1573/1568: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 1573/1568
| Monzo = -5 0 0 -2 2 1
| Cents = 5.51173
| Name = lambeth comma
| Name = lambeth comma
| Color name =  
| Color name = 3o1oorr-2, thobiloru negative 2nd
| FJS name =
| Comma = yes
| Sound =  
}}
}}
'''1573/1568''', the '''lambeth comma''', is a [[13-limit]] (or 2.7.11.13 subgroup) [[small comma]] measuring about 5.5 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s falls short of [[13/8]].  
'''1573/1568''', the '''lambeth comma''', is a [[13-limit]] (or 2.7.11.13 subgroup) [[small comma]] measuring about 5.5 [[cent]]s. It is the amount by which a stack of two [[14/11]]'s falls short of [[13/8]].  
The name comes from the place where [[Flora Canou]] dwelled when she named the comma in January 2022.


== Temperaments ==
== Temperaments ==
Tempering it out leads to a form of the '''lambeth temperament''', and enables [[lambeth chords]], the [[essentially tempered chords]] in the [[13-odd-limit]].  
Tempering it out leads to a form of the '''lambeth temperament''', and enables [[lambeth chords]], the [[essentially tempered chord]]s in the [[13-odd-limit]].  


Subgroup: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


[[Mapping]]: <br>
[[Mapping]]: <br>
[{{val| 1 0 0 0 0 5 }}, <br>
{| class="right-all"
{{val| 0 1 0 0 0 0 }}, <br>
|-
{{val| 0 0 1 0 0 0 }}, <br>
| [⟨ || 1 || 0 || 0 || 0 || 0 || 5 || ],
{{val| 0 0 0 1 0 2 }}, <br>
|-
{{val| 0 0 0 0 1 -2 }}]
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || -2 || ]]
|}
 
: mapping generators: ~2, ~3, ~5, ~7, ~11
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2, ~5/4, ~7/4 = 969.7592, ~11/8 = 549.9007, ~13/8 = 839.7169


Mapping generators: ~2, ~3, ~5, ~7, ~11
{{Optimal ET sequence|legend=1| 17c, 22f, 26, 29, 31, 43, 46, 60e, 63, 68, 72, 103, 111, 140, 183, 212, 243e, 315ef, 323, 395f, 426e, 638eef }}


{{Val list|legend=1| 17c, 22f, 26, 29, 31, 43, 46, 60e, 63, 68, 72, 103, 111, 140, 183, 212, 243e, 315ef, 323, 395f, 426e, 638eef }}
== Etymology ==
The lambeth comma was named by [[Flora Canou]] in January 2022, referring to the [[Wikipedia: London Borough of Lambeth|London Borough of Lambeth]], where she dwelled at the time.


== See also ==
== See also ==
* [[Small comma]]
* [[Small comma]]


[[Category:13-limit]]
[[Category:Small commas]]
[[Category:Lambeth]]
[[Category:Lambeth]]
[[Category:Commas named after place names]]

Latest revision as of 18:57, 28 July 2025

Interval information
Ratio 1573/1568
Factorization 2-5 × 7-2 × 112 × 13
Monzo [-5 0 0 -2 2 1
Size in cents 5.511734¢
Name lambeth comma
Color name 3o1oorr-2, thobiloru negative 2nd
FJS name [math]\displaystyle{ \text{M}{-2}^{11,11,13}_{7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 21.234
Weil norm (log2 max(n, d)) 21.2386
Wilson norm (sopfr(nd)) 59
Comma size small
Open this interval in xen-calc

1573/1568, the lambeth comma, is a 13-limit (or 2.7.11.13 subgroup) small comma measuring about 5.5 cents. It is the amount by which a stack of two 14/11's falls short of 13/8.

Temperaments

Tempering it out leads to a form of the lambeth temperament, and enables lambeth chords, the essentially tempered chords in the 13-odd-limit.

Subgroup: 2.3.5.7.11.13

Mapping:

[⟨ 1 0 0 0 0 5 ],
0 1 0 0 0 0 ],
0 0 1 0 0 0 ],
0 0 0 1 0 2 ],
0 0 0 0 1 -2 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11

Optimal tuning (CTE): ~2 = 1\1, ~3/2, ~5/4, ~7/4 = 969.7592, ~11/8 = 549.9007, ~13/8 = 839.7169

Optimal ET sequence17c, 22f, 26, 29, 31, 43, 46, 60e, 63, 68, 72, 103, 111, 140, 183, 212, 243e, 315ef, 323, 395f, 426e, 638eef

Etymology

The lambeth comma was named by Flora Canou in January 2022, referring to the London Borough of Lambeth, where she dwelled at the time.

See also