Septimagic comma: Difference between revisions

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'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup|no-fives]] [[7-limit]] [[comma]] of measuring 20.7 [[cent]]s. It is the difference between five [[14/9]]s and ~~two~~ [[3/1]]s.

'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup|no-fives]] [[7-limit]] [[comma]] measuring 20.7 [[cent]]s. It is the difference between a stack of five [[14/9]]'s and [[9/1]].

== 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. Magi is the no-five restriction of ~~the~~ [[~~Magic|~~magic ~~temperament]].~~

[[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 [[magic]].

~~=== 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 ==

~~The word ''septimagic'' is~~ a contraction of ''septimal magic'' into a single word.

This comma was named by [[Xenllium]] in 2026 as a contraction of ''septimal magic'' into a single word.

== See also ==

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 }}
-'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup|no-fives]] [[7-limit]] [[comma]] of measuring 20.7 [[cent]]s. It is the difference between five [[14/9]]s and two [[3/1]]s.
+'''537824/531441''', the '''septimagic comma''' or '''magi comma''' is a [[2.3.7 subgroup|no-fives]] [[7-limit]] [[comma]] measuring 20.7 [[cent]]s. It is the difference between a stack of five [[14/9]]'s and [[9/1]].
 == 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. Magi is the no-five restriction of the [[Magic|magic temperament]].
+[[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 [[magic]].
-=== 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 ==
-The word ''septimagic'' is a contraction of ''septimal magic'' into a single word.
+This comma was named by [[Xenllium]] in 2026 as a contraction of ''septimal magic'' into a single word.
 == See also ==