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Gallery of just intervals: Difference between revisions

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Line 28: Line 28:
| [[1/1]]
| [[1/1]]
| 0.000000
| 0.000000
| <ref group=note>The [[Sagittal]] column shows a pitch-class-sensitive [[Sagittal_notation#Athenian|Athenian]] [[Sagittal_notation#Evo|Evo]] notation with 1/1 = C. A white notehead {{sagittal|nhhf|size=300%}} indicates exact notation while black {{sagittal|nhbl|size=300%}} indicates approximate (typically within 2&#x202F;¢).</ref>&numsp;{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| <ref group=note>The [[Sagittal]] column shows a pitch-class-sensitive [[Sagittal_notation#Athenian|Athenian]] [[Sagittal_notation#Evo|Evo]] notation with 1/1 = C. A white notehead {{sagittal|nhhf|size=300%}} indicates exact notation while black {{sagittal|nhbl|size=300%}} indicates approximation (typically within 2&#x202F;¢).</ref>&numsp;{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| w1, wa unison
| w1, wa unison
| P1&numsp;&numsp;<ref group=note>If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them.</ref>
| P1&numsp;&numsp;<ref group=note>If any [[FJS]] names are missing, please [https://misotanni.github.io/fjs/en/calc.html add] them.</ref>
Line 35: Line 35:
| [[32805/32768]]
| [[32805/32768]]
| 1.953721
| 1.953721
| {{sagittal| \! }}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| \! |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| Ly-2, Layo comma
| Ly-2, Layoma
| d-2<sup>5</sup>
| d-2<sup>5</sup>
| schisma ({{Monzo|-15, 8, 1}})
| schisma ({{Monzo|-15, 8, 1}})
Line 43: Line 43:
| 6.775876
| 6.775876
| {{sagittal| |( |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| |( |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| 17ug1, Sugu comma
| 17ug1, Suguma
| P1<sub>85</sub>
| P1<sub>85</sub>
| charisma, charic comma, septendecimal kleisma
| charisma, charic comma, septendecimal kleisma
Line 49: Line 49:
| [[225/224]]
| [[225/224]]
| 7.711523
| 7.711523
| {{sagittal| ~!( }}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| ~!( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| ryy-2, Ruyoyo comma
| ryy-2, Ruyoyoma
| d-2<sup>25</sup><sub>7</sub>
| d-2<sup>25</sup><sub>7</sub>
| septimal kleisma, marvel comma ({{Monzo|-5, 2, 2, -1}})
| septimal kleisma, marvel comma ({{Monzo|-5, 2, 2, -1}})
Line 57: Line 57:
| 13.79477
| 13.79477
| {{sagittal| (|( |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| {{sagittal| (|( |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| zg<sup>3</sup>2, Zotrigu comma
| zg<sup>3</sup>2, Zotriguma
| d2<sup>7</sup><sub>125</sub>
| d2<sup>7</sup><sub>125</sub>
| septimal semicomma, starling comma ({{Monzo|1, 2, -3, 1}})
| septimal semicomma, starling comma ({{Monzo|1, 2, -3, 1}})
Line 64: Line 64:
| 17.39948
| 17.39948
| {{sagittal| ~|( |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| ~|( |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| 1uyy1, Luyoyo comma
| 1uyy1, Luyoyoma
| A1<sup>25</sup><sub>11</sub>
| A1<sup>25</sup><sub>11</sub>
| Ptolemy's comma, ptolemisma
| Ptolemy's comma, ptolemisma
Line 71: Line 71:
| 17.57613
| 17.57613
| {{sagittal| !( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| !( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| 1orr-2, Loruru comma
| 1orr-2, Loruruma
| m-2<sup>11</sup><sub>49</sub>
| m-2<sup>11</sup><sub>49</sub>
| mothwellsma
| mothwellsma
Line 78: Line 78:
| 19.55257
| 19.55257
| {{sagittal| //| |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| {{sagittal| //| |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| sgg2, Sagugu comma
| sgg2, Saguguma
| d2<sub>25</sub>
| d2<sub>25</sub>
| diaschisma ({{Monzo|11, -4, -2}})
| diaschisma ({{Monzo|11, -4, -2}})
Line 85: Line 85:
| 21.50629
| 21.50629
| {{sagittal| /| |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| /| |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| g1, Gu comma
| g1, Guma
| P1<sub>5</sub>
| P1<sub>5</sub>
| meantone comma, syntonic comma, Didymus comma
| meantone comma, syntonic comma, Didymus comma
Line 92: Line 92:
| 23.46001
| 23.46001
| {{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| LLw-2, Lalawa comma
| LLw-2, Lalawama
| d-2
| d-2
| Pythagorean comma, ditonic comma ({{Monzo|-19, 12}})
| Pythagorean comma, ditonic comma ({{Monzo|-19, 12}})
Line 99: Line 99:
| 26.43157
| 26.43157
| {{sagittal| |) |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| 3u1og1, Thulogu comma
| 3u1og1, Thuloguma
| P1<sup>11</sup><sub>65</sub>
| P1<sup>11</sup><sub>65</sub>
| winmeanma
| winmeanma
Line 106: Line 106:
| 26.84138
| 26.84138
| {{sagittal| |) |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| 3oy1, Thoyo comma
| 3oy1, Thoyoma
| P1<sup>65</sup>
| P1<sup>65</sup>
| wilsorma, 13th-partial chroma
| wilsorma, 13th-partial chroma
Line 113: Line 113:
| 27.26409
| 27.26409
| {{sagittal| |) |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| r1, Ru comma
| r1, Ruma
| P1<sub>7</sub>
| P1<sub>7</sub>
| septimal comma, Archytas' comma
| septimal comma, Archytas' comma
Line 120: Line 120:
| 29.61357
| 29.61357
| {{sagittal| |( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| |( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| Ly<span style="vertical-align: super;">5</span>-2, Laquinyo comma
| Ly<span style="vertical-align: super;">5</span>-2, Laquinyoma
| dd-2<sup>3125</sup>
| dd-2<sup>3125</sup>
| magic comma, small diesis ({{Monzo|-10, -1, 5}})
| magic comma, small diesis ({{Monzo|-10, -1, 5}})
Line 127: Line 127:
| 34.97562
| 34.97562
| {{sagittal| )|( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| )|( |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| rryy-2, Biruyo comma
| rryy-2, Biruyoma
| d-2<sup>25</sup><sub>49</sub>
| d-2<sup>25</sup><sub>49</sub>
| small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
| small septimal diesis, small septimal sixth-tone, septimal tritonic diesis, jubilisma
Line 134: Line 134:
| 35.69681
| 35.69681
| {{sagittal| \!/ |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| {{sagittal| \!/ |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| zz2, Zozo comma
| zz2, Zozoma
| m2<sup>49</sup>
| m2<sup>49</sup>
| large septimal diesis, large septimal sixth-tone, slendro diesis, semaphoresma
| large septimal diesis, large septimal sixth-tone, slendro diesis, semaphoresma
Line 141: Line 141:
| 38.90577
| 38.90577
| {{sagittal|(|(|size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal|(|(|size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| 1uy1, Luyo comma
| 1uy1, Luyoma
| A1<sup>5</sup><sub>11</sub>
| A1<sup>5</sup><sub>11</sub>
| undecimal 1/5 tone
| undecimal 1/5 tone
Line 148: Line 148:
| 41.05886
| 41.05886
| {{sagittal| (|\ |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| {{sagittal| (|\ |size=300%}}{{sagittal| bb |size=300%}}{{sagittal|ntDhf|size=400%}}&numsp;&numsp;
| g<span style="vertical-align: super;">3</span>2, Trigu comma
| g<span style="vertical-align: super;">3</span>2, Triguma
| d2<sub>125</sub>
| d2<sub>125</sub>
| diesis, minor diesis, augmented comma, enharmonic comma ({{Monzo|7, 0, -3}})
| diesis, minor diesis, augmented comma, enharmonic comma ({{Monzo|7, 0, -3}})
Line 155: Line 155:
| 43.40834
| 43.40834
| {{sagittal| //| |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| //| |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| Lzyy1, Lazoyoyo comma
| Lzyy1, Lazoyoyoma
| A1<sup>175</sup>
| A1<sup>175</sup>
| Avicenna's enharmonic diesis, avicennma ({{Monzo|-9, 1, 2, 1}})
| Avicenna's enharmonic diesis, avicennma ({{Monzo|-9, 1, 2, 1}})
Line 162: Line 162:
| 48.34767
| 48.34767
| {{sagittal| (!/ |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| (!/ |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| L3o1, Latho comma
| L3o1, Lathoma
| P1<sup>13</sup>
| P1<sup>13</sup>
| tridecimal quartertone, tridecimal flattone comma
| tridecimal quartertone, tridecimal flattone comma
Line 169: Line 169:
| 48.77038
| 48.77038
| {{sagittal| /|) |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| /|) |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| rg1, Rugu comma
| rg1, Ruguma
| P1<sub>35</sub>
| P1<sub>35</sub>
| septimal quarter tone, double comma
| septimal quarter tone, double comma
Line 176: Line 176:
| 49.16614
| 49.16614
| {{sagittal| (!/ |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| {{sagittal| (!/ |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntCbl|size=400%}}&numsp;&numsp;
| y<span style="vertical-align: super;">3</span>1, Triyo comma
| y<span style="vertical-align: super;">3</span>1, Triyoma
| A1<sup>125</sup>
| A1<sup>125</sup>
| porcupine comma ({{Monzo|1, -5, 3}})
| porcupine comma ({{Monzo|1, -5, 3}})
Line 183: Line 183:
| 50.72410
| 50.72410
| {{sagittal| |) |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal| # |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| Lr-2, Laru comma
| Lr-2, Laruma
| d-2<sub>7</sub>
| d-2<sub>7</sub>
| Harrison's comma ({{Monzo|-13, 10, 0, -1}})
| Harrison's comma ({{Monzo|-13, 10, 0, -1}})
Line 213: Line 213:
| z2, zo 2nd
| z2, zo 2nd
| m2<sup>7</sup>
| m2<sup>7</sup>
| small septimal chroma, septimal third-tone, subminor second, septimal minor second
| septimal third-tone, subminor second, septimal minor second
|-
|-
| [[27/26]]
| [[27/26]]
Line 276: Line 276:
| zg2, zogu 2nd
| zg2, zogu 2nd
| m2<sup>7</sup><sub>5</sub>
| m2<sup>7</sup><sub>5</sub>
| minor semitone, large septimal chroma
| septimal chromatic semitone, aberschismic diatonic semitone, minor diatonic semitone
|-
|-
| [[20/19]]
| [[20/19]]
Line 290: Line 290:
| sw2, sawa 2nd
| sw2, sawa 2nd
| m2
| m2
| Pythagorean limma, Pythagorean diatonic semitone, Pythagorean minor second ({{Monzo|8, -5}})
| Pythagorean limma, Pythagorean diatonic semitone, Pythagorean minor second ({{monzo| 8 -5 }})
|-
|-
| [[135/128]]
| [[135/128]]
Line 332: Line 332:
| Lw1, lawa unison
| Lw1, lawa unison
| A1
| A1
| apotome, Pythagorean chromatic semitone, Pythagorean augmented unison ({{Monzo|-11, 7}})
| Pythagorean apotome, Pythagorean chromatic semitone, Pythagorean augmented unison ({{monzo| -11 7 }})
|-
|-
| [[77/72]]
| [[77/72]]
Line 346: Line 346:
| ry1, ruyo unison
| ry1, ruyo unison
| A1<sup>5</sup><sub>7</sub>
| A1<sup>5</sup><sub>7</sub>
| septimal diatonic semitone
| septimal diatonic semitone, aberschismic chromatic semitone, major chromatic semitone
|-
|-
| [[14/13]]
| [[14/13]]
Line 493: Line 493:
| 1orry1, loruruyo unison
| 1orry1, loruruyo unison
| A1<sup>55</sup><sub>49</sub>
| A1<sup>55</sup><sub>49</sub>
| werckismic tone
| werckismic major second
|-
|-
| [[64/57]]
| [[64/57]]
Line 1,095: Line 1,095:
| 17oy4, soyo 4th
| 17oy4, soyo 4th
| P4<sup>85</sup>
| P4<sup>85</sup>
| archagall fourth, septendecimal harmonic fourth
| charismic fourth, septendecimal harmonic fourth
|-
|-
| [[117/88]]
| [[117/88]]
Line 1,102: Line 1,102:
| 3o1u4, tholu 4th
| 3o1u4, tholu 4th
| P4<sup>13</sup><sub>11</sub>
| P4<sup>13</sup><sub>11</sub>
| minthmic fourth ({{Monzo|-3, 2, 0, 0, -1, 1}})
| major-minthmic fourth ({{monzo|-3 2 0 0 -1 1}})
|-
|-
| [[4/3]]
| [[4/3]]
Line 1,522: Line 1,522:
| sg6, sagu 6th
| sg6, sagu 6th
| d6<sub>5</sub>
| d6<sub>5</sub>
| Kirnberger's fifth ("[[12edo|12-EDO]]"-esque fifth)
| Kirnberger's fifth ("[[12edo]]"-esque fifth)
|-
|-
| [[3/2]]
| [[3/2]]
Line 1,536: Line 1,536:
| 3o1uuz6, tholuluzo 6th
| 3o1uuz6, tholuluzo 6th
| m6<sup>7,13</sup><sub>11,11</sub>
| m6<sup>7,13</sup><sub>11,11</sub>
| tridecimal gentle fifth ({{Monzo|1, 0, 0, 1, -2, 1}})
| minor-minthmic fifth ({{monzo| 1 0 0 1 -2 1}})
|-
|-
| [[176/117]]
| [[176/117]]
Line 1,543: Line 1,543:
| 3u1o5, thulo 5th
| 3u1o5, thulo 5th
| P5<sup>11</sup><sub>13</sub>
| P5<sup>11</sup><sub>13</sub>
| minthmic fifth ({{Monzo|4, -2, 0, 0, 1, -1}})
| major-minthmic fifth ({{monzo| 4 -2 0 0 1 -1 }})
|-
|-
| [[128/85]]
| [[128/85]]
Line 1,550: Line 1,550:
| 17ug5, sugu 5th
| 17ug5, sugu 5th
| P5<sub>85</sub>
| P5<sub>85</sub>
| archagall fifth, septendecimal subharmonic fifth
| charismic fifth, septendecimal subharmonic fifth
|-
|-
| [[245/162]]
| [[245/162]]
Line 1,982: Line 1,982:
|1017.596
|1017.596
| {{sagittal| /| |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| /| |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
|g5, gu 7th
|g7, gu 7th
|m7<sub>5</sub>
|m7<sub>5</sub>
|classic minor seventh, large minor seventh
|classic minor seventh, large minor seventh
Line 2,056: Line 2,056:
|tridecimal submajor seventh, 16/3-tone
|tridecimal submajor seventh, 16/3-tone
|-
|-
|[[28/15]]
| [[28/15]]
|1080.557
| 1080.557
| {{sagittal| !( |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| !( |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
|zg8, zogu octave
| zg8, zogu octave
|d8<sup>7</sup><sub>5</sub>
| d8<sup>7</sup><sub>5</sub>
| grave major seventh, octave minus a ruyo aug unison
| septimal grave major seventh, aberschismic diminished octave
|-
|-
|[[15/8]]
|[[15/8]]
Line 2,099: Line 2,099:
|-
|-
|[[19/10]]
|[[19/10]]
|1111.200
|1111.199
| {{sagittal| |) |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal| b |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
|19og8, nogu 8ve
|19og8, nogu 8ve
Line 2,105: Line 2,105:
|undevicesimal diminished octave, Eratosthenes' major seventh
|undevicesimal diminished octave, Eratosthenes' major seventh
|-
|-
|[[40/21]]
| [[40/21]]
|1115.533
| 1115.533
| {{sagittal| |( |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| |( |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
|ry7, ruyo 7th
| ry7, ruyo 7th
|M7<sup>5</sup><sub>7</sub>
| M7<sup>5</sup><sub>7</sub>
|septimal acute major seventh
| septimal acute major seventh, aberschismic major seventh
|-
|-
|[[61/32]]
|[[61/32]]
Line 2,154: Line 2,154:
|lesser tridecimal diminished octave
|lesser tridecimal diminished octave
|-
|-
|[[27/14]]
| [[27/14]]
|1137.039
| 1137.039
| {{sagittal| |) |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
| {{sagittal| |) |size=300%}}{{sagittal|ntBhf|size=400%}}&numsp;&numsp;
|r7, ru 7th
| r7, ru 7th
| M7<sub>7</sub>
| M7<sub>7</sub>
|supermajor seventh, septimal major seventh
| supermajor seventh, septimal major seventh
|-
|-
|[[31/16]]
|[[31/16]]
Line 2,238: Line 2,238:
| [[27/13]]
| [[27/13]]
| 1265.337
| 1265.337
| <ref group=note>The [[Sagittal]] column shows a pitch-class-sensitive [[Sagittal_notation#Athenian|Athenian]] [[Sagittal_notation#Evo|Evo]] notation with 1/1 = C. A white notehead {{sagittal|nhhf|size=300%}} indicates exact notation while black {{sagittal|nhbl|size=300%}} indicates approximate (typically within 2&#x202F;¢).</ref>&hairsp;&hairsp;{{sagittal| (|\ |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| <ref group=note>The [[Sagittal]] column shows a pitch-class-sensitive [[Sagittal_notation#Athenian|Athenian]] [[Sagittal_notation#Evo|Evo]] notation with 1/1 = C. A white notehead {{sagittal|nhhf|size=300%}} indicates exact notation while black {{sagittal|nhbl|size=300%}} indicates approximation (typically within 2&#x202F;¢).</ref>&hairsp;&hairsp;{{sagittal| (|\ |size=300%}}{{sagittal|ntChf|size=400%}}&numsp;&numsp;
| 3u8
| 3u8
| thu8ve&numsp;&numsp;&numsp;&numsp;&numsp;<ref group=note>In the color names, "co" or "c" stands for compound, {{w|Interval (music) #Compound intervals|a conventional music term}}.</ref>
| thu8ve&numsp;&numsp;&numsp;&numsp;&numsp;<ref group=note>In the color names, "co" or "c" stands for compound, {{w|Interval (music) #Compound intervals|a conventional music term}}.</ref>
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