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

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Contribution (talk | contribs)
3,348 edits
Contribution (talk | contribs)
3,348 edits
Undo revision 123203 by Contribution (talk)
Tag: Undo
Line 110: Line 110:


== 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 232: Line 340:
| 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]]
|}
|}

Revision as of 18:18, 3 September 2023

Modes

Modes of limited transposition

Period Modes
1\12 1
2\12 2
3\12 3 ; 1 2
4\12 4 ; 1 3 ; 1 1 2
6\12 6 ; 1 5 ; 2 4 ; 1 1 4 ; 1 2 3 ; 1 3 2 ; 1 1 1 3 ; 1 1 2 2 ; 1 1 1 1 2
12\12 12

Nonatonic modes (tempering out 32805/32768)

Alteration Modes
Schisma 2 2 1 1 1 2 1 1 1

Heptatonic modes (tempering out 5120/5103)

Alteration Modes
Ion 2 2 1 2 2 2 1
Ion b3 2 1 2 2 2 2 1
Ion b6 2 2 1 2 1 3 1
Ion b3 b6 2 1 2 2 1 3 1
Ion b2 1 3 1 2 2 2 1
Ion b2 b3 1 2 2 2 2 2 1
Ion b2 b6 1 3 1 2 1 3 1
Ion b2 b3 b6 1 2 2 2 1 3 1

Pentatonic modes (tempering out 81/80)

Alteration Modes
Tetra 2 5 2 3
Penta MOS 2 2 3 2 3
Penta b7 9 3 3 2 2 2
Penta #5 9 #11 2 2 4 2 2

Blues scales (tempering out 2048/2025)

Added notes Modes
#1 b3 #5/b6 1 1 1 1 3 1 1 3
#1 b3 1 1 1 1 3 2 3
#1 1 1 2 3 2 3
b3 2 1 1 3 2 3
None 2 2 3 2 3


Tempered commas

Selected 7-limit commas tempered out in 12-tet
Ratio Factorization Cents Limit - Cents 1 / Factorization 1 / Ratio
81/80 2-4 • 34 • 5-1 21.506 5 -21.506 24 • 3-4 • 51 80/81
128/125 27 • 5-3 41.059 5 -41.059 2-7 • 53 125/128
648/625 23 • 34 • 5-4 62.565 5 -62.565 2-3 • 3-4 • 54 625/648
2048/2025 211 • 3-4 • 5-2 19.553 5 -19.553 2-11 • 34 • 52 2025/2048
6561/6250 2-1 • 38 • 5-5 84.071 5 -84.071 21 • 3-8 • 55 6250/6561
32805/32768 2-15 • 38 • 51 1.954 5 -1.954 215 • 3-8 • 5-1 32768/32805
36/35 22 • 32 • 5-1 • 7-1 48.770 7 -48.770 2-2 • 3-2 • 51 • 71 35/36
50/49 21 • 52 • 7-2 34.976 7 -34.976 2-1 • 5-2 • 72 49/50
64/63 26 • 3-2 • 7-1 27.264 7 -27.264 2-6 • 32 • 71 63/64
126/125 21 • 32 • 5-3 • 71 13.795 7 -13.795 2-1 • 3-2 • 53 • 7-1 125/126
225/224 2-5 • 32 • 52 • 7-1 7.712 7 -7.712 25 • 3-2 • 5-2 • 71 224/225
256/245 28 • 5-1 • 7-2 76.034 7 -76.034 2-8 • 51 • 72 245/256


All commas tempered out throughout series of 5-odd-limit intervals with all notes distinct, in 12-tet
Ratio Factorization Cents Limit - Cents 1 / Factorization 1 / Ratio
81/80 2-4 • 34 • 5-1 21.506 5 -21.506 24 • 3-4 • 51 80/81
128/125 27 • 5-3 41.059 5 -41.059 2-7 • 53 125/128
648/625 23 • 34 • 5-4 62.565 5 -62.565 2-3 • 3-4 • 54 625/648
2048/2025 211 • 3-4 • 5-2 19.553 5 -19.553 2-11 • 34 • 52 2025/2048
6561/6250 2-1 • 38 • 5-5 84.071 5 -84.071 21 • 3-8 • 55 6250/6561
32805/32768 2-15 • 38 • 51 1.954 5 -1.954 215 • 3-8 • 5-1 32768/32805
82944/78125 210 • 34 • 5-7 103.624 5 -103.624 2-10 • 3-4 • 57 78125/82944
262144/253125 218 • 3-4 • 5-5 60.611 5 -60.611 2-18 • 34 • 55 253125/262144
531441/500000 2-5 • 312 • 5-6 105.578 5 -105.578 25 • 3-12 • 56 500000/531441
531441/524288 2-19 • 312 23.460 3 -23.460 219 • 3-12 524288/531441
2125764/1953125 22 • 312 • 5-9 146.637 5 -146.637 2-2 • 3-12 • 59 1953125/2125764
10616832/9765625 217 • 34 • 5-10 144.683 5 -144.683 2-17 • 3-4 • 510 9765625/10616832
33554432/31640625 225 • 3-4 • 5-8 101.670 5 -101.670 2-25 • 34 • 58 31640625/33554432
53747712/48828125 213 • 38 • 5-11 166.189 5 -166.189 2-13 • 3-8 • 511 48828125/53747712
Retrieved from "https://en.xen.wiki/index.php?title=User:Contribution/Exploring_Selected_Modes_in_12-EDO&oldid=123204"