User:Eliora/Tricesimoprimal miracloid: Difference between revisions
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'''Tricesimoprimal miracloid''' is a rank-2 microtemperament which is generated with the [[31/29]] interval, otherwise known as tricesimoprimal semitone, and it is named miracloid because the generator interval is located within the miracle temperament spectrum. It can be described as the 52 & 1789 temperament. 52edo is notable because it represents 31/29 with exceptionally high precision. | |||
The 52-note scale of tricesimoprimal miracloid can hence be viewed as a [[circulating temperament]] for 52edo. | |||
== Temperament data == | |||
Subgroup: 2.5.7.11.19.29.31 | |||
Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688 | |||
{{mapping|legend=2|1 419 48 177 157 624 625|0 -461 -50 -192 -169 -685 -686}} | |||
: mapping generators: ~58/31 = 1084.628 | |||
WE tuning: 1200.008 1084.636 | |||
CWE tuning: 1200.000 1084.628 | |||
[[Support]]ing [[ET]]s: {{EDOs|52, 1737, 1789, 1841h}} | |||
Badness: 4.513 | |||
== Theory == | == Theory == | ||
Tricesimoprimal miracloid is produced with the interval of 31/29 as the generator, and a circle of 52 such intervals barely noticeably closes at the octave. | Tricesimoprimal miracloid is produced with the interval of 31/29 as the generator, and a circle of 52 such intervals barely noticeably closes at the octave. | ||
As such, the playing cards notation will be used for the 52 note MOS. | As such, the playing cards notation will be used for the 52 note MOS. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
|A'''♣''' | ! Note | ||
|0 | ! Generators up | ||
|1/1 | ! Interval | ||
|- | |||
| A'''♣''' | |||
| 0 | |||
| 1/1 | |||
|- | |- | ||
|6'''♣''' | | 6'''♣''' | ||
|1 | | 1 | ||
|31/29 | | 31/29 | ||
|- | |- | ||
|J'''♣''' | | J'''♣''' | ||
|2 | | 2 | ||
| | | | ||
|- | |- | ||
|3♠ | | 3♠ | ||
|3 | | 3 | ||
|neutral third | | neutral third | ||
|- | |- | ||
|8♠ | | 8♠ | ||
|4 | | 4 | ||
| | | | ||
|- | |- | ||
|K♠ | | K♠ | ||
|5 | | 5 | ||
| | | | ||
|- | |- | ||
|5♦ | | 5♦ | ||
|6 | | 6 | ||
|meantone fifth | | meantone fifth | ||
|- | |- | ||
|10♦ | | 10♦ | ||
|7 | | 7 | ||
| | | | ||
|- | |- | ||
|2♥ | | 2♥ | ||
|8 | | 8 | ||
| | | | ||
|- | |- | ||
|7♥ | | 7♥ | ||
|9 | | 9 | ||
| | | | ||
|- | |- | ||
|Q♥ | | Q♥ | ||
|10 | | 10 | ||
| | | | ||
|} | |} | ||
Latest revision as of 17:47, 17 August 2026
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Tricesimoprimal miracloid is a rank-2 microtemperament which is generated with the 31/29 interval, otherwise known as tricesimoprimal semitone, and it is named miracloid because the generator interval is located within the miracle temperament spectrum. It can be described as the 52 & 1789 temperament. 52edo is notable because it represents 31/29 with exceptionally high precision.
The 52-note scale of tricesimoprimal miracloid can hence be viewed as a circulating temperament for 52edo.
Temperament data
Subgroup: 2.5.7.11.19.29.31
Comma list: 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688
Subgroup-val mapping: [⟨1 419 48 177 157 624 625], ⟨0 -461 -50 -192 -169 -685 -686]]
- mapping generators: ~58/31 = 1084.628
WE tuning: 1200.008 1084.636 CWE tuning: 1200.000 1084.628
Supporting ETs: 52, 1737, 1789, 1841h
Badness: 4.513
Theory
Tricesimoprimal miracloid is produced with the interval of 31/29 as the generator, and a circle of 52 such intervals barely noticeably closes at the octave. As such, the playing cards notation will be used for the 52 note MOS.
| Note | Generators up | Interval |
|---|---|---|
| A♣ | 0 | 1/1 |
| 6♣ | 1 | 31/29 |
| J♣ | 2 | |
| 3♠ | 3 | neutral third |
| 8♠ | 4 | |
| K♠ | 5 | |
| 5♦ | 6 | meantone fifth |
| 10♦ | 7 | |
| 2♥ | 8 | |
| 7♥ | 9 | |
| Q♥ | 10 |