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. | ||
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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 |