1225/1224: Difference between revisions

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== Temperaments ==
== Temperaments ==
Tempering out this comma in the 17-limit results in the '''noellismic temperament''', where [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support this temperament below.  
Tempering out this comma in the 17-limit results in the '''noellismic temperament''', or in the 2.3.5.7.17 subgroup, the '''noellic temperament'''. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.  


=== Noellismic ===
[[Subgroup]]: 2.3.5.7.11.13.17
[[Subgroup]]: 2.3.5.7.11.13.17


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Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277


{{Val list|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
{{Val list|legend=1| 19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
=== Noellic ===
Subgroup: 2.3.5.7.17
Sval mapping:
<br>[{{val| 1 0 0 0 -3 }}
<br>{{val| 0 1 0 0 -2 }}
<br>{{val| 0 0 1 0 2 }}
<br>{{val| 0 0 0 1 2 }}
Sval mapping generators: ~2, ~3, ~5, ~7
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468
Optimal GPV sequence: {{val list| 19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}


== Etymology ==
== Etymology ==

Revision as of 15:14, 10 February 2023

Interval information
Ratio 1225/1224
Factorization 2-3 × 3-2 × 52 × 72 × 17-1
Monzo [-3 -2 2 2 0 0 -1⟩
Size in cents 1.413829¢
Name noellisma
Color name 17uzzyy1, subizoyo 1sn,
Subizoyo comma
FJS name [math]\displaystyle{ \text{A1}^{5,5,7,7}_{17} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 20.516
Weil norm (log2 max(n, d)) 20.5171
Wilson norm (sopfr(nd)) 53
Comma size unnoticeable
S-expressions S35,
S49⋅S50
Open this interval in xen-calc

1225/1224, the noellisma, is a 17-limit (also 2.3.5.7.17 subgroup) comma measuring about 1.41 cents. It is the difference between 35/34 and 36/35, and between 49/48 and 51/50.

Commatic relations

In terms of commas, it is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

Temperaments

Tempering out this comma in the 17-limit results in the noellismic temperament, or in the 2.3.5.7.17 subgroup, the noellic temperament. In either case 18/17 is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

Noellismic

Subgroup: 2.3.5.7.11.13.17

Mapping:
[⟨1 0 0 0 0 0 -3]
⟨0 1 0 0 0 0 -2]
⟨0 0 1 0 0 0 2]
⟨0 0 0 1 0 0 2]
⟨0 0 0 0 1 0 0]
⟨0 0 0 0 0 1 0]

Mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277

Template:Val list

Noellic

Subgroup: 2.3.5.7.17

Sval mapping:
[⟨1 0 0 0 -3]
⟨0 1 0 0 -2]
⟨0 0 1 0 2]
⟨0 0 0 1 2]

Sval mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

Optimal GPV sequence: Template:Val list

Etymology

The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

See also

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