289/288: Difference between revisions

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 {{Infobox Interval
-| Icon =
+| Name = semitonisma, septendecimal semitones comma, septendecimal 6-cent comma
-| Ratio = 289/288
+| Color name = 17oo2, soso 2nd,<br>Soso comma
-| Monzo = -5 -2 0 0 0 0 2
+| Comma = yes
-| Cents = 6.00082
-| Name = septendecimal semitones comma, <br>septendecimal 6-cent comma
-| Color name = soso comma
-| FJS name = d2<sup>17,17</sup>
-| Sound =
 }}
-'''289/288''', the '''septendecimal semitones comma''' or the '''septendecimal 6-cent comma''', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], as well as between [[17/12]] and [[24/17]]. Tempering it out leads the [[octave]] split into two equal parts, each representing 17/12~24/17. Odd EDOs cannot temper it out.
+'''289/288''', the '''semitonisma''', also described as the ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'', is a [[17-limit]] (also 2.3.17 [[subgroup]]) [[superparticular]] [[comma]] of about 6 [[cent]]s. It is the difference between [[17/16]] and [[18/17]], the two septendecimal semitones, as well as between [[17/12]] and [[24/17]], the two septendecimal tritones. It is also the difference between two stacked [[17/16]] and [[9/8]].
+== Commatic relations ==
+This comma identifies itself as the difference between the following superparticular pairs:
+* [[85/84]] and [[120/119]]
+* [[136/135]] and [[256/255]]
+* [[273/272]] and [[4914/4913]]
+It factors into the following superparticular pairs:
+* [[561/560]] and [[595/594]]
+* [[442/441]] and [[833/832]]
+* [[385/384]] and [[1156/1155]]
+* [[325/324]] and [[2601/2600]]
+== Temperaments ==
+Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
+=== Semitonic ===
+See [[No-fives subgroup temperaments #Semitonic]].
+=== Semitonismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 2 || 0 || 0 || 0 || 0 || 0 || 5 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~17/12, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8
+{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}*
+<nowiki>*</nowiki> [[optimal patent val]]: [[280edo|280]]
+== Etymology ==
+The semitonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''septendecimal semitones comma'' into a single word consisting of Latin ''semi'' ("half") and ''tonus'' ("tone"). However, ''septendecimal semitones comma'' and ''septendecimal 6-cent comma'' were attested much earlier.
 == See also ==
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 * [[List of superparticular intervals]]
-[[Category:Interval ratio]]
+[[Category:Semitonismic]]
-[[Category:17-limit]]
+[[Category:Commas named for the intervals they stack]]
-[[Category:Small comma]]
-[[Category:Superparticular]]