Septimagic comma: Difference between revisions
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Created page with "{{Infobox interval | Ratio = 537824/531441 | Name = septimagic comma, magi comma | Color name = sz<sup>5</sup>4, saquinzo 4th | Comma = yes }} '''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a no-fives 7-limit comma of measuring 20.7 cents. It is the difference between five 14/9s and two 3/1s. == Temperaments == Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and..." Tags: Mobile edit Mobile web edit |
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== Temperaments == | == Temperaments == | ||
Tempering out this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and the '''[[No-fives subgroup temperaments #Magi|magi temperament]]''' in its minimal prime subgroup of 2.3.7. | [[Tempering out]] this comma gives the rank-3 '''septimagic temperament''' in the full 7-limit, and the '''[[No-fives subgroup temperaments #Magi|magi temperament]]''' in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of the [[Magic|magic temperament]]. | ||
=== Septimagic === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 537824/531441 | |||
{{Mapping|legend=1| 1 0 0 -1 | 0 5 0 12 | 0 0 1 0 }} | |||
: Mapping generators: ~2, ~243/196, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2 = 1199.822{{c}}, ~243/196 = 380.604{{c}}, ~5 = 2786.312{{c}} | |||
* [[CWE]]: ~2 = 1200.000{{c}}, ~243/196 = 380.638{{c}}, ~5 = 2786.523{{c}} | |||
{{Optimal ET sequence|legend=1| 19, 41, 104c, 126, 145, 167, 186 }} | |||
[[Badness]] (Sintel): 11.758 | |||
== Etymology == | == Etymology == | ||
Revision as of 02:02, 18 January 2026
| Interval information |
magi comma
537824/531441, the septimagic comma or magi comma is a no-fives 7-limit comma of measuring 20.7 cents. It is the difference between five 14/9s and two 3/1s.
Temperaments
Tempering out this comma gives the rank-3 septimagic temperament in the full 7-limit, and the magi temperament in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of the magic temperament.
Septimagic
Subgroup: 2.3.5.7
Comma list: 537824/531441
Mapping: [⟨1 0 0 -1], ⟨0 5 0 12], ⟨0 0 1 0]]
- Mapping generators: ~2, ~243/196, ~5
- WE: ~2 = 1199.822 ¢, ~243/196 = 380.604 ¢, ~5 = 2786.312 ¢
- CWE: ~2 = 1200.000 ¢, ~243/196 = 380.638 ¢, ~5 = 2786.523 ¢
Optimal ET sequence: 19, 41, 104c, 126, 145, 167, 186
Badness (Sintel): 11.758
Etymology
The word septimagic is a contraction of septimal magic into a single word.