Unnoticeable comma: Difference between revisions
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'''Unnoticeable commas''' are very small intervals. These [[comma]]s are called "unnoticeable" because, being equal to or less than 3.5 cents, they are smaller than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] (just-noticeable difference) of human pitch perception, as illustrated by the research of [[ | '''Unnoticeable commas''' are very small intervals. These [[comma]]s are called "unnoticeable" because, being equal to or less than 3.5 cents, they are smaller than the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] ([[just-noticeable difference]]) of human pitch perception, as illustrated by the research of [[Aaron Andrew Hunt]]. It is improbable that even a trained listener would be able to notice these intervals, and as such they a prime target for psychoacoustically informed [[Microtempering|microtempering]]. (However, a considerably larger comma can be unnoticeable in an [[adaptive just intonation|adaptive]] tuning context. Instead of one large pitch shift of the entire comma, there can be many small pitch shifts of a fraction of a comma, one per chord change.) | ||
For commas over 100 cents in size, see [[Large comma]]; for commas in between 30 and 100 cents in size, see [[Medium comma]]; and for commas over 3.5 cents in size, see [[Small comma]]. | For commas over 100 cents in size, see [[Large comma]]; for commas in between 30 and 100 cents in size, see [[Medium comma]]; and for commas over 3.5 cents in size, see [[Small comma]]. | ||
Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[conventions|convention]] elsewhere on the wiki. Except for the 3-limit commas, the [[ | Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[conventions|convention]] elsewhere on the wiki. Except for the 3-limit commas, the [[color notation|color name]] refers to both the comma and the temperament created when it is tempered out. | ||
== List of commas, by prime limit == | == List of commas, by prime limit == | ||
Line 29: | Line 29: | ||
| {{monzo| 485 -306 }} | | {{monzo| 485 -306 }} | ||
| 1.7697 | | 1.7697 | ||
| | | | ||
|- | |- | ||
| [[Satanic comma]] | | [[Satanic comma]] | ||
Line 136: | Line 136: | ||
| [[Gene Ward Smith]] (2003) | | [[Gene Ward Smith]] (2003) | ||
|- | |- | ||
|[[Neon comma]] | | [[Neon comma]] | ||
|Laquinquinbigu | | Laquinquinbigu | ||
| | | | ||
| | | | ||
| | | {{monzo| 21 60 -50 }} | ||
|1.6144 | | 1.6144 | ||
|[[Eliora]] (2024) | | [[Eliora]] (2024) | ||
|- | |- | ||
| [[Septendecima]] | | [[Septendecima]] | ||
Line 192: | Line 192: | ||
| [[User:Xenllium|Xenllium]] (2022) | | [[User:Xenllium|Xenllium]] (2022) | ||
|- | |- | ||
|[[Niobium comma]] | | [[Niobium comma]] | ||
| | | | ||
| | | | ||
| | | | ||
| | | {{Monzo| -875 492 41 }} | ||
|0.72269 | | 0.72269 | ||
|[[Eliora]] (2023) | | [[Eliora]] (2023) | ||
|- | |- | ||
| [[Kwazy comma]] | | [[Kwazy comma]] | ||
Line 302: | Line 302: | ||
| {{Monzo| 161 -84 -12 }} | | {{Monzo| 161 -84 -12 }} | ||
| 0.015361 | | 0.015361 | ||
| | | | ||
|- | |- | ||
| Selenia | | Selenia | ||
Line 409: | Line 409: | ||
| {{Monzo| -16 1 5 1 }} | | {{Monzo| -16 1 5 1 }} | ||
| 2.3495 | | 2.3495 | ||
|[[Gene Ward Smith]] (2005) | | [[Gene Ward Smith]] (2005) | ||
|- | |- | ||
| [[Forge comma]] | | [[Forge comma]] | ||
Line 419: | Line 419: | ||
| [[Dawson Berry]] (2022) | | [[Dawson Berry]] (2022) | ||
|- | |- | ||
|[[109-7-comma]] | | [[109-7-comma]] | ||
| | | | ||
|L<sup>16</sup>z<sup>109</sup>39 | | L<sup>16</sup>z<sup>109</sup>39 | ||
| | | | ||
| | | {{Monzo| -306 0 0 109 }} | ||
|2.0238 | | 2.0238 | ||
|[[Eliora]] (2024) | | [[Eliora]] (2024) | ||
|- | |- | ||
| [[Neptunisma]] | | [[Neptunisma]] | ||
Line 457: | Line 457: | ||
| {{Monzo| -11 2 7 -3 }} | | {{Monzo| -11 2 7 -3 }} | ||
| 1.6283 | | 1.6283 | ||
| | | | ||
|- | |- | ||
| [[Skeetsma]] | | [[Skeetsma]] | ||
Line 467: | Line 467: | ||
| [[User:Jerdle|Jerdle]] (2021) | | [[User:Jerdle|Jerdle]] (2021) | ||
|- | |- | ||
|[[Breeze comma]] | | [[Breeze comma]] | ||
|Laquadru-atriyo | | Laquadru-atriyo | ||
|Lr<sup>4</sup>y<sup>3</sup>-4 | | Lr<sup>4</sup>y<sup>3</sup>-4 | ||
|2460375 / 2458624 | | 2460375 / 2458624 | ||
| | | {{Monzo| -10 9 3 -4 }} | ||
|1.2325 | | 1.2325 | ||
|[[Tristan Bay]] (2024) | | [[Tristan Bay]] (2024) | ||
|- | |- | ||
| [[Wizma]] | | [[Wizma]] | ||
Line 545: | Line 545: | ||
| {{Monzo| -1 -7 4 1 }} | | {{Monzo| -1 -7 4 1 }} | ||
| 0.39576 | | 0.39576 | ||
| | | | ||
|- | |- | ||
| [[Septiruthenia]], septimal ruthenia | | [[Septiruthenia]], septimal ruthenia | ||
Line 617: | Line 617: | ||
| {{Monzo| -4 17 1 -9 }} | | {{Monzo| -4 17 1 -9 }} | ||
| 0.11557 | | 0.11557 | ||
| | | | ||
|- | |- | ||
| [[Nommisma]] | | [[Nommisma]] | ||
Line 633: | Line 633: | ||
| {{Monzo| 3 -13 10 -2 }} | | {{Monzo| 3 -13 10 -2 }} | ||
| 0.070314 | | 0.070314 | ||
| | | | ||
|- | |- | ||
| 171&1547&4973 comma | | 171&1547&4973 comma | ||
Line 724: | Line 724: | ||
| {{Monzo| 9 -2 -4 0 1 }} | | {{Monzo| 9 -2 -4 0 1 }} | ||
| 2.1531 | | 2.1531 | ||
| | | | ||
|- | |- | ||
| [[Nexus comma]], nexisma | | [[Nexus comma]], nexisma | ||
Line 734: | Line 734: | ||
| [[Dawson Berry]] (2020) | | [[Dawson Berry]] (2020) | ||
|- | |- | ||
|[[Reef comma]] | | [[Reef comma]] | ||
|Salubizogu | | Salubizogu | ||
|s1uzzgg3 | | s1uzzgg3 | ||
|200704/200475 | | 200704/200475 | ||
| | | {{Monzo| 12 -6 -2 2 -1 }} | ||
|1.9764 | | 1.9764 | ||
|[[Dawson Berry]] (2022) | | [[Dawson Berry]] (2022) | ||
|- | |- | ||
| [[41503/41472|Argyria]], tinge | | [[41503/41472|Argyria]], tinge | ||
Line 780: | Line 780: | ||
| {{Monzo| -8 3 -4 2 2 }} | | {{Monzo| -8 3 -4 2 2 }} | ||
| 0.89784 | | 0.89784 | ||
| [[User:Tristanbay|Tristan Bay]] (2024) for | | [[User:Tristanbay|Tristan Bay]] (2024) for ''seascape comma'' | ||
|- | |- | ||
| Sesdecal | | Sesdecal | ||
Line 814: | Line 814: | ||
| | | | ||
|- | |- | ||
|[[Sossmarvel comma]] | | [[Sossmarvel comma]] | ||
| Trila-lusepruyoyo | | Trila-lusepruyoyo | ||
| L<sup>3</sup>1ur<sup>7</sup>y<sup>14</sup>-8 | | L<sup>3</sup>1ur<sup>7</sup>y<sup>14</sup>-8 | ||
| 9730975341796875 / 9726998192586752 | | 9730975341796875 / 9726998192586752 | ||
|{{Monzo| -30 13 14 -7 -1 }} | | {{Monzo| -30 13 14 -7 -1 }} | ||
| 0.70772 | | 0.70772 | ||
|[[Dawson Berry]] (2022) | | [[Dawson Berry]] (2022) | ||
|- | |- | ||
| [[3025/3024|Lehmerisma]] | | [[3025/3024|Lehmerisma]] | ||
Line 830: | Line 830: | ||
| [[Gene Ward Smith]] (2004) | | [[Gene Ward Smith]] (2004) | ||
|- | |- | ||
|[[Ptolemi-nicema]] | | [[Ptolemi-nicema]] | ||
| Quinbisa-twethetriluyoyo | | Quinbisa-twethetriluyoyo | ||
| s<sup>10</sup>1u<sup>69</sup>y<sup>138</sup>-8 | | s<sup>10</sup>1u<sup>69</sup>y<sup>138</sup>-8 | ||
| | | | ||
|{{Monzo| 137 -138 138 0 -69 }} | | {{Monzo| 137 -138 138 0 -69 }} | ||
| 0.56437 | | 0.56437 | ||
|[[User:Eliora|Eliora]] (2023) | | [[User:Eliora|Eliora]] (2023) | ||
|- | |- | ||
| [[Elysia]] | | [[Elysia]] | ||
Line 870: | Line 870: | ||
| | | | ||
|- | |- | ||
|[[Countercentisma]] | | [[Countercentisma]] | ||
| | | | ||
| | | | ||
| | | | ||
|{{Monzo| -1 -3300 2700 0 -300 }} | | {{Monzo| -1 -3300 2700 0 -300 }} | ||
| 0.14187 | | 0.14187 | ||
|[[User:CompactStar|CompactStar]] (2024) | | [[User:CompactStar|CompactStar]] (2024) | ||
|- | |- | ||
|[[Spoob]] | | [[Spoob]] | ||
|Tribiluzozogu | | Tribiluzozogu | ||
|1u<sup>6</sup>z<sup>12</sup>g<sup>6</sup>8 | | 1u<sup>6</sup>z<sup>12</sup>g<sup>6</sup>8 | ||
|27682574402 / 27680640625 | | 27682574402 / 27680640625 | ||
| | | {{Monzo|1 0 -6 12 -6 }} | ||
|0.12094 | | 0.12094 | ||
|[[User:Eliora|Eliora]] (2023) | | [[User:Eliora|Eliora]] (2023) | ||
|- | |- | ||
| [[Syntonisma]] | | [[Syntonisma]] | ||
Line 900: | Line 900: | ||
| {{Monzo| -1 -11 -1 0 6 }} | | {{Monzo| -1 -11 -1 0 6 }} | ||
| 0.088931 | | 0.088931 | ||
| | | | ||
|- | |- | ||
| Parisma | | Parisma | ||
Line 1,007: | Line 1,007: | ||
| {{Monzo| 0 2 2 1 -2 -1 }} | | {{Monzo| 0 2 2 1 -2 -1 }} | ||
| 2.1998 | | 2.1998 | ||
| | | | ||
|- | |- | ||
| [[1001/1000|Sinbadma]] | | [[1001/1000|Sinbadma]] | ||
Line 1,015: | Line 1,015: | ||
| {{Monzo| -3 0 -3 1 1 1 }} | | {{Monzo| -3 0 -3 1 1 1 }} | ||
| 1.7303 | | 1.7303 | ||
| | | | ||
|- | |- | ||
| [[4459/4455|Tristanisma]] | | [[4459/4455|Tristanisma]] | ||
Line 1,065: | Line 1,065: | ||
| | | | ||
|- | |- | ||
|[[Pseudovishnuzma]] | | [[Pseudovishnuzma]] | ||
| Sasa-thozosepbigu | | Sasa-thozosepbigu | ||
| ss3ozg<sup>14</sup>5 | | ss3ozg<sup>14</sup>5 | ||
| 6106906624 / 6103515625 | | 6106906624 / 6103515625 | ||
|{{Monzo| 26 0 -14 1 0 1 }} | | {{Monzo| 26 0 -14 1 0 1 }} | ||
| 0.96157 | | 0.96157 | ||
|[[User:Eliora|Eliora]] (2023) | | [[User:Eliora|Eliora]] (2023) | ||
|- | |- | ||
| [[Sercloreminisma]] | | [[Sercloreminisma]] | ||
Line 1,103: | Line 1,103: | ||
| {{Monzo| 12 -2 -1 -1 0 -1 }} | | {{Monzo| 12 -2 -1 -1 0 -1 }} | ||
| 0.42272 | | 0.42272 | ||
| | | | ||
|- | |- | ||
| [[4225/4224|Leprechaun comma]] | | [[4225/4224|Leprechaun comma]] | ||
Line 1,284: | Line 1,284: | ||
| [[Eliora]] (2022) | | [[Eliora]] (2022) | ||
|- | |- | ||
|[[24576/24565|Mavka comma]], archagallisma | | [[24576/24565|Mavka comma]], archagallisma | ||
|Trisu-agu | | Trisu-agu | ||
|17u<sup>3</sup>g-2 | | 17u<sup>3</sup>g-2 | ||
|24576/24565 | | 24576/24565 | ||
| | | {{Monzo| 13 1 -1 0 0 0 -3 }} | ||
|0.77506 | | 0.77506 | ||
|[[Eliora]] (2022) for ''mavka comma'' | | [[Eliora]] (2022) for ''mavka comma'' | ||
|- | |- | ||
| [[2431/2430|Heptacircle comma]] | | [[2431/2430|Heptacircle comma]] | ||
Line 1,316: | Line 1,316: | ||
| [[Flora Canou]] (2023) | | [[Flora Canou]] (2023) | ||
|- | |- | ||
| [[4914/4913|Baladisma | | [[4914/4913|Baladisma]] | ||
]] | |||
| Trisu-athozo | | Trisu-athozo | ||
| 17u<sup>3</sup>3oz-2 | | 17u<sup>3</sup>3oz-2 | ||
Line 1,341: | Line 1,340: | ||
| [[User:Xenllium|Xenllium]] (2023) | | [[User:Xenllium|Xenllium]] (2023) | ||
|- | |- | ||
| Centisma | | [[Centisma]] | ||
| quinquinquadquadso | | quinquinquadquadso | ||
| 17o<sup>400</sup>194 | | 17o<sup>400</sup>194 | ||
| | | | ||
| 2.3.17 {{Monzo|-1001 -400 400}} | | 2.3.17 {{Monzo| -1001 -400 400 }} | ||
| 0.16345 | | 0.16345 | ||
| CompactStar (2023) | | CompactStar (2023) | ||
Line 1,448: | Line 1,447: | ||
| [[User:Xenllium|Xenllium]] (2023) | | [[User:Xenllium|Xenllium]] (2023) | ||
|- | |- | ||
|[[Mercurial comma]] | | [[Mercurial comma]] | ||
|Quinnosu-abiruyo | | Quinnosu-abiruyo | ||
|19o<sup>5</sup>17u<sup>5</sup>rryy-3 | | 19o<sup>5</sup>17u<sup>5</sup>rryy-3 | ||
|557122275 / 556583944 | | 557122275 / 556583944 | ||
| | | {{Monzo| -3 2 2 -2 0 0 -5 5 }} | ||
|1.6736 | | 1.6736 | ||
|[[User:Yourmusic Productions|Yourmusic Productions]] (2020) | | [[User:Yourmusic Productions|Yourmusic Productions]] (2020) | ||
|- | |- | ||
| [[1216/1215|Password, Eratosthenes' comma]] | | [[1216/1215|Password, Eratosthenes' comma]] | ||
Line 1,966: | Line 1,965: | ||
| [[User:Xenllium|Xenllium]] (2023) | | [[User:Xenllium|Xenllium]] (2023) | ||
|- | |- | ||
|[[961/960|Trricesimoprimal quarter-tones comma]] | | [[961/960|Trricesimoprimal quarter-tones comma]] | ||
|Bithiwo-agu | | Bithiwo-agu | ||
| | | | ||
|961/960 | | 961/960 | ||
|2.3.5.31 [-6 -1 -1 2⟩ | | 2.3.5.31 [-6 -1 -1 2⟩ | ||
|1.8024 | | 1.8024 | ||
|[[Godtone]] (2024) | | [[Godtone]] (2024) | ||
|- | |- | ||
| [[1024/1023|Kibisma]] | | [[1024/1023|Kibisma]] | ||
Line 1,980: | Line 1,979: | ||
| 2.3.11.31 {{Monzo| 10 -1 -1 -1 }} | | 2.3.11.31 {{Monzo| 10 -1 -1 -1 }} | ||
| 1.6915 | | 1.6915 | ||
|[[User:Xenllium|Xenllium]] (2023) | | [[User:Xenllium|Xenllium]] (2023) | ||
|- | |- | ||
|[[1025/1024|Kilobytisma]] | | [[1025/1024|Kilobytisma]] | ||
|Fowoyoyo | | Fowoyoyo | ||
|41oyy-2 | | 41oyy-2 | ||
|1025/1024 | | 1025/1024 | ||
|2.5.41 [-10 2 1⟩ | | 2.5.41 [-10 2 1⟩ | ||
|1.6898 | | 1.6898 | ||
|[[CompactStar]] (2024) | | [[CompactStar]] (2024) | ||
|- | |- | ||
| [[1682/1681|Shaftesburisma]] | | [[1682/1681|Shaftesburisma]] | ||
Line 2,006: | Line 2,005: | ||
| [[User:Kaiveran|Kaiveran]] (2023) | | [[User:Kaiveran|Kaiveran]] (2023) | ||
|- | |- | ||
|[[Magnetisma]] | | [[Magnetisma]] | ||
|Tritrila-quinquadtrifo thutweno | | Tritrila-quinquadtrifo thutweno | ||
|L<sup>9</sup>43u<sup>60</sup>29o<sup>60</sup>-8 | | L<sup>9</sup>43u<sup>60</sup>29o<sup>60</sup>-8 | ||
| | | | ||
|2.3.29.43 | | 2.3.29.43 {{monzo| -61 60 60 -60 }} | ||
|0.86936 | | 0.86936 | ||
|[[User:Eliora|Eliora]] (2022) | | [[User:Eliora|Eliora]] (2022) | ||
|- | |- | ||
| [[2520/2519|Platonisma]] | | [[2520/2519|Platonisma]] | ||
Line 2,018: | Line 2,017: | ||
| | | | ||
| 2520/2519 | | 2520/2519 | ||
| 2.3.5.7.11.229 {{ | | 2.3.5.7.11.229 {{monzo| 3 2 1 1 -1 -1 }} | ||
| 0.68713 | | 0.68713 | ||
| [[User:Eliora|Eliora]] (2022) | | [[User:Eliora|Eliora]] (2022) | ||
Line 2,054: | Line 2,053: | ||
| [[User:Xenllium|Xenllium]] (2023) | | [[User:Xenllium|Xenllium]] (2023) | ||
|- | |- | ||
|[[5041/5040|Third brown pair comma]], 19th highly compositema | | [[5041/5040|Third brown pair comma]], 19th highly compositema | ||
| | | | ||
|71oorg1 | | 71oorg1 | ||
|5041/5040 | | 5041/5040 | ||
|2.3.5.7.71 | | 2.3.5.7.71 {{monzo| -4 -2 -1 -1 2 }} | ||
|0.34347 | | 0.34347 | ||
|[[Eliora]] (2022) | | [[Eliora]] (2022) | ||
|- | |- | ||
| [[5292/5291|Bullionisma]] | | [[5292/5291|Bullionisma]] | ||
Line 2,098: | Line 2,097: | ||
| 41u23u19o3o1uz2 | | 41u23u19o3o1uz2 | ||
| 10374/10373 | | 10374/10373 | ||
| 2.3.7.11.13.19.23.41 {{monzo|1 1 1 -1 1 1 -1 -1}} | | 2.3.7.11.13.19.23.41 {{monzo| 1 1 1 -1 1 1 -1 -1 }} | ||
| 0.16689 | | 0.16689 | ||
| [[Francium]] (2024) | | [[Francium]] (2024) | ||
Line 2,110: | Line 2,109: | ||
| [[Francium]] (2024) | | [[Francium]] (2024) | ||
|- | |- | ||
|[[Berylisma]] | | [[Berylisma]] | ||
|Quadthisolu | | Quadthisolu | ||
|37o<sup>4</sup>1u<sup>4</sup>4 | | 37o<sup>4</sup>1u<sup>4</sup>4 | ||
|1874161 / 1874048 | | 1874161 / 1874048 | ||
|2.11.37 | | 2.11.37 {{monzo| -7 -4 4 }} | ||
|0.10439 | | 0.10439 | ||
|[[User:Jerdle|Jerdle]] (2023) | | [[User:Jerdle|Jerdle]] (2023) | ||
|- | |- | ||
| [[Totziensisma]] | | [[Totziensisma]] | ||
| Thiwotwetholurutrigu | | Thiwotwetholurutrigu | ||
|31o23o1urg<sup>3</sup>1 | | 31o23o1urg<sup>3</sup>1 | ||
| 19251/19250 | | 19251/19250 | ||
| 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 0 0 0 1 0 1 }} | | 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 0 0 0 1 0 1 }} | ||
Line 2,182: | Line 2,181: | ||
| [[Budjarn Lambeth]] (2023) | | [[Budjarn Lambeth]] (2023) | ||
|- | |- | ||
|[[Odyssey comma]] | | [[Odyssey comma]] | ||
|Bitwenotwetho-athulurutrigu | | Bitwenotwetho-athulurutrigu | ||
|29oo23oo3u1urg<sup>3</sup>2 | | 29oo23oo3u1urg<sup>3</sup>2 | ||
|4004001/4004000 | | 4004001/4004000 | ||
|2.3.5.7.11.13.23.29 {{ | | 2.3.5.7.11.13.23.29 {{monzo| -5 2 -3 -1 -1 -1 0 0 2 2 }} | ||
|0.00043238 | | 0.00043238 | ||
|[[Tristan Bay]] (2024) | | [[Tristan Bay]] (2024) | ||
|- | |- | ||
| [[Borcherdsma]] | | [[Borcherdsma]] | ||
Line 2,194: | Line 2,193: | ||
| | | | ||
| 160 561 400 000 / 160 561 399 999 | | 160 561 400 000 / 160 561 399 999 | ||
| 2.5.7.11.13.19.29.31.47.59.71 {{ | | 2.5.7.11.13.19.29.31.47.59.71 {{monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }} | ||
| 1.0783 × 10<sup>-8</sup> | | 1.0783 × 10<sup>-8</sup> | ||
| [[User:Akselai|Akselai]] (2024) | | [[User:Akselai|Akselai]] (2024) |