1225/1224: Difference between revisions

VisualWikitext

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 {{Infobox Interval
-| Icon =
+| Name = noellisma
-| Ratio = 1225/1224
+| Color name = 17uzzyy1, subizoyo 1sn,<br>Subizoyo comma
-| Monzo = -3 -2 2 2 0 0 -1
+| Comma = yes
-| Cents = 1.41383
-| Name = noema
-| Color name =
-| Sound =
 }}
-'''1225/1224''', the '''noema''', is a [[17-limit]] (also 2.3.5.7.17 subgroup) [[comma]] measuring about 1.41 [[cent]]s. It is the difference between [[35/34]] and [[36/35]].
+'''1225/1224''', the '''noellisma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] (also 2.3.5.7.17-[[subgroup]]) [[comma]] measuring about 1.41 [[cent]]s. It is the amount by which a stack of two [[7/6]] subminor thirds exceeds [[34/25]], and the amount by which a stack of two [[35/24]] subfifths exceeds [[17/8]], one octave above [[17/16]]. It is also the difference between [[35/34]] and [[36/35]], and between [[49/48]] and [[51/50]].
+== Commatic relations ==
+This comma is the difference between the following superparticular pairs:
+* [[273/272]] and [[351/350]]
+* [[325/324]] and [[442/441]]
+* [[375/374]] and [[540/539]]
+* [[385/384]] and [[561/560]]
+* [[595/594]] and [[1156/1155]]
+* [[625/624]] and [[1275/1274]]
+* [[715/714]] and [[1716/1715]]
+* [[833/832]] and [[2601/2600]]
+* [[1089/1088]] and [[9801/9800]]
+It factors into the following superparticular pairs:
+* [[2401/2400]] and [[2500/2499]]
+* [[2058/2057]] and [[3025/3024]]
+* [[1701/1700]] and [[4375/4374]]
+* [[1275/1274]] and [[31213/31212]]
 == Temperaments ==
-Tempering out this comma results in [[18/17]] being split into two equal parts, each representing 35/34~36/35, and enables the [[25-odd-limit]] essentially tempered '''noemic chords'''.
+[[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.
+Since 1225/1224 factors as (2401/2400)⋅(2500/2499), it would make sense to temper them both out, so noellic can be further tempered to a simple extension of [[breed (temperament)|breed]] that adds prime 17, though it loses accuracy when compared to breed.
+=== Noellic ===
+[[Subgroup]]: 2.3.5.7.17
+{{Mapping|legend=2| 1 0 0 0 -3 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 2 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}}
+{{Optimal ET sequence|legend=1| 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }}
+[[Badness]] (Sintel): 0.0985
+=== Noellismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -3 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}}, ~11/8 = 551.1747{{c}}, ~13/8 = 840.3844{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}}, ~11/8 = 551.2309{{c}}, ~13/8 = 840.4346{{c}}
+{{Optimal ET sequence|legend=1| 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }}
+[[Badness]] (Sintel): 0.578
+== Etymology ==
+The noellisma was named by [[Flora Canou]] in 2022. The name derives from ''Noel'', for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:17-limit]]
+[[Category:Noellismic]]
-[[Category:Unnoticeable comma]]
+[[Category:Commas referencing a famous use of a number]]
-[[Category:Superparticular]]
-[[Category:Noemic]]