3381/3380: Difference between revisions

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'''3381/3380''', the '''mikkolisma''', is a [[23-limit]] [[superparticular ratio|superparticular comma]] of about 0.51 [[cent]]s. It is the amount by which a stack consisting of [[23/21]] and two [[14/13]]'s succeed [[80/63]].
'''3381/3380''', the '''mikkolisma''', is a [[23-limit]] [[superparticular ratio|superparticular comma]] of about 0.51 [[cent]]s. It is the amount by which a stack consisting of [[23/21]] and two [[14/13]]'s succeed [[80/63]].
== Commatic relationships ==
This comma is the difference between following superparticular pairs:
* [[196/195]] and [[208/207]]
* [[441/440]] and [[507/506]]
* [[833/832]] and [[1105/1104]]
* [[2646/2645]] and [[12168/12167]]
It factors into the following superparticular pairs:
* [[3888/3887]] and [[25921/25920]]
* [[3969/3968]] and [[22816/22815]]
* [[5292/5291]] and [[9361/9360]]
== Temperaments ==
Tempering out the comma leads to the rank-8 temperament '''mikkolismic'''. Using the 2.3.5.7.13.23 subgroup leads to the rank-5 temperament '''mikkolic'''.
=== Mikkolismic ===
[[Subgroup]]: 2.3.5.7.11.13.17.19.23
[[Comma list]]: 3381/3380
[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0|| 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0|| 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || -2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~11/8 = 551.318, ~13/8 = 840.650, ~17/16 = 104.955, ~19/16 = 297.513
{{Optimal ET sequence|legend=1| 6fhi, 7deefghi, 7dfghi, 8d, 9, 10e, 10, 10h, 12fi, 16h, 16, 17cg, 17cgh, 19egh, 19, 22fh, 26i, 29g, 38df, 39dfgi, 41i, 46, 58hi, 62, 68, 72hi, 72i, 84, 87, 94, 111, 130, 140, 152fg, 159, 198, 198g, 217, 243e, 270, 282, 311, 373g, 422, 525, 581, 742i, 814, 954h, 1106, 1282, 1323, 1395, 1677e, 1696, 1768gi, 1920, 2874hi, 3202, 3513, 5011di, 6293di }}
=== Mikkolic ===
[[Subgroup]]: 2.3.5.7.13.23
[[Comma list]]: 3381/3380
[[Mapping]]: <br>
{| class="right-all"
| [⟨ || 1 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 ||  0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 ||  0 || -2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 2 || ]
|}
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~13/8 = 840.650
{{Optimal ET sequence|legend=1| 7dfi, 8d, 9, 10, 12fi, 16, 17c, 19, 27, 29, 36, 39dfi, 41i, 45fi, 46, 58i, 68, 84, 103, 111, 113, 130, 198, 224, 243, 311, 373, 441, 1012, 1106, 1236, 1395, 1677, 1920, 2118, 2361, 2631, 3072, 4327 }}


== Etymology ==
== Etymology ==
The name ''mikkolisma'' was named by [[Francium]] in 2024. It refers to [[Wikipedia:3381 Mikkola|3381 Mikkola]], the asteroid. [[User:Xenllium|Xenllium]] proposed the name ''seminaiadvice comma'' in 2023.
The name ''mikkolisma'' was named by [[Francium]] in 2024. It refers to [[Wikipedia:3381 Mikkola|3381 Mikkola]], the asteroid. Which was in turn named after a Finnish astronomer. [[User:Xenllium|Xenllium]] proposed the name ''seminaiadvice comma'' in 2023.


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
[[Category:Commas named after asteroids]]
[[Category:Commas named after individuals]]

Latest revision as of 01:15, 4 November 2024

Interval information
Ratio 3381/3380
Factorization 2-2 × 3 × 5-1 × 72 × 13-2 × 23
Monzo [-2 1 -1 2 0 -2 0 0 1⟩
Size in cents 0.5121237¢
Name mikkolisma
Color name 23o3uuzzg2,
twethothuthuzozogu 2nd
FJS name [math]\displaystyle{ \text{A1}^{7,7,23}_{5,13,13} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 23.446
Weil norm (log2 max(n, d)) 23.4465
Wilson norm (sopfr(nd)) 75
Comma size unnoticeable
Open this interval in xen-calc

3381/3380, the mikkolisma, is a 23-limit superparticular comma of about 0.51 cents. It is the amount by which a stack consisting of 23/21 and two 14/13's succeed 80/63.

Commatic relationships

This comma is the difference between following superparticular pairs:

It factors into the following superparticular pairs:

Temperaments

Tempering out the comma leads to the rank-8 temperament mikkolismic. Using the 2.3.5.7.13.23 subgroup leads to the rank-5 temperament mikkolic.

Mikkolismic

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 3381/3380

Mapping:

[⟨ 1 0 0 0 0 0 0 0 2 ],
⟨ 0 1 0 0 0 0 0 0 -1 ],
⟨ 0 0 1 0 0 0 0 0 1 ],
⟨ 0 0 0 1 0 0 0 0 -2 ],
⟨ 0 0 0 0 1 0 0 0 0 ],
⟨ 0 0 0 0 0 1 0 0 2 ],
⟨ 0 0 0 0 0 0 1 0 0 ],
⟨ 0 0 0 0 0 0 0 1 0 ]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~11/8 = 551.318, ~13/8 = 840.650, ~17/16 = 104.955, ~19/16 = 297.513

Optimal ET sequence: 6fhi, 7deefghi, 7dfghi, 8d, 9, 10e, 10, 10h, 12fi, 16h, 16, 17cg, 17cgh, 19egh, 19, 22fh, 26i, 29g, 38df, 39dfgi, 41i, 46, 58hi, 62, 68, 72hi, 72i, 84, 87, 94, 111, 130, 140, 152fg, 159, 198, 198g, 217, 243e, 270, 282, 311, 373g, 422, 525, 581, 742i, 814, 954h, 1106, 1282, 1323, 1395, 1677e, 1696, 1768gi, 1920, 2874hi, 3202, 3513, 5011di, 6293di

Mikkolic

Subgroup: 2.3.5.7.13.23

Comma list: 3381/3380

Mapping:

[⟨ 1 0 0 0 0 2 ],
⟨ 0 1 0 0 0 -1 ],
⟨ 0 0 1 0 0 1 ],
⟨ 0 0 0 1 0 -2 ],
⟨ 0 0 0 0 1 2 ]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.338, ~7/4 = 968.756, ~13/8 = 840.650

Optimal ET sequence: 7dfi, 8d, 9, 10, 12fi, 16, 17c, 19, 27, 29, 36, 39dfi, 41i, 45fi, 46, 58i, 68, 84, 103, 111, 113, 130, 198, 224, 243, 311, 373, 441, 1012, 1106, 1236, 1395, 1677, 1920, 2118, 2361, 2631, 3072, 4327

Etymology

The name mikkolisma was named by Francium in 2024. It refers to 3381 Mikkola, the asteroid. Which was in turn named after a Finnish astronomer. Xenllium proposed the name seminaiadvice comma in 2023.

See also

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