Nexus comma: Difference between revisions
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Switched the order of this comma's names in anticipation of this article being potentially moved from "Nexuma" to "Nexus comma", as the latter name seems to be more easily accepted, plus the possibility of this comma having additional similar names |
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| Monzo = -16 -3 0 0 6 | | Monzo = -16 -3 0 0 6 | ||
| Cents = 2.04265 | | Cents = 2.04265 | ||
| Name = | | Name = nexus comma, <br> nexuma | ||
| Color name = | | Color name = | ||
| FJS name = | | FJS name = | ||
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The ''' | The '''nexus comma''', otherwise known as the '''nexuma''', is an [[11-limit]] [[unnoticeable comma]] with a ratio of '''1771561/1769472''' and a value of approximately 2 cents. It is the sum of the [[32805/32768|schisma]] and the [[parimo]], the difference between the [[243/242|rastma]] and the [[Alpharabian comma]], and the amount by which a stack of three [[128/121]] Alpharabian diatonic semitones falls short of a [[32/27]] minor third. Tempering it out leads to the joining of the [[11-limit]] and the [[3-limit]], a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the "'''nexus temperament'''"- the source of this comma's names. While the importance of the 3-limit is generally accepted (see [[Pythagorean tuning]], [[circle of fifths]], [[FJS]], [[Helmholtz-Ellis notation]]), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of [[128/121|diatonic semitones]] (see [[Alpharabian tuning]]). For a list of temperaments that temper out the nexuma, see [[nexus family]]. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
Revision as of 18:02, 26 December 2020
| Interval information |
nexuma
The nexus comma, otherwise known as the nexuma, is an 11-limit unnoticeable comma with a ratio of 1771561/1769472 and a value of approximately 2 cents. It is the sum of the schisma and the parimo, the difference between the rastma and the Alpharabian comma, and the amount by which a stack of three 128/121 Alpharabian diatonic semitones falls short of a 32/27 minor third. Tempering it out leads to the joining of the 11-limit and the 3-limit, a fact which, in light of the importance of both p-limits, lends itself to this temperament being dubbed the "nexus temperament"- the source of this comma's names. While the importance of the 3-limit is generally accepted (see Pythagorean tuning, circle of fifths, FJS, Helmholtz-Ellis notation), it can be derived mathematically that the 11-limit is an excellent basis for quartertones in terms of ratio simplicity, and the 11-limit can be shown to host a clear sequence of intervals in which every other member is the octave complement of what is effectively a stack of diatonic semitones (see Alpharabian tuning). For a list of temperaments that temper out the nexuma, see nexus family.