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== List of projection pairs ==
== List of projection pairs ==
=== 5-limit ===
=== 5-limit ===
* [[Negri comma|16875/16384]]: <code>3 50625/16384, 5 16384/3375</code> to 2.15
{| class="wikitable"
* [[250/243]]: <code>3 729/250, 5 59049/12500</code> to 2.9/5
|+ Projection pairs for 5-limit temperaments
* [[Magic comma|3125/3072]]: <code>3 3125/1024</code>
|-
* [[Tetracot comma|20000/19683]]: <code>3 20000/6561, 5 2000000000/387420489</code> to 2.9/5
! Temperament !! Associated comma !! Projection pair !! Target subgroup
* [[81/80]]: <code>5 81/16</code>
|-
* [[Würschmidt comma|393216/390625]]: <code>3 390625/131072</code>
| [[Negri]] || [[16875/16384]] || <code>3 50625/16384, 5 16384/3375</code> || 2.15
* [[Semicomma|2109375/2097152]]: <code>3 13348388671875/4398046511104, 5 2097152/421875</code> to 2.75
|-
* [[15625/15552]]: <code>3 46656/15625, 5 15552/3125</code> to 2.5/3
| [[Porcupine]] || [[250/243]] || <code>3 729/250, 5 59049/12500</code> || 2.9/5
* [[Schisma|32805/32768]]: <code>5 32768/6561</code>
|-
| [[Magic]] || [[3125/3072]] || <code>3 3125/1024</code> || 2.5
|-
| [[Tetracot]] || [[20000/19683]] || <code>3 20000/6561, 5 2000000000/387420489</code> || 2.9/5
|-
| [[Meantone]] || [[81/80]] || <code>5 81/16</code> || 2.3
|-
| [[Würschmidt]] || [[393216/390625]] || <code>3 390625/131072</code> || 2.5
|-
| [[Orson]] || [[2109375/2097152]] || <code>3 13348388671875/4398046511104, 5 2097152/421875</code> || 2.75
|-
| [[Hanson]] || [[15625/15552]] || <code>3 46656/15625, 5 15552/3125</code> || 2.5/3
|-
| [[Helmholtz]] || [[32805/32768]] || <code>5 32768/6561</code> || 2.3
|}


=== 7-limit ===
=== 7-limit ===
* [[1029/1000]]: <code>3 1000/343</code> to 2.5.7
{| class="wikitable"
* [[36/35]]: <code>7 36/5</code>
|+ Projection pairs for 7-limit temperaments
* [[525/512]]: <code>7 512/75</code>
|-
* [[49/48]]: <code>3 49/16</code> to 2.5.7
! Temperament !! Associated comma !! Projection pair !! Target subgroup
* [[686/675]]: <code>5 3375/686, 7 675/98</code> to 2.3.7/5
|-
* [[64/63]]: <code>7 64/9</code>
| [[Keegic]] || [[1029/1000]] || <code>3 1000/343</code> || 2.5.7
* [[Blackjackisma|854296875/843308032]]: <code>5 843308032/170859375, 7 5903156224/854296875</code> to 2.3.7/5
|-
* [[Squalentine comma|64827/64000]]: <code>5 320000/64827, 7 64000/9261</code> to 2.3.7/5
| [[Mint]] || [[36/35]] || <code>7 36/5</code> || 2.3.5
* [[875/864]]: <code>7 864/125</code>
|-
* [[3125/3087]]: <code>5 15625/3087, 7 9765625/1361367</code> to 2.3.25/7
| [[Avicennmic]] || [[525/512]] || <code>7 512/75</code> || 2.3.5
* [[2430/2401]]: <code>5 2401/486</code> to 2.3.7
|-
* [[Trimyna comma|50421/50000]]: <code>3 50000/16807</code> to 2.5.7
| [[Semaphoresmic]] || [[49/48]] || <code>3 49/16</code> || 2.5.7
* [[245/243]]: <code>5 243/49</code> to 2.3.7
|-
* [[126/125]]: <code>7 125/18</code>
| [[Sengic]] || [[686/675]] || <code>5 3375/686, 7 675/98</code> || 2.3.7/5
* [[4000/3969]]: <code>5 3969/800, 7 27783/4000</code> to 2.3.7/5
|-
* [[1728/1715]]: <code>5 1728/343</code> to 2.3.7
| [[Archytas]] || [[64/63]] || <code>7 64/9</code> || 2.3.5
* [[1029/1024]]: <code>3 1024/343</code> to 2.5.7
|-
* [[225/224]]: <code>7 225/32</code>
| [[Blackjackismic]] || [[Blackjackisma|854296875/843308032]] || <code>5 843308032/170859375, 7 5903156224/854296875</code> || 2.3.7/5
* [[Cataharry comma|19683/19600]]: <code>3 19600/6561, 7 1033052339200000000/150094635296999121</code> to 2.5.81/7
|-
* [[Mirkwai comma|16875/16807]]: <code>5 84375/16807, 7 16875/2401</code> to 2.3.7/5
| [[Squalentine]] || [[64827/64000]] || <code>5 320000/64827, 7 64000/9261</code> || 2.3.7/5
* [[Hemimage comma|10976/10935]]: <code>5 10976/2187</code> to 2.3.7
|-
* [[3136/3125]]: <code>5 3136/625, 7 68841472/9765625</code> to 2.3.25/7
| [[Keemic]] || [[875/864]] || <code>7 864/125</code> || 2.3.5
* [[5120/5103]]: <code>7 5120/729</code>
|-
* [[6144/6125]]: <code>3 6125/2048</code> to 2.5.7
| [[Gariboh]] || [[3125/3087]] || <code>5 15625/3087, 7 9765625/1361367</code> || 2.3.25/7
* [[Garischisma|33554432/33480783]]: <code>7 33554432/4782969</code>
|-
* [[Wadisma|201768035/201326592]]: <code>5 201326592/40353607</code> to 2.3.7
| [[Nuwell]] || [[2430/2401]] || <code>5 2401/486</code> || 2.3.7
* [[Quasiorwellisma|29360128/29296875]]: <code>7 29296875/4194304</code>
|-
* [[Horwell comma|65625/65536]]: <code>7 65536/9375</code>
| [[Trimyna]] || [[50421/50000]] || <code>3 50000/16807</code> || 2.5.7
* [[Meter|703125/702464]]: <code>5 702464/140625, 7 3454189699072/494384765625</code> to 2.3.25/7
|-
* [[Wizma|420175/419904]]: <code>5 882735153125/176319369216, 7 419904/60025</code> to 2.3.245
| [[Sensamagic]] || [[245/243]] || <code>5 243/49</code> || 2.3.7
* [[2401/2400]]: <code>3 2401/800</code> to 2.5.7
|-
* [[4375/4374]]: <code>7 4374/625</code>
| [[Starling]] || [[126/125]] || <code>7 125/18</code> || 2.3.5
|-
| [[Octagar]] || [[4000/3969]] || <code>5 3969/800, 7 27783/4000</code> || 2.3.7/5
|-
| [[Orwellismic]] || [[1728/1715]] || <code>5 1728/343</code> || 2.3.7
|-
| [[Gamelismic]] || [[1029/1024]] || <code>3 1024/343</code> || 2.5.7
|-
| [[Marvel]] || [[225/224]] || <code>7 225/32</code> || 2.3.5
|-
| [[Cataharry]] || [[19683/19600]] || <code>3 19600/6561, 7 1033052339200000000/150094635296999121</code> || 2.5.81/7
|-
| [[Mirkwai]] || [[16875/16807]] || <code>5 84375/16807, 7 16875/2401</code> || 2.3.7/5
|-
| [[Hemimage]] || [[10976/10935]] || <code>5 10976/2187</code> || 2.3.7
|-
| [[Hemimean]] || [[3136/3125]] || <code>5 3136/625, 7 68841472/9765625</code> || 2.3.25/7
|-
| [[Hemifamity]] || [[5120/5103]] || <code>7 5120/729</code> || 2.3.5
|-
| [[Porwell]] || [[6144/6125]] || <code>3 6125/2048</code> || 2.5.7
|-
| [[Garischismic]] || [[33554432/33480783]] || <code>7 33554432/4782969</code> || 2.3.5
|-
| [[Wadismic]] || [[201768035/201326592]] || <code>5 201326592/40353607</code> || 2.3.7
|-
| [[Quasiorwellismic]] || [[29360128/29296875]] || <code>7 29296875/4194304</code> || 2.3.5
|-
| [[Horwell]] || [[65625/65536]] || <code>7 65536/9375</code> || 2.3.5
|-
| [[Metric]] || [[703125/702464]] || <code>5 702464/140625, 7 3454189699072/494384765625</code> || 2.3.25/7
|-
| [[Wizmic]] || [[420175/419904]] || <code>5 882735153125/176319369216, 7 419904/60025</code> || 2.3.245
|-
| [[Breed]] || [[2401/2400]] || <code>3 2401/800</code> || 2.5.7
|-
| [[Ragismic]] || [[4375/4374]] || <code>7 4374/625</code> || 2.3.5
|}


=== 11-limit ===
=== 11-limit ===
* [[33/32]]: <code>11 32/3</code>
{| class="wikitable"
* [[45/44]]: <code>11 45/4</code>
|+ Projection pairs for 11-limit temperaments
* [[55/54]]: <code>11 54/5</code>
|-
* [[56/55]]: <code>11 56/5</code>
! Temperament !! Associated comma !! Projection pair !! Target subgroup
* [[245/242]]: <code>5 242/49</code> to 2.3.7.11
|-
* [[99/98]]: <code>11 98/9</code>
|  || [[33/32]] || <code>11 32/3</code> || 2.3.5.7
* [[100/99]]: <code>11 100/9</code>
|-
* [[121/120]]: <code>5 121/24</code> to 2.3.7.11
| [[Cake]] || [[45/44]] || <code>11 45/4</code> || 2.3.5.7
* [[1331/1323]]: <code>7 9261/1331, 11 1323/121</code> to 2.3.5.11/7
|-
* [[176/175]]: <code>11 175/16</code>
|  || [[55/54]] || <code>11 54/5</code> || 2.3.5.7
* [[896/891]]: <code>11 896/81</code>
|-
* [[4375/4356]]: <code>7 4356/625</code> to 2.3.5.11
|  || [[56/55]] || <code>11 56/5</code> || 2.3.5.7
* [[Semicanousma|14641/14580]]: <code>5 14641/2916</code> to 2.3.7.11
|-
* [[243/242]]: <code>3 242/81, 11 644204/59049</code> to 2.5.7.11/9
| [[Frostmic]] || [[245/242]] || <code>5 242/49</code> || 2.3.7.11
* [[3388/3375]]: <code>7 3375/484</code> to 2.3.5.11
|-
* [[385/384]]: <code>11 384/35</code>
| [[Mothwellsmic]] || [[99/98]] || <code>11 98/9</code> || 2.3.5.7
* [[8019/8000]]: <code>11 8000/729</code>
|-
* [[441/440]]: <code>11 441/40</code>
| [[Ptolemismic]] || [[100/99]] || <code>11 100/9</code> || 2.3.5.7
* [[1375/1372]]: <code>11 1372/125</code>
|-
* [[6250/6237]]: <code>11 6250/567</code>
| [[Biyatismic]] || [[121/120]] || <code>5 121/24</code> || 2.3.7.11
* [[540/539]]: <code>11 540/49</code>
|-
* [[4000/3993]]: <code>3 4000/1331</code> to 2.5.7.11
|  || [[1331/1323]] || <code>7 9261/1331, 11 1323/121</code> || 2.3.5.11/7
* [[Symbiotic comma|19712/19683]]: <code>11 19683/1792</code>
|-
* [[5632/5625]]: <code>11 5625/512</code>
| [[Valinorsmic]] || [[176/175]] || <code>11 175/16</code> || 2.3.5.7
* [[Argyria|41503/41472]]: <code>7 41472/5929, 11 456533/41472</code> to 2.3.5.77
|-
* [[3025/3024]]: <code>7 3025/432</code> to 2.3.5.11
| [[Pentacircle]] || [[896/891]] || <code>11 896/81</code> || 2.3.5.7
|-
|  || [[4375/4356]] || <code>7 4356/625</code> || 2.3.5.11
|-
| [[Semicanousmic]] || [[14641/14580]] || <code>5 14641/2916</code> || 2.3.7.11
|-
| [[Rastmic]] || [[243/242]] || <code>3 242/81, 11 644204/59049</code> || 2.5.7.11/9
|-
|  || [[3388/3375]] || <code>7 3375/484</code> || 2.3.5.11
|-
| [[Keenanismic]] || [[385/384]] || <code>11 384/35</code> || 2.3.5.7
|-
| [[Trimitone]] || [[8019/8000]] || <code>11 8000/729</code> || 2.3.5.7
|-
| [[Werckismic]] || [[441/440]] || <code>11 441/40</code> || 2.3.5.7
|-
|  || [[1375/1372]] || <code>11 1372/125</code> || 2.3.5.7
|-
|  || [[6250/6237]] || <code>11 6250/567</code> || 2.3.5.7
|-
| [[Swetismic]] || [[540/539]] || <code>11 540/49</code> || 2.3.5.7
|-
|  || [[4000/3993]] || <code>3 4000/1331</code> || 2.5.7.11
|-
| [[Symbiotic]] || [[19712/19683]] || <code>11 19683/1792</code> || 2.3.5.7
|-
|  || [[5632/5625]] || <code>11 5625/512</code> || 2.3.5.7
|-
| [[Argyric]] || [[41503/41472]] || <code>7 41472/5929, 11 456533/41472</code> || 2.3.5.77
|-
| [[Lehmerismic]] || [[3025/3024]] || <code>7 3025/432</code> || 2.3.5.11
|}


[[Category:Lists of intervals]]
[[Category:Lists of intervals]]
[[Category:Just intonation]]
[[Category:Just intonation]]
[[Category:Method]]
[[Category:Method]]
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