User:Contribution/Exploring Selected Modes in 19-EDO: Difference between revisions

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== Mapping ==
sharpness = 1
L = 3 ; s = 2
{| class="wikitable center-all"
!Degree
!Notation
!Approximate Ratios
!Approximate Ratios
!Notation
!Degree
|-
|0
|P1
|<u>1/1</u>
|<u>2/1</u>
|P8
|19
|-
|1
|A1, d2
|
|
|A7, d8
|18
|-
|2
|m2
|16/15, 15/14, <u>14/13</u>, 13/12
|24/13, <u>13/7</u>, 28/15, 15/8
|M7
|17
|-
|3
|M2
|<u>10/9</u>, 9/8
|16/9, <u>9/5</u>
|m7
|16
|-
|4
|A2, d3
|8/7, <u>15/13</u>, 7/6
|12/7, <u>26/15,</u> 7/4
|A6, d7
|15
|-
|5
|m3
|<u>6/5</u>
|<u>5/3</u>
|M6
|14
|-
|6
|M3
|16/13, <u>5/4</u>
|<u>8/5</u>, 13/8
|m6
|13
|-
|7
|A3, d4
|<u>9/7</u>, 13/10
|20/13, <u>14/9</u>
|A5, d6
|12
|-
|8
|P4
|<u>4/3</u>
|<u>3/2</u>
|P5
|11
|-
|9
|A4
|<u>18/13</u>, 7/5
|10/7, <u>13/9</u>
|d5
|10
|}
== Rank-2 5-limit temperaments ==
== Rank-2 5-limit temperaments ==
{| class="wikitable"
{| class="wikitable"
Line 58: Line 141:
!Period
!Period
!Generator
!Generator
!Modes
!Necklace
!Names
!Proposed Name
|-
|-
|19\19
|19\19
|2\19
|2\19
|2 2 2 2 2 1 2 2 2 2
|2 2 2 2 2 1 2 2 2 2
|Negri[10]
|Negri[10]@19edo
|-
|-
|19\19
|19\19
|3\19
|3\19
|1 2 1 2 1 2 1 2 1 2 1 2 1
|1 2 1 2 1 2 1 2 1 2 1 2 1
|Unsmate[13]
|Unsmate[13]@19edo
|-
|-
| rowspan="2" |19\19
| rowspan="2" |19\19
| rowspan="2" |4\19
| rowspan="2" |4\19
|3 1 3 1 3 1 3 1 3
|3 1 3 1 3 1 3 1 3
|Hogzilla[9]
|Hogzilla[9]@19edo
|-
|-
|1 2 1 1 2 1 2 1 1 2 1 1 2 1
|1 2 1 1 2 1 2 1 1 2 1 1 2 1
|Hogzilla[14]
|Hogzilla[14]@19edo
|-
|-
| rowspan="2" |19\19
| rowspan="2" |19\19
| rowspan="2" |5\19
| rowspan="2" |5\19
|1 3 1 1 3 1 3 1 1 3 1
|1 3 1 1 3 1 3 1 1 3 1
|Kleismic[11]
|Kleismic[11]@19edo
|-
|-
|1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
|1 2 1 1 1 2 1 1 1 2 1 1 1 2 1
|Kleismic[15]
|Kleismic[15]@19edo
|-
|-
| rowspan="3" |19\19
| rowspan="3" |19\19
| rowspan="3" |6\19
| rowspan="3" |6\19
|1 4 1 1 4 1 1 1 4 1
|1 4 1 1 4 1 1 1 4 1
|Magic[10]
|Magic[10]@19edo
|-
|-
|1 1 3 1 1 1 3 1 1 1 3 1 1
|1 1 3 1 1 1 3 1 1 1 3 1 1
|Magic[13]
|Magic[13]@19edo
|-
|-
|1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1
|1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1
|Magic[16]
|Magic[16]@19edo
|-
|-
|19\19
|19\19
|7\19
|7\19
|2 1 2 2 2 1 2 2 2 1 2
|2 1 2 2 2 1 2 2 2 1 2
|Sensi[11]
|Sensi[11]@19edo
|-
|-
|19\19
|19\19
|8\19
|8\19
|2 1 2 1 2 2 1 2 1 2 1 2
|2 1 2 1 2 2 1 2 1 2 1 2
|Meantone[12]
|Meantone[12]@19edo
|-
|-
|1\19
|1\19
Line 112: Line 195:
|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|19edo
|19edo
|}
== Mapping ==
sharpness = 1
L = 3 ; s = 2
{| class="wikitable center-all"
!Degree
!Notation
!Approximate Ratios
!Approximate Ratios
!Notation
!Degree
|-
|0
|P1
|<u>1/1</u>
|<u>2/1</u>
|P8
|19
|-
|1
|A1, d2
|
|
|A7, d8
|18
|-
|2
|m2
|16/15, 15/14, <u>14/13</u>, 13/12
|24/13, <u>13/7</u>, 28/15, 15/8
|M7
|17
|-
|3
|M2
|<u>10/9</u>, 9/8
|16/9, <u>9/5</u>
|m7
|16
|-
|4
|A2, d3
|8/7, <u>15/13</u>, 7/6
|12/7, <u>26/15,</u> 7/4
|A6, d7
|15
|-
|5
|m3
|<u>6/5</u>
|<u>5/3</u>
|M6
|14
|-
|6
|M3
|16/13, <u>5/4</u>
|<u>8/5</u>, 13/8
|m6
|13
|-
|7
|A3, d4
|<u>9/7</u>, 13/10
|20/13, <u>14/9</u>
|A5, d6
|12
|-
|8
|P4
|<u>4/3</u>
|<u>3/2</u>
|P5
|11
|-
|9
|A4
|<u>18/13</u>, 7/5
|10/7, <u>13/9</u>
|d5
|10
|}
|}

Latest revision as of 09:47, 3 July 2026

Mapping

sharpness = 1

L = 3 ; s = 2

Degree Notation Approximate Ratios Approximate Ratios Notation Degree
0 P1 1/1 2/1 P8 19
1 A1, d2 A7, d8 18
2 m2 16/15, 15/14, 14/13, 13/12 24/13, 13/7, 28/15, 15/8 M7 17
3 M2 10/9, 9/8 16/9, 9/5 m7 16
4 A2, d3 8/7, 15/13, 7/6 12/7, 26/15, 7/4 A6, d7 15
5 m3 6/5 5/3 M6 14
6 M3 16/13, 5/4 8/5, 13/8 m6 13
7 A3, d4 9/7, 13/10 20/13, 14/9 A5, d6 12
8 P4 4/3 3/2 P5 11
9 A4 18/13, 7/5 10/7, 13/9 d5 10

Rank-2 5-limit temperaments

Period Generator Temperaments 5-limit commas
19\19 1\19 Unicorn 1594323/1562500
19\19 2\19 Negri 16875/16384
19\19 3\19 Unsmate 17578125/16777216
19\19 4\19 Hogzilla 4428675/4194304
19\19 5\19 Kleismic 15625/15552
19\19 6\19 Magic 3125/3072
19\19 7\19 Sensi 78732/78125
19\19 8\19 Meantone 81/80
19\19 9\19 Stump 273375/262144

MOS Modes

Period Generator Necklace Proposed Name
19\19 2\19 2 2 2 2 2 1 2 2 2 2 Negri[10]@19edo
19\19 3\19 1 2 1 2 1 2 1 2 1 2 1 2 1 Unsmate[13]@19edo
19\19 4\19 3 1 3 1 3 1 3 1 3 Hogzilla[9]@19edo
1 2 1 1 2 1 2 1 1 2 1 1 2 1 Hogzilla[14]@19edo
19\19 5\19 1 3 1 1 3 1 3 1 1 3 1 Kleismic[11]@19edo
1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 Kleismic[15]@19edo
19\19 6\19 1 4 1 1 4 1 1 1 4 1 Magic[10]@19edo
1 1 3 1 1 1 3 1 1 1 3 1 1 Magic[13]@19edo
1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 Magic[16]@19edo
19\19 7\19 2 1 2 2 2 1 2 2 2 1 2 Sensi[11]@19edo
19\19 8\19 2 1 2 1 2 2 1 2 1 2 1 2 Meantone[12]@19edo
1\19 1\19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 19edo
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