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User:Contribution/Exploring Selected Modes in 12-EDO: Difference between revisions

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== Tempered commas ==
== Tempered commas ==
{| class="wikitable center-all left-2 right-3 right-5 left-6"
|+style=white-space:nowrap| Selected 7-limit commas tempered out in 12-tet
! Ratio
! Factorization
! Cents
! Limit
! - Cents
! 1 / Factorization
! 1 / Ratio
|-
| [[81/80]]
| 2<sup>-4</sup> • 3<sup>4</sup> • 5<sup>-1</sup>
| 21.506
| 5
| -21.506
| 2<sup>4</sup> • 3<sup>-4</sup> • 5<sup>1</sup>
| [[80/81]]
|-
| [[128/125]]
| 2<sup>7</sup> • 5<sup>-3</sup>
| 41.059
| 5
| -41.059
| 2<sup>-7</sup> • 5<sup>3</sup>
| [[125/128]]
|-
| [[648/625]]
| 2<sup>3</sup> • 3<sup>4</sup> • 5<sup>-4</sup>
| 62.565
| 5
| -62.565
| 2<sup>-3</sup> • 3<sup>-4</sup> • 5<sup>4</sup>
| [[625/648]]
|-
| [[2048/2025]]
| 2<sup>11</sup> • 3<sup>-4</sup> • 5<sup>-2</sup>
| 19.553
| 5
| -19.553
| 2<sup>-11</sup> • 3<sup>4</sup> • 5<sup>2</sup>
| [[2025/2048]]
|-
|[[6561/6250]]
|2<sup>-1</sup> • 3<sup>8</sup> • 5<sup>-5</sup>
|84.071
|5
| -84.071
|2<sup>1</sup> • 3<sup>-8</sup> • 5<sup>5</sup>
|[[6250/6561]]
|-
|[[32805/32768]]
|2<sup>-15</sup> • 3<sup>8</sup> • 5<sup>1</sup>
|1.954
|5
| -1.954
|2<sup>15</sup> • 3<sup>-8</sup> • 5<sup>-1</sup>
|[[32768/32805]]
|-
| [[36/35]]
| 2<sup>2</sup> • 3<sup>2</sup> • 5<sup>-1</sup> • 7<sup>-1</sup>
| 48.770
| 7
| -48.770
| 2<sup>-2</sup> • 3<sup>-2</sup> • 5<sup>1</sup> • 7<sup>1</sup>
| [[35/36]]
|-
| [[50/49]]
| 2<sup>1</sup> • 5<sup>2</sup> • 7<sup>-2</sup>
| 34.976
| 7
| -34.976
| 2<sup>-1</sup> • 5<sup>-2</sup> • 7<sup>2</sup>
| [[49/50]]
|-
| [[64/63]]
| 2<sup>6</sup> • 3<sup>-2</sup> • 7<sup>-1</sup>
| 27.264
| 7
| -27.264
| 2<sup>-6</sup> • 3<sup>2</sup> • 7<sup>1</sup>
| [[63/64]]
|-
| [[126/125]]
| 2<sup>1</sup> • 3<sup>2</sup> • 5<sup>-3</sup> • 7<sup>1</sup>
| 13.795
| 7
| -13.795
| 2<sup>-1</sup> • 3<sup>-2</sup> • 5<sup>3</sup> • 7<sup>-1</sup>
| [[125/126]]
|-
| [[225/224]]
| 2<sup>-5</sup> • 3<sup>2</sup> • 5<sup>2</sup> • 7<sup>-1</sup>
| 7.712
| 7
| -7.712
| 2<sup>5</sup> • 3<sup>-2</sup> • 5<sup>-2</sup> • 7<sup>1</sup>
| [[224/225]]
|-
| [[256/245]]
| 2<sup>8</sup> • 5<sup>-1</sup> • 7<sup>-2</sup>
| 76.034
| 7
| -76.034
| 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| [[245/256]]
|}


{| class="wikitable center-all left-2 right-3 right-5 left-6 mw-collapsible mw-collapsed"
{| class="wikitable center-all left-2 right-3 right-5 left-6 mw-collapsible mw-collapsed"
Line 340: Line 232:
| 2<sup>-13</sup> • 3<sup>-8</sup> • 5<sup>11</sup>
| 2<sup>-13</sup> • 3<sup>-8</sup> • 5<sup>11</sup>
| [[48828125/53747712]]
| [[48828125/53747712]]
|}
{| class="wikitable center-all left-2 right-3 right-5 left-6"
|+style=white-space:nowrap| Selected 7-limit commas tempered out in 12-tet
! Ratio
! Factorization
! Cents
! Limit
! - Cents
! 1 / Factorization
! 1 / Ratio
| [[36/35]]
| 2<sup>2</sup> • 3<sup>2</sup> • 5<sup>-1</sup> • 7<sup>-1</sup>
| 48.770
| 7
| -48.770
| 2<sup>-2</sup> • 3<sup>-2</sup> • 5<sup>1</sup> • 7<sup>1</sup>
| [[35/36]]
|-
| [[50/49]]
| 2<sup>1</sup> • 5<sup>2</sup> • 7<sup>-2</sup>
| 34.976
| 7
| -34.976
| 2<sup>-1</sup> • 5<sup>-2</sup> • 7<sup>2</sup>
| [[49/50]]
|-
| [[64/63]]
| 2<sup>6</sup> • 3<sup>-2</sup> • 7<sup>-1</sup>
| 27.264
| 7
| -27.264
| 2<sup>-6</sup> • 3<sup>2</sup> • 7<sup>1</sup>
| [[63/64]]
|-
| [[126/125]]
| 2<sup>1</sup> • 3<sup>2</sup> • 5<sup>-3</sup> • 7<sup>1</sup>
| 13.795
| 7
| -13.795
| 2<sup>-1</sup> • 3<sup>-2</sup> • 5<sup>3</sup> • 7<sup>-1</sup>
| [[125/126]]
|-
| [[225/224]]
| 2<sup>-5</sup> • 3<sup>2</sup> • 5<sup>2</sup> • 7<sup>-1</sup>
| 7.712
| 7
| -7.712
| 2<sup>5</sup> • 3<sup>-2</sup> • 5<sup>-2</sup> • 7<sup>1</sup>
| [[224/225]]
|-
| [[256/245]]
| 2<sup>8</sup> • 5<sup>-1</sup> • 7<sup>-2</sup>
| 76.034
| 7
| -76.034
| 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| [[245/256]]
|}
|}
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