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 [[Aaron_Andrew_Hunt|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.)  
'''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 [[Color notation|color name]] refers to both the comma and the temperament created when it is tempered out.
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
| [[User:Royalmilktea|Royalmilktea]] (2022)
|  
|-
|-
| [[Satanic comma]]
| [[Satanic comma]]
Line 136: Line 136:
| [[Gene Ward Smith]] (2003)
| [[Gene Ward Smith]] (2003)
|-
|-
|[[Neon comma]]
| [[Neon comma]]
|Laquinquinbigu
| Laquinquinbigu
|
|
|
|
|[21 60 -50⟩
| {{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]]
|
|
|
|
|
|
|[-875 492 41⟩
| {{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
|[[User:Xenllium|Xenllium]] (2019)
|  
|-
|-
| 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
|
|
|[-306 0 0 109⟩
| {{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
|[[Dawson Berry]] (2020)
|  
|-
|-
| [[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
|[-10 9 3 -4⟩
| {{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
|[[User:Xenllium|Xenllium]] (2019)
|  
|-
|-
| [[Septiruthenia]], septimal ruthenia
| [[Septiruthenia]], septimal ruthenia
Line 617: Line 617:
| {{Monzo| -4 17 1 -9 }}
| {{Monzo| -4 17 1 -9 }}
| 0.11557
| 0.11557
| [[User:Royalmilktea|Royalmilktea]] (2022)
|  
|-
|-
| [[Nommisma]]
| [[Nommisma]]
Line 633: Line 633:
| {{Monzo| 3 -13 10 -2 }}
| {{Monzo| 3 -13 10 -2 }}
| 0.070314
| 0.070314
| [[User:Royalmilktea|Royalmilktea]] (2022)
|  
|-
|-
| 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
| [[User:Royalmilktea|Royalmilktea]] (2022)
|  
|-
|-
| [[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
|[12 -6 -2 2 -1⟩
| {{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 s''eascape comma''
| [[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
|[ 1 0 -6 12 -6⟩
| {{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
| [[Dawson Berry]] (2020)
|  
|-
|-
| 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
| [[Dawson Berry]] (2022)
|  
|-
|-
| [[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
| [[Dawson Berry]] (2021)
|  
|-
|-
| [[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
| [[User:CritDeathX|Nicolai]] (2020)
|  
|-
|-
| [[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
|[13 1 -1 0 0 0 -3⟩
| {{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
|[-3 2 2 -2 0 0 -5 5⟩
| {{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 [-61 60 60 -60⟩
| 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 {{Monzo| 3 2 1 1 -1 -1 }}
| 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 [-4 -2 -1 -1 2⟩
| 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 [-7 -4 4⟩
| 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 {{Monzo|-5 2 -3 -1 -1 -1 0 0 2 2}}
| 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 {{Monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }}
| 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)