FloraC: + name

2025-10-30T10:27:30Z

+ name

← Older revision		Revision as of 10:27, 30 October 2025
Line 391:		Line 391:
	\| (2×13<sup>2</sup>×29)/(3<sup>2</sup>×11)<sup>2</sup>		\| (2×13<sup>2</sup>×29)/(3<sup>2</sup>×11)<sup>2</sup>
	\| 2.3.11.13.29 {{monzo\| 1 -4 -2 2 1 }}		\| 2.3.11.13.29 {{monzo\| 1 -4 -2 2 1 }}
	\|		\| Kakisma
	\|		\|
	\|-		\|-

Fredg999: Categories

2025-07-22T20:14:13Z

Fredg999: Split from List of superparticular intervals, as discussed on the talk page

2025-07-22T20:12:12Z

Split from List of superparticular intervals, as discussed on the talk page

New page

{{Breadcrumb}}
== 29-limit ==
{| 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>
|-
| [[29/28]]
| 60.751
| 29/(22×7)
| 2.7.29 {{monzo| -2 -1 1 }}
| Vicesimononal thirdtone, vicesimononal subchroma, large vicesimononal quartertone, large vicesimononal 2/7-tone
|
|-
| [[30/29]]
| 58.692
| (2×3×5)/29
| 2.3.5.29 {{monzo| 1 1 1 -1 }}
| Small vicesimononal quartertone, small vicesimononal 2/7-tone
|
|-
| [[58/57]]
| 30.109
| (2×29)/(3×19)
| 2.3.19.29 {{monzo| 1 -1 -1 1 }}
| Vicesimononal 1/7-tone
|
|-
| [[88/87]]
| 19.786
| (23×11)/(3×29)
| 2.3.11.29 {{monzo| 3 -1 1 -1 }}
| Vicesimononal 1/10-tone, farewell comma
|
|-
| [[116/115]]
| 14.989
| (22×29)/(5×23)
| 2.5.23.29 {{monzo| 2 -1 -1 1 }}
| Sironisma
|
|-
| [[117/116]]
| 14.860
| (32×13)/(22×29)
| 2.3.13.29 {{monzo| -2 2 1 -1 }}
| Lomisma
|
|-
| [[145/144]]
| 11.981
| (5×29)/(22×3)2
| 2.3.5.29 {{monzo| -4 -2 1 1 }}
| Adeonisma, 29th-partial chroma
|
|-
| [[175/174]]
| 9.9211
| (52×7)/(2×3×29)
| 2.3.5.7.29 {{monzo| -1 -1 2 1 -1 }}
| Major chthonovinema
|
|-
| [[204/203]]
| 8.5073
| (22×3×17)/(7×29)
| 2.3.7.17.29 {{monzo| 2 1 -1 1 -1 }}
| Kallistisma
|
|-
| [[232/231]]
| 7.4783
| (23×29)/(3×7×11)
| 2.3.7.11.29 {{monzo| 3 -1 -1 -1 1 }}
| Major paravinema
|
|-
| [[261/260]]
| 6.6458
| (32×29)/(22×5×13)
| 2.3.5.13.29 {{monzo| -2 2 -1 -1 1 }}
| Major vinetonema
|
|-
| [[290/289]]
| 5.9801
| (2×5×29)/172
| 2.5.17.29 {{monzo| 1 1 -2 1 }}
| Brunisma
|
|-
| [[320/319]]
| 5.4186
| (26×5)/(11×29)
| 2.5.11.29 {{monzo| 6 1 -1 -1 }}
| Minor paravinema
|
|-
| [[378/377]]
| 4.5861
| (2×33×7)/(13×29)
| 2.3.7.13.29 {{monzo| 1 3 1 -1 -1 }}
| Major semivinema
|
|-
| [[406/405]]
| 4.2694
| (2×7×29)/(34×5)
| 2.3.5.7.29 {{monzo| 1 -4 -1 1 1 }}
| Minor semivinema
|
|-
| [[494/493]]
| 3.5081
| (2×13×19)/(17×29)
| 2.13.17.19.29 {{monzo| 1 1 -1 1 -1 }}
| Minor vinetonema
|
|-
| [[551/550]]
| 3.1448
| (19×29)/(2×52×11)
| 2.5.11.19.29 {{monzo| -1 -2 -1 1 1 }}
| Minor chthonovinema
|
|-
| [[552/551]]
| 3.1391
| (23×3×23)/(19×29)
| 2.3.19.23.29 {{monzo| 3 1 -1 1 -1 }}
| Sigelindisma
|
|-
| [[609/608]]
| 2.8451
| (3×7×29)/(25×19)
| 2.3.7.19.29 {{monzo| -5 1 1 -1 1 }}
| Vineyard comma
|
|-
| [[638/637]]
| 2.7157
| (2×11×29)/(72×13)
| 2.7.11.13.29 {{monzo| 1 -2 1 -1 1 }}
| Moirisma
|
|-
| [[726/725]]
| 2.3863
| (2×3×112)/(52×29)
| 2.3.5.11.29 {{monzo| 1 1 -2 2 -1 }}
| Joellisma
|
|-
| [[783/782]]
| 2.2124
| (33×29)/(2×17×23)
| 2.3.17.23.29 {{monzo| -1 3 -1 -1 1 }}
| Norisma
|
|-
| [[784/783]]
| 2.2096
| (22×7)2/(33×29)
| 2.3.7.29 {{monzo| 4 -3 2 -1 }}
| Biminorisma, spoogalactic comma
| S28
|-
| [[841/840]]
| 2.0598
| 292/(23×3×5×7)
| 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}
| Arabellisma
| S29
|-
| [[1015/1014]]
| 1.7065
| (5×7×29)/(2×3×132)
| 2.3.5.7.13.29 {{monzo| -1 -1 1 1 -2 1 }}
| Christisma
|
|-
| [[1045/1044]]
| 1.6575
| (5×11×19)/((2×3)2×29)
| 2.3.5.11.19.29 {{monzo| -2 -2 1 1 1 -1 }}
| Michelisma
|
|-
| [[1276/1275]]
| 1.3573
| (22×11×29)/(3×52×17)
| 2.3.5.11.17.29 {{monzo| 2 -1 -2 1 -1 1 }}
| Ucclisma
|
|-
| [[1450/1449]]
| 1.1944
| (2×52×29)/(32×7×23)
| 2.3.5.7.23.29 {{monzo| 1 -2 2 -1 -1 1 }}
| Raimondisma
|
|-
| [[1596/1595]]
| 1.0851
| (22×3×7×19)/(5×11×29)
| 2.3.5.7.11.19.29 {{monzo| 2 1 -1 1 -1 1 -1 }}
| Itzigsohnisma
|
|-
| [[1625/1624]]
| 1.0657
| (53×13)/(23×7×29)
| 2.5.7.13.29 {{monzo| -3 3 -1 1 -1 }}
| Norcma
|
|-
| [[1683/1682]]
| 1.0290
| (32×11×17)/(2×292)
| 2.3.11.17.29 {{monzo| -1 2 1 1 -2 }}
| Castafiorisma
|
|-
| [[2001/2000]]
| 0.86540
| (3×23×29)/(24×53)
| 2.3.5.23.29 {{monzo| -4 1 -3 1 1 }}
| Major discoverisma
|
|-
| [[2002/2001]]
| 0.86497
| (2×7×11×13)/(3×23×29)
| 2.3.7.11.13.23.29 {{monzo| 1 -1 1 1 1 -1 -1 }}
| Minor discoverisma
|
|-
| [[2176/2175]]
| 0.79579
| (27×17)/(3×52×29)
| 2.3.5.17.29 {{monzo| 7 -1 -2 1 -1 }}
| Donarisma
|
|-
| [[2205/2204]]
| 0.78532
| ((3×7)/2)2×(5/(19×29))
| 2.3.5.7.19.29 {{monzo| -2 2 1 2 -1 -1 }}
| Glinkisma
|
|-
| [[2262/2261]]
| 0.76552
| (2×3×13×29)/(7×17×19)
| 2.3.7.13.17.19.29 {{monzo| 1 1 -1 1 -1 -1 1 }}
| Mitidikisma
|
|-
| [[2465/2464]]
| 0.70247
| (5×17×29)/(25×7×11)
| 2.5.7.11.17.29 {{monzo| -5 1 -1 -1 1 1 }}
| Laservine comma
|
|-
| [[2640/2639]]
| 0.65589
| (24×3×5×11)/(7×13×29)
| 2.3.5.7.11.13.29 {{monzo| 4 1 1 -1 1 -1 -1 }}
| Hällströmisma
|
|-
| [[2755/2754]]
| 0.62851
| (5×19×29)/(2×34×17)
| 2.3.5.17.19.29 {{monzo| -1 -4 1 -1 1 1 }}
| Avicema
|
|-
| [[2784/2783]]
| 0.62196
| (25×3×29)/(112×23)
| 2.3.11.23.29 {{monzo| 5 1 -2 -1 1 }}
| Domeykisma
|
|-
| [[3249/3248]]
| 0.53293
| (3×19)2/(24×7×29)
| 2.3.7.19.29 {{monzo| -4 2 -1 2 -1 }}
| Musashinisma, Musashino comma
| S57
|-
| [[3451/3450]]
| 0.50173
| (7×17×29)/(2×3×52×23)
| 2.3.5.7.17.23.29 {{monzo| -1 -1 -2 1 1 -1 1 }}
| Mentorisma
|
|-
| [[3510/3509]]
| 0.49330
| (2×33×5×13)/(112×29)
| 2.3.5.11.13.29 {{monzo| 1 3 1 -2 1 -1 }}
| Veederisma
|
|-
| [[4641/4640]]
| 0.37307
| (3×7×13×17)/(25×5×29)
| 2.3.5.7.13.17.29 {{monzo| -5 1 -1 1 1 1 -1 }}
| Vinecute comma
|
|-
| [[4785/4784]]
| 0.36184
| (3×5×11×29)/(24×13×23)
| 2.3.5.11.13.23.29 {{monzo| -4 1 1 1 -1 -1 1 }}
| Petrovsma
|
|-
| [[4901/4900]]
| 0.35328
| (13/(2×5×7))2×29
| 2.5.7.13.29 {{monzo| -2 -2 -2 2 1 }}
| Large grapevine comma
|
|-
| [[5104/5103]]
| 0.33922
| (24×11×29)/(36×7)
| 2.3.7.11.29 {{monzo| 4 -6 -1 1 1 }}
|
|
|-
| [[5888/5887]]
| 0.29405
| (28×23)/(7×292)
| 2.7.23.29 {{monzo| 8 -1 1 -2 }}
| Vinocular comma
|
|-
| [[5916/5915]]
| 0.29266
| (22×3×17×29)/(5×7×132)
| 2.3.5.7.13.17.29 {{monzo| 2 1 -1 -1 -2 1 1 }}
| Woudisma
|
|-
| [[6670/6669]]
| 0.25957
| (2×5×23×29)/(33×13×19)
| 2.3.5.13.19.23.29 {{monzo| 1 -3 1 -1 -1 1 1 }}
|
|
|-
| [[7106/7105]]
| 0.24365
| (2×11×17×19)/(5×72×29)
| 2.5.7.11.17.19.29 {{monzo| 1 -1 -2 1 1 1 -1 }}
|
|
|-
| [[7425/7424]]
| 0.23318
| (33×52×11)/(28×29)
| 2.3.5.11.29 {{monzo| -8 3 2 1 -1 }}
| Small grapevine comma
|
|-
| [[7889/7888]]
| 0.21946
| (73×23)/(24×17×29)
| 2.7.17.23.29 {{monzo| -4 3 -1 1 -1 }}
|
|
|-
| [[8671/8670]]
| 0.19967
| (13×23×29)/(2×3×5×172)
| 2.3.5.13.17.23.29 {{monzo| -1 -1 -1 1 -2 1 1 }}
| Vinous comma, vinousma
|
|-
| [[9802/9801]]
| 0.17663
| (2×132×29)/(32×11)2
| 2.3.11.13.29 {{monzo| 1 -4 -2 2 1 }}
|
|
|-
| [[10557/10556]]
| 0.16400
| (33×17×23)/(22×7×13×29)
| 2.3.7.13.17.23.29 {{monzo| -2 3 -1 -1 1 1 -1 }}
| Rowlandisma
|
|-
| 11340/11339
| 0.15267
| (22×34×5×7)/(17×23×29)
| 2.3.5.7.17.23.29 {{monzo| 2 4 1 1 -1 -1 -1 }}
|
|
|-
| [[Uma|12006/12005]]
| 0.14420
| (2×32×23×29)/(5×74)
| 2.3.5.7.23.29 {{monzo| 1 2 -1 -4 1 1 }}
| Uma, umic comma
|
|-
| 12673/12672
| 0.13661
| (19×23×29)/(27×32×11)
| 2.3.11.19.23.29 {{monzo| -7 -2 -1 1 1 1 }}
|
|
|-
| 13225/13224
| 0.13091
| (5×23)2/(23×3×19×29)
| 2.3.5.19.23.29 {{monzo| -3 -1 2 -1 2 -1 }}
|
| S115
|-
| 13311/13310
| 0.13007
| (33×17×29)/(2×5×113)
| 2.3.5.11.17.29 {{monzo| -1 3 -1 -3 1 1 }}
|
|
|-
| 13312/13311
| 0.13006
| (210×13)/(33×17×29)
| 2.3.13.17.29 {{monzo| 10 -3 1 -1 -1 }}
|
|
|-
| 13456/13455
| 0.12866
| (22×29)2/(32×5×13×23)
| 2.3.5.13.23.29 {{monzo| 4 -2 -1 -1 -1 2 }}
|
| S116
|-
| 19228/19227
| 0.090039
| (22×11×19×23)/(3×13×17×29)
| 2.3.11.13.17.19.23.29 {{monzo| 2 -1 1 -1 -1 1 1 -1 }}
|
|
|-
| 20736/20735
| 0.083491
| (22×3)4/(5×11×13×29)
| 2.3.5.11.13.29 {{monzo| 8 4 -1 -1 -1 -1 }}
|
| S144
|-
| 23751/23750
| 0.072893
| (32×7×13×29)/(2×54×19)
| 2.3.5.7.13.19.29 {{monzo| -1 2 -4 1 1 -1 1 }}
|
|
|-
| 24795/24794
| 0.069823
| (32×5×19×29)/(2×72×11×23)
| 2.3.5.7.11.19.23.29 {{monzo| -1 2 1 -2 -1 1 -1 1 }}
|
|
|-
| [[Vuillafansisma|25840/25839]]
| 0.067000
| (24×5×17×19)/(34×11×29)
| 2.3.5.11.17.19.29 {{monzo| 4 -4 1 -1 1 1 -1 }}
| Vuillafansisma
|
|-
| 27000/26999
| 0.064121
| (2×3×5)3/(72×19×29)
| 2.3.5.7.19.29 {{monzo| 3 3 3 -2 -1 -1 }}
|
|
|-
| 30625/30624
| 0.056531
| (52×7)2/(25×3×11×29)
| 2.3.5.7.11.29 {{monzo| -5 -1 4 2 -1 -1 }}
|
| S175
|-
| 30856/30855
| 0.056108
| (23×7×19×29)/(3×5×112×17)
| 2.3.5.7.11.17.19.29 {{monzo| 3 -1 -1 1 -2 -1 1 1 }}
|
|
|-
| 35322/35321
| 0.049014
| (2×3×7×292)/(11×132×19)
| 2.3.7.11.13.19.29 {{monzo| 1 1 1 -1 -2 -1 2 }}
|
|
|-
| 47125/47124
| 0.036737
| (53×13×29)/((2×3)2×7×11×17)
| 2.3.5.7.11.13.17.29 {{monzo| -2 -2 3 -1 -1 1 -1 1 }}
|
|
|-
| 53361/53360
| 0.032444
| (3×7×11)2/(24×5×23×29)
| 2.3.5.7.11.23.29 {{monzo| -4 2 -1 2 2 -1 -1 }}
|
| S231
|-
| 72501/72500
| 0.023879
| (3×11×133)/((2×52)2×29)
| 2.3.5.11.13.29 {{monzo| -2 1 -4 1 3 -1 }}
|
|
|-
| 83521/83520
| 0.020728
| 174/((23×3)2×5×29)
| 2.3.5.17.29 {{monzo| -6 -2 -1 4 -1 }}
|
| S289
|-
| 87465/87464
| 0.019794
| (3×5×73×17)/(23×13×292)
| 2.3.5.7.13.17.29 {{monzo| -3 1 1 3 -1 1 -2 }}
|
|
|-
| 136851/136850
| 0.012651
| (3×112×13×29)/(2×52×7×17×23)
| 2.3.5.7.11.13.17.23.29 {{monzo| -1 1 -2 -1 2 1 -1 -1 1 }}
|
|
|-
| 158950/158949
| 0.010892
| (2×(5×17)2×11)/(33×7×292)
| 2.3.5.7.11.17.29 {{monzo| 1 -3 2 -1 1 2 -2 }}
|
|
|-
| 166635/166634
| 0.010389
| ((3×23)2×5×7)/(2×132×17×29)
| 2.3.5.7.13.17.23.29 {{monzo| -1 2 1 1 -2 -1 2 -1 }}
|
|
|-
| 168751/168750
| 0.010259
| (11×232×29)/(2×33×55)
| 2.3.5.11.23.29 {{monzo| -1 -3 -5 1 2 1 }}
|
|
|-
| 176001/176000
| 0.0098365
| (3×7×172×29)/(27×53×11)
| 2.3.5.7.11.17.29 {{monzo| -7 1 -3 1 -1 2 1 }}
|
|
|-
| 176176/176175
| 0.0098268
| (24×7×112×13)/(35×52×29)
| 2.3.5.7.11.13.29 {{monzo| 4 -5 -2 1 2 1 -1 }}
|
|
|-
| 184093/184092
| 0.0094042
| ((7×17)2×13)/((2×23)2×3×29)
| 2.3.7.13.17.23.29 {{monzo| -2 -1 2 1 2 -2 -1 }}
|
|
|-
| 240787/240786
| 0.0071899
| (192×23×29)/(2×(3×7)3×13)
| 2.3.7.13.19.23.29 {{monzo| -1 -3 -3 -1 2 1 1 }}
|
|
|-
| 244036/244035
| 0.0070942
| (2×13×19)2/(32×5×11×17×29)
| 2.3.5.11.13.17.19.29 {{monzo| 2 -2 -1 -1 2 -1 2 -1 }}
|
| S494
|-
| 303601/303600
| 0.0057023
| ((19×29)/(22×5))2/(3×11×23)
| 2.3.5.11.19.23.29 {{monzo| -4 -1 -2 -1 2 -1 2 }}
|
| S551
|-
| 410670/410669
| 0.0042156
| (2×35×5×132)/((7×17)2×29)
| 2.3.5.7.13.17.29 {{monzo| 1 5 1 -2 2 -2 -1 }}
|
|
|-
| 418761/418760
| 0.0041342
| ((3×17)2×7×23)/(23×5×192×29)
| 2.3.5.7.17.19.23.29 {{monzo| -3 2 -1 1 2 -2 1 -1 }}
|
|
|-
| 613089/613088
| 0.0028238
| (33×29)2/(25×72×17×23)
| 2.3.7.17.23.29 {{monzo| -5 6 -2 -1 -1 2 }}
|
| S783
|-
| 949026/949025
| 0.0018242
| (2×3×13×233)/(52×7×11×17×29)
| 2.3.5.7.11.13.17.23.29 {{monzo| 1 1 -2 -1 -1 1 -1 3 -1 }}
|
|
|-
| 1163800/1163799
| 0.0014876
| (23×(5×23)2×11)/(32×73×13×29)
| 2.3.5.7.11.13.23.29 {{monzo| 3 -2 2 -3 1 -1 2 -1 }}
|
|
|-
| 1235169/1235168
| 0.0014016
| (35×13×17×23)/(25×113×29)
| 2.3.11.13.17.23.29 {{monzo| -5 5 -3 1 1 1 -1 }}
|
|
|-
| 1243840/1243839
| 0.0013918
| ((23×13)2×5×23)/(3×17×293)
| 2.3.5.13.17.23.29 {{monzo| 6 -1 1 2 -1 1 -3 }}
|
|
|-
| 1625625/1625624
| 0.0010650
| (3×52×17)2/(23×72×11×13×29)
| 2.3.5.7.11.13.17.29 {{monzo| -3 2 4 -2 -1 -1 2 -1 }}
|
| S1275
|-
| 1852201/1852200
| 0.00093469
| (13×173×29)/((2×3×7)3×52)
| 2.3.5.7.13.17.29 {{monzo| -3 -3 -2 -3 1 3 1 }}
|
|
|-
| 2697696/2697695
| 0.00064175
| (25×32×17×19×29)/(5×73×112×13)
| 2.3.5.7.11.13.17.19.29 {{monzo| 5 2 -1 -3 -2 -1 1 1 1 }}
|
|
|-
| [[Odyssey comma|4004001/4004000]]
| 0.00043238
| (3×23×29)2/(25×53×7×11×13)
| 2.3.5.7.11.13.23.29 {{monzo| -5 2 -3 -1 -1 -1 2 2 }}
| Odyssey comma
| S2001
|-
| 4090625/4090624
| 0.00042322
| (55×7×11×17)/((24×29)2×19)
| 2.5.7.11.17.19.29 {{monzo| -8 5 1 1 1 -1 -2 }}
|
|
|-
| 8268800/8268799
| 0.00020937
| ((25×5)2×17×19)/((7×23)2×11×29)
| 2.5.7.11.17.19.23.29 {{monzo| 10 2 -2 -1 1 1 -2 -1 }}
|
|
|-
| 10556001/10556000
| 0.00016400
| (3×19)4/(25×53×7×13×29)
| 2.3.5.7.13.19.29 {{monzo| -5 4 -3 -1 -1 4 -1 }}
|
| S3249
|-
| 18085705/18085704
| 9.5724×10-5
| (5×11×17×23×292)/((2×7×13)3×3)
| 2.3.5.7.11.13.17.23.29 {{monzo| -3 -1 1 -3 1 -3 1 1 2 }}
|
|
|-
| 96059601/96059600
| 1.8022×10-5
| (32×11)4/((22×5×7×13)2×29)
| 2.3.5.7.11.13.29 {{monzo| -4 8 -2 -2 4 -2 -1 }}
|
| S9801
|-
| 177182721/177182720
| 9.7709×10-6
| (33×17×29)2/(211×5×113×13)
| 2.3.5.11.13.17.29 {{monzo| -11 6 -1 -3 -1 2 2 }}
|
| S13311
|}

== Notes ==
<references/>

← Older revision		Revision as of 20:14, 22 July 2025
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	== Notes ==		== Notes ==
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			[[Category:Lists of intervals]]
			[[Category:Superparticular ratios\|*]]

List of superparticular intervals/29-limit - Revision history

FloraC: + name

Fredg999: Categories

Fredg999: Split from List of superparticular intervals, as discussed on the talk page