Francium: Created page with "{{Infobox Interval | Ratio = 17545/17544 | Name = manheimisma | Color name = 43u29o17u1ooy-2
fothutwenosuloloyo negative 2nd | Comma = yes }} '''17545/17544''', the '''m..."

2024-11-04T20:49:43Z

Created page with "{{Infobox Interval | Ratio = 17545/17544 | Name = manheimisma | Color name = 43u29o17u1ooy-2 <br> fothutwenosuloloyo negative 2nd | Comma = yes }} '''17545/17544''', the '''m..."

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{{Infobox Interval
| Ratio = 17545/17544
| Name = manheimisma
| Color name = 43u29o17u1ooy-2 <br> fothutwenosuloloyo negative 2nd
| Comma = yes
}}

'''17545/17544''', the '''manheimisma''', is a [[43-limit]] [[superparticular ratio|superparticular comma]] of about 0.1 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[1463/1462]] and [[1596/1595]]
* [[1936/1935]] and [[2176/2175]]
* [[2925/2924]] and [[3510/3509]]
* [[7569/7568]] and [[13311/13310]]

It can be factored into the following superparticular commas:
* [[20125/20124]] and [[136851/136850]]
* [[25025/25024]] and [[58696/58695]]
* [[27951/27950]] and [[47125/47124]]

== Temperaments ==
Tempering out this comma in the full 43-limit leads to the rank-13 temperament '''manheimismic'''. Using the 2.3.5.11.17.29.43 subgroup leads to the rank-6 temperament '''manheimic'''.

=== Manheimismic ===

[[Subgroup]]. 2.3.5.7.11.13.17.19.23.29.31.37.41.43

[[Comma list]]: 17545/17544

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 2 || 3 || 3 || 4 || 4 || 4 || 4 || 4 || 5 || 5 || 4 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ],
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.957, ~5/4 = 386.309, ~7/4 = 968.826, ~11/8 = 551.299, ~13/8 = 840.528, ~17/16 = 104.969, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.559, ~31/16 = 1145.036, ~37/32 = 251.344, ~41/32 = 429.062

=== Manheimic ===

[[Subgroup]]: 2.3.5.11.17.29.43

[[Comma list]]: 17545/17544

[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 1 || 2 || 3 || 4 || 4 || 4 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.957, ~5/4 = 386.309, ~11/8 = 551.299, ~17/16 = 104.969, ~29/16 = 1029.559

{{Optimal ET sequence|legend=1| 6j, 7gjjn, 7g, 10n, 12enn, 12gjn, 14cggjjn, 14cn, 15n, 16jn, 17cgn, 19egnn, 19, 22, 31gj, 31, 34n, 46j, 53gn, 56, 65, 118, 183, 414, 422, 487, 597, 605, 653, 677, 718, 764j, 836, 1019, 1513, 1600, 1783, 2000, 2231, 2349, 2414, 2836, 3737, 3920, 4197, 4436, 4619, 5520, 7033, 10139 }}

== Etymology ==
The manheimisma was named by [[Francium]] in 2024. It refers to the postal code of Manheim, Pennsylvania.

== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]

[[Category:Commas named after place names]]

Manheimisma - Revision history

Francium: Created page with "{{Infobox Interval | Ratio = 17545/17544 | Name = manheimisma | Color name = 43u29o17u1ooy-2 fothutwenosuloloyo negative 2nd | Comma = yes }} '''17545/17544''', the '''m..."

Francium: Created page with "{{Infobox Interval | Ratio = 17545/17544 | Name = manheimisma | Color name = 43u29o17u1ooy-2
fothutwenosuloloyo negative 2nd | Comma = yes }} '''17545/17544''', the '''m..."