User:Moremajorthanmajor/7L 2s (major tenth-equivalent): Difference between revisions

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This page is about of a [[MOSScales|MOSScale]] with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).
This page is about a [[MOS scale]] with a period of a major tenth and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).


{{Infobox MOS|Equave=5/2|Pattern=LLLsLLLLs|nLargeSteps=7|nSmallSteps=2|Name=Superdiatonic}}
==Name==
The author suggests the name '''Terra Rubra''' for this scale.


==Name==
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
==Temperaments==
==Temperaments==
If you're looking for highly accurate scales (that is, ones that approximate gamelan closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, if 688 cents is an acceptable ‘25/17' to you), then the harmonic entropy minimum of Terra Rubra is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Terra Rubra Superdiatonic" or simply 'Superdiatonic'.
 
=== Terra Rubra-Meantone ===
[[Subgroup]]: 5/2.2.3
 
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~3/2 = 696.8737¢
 
[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]
 
[[Optimal ET sequence]]: [[9ed5/2]], [[16ed5/2]], [[25ed5/2]]
 
=== Terra Rubra-Superpyth ===
[[Subgroup]]: 18/7.2.3
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~3/2 = 708.4011¢
 
[[Mapping]]: [⟨1 1 1], ⟨0 -2 -1]]
 
[[Optimal ET sequence]]: [[7ed18/7]], [[16ed18/7]], [[23ed18/7]], [[30ed18/7]]
 
==Scale tree==
==Scale tree==
{| class="wikitable"
{| class="wikitable"
|-
|-
! colspan="3" |Generator
!Generator
! |<span style="display: block; text-align: center;">'''Generator size (normalized )'''</span>
! |Generator size
!<span style="display: block; text-align: center;">'''Generator size (ed4\3)'''</span>
!L
! |Pentachord steps
!s
! |Comments
!Comments
|-
|-
| |4\[[7edo|7]]
| |4\[[7ed5/2|7]]
| |
| |<u>960.000</u>
| |
|1
| |<u>960</u>
|0
|''914.285…''
|
| |<nowiki>1 1|1 0</nowiki>
| |
|-
|-
|25\44
|25\44
|
|<u>937.500</u>
|
|6
|<u>937.5</u>
|1
|''909.{{Overline|09}}''
|<nowiki>6 6|6 1</nowiki>
|
|
|-
|-
|
|71\129
|71\125
|<u>936.263</u>
|
|17
|<u>936.263…</u>
|3
|''908.8''
|<nowiki>17 17|17 3</nowiki>
|
|
|-
|-
|
|46\81
|46\81
|
|<u>935.593</u>
|<u>935.593…</u>
|11
|''908.641…''
|2
|<nowiki>11 11|11 2</nowiki>
|
|
|-
|-
|
|67\118
|67\118
|
|<u>934.884</u>
|<u>934.883…</u>
|16
|''908.474…''
|3
|<nowiki>16 16|16 3</nowiki>
|
|
|-
|-
| |21\37
| |21\37
| |
| |<u>933.333</u>
| |
|5
| |<u>933.{{Overline|3}}</u>
|1
|''908.{{Overline|108}}''
| |<nowiki>5 5|5 1</nowiki>
| |
| |
|-
|-
|
|80\141
|80\141
|
|<u>932.039</u>
|<u>932.038…</u>
|19
|''907.801…''
|4
|<nowiki>19 19|19 4</nowiki>
|
|
|-
|-
|
|59\104
|59\104
|
|<u>931.579</u>
|<u>931.579…</u>
|14
|''907.692…''
|3
|<nowiki>14 14|14 3</nowiki>
|
|
|-
|-
|
|38\67
|38\67
|
|<u>930.612</u>
|<u>930.612…</u>
|9
|''907.462…''
|2
|<nowiki>9 9|9 2</nowiki>
|
|
|-
|-
|
|55\97
|55\97
|
|<u>929.577</u>
|<u>929.577…</u>
|13
|''907.216…''
|3
|<nowiki>13 13|13 3</nowiki>
|
|
|-
|-
|
|72\127
|72\127
|
|<u>929.032</u>
|<u>929.032…</u>
|17
|''907.086…''
|4
|<nowiki>17 17|17 4</nowiki>
|
|
|-
|-
|
|89\157
|89\157
|
|<u>928.696</u>
|<u>928.695…</u>
|21
|''907.006…''
|5
|<nowiki>21 21|21 5</nowiki>
|
|
|-
|-
| |17\30
| |17\30
| |<u>927.273</u>
|4
|1
| |
| |
| |
| |<u>927.{{Overline|27}}</u>
|''906.{{Overline|6}}''
| |<nowiki>4 4|4 1</nowiki>
| |L/s = 4
|-
|-
|
|115\203
|115\203
|
|<u>926.174</u>
|<u>926.174…</u>
|27
|''906.403…''
|7
|<nowiki>27 27|27 7</nowiki>
|
|
|-
|-
|
|98\173
|98\173
|
|<u>925.984</u>
|<u>925.984…</u>
|23
|''906.358…''
|6
|<nowiki>23 23|23 6</nowiki>
|
|
|-
|-
|
|81\143
|81\143
|
|<u>925.714</u>
|<u>925.714…</u>
|19
|''906.293…''
|5
|<nowiki>19 19|19 5</nowiki>
|
|
|-
|-
|
|64\113
|64\113
|
|<u>925.301</u>
|<u>925.301…</u>
|15
|''906.194…''
|4
|<nowiki>15 15|15 4</nowiki>
|
|
|-
|-
|
|47\83
|47\83
|
|<u>924.590</u>
|<u>924.591…</u>
|11
|''906.024…''
|3
|<nowiki>11 11|11 3</nowiki>
|
|
|-
|-
| |
| |30\53
| |30\53
| |
| |<u>923.077</u>
| |<u>923.076…</u>
|7
|''905.660…''
|2
| |<nowiki>7 7|7 2</nowiki>
| |
| |
|-
|-
|
|
|73\129
|73\129
|<u>922.105…</u>
|<u>922.105</u>
|''905.426…''
|17
|<nowiki>17 17|17 5</nowiki>
|5
|
|
|-
|-
| |
| |43\76
| |43\76
| |
| |<u>921.429</u>
| |<u>921.428…</u>
|10
|''905.263…''
|3
| |<nowiki>10 10|10 3</nowiki>
| |
| |
|-
|-
| |
| |56\99
| |56\99
| |
| |<u>920.548</u>
| |<u>920.547…</u>
|13
|''905.{{Overline|05}}''
|4
| |<nowiki>13 13|13 4</nowiki>
| |
| |
|-
|-
| |
| |69\122
| |69\122
| |
| |<u>920.000</u>
| |<u>920</u>
|16
|''904.918…''
|5
| |<nowiki>16 16|16 5</nowiki>
| |
| |
|-
|-
| |
| |82\145
| |82\145
| |
| |<u>919.626</u>
| |<u>919.626…</u>
|19
|''904.827…''
|6
| |<nowiki>19 19|19 6</nowiki>
| |
| |
|-
|-
| |
| |95\168
| |95\168
| |
| |<u>919.355</u>
| |<u>919.354…</u>
|22
|''904.761…''
|7
| |<nowiki>22 22|22 7</nowiki>
| |
| |
|-
|-
| |
| |
| |<u>919.340</u>
|π
|1
| |
| |
| |
| |<u>919.340…</u>
|''904.758…''
| |<nowiki>π π|π 1</nowiki>
| |L/s = π
|-
|-
| |
| |108\191
| |108\191
| |
| |<u>919.149</u>
| |<u>919.148…</u>
|25
|''904.712…''
|8
| |<nowiki>25 25|25 8</nowiki>
| |
| |
|-
|-
| |
| |121\214
| |121\214
| |
| |<u>918.987</u>
| |<u>918.987…</u>
|28
|''904.672…''
|9
| |<nowiki>28 28|28 9</nowiki>
| |28;9 Superdiatonic 1/28-tone
|-
| |
| |134\237
| |
| |<u>918.857…</u>
|''904.642…''
| |<nowiki>31 31|31 10</nowiki>
| |
| |
|-
|-
| |13\23
| |13\23
| |<u>917.647</u>
|3
|1
| |
| |
| |
| |<u>917.647…</u>
|''904.347…''
| |<nowiki>3 3|3 1</nowiki>
| |Terra Rubra 1/3-tone
|-
| |
| |126\223
| |
| |<u>916.{{Overline|36}}</u>
|''904.035…''
| |<nowiki>29 29|29 10</nowiki>
| |Terra Rubra <span style="font-size: 12.8000001907349px;"><big>1/29-tone</big></span>
|-
| |
| |113\200
| |
| |<u>916.{{Overline|216}}</u>
|''904''
| |<nowiki>26 26|26 9</nowiki>
| |Terra Rubra <span style="font-size: 12.8000001907349px;"><big>1/26-tone</big></span>
|-
|-
| |
| |100\177
| |100\177
| |
| |<u>916.031</u>
| |<u>916.030…</u>
|23
|''903.954…''
|8
| |<nowiki>23 23|23 8</nowiki>
| |
| |
|-
|-
| |
| |87\154
| |87\154
| |
| |<u>915.789</u>
| |<u>915.789…</u>
|20
|''903.896…''
|7
| |<nowiki>20 20|20 7</nowiki>
| |
| |
|-
|-
| |
| |74\131
| |74\131
| |<u>915.464</u>
|17
|6
| |
| |
| |<u>915.463…</u>
|''903.816…''
| |<nowiki>17 17|17 6</nowiki>
| |Terra Rubra 1/17-tone
|-
|-
| |
| |61\108
| |61\108
| |<u>915.000</u>
|14
|5
| |
| |
| |<u>915</u>
|''903.{{Overline|703}}''
| |<nowiki>14 14|14 5</nowiki>
| |Terra Rubra 1/14-tone
|-
|-
| |
| |
| |109\193
| |<u>914.685…</u>
|''903.626…''
| |<nowiki>25 25|25 9</nowiki>
| |Terra Rubra 1/25-tone
|-
| |
| |48\85
| |48\85
| |<u>914.286</u>
|11
|4
| |
| |
| |<u>914.286…</u>
|''903.529…''
| |<nowiki>11 11|11 4</nowiki>
| |Terra Rubra 1/11-tone
|-
|-
| |
| |
| |
| |<u>913.821</u>
| |
|e
| |<u>913.820…</u>
|1
|''903.415…''
| |<nowiki>e e|e 1</nowiki>
| |L/s = e
| |L/s = e
|-
|-
| |
| |35\62
| |35\62
| |<u>913.043</u>
|8
|3
| |
| |
| |<u>913.043…</u>
|''903.225…''
| |<nowiki>8 8|8 3</nowiki>
| |Terra Rubra 1/8-tone
|-
|-
| |
| |
| |
| |<u>912.287</u>
| |92\163
|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>+1
| |<u>912.396…</u>
|1
|''903.067…''
| |Split <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> superdiatonic relation
| |<nowiki>21 21|21 8</nowiki>
| |21;8 Superdiatonic 1/21-tone
|-
|-
| |57\101
| |<u>912.000</u>
|13
|5
| |
| |
| |
| |
| |<u>912.286…</u>
|''903.040…''
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ+1 φ+1|φ+1 1</nowiki></span>
| |Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)
|-
| |
| |
| |57\101
| |<u>912</u>
|''902.970…''
| |<nowiki>13 13|13 5</nowiki>
| |13;5 Superdiatonic 1/13-tone
|-
|-
|
|
|79\140
|79\140
|<u>911.538…</u>
|<u>911.538</u>
|''902.857…''
|18
|<nowiki>18 18|18 7</nowiki>
|7
|
|
|-
|-
| |
| |22\39
| |22\39
| |<u>910.345</u>
|5
|2
| |
| |
| |<u>910.344…</u>
|''902.564…''
| |<nowiki>5 5|5 2</nowiki>
| |Terra Rubra 1/5-tone
|-
|-
| |75\133
| |<u>909.091</u>
|17
|7
| |
| |
| |
| |75\133
| |<u>909.0̄9̄</u>
|''902.255…''
| |<nowiki>17 17|17 7</nowiki>
| |17;7 Superdiatonic 1/17-tone
|-
|-
| |
| |
| |53\94
| |53\94
| |<u>908.571…</u>
| |<u>908.571</u>
|''902.127…''
|12
| |<nowiki>12 12|12 5</nowiki>
|5
| |
| |
|-
|-
| |
| |31\55
| |31\55
| |<u>907.317</u>
|7
|3
| |
| |
| |<u>907.317…</u>
|''901.{{Overline|81}}''
| |<nowiki>7 7|7 3</nowiki>
| |7;3 Superdiatonic 1/7-tone
|-
|-
|
|
|71\126
|71\126
|<u>906.382…</u>
|<u>906.383</u>
|''901.587…''
|16
|<nowiki>16 16|16 7</nowiki>
|7
|
|
|-
|-
| |
| |40\71
| |40\71
| |<u>905.660</u>
|9
|4
| |
| |
| |<u>905.660…</u>
|''901.408…''
| |<nowiki>9 9|9 4</nowiki>
| |9;4 Superdiatonic 1/9-tone
|-
| |
| |49\87
| |
| |<u>904.615…</u>
|''901.149…''
| |<nowiki>11 11|11 5</nowiki>
| |11;5 Superdiatonic 1/11-tone
|-
|-
| |…
| |…
|…
|…
| |
| |
| |58\103
| |
| |<u>903.896…</u>
|''900.970…''
| |<nowiki>13 13|13 6</nowiki>
| |13;6 Superdiatonic 1/13-tone
|-
|
|67\119
|
|<u>903.370…</u>
|''900.840…''
|<nowiki>15 15|15 7</nowiki>
|
|-
|
|76\135
|
|<u>902.970…</u>
|''900.{{Overline|740}}''
|<nowiki>17 17|17 7</nowiki>
|
|-
|-
|
|229\305
|85\151
|<u>900.983</u>
|
|51
|<u>902.654…</u>
|25
|''900.662…''
|<nowiki>19 19|19 9</nowiki>
|
|-
|
|94\167
|
|<u>902.4</u>
|''900.598…''
|<nowiki>21 21|21 10</nowiki>
|
|-
|
|103\183
|
|<u>902.189…</u>
|''900.564…''
|<nowiki>23 23|23 11</nowiki>
|
|-
|
|112\199
|
|<u>902.013…</u>
|''900.502…''
|<nowiki>25 25|25 12</nowiki>
|
|-
|
|121\215
|
|<u>901.863…</u>
|''900.465…''
|<nowiki>27 27|27 13</nowiki>
|
|
|-
|-
| |9\16
| |9\16
| |
| |<u>900.000</u>
| |
|2
| |<u>900</u>
|1
|''900''
| |<nowiki>2 2|2 1</nowiki>
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
|-
|-
|
|230\397
|230\409
|<u>899.023</u>
|
|51
|<u>899.022…</u>
|26
|''898.755…''
|<nowiki>51 51|51 26</nowiki>
|
|-
|
|221\393
|
|<u>898.983…</u>
|''889.745…''
|<nowiki>49 49|49 25</nowiki>
|
|-
|
|212\377
|
|<u>898.939…</u>
|''899.734…''
|<nowiki>47 47|47 24</nowiki>
|
|-
|
|203\361
|
|<u>898.892…</u>
|''899.722…''
|<nowiki>45 45|45 23</nowiki>
|
|-
|
|194\345
|
|<u>898.841…</u>
|''899.710…''
|<nowiki>43 43|43 22</nowiki>
|
|-
|
|185\329
|
|<u>898.785…</u>
|''899.696…''
|<nowiki>41 41|41 21</nowiki>
|
|-
|
|176\313
|
|<u>898.723…</u>
|''899.680…''
|<nowiki>39 39|39 20</nowiki>
|
|-
|
|167\297
|
|<u>898.654…</u>
|''899.663…''
|<nowiki>37 37|37 19</nowiki>
|
|-
|
|158\281
|
|<u>898.578…</u>
|''899.644…''
|<nowiki>35 35|35 18</nowiki>
|
|-
|
|149\265
|
|<u>898.492…</u>
|''899.622…''
|<nowiki>33 33|33 17</nowiki>
|
|-
|
|140\249
|
|<u>898.395…</u>
|''899.598…''
|<nowiki>31 31|31 16</nowiki>
|
|-
|
|131\233
|
|<u>898.285…</u>
|''899.570…''
|<nowiki>29 29|29 15</nowiki>
|
|-
|
|122\217
|
|<u>898.159…</u>
|''899.539…''
|<nowiki>27 27|27 14</nowiki>
|
|-
|
|113\201
|
|<u>898.013…</u>
|''899.502…''
|<nowiki>25 25|25 13</nowiki>
|
|-
|
|104\185
|
|<u>897.841…</u>
|''899.459…''
|<nowiki>23 23|23 12</nowiki>
|
|-
|
|95\169
|
|<u>897.637…</u>
|''899.408…''
|<nowiki>21 21|21 11</nowiki>
|
|-
|
|86\153
|
|<u>897.391…</u>
|''899.346…''
|<nowiki>19 19|19 10</nowiki>
|
|
|-
|-
|
|…
|77\137
|…
|
|…
|<u>897.087…</u>
|…
|''899.270…''
|<nowiki>17 17|17 9</nowiki>
|
|
|-
|-
|
|68\121
|
|<u>896.703…</u>
|''899.173…''
|<nowiki>15 15|15 8</nowiki>
|
|-
| |
| |59\105
| |
| |<u>896.202…</u>
|''899.047…''
| |<nowiki>13 13|13 7</nowiki>
| |Terra Rubra 1/13-tone
|-
| |
| |50\89
| |
| |<u>895.522…</u>
|''898.876…''
| |<nowiki>11 11|11 6</nowiki>
| |Terra Rubra 1/11-tone
|-
| |
| |41\73
| |41\73
| |<u>894.545</u>
|9
|5
| |
| |
| |<u>894.5̄4̄</u>
|''898.630…''
| |<nowiki>9 9|9 5</nowiki>
| |Terra Rubra 1/9-tone
|-
|-
| |
| |32\57
| |32\57
| |
| |<u>893.023</u>
| |<u>893.023…</u>
|7
|''898.245…''
|4
| |<nowiki>7 7|7 4</nowiki>
| |<span style="font-size: 12.8000001907349px;"><big>the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b'</big></span>
| |Terra Rubra 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b')</span>
|-
|-
| |
| |
| |<u>892.459</u>
|
|
| |
| |
| |
| |<u>892.459…</u>
|''898.102…''
| |<span style="background-color: #ffffff;"><nowiki>√3 √3|√3 1</nowiki></span>
| |
|-
|-
| |
|87\155
| |
|<u>892.307</u>
|19
|11
|
|-
| |55\98
| |55\98
| |<u>891.{{Overline|891}}</u>
| |<u>891.892</u>
|''897.959…''
|12
| |<nowiki>12 12|12 7</nowiki>
|7
| |
|-
| |
| |
| |
| |78\139
| |<u>891.428…</u>
|''897.841…''
| |<nowiki>17 17|17 10</nowiki>
| |Terra Rubra 1/17-tone
|-
|-
| |
| |23\41
| |23\41
| |
| |<u>890.323</u>
| |<u>890.323…</u>
|5
|''897.560…''
|3
| |<nowiki>5 5|5 3</nowiki>
| |Golden Terra Rubra 1/5-tone
| |5;3 Golden Terra Rubra 1/5-tone
|-
|-
|
|
|83\148
|83\148
|<u>889.285…</u>
|<u>889.286</u>
|''897.{{Overline|297}}''
|18
|<nowiki>18 18|18 11</nowiki>
|11
|
|
|-
|-
| |
| |
| |60\107
| |60\107
| |<u>888.{{Overline|8}}</u>
| |<u>888.889</u>
|''897.196…''
|13
| |<nowiki>13 13|13 8</nowiki>
|8
| |13;8 Golden Terra Rubra 1/13-tone
| |Golden Terra Rubra 1/13-tone
|-
|-
| |
| |
| |
| |<u>888.643</u>
| |
|<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span>
| |<u>888.643…</u>
|1
|''897.133…''
| |<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;"><nowiki>φ φ|φ 1</nowiki></span>
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
| |GOLDEN Terra Rubra (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span>
|-
|-
| |
| |
| |97\173
| |<u>888.549…</u>
|''897.109…''
| |<nowiki>21 21|21 13</nowiki>
| |21;13 Golden Terra Rubra 1/21-tone
|-
| |
| |37\66
| |37\66
| |
| |<u>888.000</u>
| |<u>888</u>
|8
|''896.{{Overline|96}}''
|5
| |<nowiki>8 8|8 5</nowiki>
| |Golden Terra Rubra 1/8-tone
| |8;5 Golden Terra Rubra 1/8-tone
|-
|-
|
|
|88\157
|88\157
|<u>887.394…</u>
|<u>887.395</u>
|''896.815…''
|19
|<nowiki>19 19|19 12</nowiki>
|12
|
|
|-
|-
| |
| |51\91
| |51\91
| |<u>886.957</u>
|11
|7
| |
| |
| |<u>886.956…</u>
|''896.703…''
| |<nowiki>11 11|11 7</nowiki>
| |11;7 Superdiatonic 1/11-tone
|-
|-
| |
| |
| |
| |<u>886.933…</u>
|''896.697…''
| |<nowiki>π π|π 2</nowiki>
| |
|-
| |
| |
| |116\207
| |<u>886.624…</u>
|''896.618…''
| |<nowiki>25 25|25 16</nowiki>
| |25;16 Superdiatonic 1/25-tone
|-
| |
| |65\116
| |65\116
| |<u>886.364</u>
|14
|9
| |
| |
| |<u>886.{{Overline|36}}</u>
|''896.551…''
| |<nowiki>14 14|14 9</nowiki>
| |14;9 Superdiatonic 1/14-tone
|-
|-
| |
| |79\141
| |79\141
| |<u>885.981</u>
|17
|11
| |
| |
| |<u>885.981…</u>
|''896.453…''
| |<nowiki>17 17|17 11</nowiki>
| |17;11 Superdiatonic 1/17-tone
|-
|-
| |
| |93\166
| |93\166
| |
| |<u>885.714</u>
| |<u>885.714…</u>
|20
|''896.385…''
|13
| |<nowiki>20 20|20 13</nowiki>
| |
| |
|-
| |
| |107\191
| |
| |<u>885.517…</u>
|''896.335…''
| |<nowiki>23 23|23 15</nowiki>
| |
|-
| |
| |121\216
| |
| |<u>885.365…</u>
|''896.{{Overline|296}}''
| |<nowiki>26 26|26 17</nowiki>
| |26;17 Superdiatonic 1/26-tone
|-
| |
| |135\241
| |
| |<u>885.245…</u>
|''896.265…''
| |<nowiki>29 29|29 19</nowiki>
| |29;19 Superdiatonic 1/29-tone
|-
|-
| |14\25
| |14\25
| |
| |<u>884.211</u>
| |
|3
| |<u>884.210…</u>
|2
|''896''
| |Golden Terra Rubra 1/3-tone
| |<nowiki>3 3|3 2</nowiki>
| |3;2 Golden Terra Rubra 1/3-tone
|-
| |
| |145\259
| |
| |<u>883.248…</u>
|''895.752…''
| |<nowiki>31 31|31 21</nowiki>
| |31;21 Superdiatonic 1/31-tone
|-
| |
| |131\234
| |
| |<u>883.146…</u>
|''895.726…''
| |<nowiki>28 28|28 19</nowiki>
| |28;19 Superdiatonic 1/28-tone
|-
|-
| |
| |117\209
| |117\209
| |
| |<u>883.019</u>
| |<u>883.018…</u>
|25
|''895.693…''
|17
| |<nowiki>25 25|25 17</nowiki>
| |
| |
|-
|-
| |
| |103\184
| |103\184
| |
| |<u>882.857</u>
| |<u>882.857…</u>
|22
|''895.652…''
|15
| |<nowiki>22 22|22 15</nowiki>
| |
| |
|-
|-
| |
| |89\159
| |89\159
| |
| |<u>882.645</u>
| |<u>882.644…</u>
|19
|''895.579…''
|13
| |<nowiki>19 19|19 13</nowiki>
| |
| |
|-
|-
| |
| |75\134
| |75\134
| |
| |<u>882.353</u>
| |<u>882.353…</u>
|16
|''895.522…''
|11
| |<nowiki>16 16|16 11</nowiki>
| |
| |
|-
|-
| |
| |61\109
| |61\109
| |
| |<u>881.928</u>
| |<u>881.927…</u>
|13
|''895.412…''
|9
| |<nowiki>13 13|13 9</nowiki>
| |
| |
|-
|-
| |
| |47\84
| |47\84
| |
| |<u>881.250</u>
| |<u>881.25</u>
|10
|''895.238…''
|7
| |<nowiki>10 10|10 7</nowiki>
| |
| |
|-
|-
|
|
|80\143
|<u>880.733…</u>
|''895.104…''
|<nowiki>17 17|17 12</nowiki>
|
|-
| |
| |33\59
| |33\59
| |
| |<u>880.000</u>
| |<u>880</u>
|7
|''894.915…''
|5
| |<nowiki>7 7|7 5</nowiki>
| |
| |
|-
|-
|
|
|85\152
|85\152
|<u>879.310…</u>
|<u>879.310</u>
|''894.736…''
|18
|<nowiki>18 18|18 13</nowiki>
|13
|
|
|-
|-
|
|52\93
|52\93
|<u>878.873</u>
|11
|8
|
|
|<u>878.873…</u>
|-
|''894.623…''
|71\127
|<nowiki>11 11|11 8</nowiki>
|<u>878.351</u>
|15
|11
|
|
|-
|-
|90\161
|<u>878.049</u>
|19
|14
|
|
|71\127
|-
|
|109\195
|<u>878.350…</u>
|<u>877.852</u>
|''894.488…''
|23
|<nowiki>15 15|15 8</nowiki>
|17
|
|
|-
|-
| |19\34
| |19\34
| |
| |<u>876.923</u>
| |
|4
| |<u>876.923…</u>
|3
|''894.117…''
| |<nowiki>4 4|4 3</nowiki>
| |
| |
|-
|-
|
|62\111
|62\111
|
|<u>875.294</u>
|<u>875.294…</u>
|13
|''893.{{Overline|693}}''
|10
|<nowiki>13 13|13 10</nowiki>
|
|
|-
|-
|
|43\77
|43\77
|
|<u>874.576</u>
|<u>874.576…</u>
|9
|''893.506…''
|7
|<nowiki>9 9|9 7</nowiki>
|
|
|-
|-
|
|67\120
|67\120
|
|<u>873.913</u>
|<u>873.913…</u>
|14
|''893.{{Overline|3}}''
|11
|<nowiki>14 14|14 11</nowiki>
|
|
|-
|-
|24\43
|24\43
|
|<u>872.727</u>
|
|5
|<u>872.{{Overline|72}}</u>
|4
|''893.023…''
|<nowiki>5 5|5 4</nowiki>
|
|
|-
|-
|
|53\95
|53\95
|
|<u>871.233</u>
|<u>871.232…</u>
|11
|''892.631…''
|9
|<nowiki>11 11|11 9</nowiki>
|
|
|-
|-
|29\52
|29\52
|
|<u>870.000</u>
|
|6
|<u>870</u>
|5
|''892.307…''
|<nowiki>6 6|6 5</nowiki>
|
|
|-
|-
| |5\[[9edo|9]]
| |5\[[9edo|9]]
| |
| |<u>857.142</u>
| |
|1
| |<u>857.142…</u>
|0
|''888.{{Overline|8}}''
| |<nowiki>1 1|1 1</nowiki>
| |
| |
|}
|}
== See also ==
[[7L 2s (5/2-equivalent)]] - idealized meantone tuning
[[7L 2s (81/32-equivalent)]] - Pythagorean tuning
[[7L 2s (28/11-equivalent)]] - Neogothic tuning
[[7L 2s (18/7-equivalent)]] - idealized Archytas tuning

Latest revision as of 19:06, 29 December 2024

This page is about a MOS scale with a period of a major tenth and 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).

Name

The author suggests the name Terra Rubra for this scale.

Temperaments

Terra Rubra-Meantone

Subgroup: 5/2.2.3

Comma list: 81/80

POL2 generator: ~3/2 = 696.8737¢

Mapping: [⟨1 1 1], ⟨0 -2 -1]]

Optimal ET sequence: 9ed5/2, 16ed5/2, 25ed5/2

Terra Rubra-Superpyth

Subgroup: 18/7.2.3

Comma list: 64/63

POL2 generator: ~3/2 = 708.4011¢

Mapping: [⟨1 1 1], ⟨0 -2 -1]]

Optimal ET sequence: 7ed18/7, 16ed18/7, 23ed18/7, 30ed18/7

Scale tree

Generator Generator size L s Comments
4\7 960.000 1 0
25\44 937.500 6 1
71\129 936.263 17 3
46\81 935.593 11 2
67\118 934.884 16 3
21\37 933.333 5 1
80\141 932.039 19 4
59\104 931.579 14 3
38\67 930.612 9 2
55\97 929.577 13 3
72\127 929.032 17 4
89\157 928.696 21 5
17\30 927.273 4 1
115\203 926.174 27 7
98\173 925.984 23 6
81\143 925.714 19 5
64\113 925.301 15 4
47\83 924.590 11 3
30\53 923.077 7 2
73\129 922.105 17 5
43\76 921.429 10 3
56\99 920.548 13 4
69\122 920.000 16 5
82\145 919.626 19 6
95\168 919.355 22 7
919.340 π 1
108\191 919.149 25 8
121\214 918.987 28 9
13\23 917.647 3 1
100\177 916.031 23 8
87\154 915.789 20 7
74\131 915.464 17 6
61\108 915.000 14 5
48\85 914.286 11 4
913.821 e 1 L/s = e
35\62 913.043 8 3
912.287 φ+1 1 Split φ superdiatonic relation
57\101 912.000 13 5
79\140 911.538 18 7
22\39 910.345 5 2
75\133 909.091 17 7
53\94 908.571 12 5
31\55 907.317 7 3
71\126 906.383 16 7
40\71 905.660 9 4
… … … …
229\305 900.983 51 25
9\16 900.000 2 1 [BOUNDARY OF PROPRIETY: smaller generators are strictly proper]
230\397 899.023 51 26
… … … …
41\73 894.545 9 5
32\57 893.023 7 4 the 'Commatic' version of Terra Rubra, because its high accuracy of the 16/15 interval, the note '2b'
892.459
87\155 892.307 19 11
55\98 891.892 12 7
23\41 890.323 5 3 Golden Terra Rubra 1/5-tone
83\148 889.286 18 11
60\107 888.889 13 8 Golden Terra Rubra 1/13-tone
888.643 φ 1 GOLDEN Terra Rubra (L/s = φ)
37\66 888.000 8 5 Golden Terra Rubra 1/8-tone
88\157 887.395 19 12
51\91 886.957 11 7
65\116 886.364 14 9
79\141 885.981 17 11
93\166 885.714 20 13
14\25 884.211 3 2 Golden Terra Rubra 1/3-tone
117\209 883.019 25 17
103\184 882.857 22 15
89\159 882.645 19 13
75\134 882.353 16 11
61\109 881.928 13 9
47\84 881.250 10 7
33\59 880.000 7 5
85\152 879.310 18 13
52\93 878.873 11 8
71\127 878.351 15 11
90\161 878.049 19 14
109\195 877.852 23 17
19\34 876.923 4 3
62\111 875.294 13 10
43\77 874.576 9 7
67\120 873.913 14 11
24\43 872.727 5 4
53\95 871.233 11 9
29\52 870.000 6 5
5\9 857.142 1 0

See also

7L 2s (5/2-equivalent) - idealized meantone tuning

7L 2s (81/32-equivalent) - Pythagorean tuning

7L 2s (28/11-equivalent) - Neogothic tuning

7L 2s (18/7-equivalent) - idealized Archytas tuning

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