4225/4224: Difference between revisions
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== Temperaments == | == Temperaments == | ||
Tempering | Tempering out this comma in the full 13-limit leads to the rank-5 '''leprechaun temperament'''. It is also tempered out in lower-rank temperaments including [[abigail]], [[newt]], [[decoid]], [[donar]], etc. Tempering it out also splits the [[33/32]] Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below. | ||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Mapping]]: | |||
<br>[{{val| 1 0 0 0 1 4 }} | |||
<br>{{val| 0 1 0 0 1 1 }} | |||
<br>{{val| 0 0 1 0 0 -1 }} | |||
<br>{{val| 0 0 0 1 0 0 }} | |||
<br>{{val| 0 0 0 0 2 1 }}] | |||
Mapping generators: ~2, ~3, ~5, ~7, ~65/48 | |||
{{Val list|legend=1| 41, 46, 53, 80, 87, 103, 121, 130, 183, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1308, 1448, 1578, 1889, 2756, 2843, 3337, 4421f, 4915f, 7758cff, 10514cdff }} | |||
== See also == | == See also == | ||
Revision as of 18:59, 13 November 2022
| Interval information |
reduced
4225/4224, the leprechaun comma, is an unnoticeable 13-limit superparticular interval. It is the difference between the following pairs:
- 65/64 and 66/65
- 169/168 and 176/175
- 325/324 and 352/351
- 2080/2079 and 4096/4095
- 3025/3024 and 10648/10647
Temperaments
Tempering out this comma in the full 13-limit leads to the rank-5 leprechaun temperament. It is also tempered out in lower-rank temperaments including abigail, newt, decoid, donar, etc. Tempering it out also splits the 33/32 Alpharabian quarter-tone in two, each part corresponding to 65/64 and 66/65. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.11.13
Mapping:
[⟨1 0 0 0 1 4]
⟨0 1 0 0 1 1]
⟨0 0 1 0 0 -1]
⟨0 0 0 1 0 0]
⟨0 0 0 0 2 1]]
Mapping generators: ~2, ~3, ~5, ~7, ~65/48