Escapade comma: Difference between revisions
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ArrowHead294 (talk | contribs) No edit summary |
These inline maths look horrible; I'm taking the liberty of reverting them. Also misc. linking improvements |
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The '''escapade comma''' ( | The '''escapade comma''' ({{monzo|legend=1| 32 -7 -9 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, (4/3)<sup>7</sup>/(5/4)<sup>9</sup>. This can also be written as (5/3)/(16/15)<sup>8</sup>, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]]. In terms of commas, it is equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]], that is, (128/125)<sup>2</sup>/((15625/15552)(81/80)<sup>3</sup>). | ||
== Temperaments == | == Temperaments == | ||
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== Etymology == | == Etymology == | ||
The escapade comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by [[Carl Lumma]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>. | The escapade comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by [[Carl Lumma]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>. | ||
== Notes == | == Notes == | ||
[[Category:Escapade]] | [[Category:Escapade]] | ||
Revision as of 15:23, 24 April 2024
| Interval information |
reduced subharmonic
The escapade comma (monzo: [32 -7 -9⟩) is a small 5-limit comma with a size of 9.492 cents. It is the difference between nine just major thirds and seven just perfect fourths, that is, (4/3)7/(5/4)9. This can also be written as (5/3)/(16/15)8, that is, the difference between a stack of eight classic diatonic semitones and a classic major sixth. In terms of commas, it is equal to two lesser dieses minus three syntonic commas and one kleisma, that is, (128/125)2/((15625/15552)(81/80)3).
Temperaments
Temperaments in the escapade family tempers out this comma.
Etymology
The escapade comma seems to have been named by Paul Erlich in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by Carl Lumma[1].