 {{monzo| -3 -1 1 }} | Large qu..."

2025-09-18T13:24:17Z

Created page with "== 41-limit (incomplete) == {| class="wikitable center-6" style="width:100%" ! width="10%" | Ratio ! width="10%" | Cents ! width="15%" | Factorization ! width="15%" | Monzo ! width="45%" | Name(s) ! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See square superparticular for details.</ref> |- | 41/40 | 42.749 | 41/(23×5) | 2.5.41 {{monzo| -3 -1 1 }} | Large qu..."

New page

== 41-limit (incomplete) ==
{| class="wikitable center-6" style="width:100%"
! width="10%" | [[Ratio]]
! width="10%" | [[Cent]]s
! width="15%" | Factorization
! width="15%" | [[Monzo]]
! width="45%" | Name(s)
! width="5%" | Meta<ref name="ssp">Denoted by S-expressions, where s''k'' is defined as (''k''/(''k'' - 1))/((''k'' + 1)/''k''). See [[square superparticular]] for details.</ref>
|-
| [[41/40]]
| 42.749
| 41/(23×5)
| 2.5.41 {{monzo| -3 -1 1 }}
| Large quadracesimoprimal 1/5-tone
|
|-
| [[42/41]]
| 41.719
| (2×3×7)/41
| 2.3.7.41 {{monzo| 1 1 1 -1 }}
| Small quadracesimoprimal 1/5-tone
|
|-
| [[82/81]]
| 21.242
| (2×41)/34
| 2.3.41 {{monzo| 1 -4 1 }}
| 41st-partial chroma
|
|-
| [[124/123]]
| 14.018
| (22×31)/(3×41)
| 2.3.31.41 {{monzo| 2 -1 1 -1 }}
|
|
|-
| [[165/164]]
| 10.524
| (3×5×11)/(22×41)
| 2.3.5.11.41 {{monzo| -2 1 1 1 -1 }}
|
|
|-
| [[205/204]]
| 8.4657
| (5×41)/(22×3×17)
| 2.3.5.17.41 {{monzo| -2 -1 1 -1 1 }}
|
|
|-
| [[246/245]]
| 7.0519
| (2×3×41)/(5×72)
| 2.3.5.7.41 {{monzo| 1 1 -1 -2 1 }}
|
|
|-
| [[247/246]]
| 7.0233
| (13×19)/(2×3×41)
| 2.3.13.19.41 {{monzo| -1 -1 1 1 -1 }}
|
|
|-
| [[287/286]]
| 6.0427
| (7×41)/(2×11×13)
| 2.7.11.13.41 {{monzo| -1 1 -1 -1 1 }}
|
|
|-
| [[288/287]]
| 6.0217
| (25×32)/(7×41)
| 2.3.7.41 {{monzo| 5 2 -1 -1 }}
|
|
|-
| [[369/368]]
| 4.6981
| (32×41)/(24×23)
| 2.3.23.41 {{monzo| -4 2 -1 1 }}
|
|
|-
| [[370/369]]
| 4.6853
| (2×5×37)/(32×41)
| 2.3.5.37.41 {{monzo| 1 -2 1 1 -1 }}
|
|
|-
| [[451/450]]
| 3.8429
| (11×41)/(2×(3×5)2)
| 2.3.5.11.41 {{monzo| -1 -2 -2 1 1 }}
|
|
|-
| [[493/492]]
| 3.5152
| (17×29)/(22×3×41)
| 2.3.17.29.41 {{monzo| -2 -1 1 1 -1 }}
|
|
|-
| [[533/532]]
| 3.2511
| (13×41)/(22×7×19)
| 2.7.13.19.41 {{monzo| -2 -1 1 -1 1 }}
|
|
|-
| [[575/574]]
| 3.0135
| (52×23)/(2×7×41)
| 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}
| Renatisma
|
|-
| [[616/615]]
| 2.8127
| (23×7×11)/(3×5×41)
| 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}
| Ellisma
|
|-
| [[697/696]]
| 2.4856
| (17×41)/(23×3×29)
| 2.3.17.29.41 {{monzo| -3 -1 1 -1 1 }}
|
|
|-
| [[780/779]]
| 2.2210
| (22×3×5×13)/(19×41)
| 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}
| Wiesentisma
|
|-
| [[820/819]]
| 2.1125
| (22×5×41)/(32×7×13)
| 2.3.5.7.13.41 {{monzo| 2 -2 1 -1 -1 1 }}
|
|
|-
| [[1025/1024]]
| 1.6898
| (52×41)/210
| 2.5.41 {{monzo| -10 2 1 }}
| Kilobytisma
|
|-
| [[1026/1025]]
| 1.6882
| (2×33×19)/(52×41)
| 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}
| Ingridisma
|
|-
| [[1148/1147]]
| 1.5087
| (22×7×41)/(31×37)
| 2.7.31.37.41 {{monzo| 2 1 -1 -1 1 }}
|
|
|-
| [[1189/1188]]
| 1.4567
| (29×41)/(22×33×11)
| 2.3.11.29.41 {{monzo| -2 -3 -1 1 1 }}
|
|
|-
| [[1190/1189]]
| 1.4554
| (2×5×7×17)/(29×41)
| 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}
| Pelagisma
|
|-
| [[1312/1311]]
| 1.3200
| (25×41)/(3×19×23)
| 2.3.19.23.41 {{monzo| 5 -1 -1 -1 1 }}
|
|
|-
| [[1353/1352]]
| 1.2800
| (3×11×41)/(23×132)
| 2.3.11.13.41 {{monzo| -3 1 1 -2 1 }}
|
|
|-
| [[1395/1394]]
| 1.2415
| (32×5×31)/(2×17×41)
| 2.3.5.17.31.41 {{monzo| -1 2 1 -1 1 -1 }}
|
|
|-
| [[1518/1517]]
| 1.1408
| (2×3×11×23)/(37×41)
| 2.3.11.23.37.41 {{monzo| 1 1 1 1 -1 -1 }}
| Rovaniemisma
|
|-
| [[1600/1599]]
| 1.0824
| (23×5)2/(3×13×41)
| 2.3.5.13.41 {{monzo| 6 -1 2 -1 -1 }}
|
| S40
|-
| [[1681/1680]]
| 1.0302
| 412/(24×3×5×7)
| 2.3.5.7.41 {{monzo| -4 -1 -1 -1 2 }}
|
| S41
|-
| [[1682/1681]]
| 1.0296
| (2×292)/412
| 2.29.41 {{monzo| 1 2 -2 }}
| Shaftesburisma
|
|-
| [[1805/1804]]
| 0.95940
| (5×192)/(22×11×41)
| 2.5.11.19.41 {{monzo| -2 1 -1 2 -1 }}
|
|
|-
| [[1886/1885]]
| 0.91818
| (2×23×41)/(5×13×29)
| 2.5.13.23.29.41 {{monzo| 1 -1 -1 1 -1 1 }}
|
|
|-
| [[1887/1886]]
| 0.91770
| (3×17×37)/(2×23×41)
| 2.3.17.23.37.41 {{monzo| -1 1 1 -1 1 -1 }}
|
|
|-
| [[2091/2090]]
| 0.82814
| (3×17×41)/(2×5×11×19)
| 2.3.5.11.17.19.41 {{monzo| -1 1 -1 -1 1 -1 1 }}
|
|
|-
| [[2255/2254]]
| 0.76790
| (5×11×41)/(2×72×23)
| 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}
| Qinghaisma
|
|-
| [[2296/2295]]
| 0.75419
| (23×7×41)/(33×5×17)
| 2.3.5.7.17.41 {{monzo| 3 -3 -1 1 -1 1 }}
|
|
|-
| [[2542/2541]]
| 0.68119
| (2×31×41)/(3×7×112)
| 2.3.7.11.31.41 {{monzo| 1 -1 -1 -2 1 1 }}
|
|
|-
| [[2584/2583]]
| 0.67011
| (23×17×19)/(32×7×41)
| 2.3.7.17.19.41 {{monzo| 3 -2 -1 1 1 -1 }}
|
|
|-
| [[2625/2624]]
| 0.65964
| (3×53×7)/(26×41)
| 2.3.5.7.41 {{monzo| -6 1 3 1 -1 }}
|
|
|-
| [[2665/2664]]
| 0.64974
| (5×13×41)/(23×32×37)
| 2.3.5.13.37.41 {{monzo| -3 -2 1 1 -1 1 }}
|
|
|-
| [[2871/2870]]
| 0.60311
| (32×11×29)/(2×5×7×41)
| 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}
| Schoberisma
|
|-
| [[3690/3689]]
| 0.46923
| (2×32×5×41)/(7×17×31)
| 2.3.5.7.17.31.41 {{monzo| 1 2 1 -1 -1 -1 1 }}
|
|
|-
| [[3773/3772]]
| 0.45891
| (73×11)/(22×23×41)
| 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}
| Smithsonianisma
|
|-
| [[4060/4059]]
| 0.42646
| (22×5×7×29)/(32×11×41)
| 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}
| Deipylosisma
|
|-
| [[4264/4263]]
| 0.40606
| (23×13×41)/(3×72×29)
| 2.3.7.13.29.41 {{monzo| 3 -1 -2 1 -1 1 }}
|
|
|-
| [[4551/4550]]
| 0.38045
| (3×37×41)/(2×52×7×13)
| 2.3.5.7.13.37.41 {{monzo| -1 1 -2 -1 -1 1 1 }}
|
|
|-
| [[4675/4674]]
| 0.37036
| (52×11×17)/(2×3×19×41)
| 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}
| Ohbokisma
|
|-
| [[4921/4920]]
| 0.35184
| (7×19×37)/(23×3×5×41)
| 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}
| Volontisma
|
|-
| [[4961/4960]]
| 0.34900
| (112×41)/(25×5×31)
| 2.5.11.31.41 {{monzo| -5 -1 2 -1 1 }}
|
|
|-
| [[5084/5083]]
| 0.34056
| (22×31×41)/(13×17×23)
| 2.13.17.23.31.41 {{monzo| 2 -1 -1 -1 1 1 }}
|
|
|-
| [[5577/5576]]
| 0.31045
| (3×11×132)/(23×17×41)
| 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}
| Priestlisma
|
|-
| [[6069/6068]]
| 0.28528
| (3×7×172)/(22×37×41)
| 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}
| Cevolanisma
|
|-
| [[6273/6272]]
| 0.27600
| (32×17×41)/(27×72)
| 2.3.7.17.41 {{monzo| -7 2 -2 1 1 }}
|
|
|-
| [[6561/6560]]
| 0.26389
| 38/(25×5×41)
| 2.3.5.41 {{monzo| -5 8 -1 -1 }}
|
| S81
|-
| [[6601/6600]]
| 0.26229
| (7×23×41)/(23×3×52×11)
| 2.3.5.7.11.23.41 {{monzo| -3 -1 -2 1 -1 1 1 }}
|
|
|-
| [[6930/6929]]
| 0.24984
| (2×32×5×7×11)/(132×41)
| 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }}
| Bedanisma
|
|-
| [[7176/7175]]
| 0.24127
| (23×3×13×23)/(52×7×41)
| 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}
| Kunijisma
|
|-
| [[7216/7215]]
| 0.23993
| (24×11×41)/(3×5×13×37)
| 2.3.5.11.13.37.41 {{monzo| 4 -1 -1 1 -1 -1 1 }}
|
|
|-
| [[7750/7749]]
| 0.22340
| (2×53×31)/(33×7×41)
| 2.3.5.7.31.41 {{monzo| 1 -3 3 -1 1 -1 }}
|
|
|-
| [[8569/8568]]
| 0.20205
| (11×19×41)/(23×32×7×17)
| 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}
| Mamelisma
|
|-
| [[8856/8855]]
| 0.19550
| ((2×3)3×41)/(5×7×11×23)
| 2.3.5.7.11.23.41 {{monzo| 3 3 -1 -1 -1 -1 1 }}
|
|
|-
| [[9472/9471]]
| 0.18278
| (28×37)/(3×7×11×41)
| 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}
| Brugesisma
|
|-
| 10045/10044
| 0.17236
| (5×72×41)/(22×34×31)
| 2.3.5.7.31.41 {{monzo| -2 -4 1 2 -1 1 }}
|
|
|-
| [[10374/10373]]
| 0.16689
| (2×3×7×13×19)/(11×23×41)
| 2.3.7.11.13.19.23.41 {{monzo| 1 1 1 -1 1 1 -1 -1}}
| Etampesisma
|
|-
| 10660/10659
| 0.16241
| (22×5×13×41)/(3×11×17×19)
| 2.3.5.11.13.17.19.41 {{monzo| 2 -1 1 -1 1 -1 -1 1 }}
|
|
|-
| [[11440/11439]]
| 0.15134
| (24×5×11×13)/(32×31×41)
| 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}
| Massironisma
|
|-
| 13776/13775
| 0.12567
| (24×3×7×41)/(52×19×29)
| 2.3.5.7.19.29.41 {{monzo| 4 1 -2 1 -1 -1 1 }}
|
|
|-
| 14145/14144
| 0.12240
| (3×5×23×41)/(26×13×17)
| 2.3.5.13.17.23.41 {{monzo| -6 1 1 -1 -1 1 1 }}
|
|
|-
| 14801/14800
| 0.11697
| (192×41)/(24×52×37)
| 2.5.19.37.41 {{monzo| -4 -2 2 -1 1 }}
|
|
|-
| [[15376/15375]]
| 0.11260
| (22×31)2/(3×53×41)
| 2.3.5.31.41 {{monzo| 4 -1 -3 2 -1 }}
| Martakisma
| S124
|-
| 15457/15456
| 0.11201
| (13×29×41)/(25×3×7×23)
| 2.3.7.13.23.29.41 {{monzo| -5 -1 -1 1 -1 1 1 }}
|
|
|-
| 16400/16399
| 0.10557
| (24×52×41)/(232×31)
| 2.5.23.31.41 {{monzo| 4 2 -2 -1 1 }}
|
|
|-
| 16524/16523
| 0.10477
| (22×35×17)/(13×31×41)
| 2.3.13.17.31.41 {{monzo| 2 5 -1 1 -1 -1 }}
|
|
|-
| 16606/16605
| 0.10426
| (2×192×23)/(34×5×41)
| 2.3.5.19.23.41 {{monzo| 1 -4 -1 2 1 -1 }}
|
|
|-
| 17425/17424
| 0.099356
| (52×17×41)/(22×3×11)2
| 2.3.5.11.17.41 {{monzo| -4 -2 2 -2 1 1 }}
|
|
|-
| [[17836/17835]]
| 0.097067
| (22×73×13)/(3×5×29×41)
| 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}
| Canupisma
|
|-
| 17918/17917
| 0.096623
| (2×172×31)/(19×23×41)
| 2.17.19.23.31.41 {{monzo| 1 2 -1 -1 1 -1 }}
|
|
|-
| 19721/19720
| 0.087789
| (13×37×41)/(23×5×17×29)
| 2.5.13.17.29.37.41 {{monzo| -3 -1 1 -1 -1 1 1 }}
|
|
|-
| 19845/19844
| 0.087240
| (34×5×72)/((2×11)2×41)
| 2.3.5.7.11.41 {{monzo| -2 4 1 2 -2 -1 }}
|
|
|-
| [[76384/76383]]
| 0.022665
| (25×7×11×31)/(34×23×41)
| 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}
| Vernonisma
|
|-
| [[Mebisma|1048576/1048575]]
| 0.0016510
| 220/(3×52×11×31×41)
| 2.3.5.11.31.41 {{monzo| 20 -1 -2 -1 -1 -1 }}
| Mebisma
| S1024
|}

== Notes ==
<references/>

[[Category:Lists of intervals]]
[[Category:Superparticular ratios]]

List of superparticular intervals/41-limit - Revision history

FloraC at 13:29, 18 September 2025

FloraC at 13:26, 18 September 2025