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#REDIRECT [[User:7L 2s (major tenth equivalent)]]
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).
 
{{Infobox MOS|Equave=5/2|Pattern=LLLsLLLLs|nLargeSteps=7|nSmallSteps=2|Name=Superdiatonic}}
 
==Name==
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
==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'.
==Scale tree==
{| class="wikitable"
|-
! colspan="3" |Generator
! |<span style="display: block; text-align: center;">'''Generator size (normalized )'''</span>
!<span style="display: block; text-align: center;">'''Generator size (ed4\3)'''</span>
! |Pentachord steps
! |Comments
|-
| |4\[[7edo|7]]
| |
| |
| |<u>960</u>
|''914.285…''
| |<nowiki>1 1|1 0</nowiki>
| |
|-
|25\44
|
|
|<u>937.5</u>
|''909.{{Overline|09}}''
|<nowiki>6 6|6 1</nowiki>
|
|-
|
|71\125
|
|<u>936.263…</u>
|''908.8''
|<nowiki>17 17|17 3</nowiki>
|
|-
|
|46\81
|
|<u>935.593…</u>
|''908.641…''
|<nowiki>11 11|11 2</nowiki>
|
|-
|
|67\118
|
|<u>934.883…</u>
|''908.474…''
|<nowiki>16 16|16 3</nowiki>
|
|-
| |21\37
| |
| |
| |<u>933.{{Overline|3}}</u>
|''908.{{Overline|108}}''
| |<nowiki>5 5|5 1</nowiki>
| |
|-
|
|80\141
|
|<u>932.038…</u>
|''907.801…''
|<nowiki>19 19|19 4</nowiki>
|
|-
|
|59\104
|
|<u>931.579…</u>
|''907.692…''
|<nowiki>14 14|14 3</nowiki>
|
|-
|
|38\67
|
|<u>930.612…</u>
|''907.462…''
|<nowiki>9 9|9 2</nowiki>
|
|-
|
|55\97
|
|<u>929.577…</u>
|''907.216…''
|<nowiki>13 13|13 3</nowiki>
|
|-
|
|72\127
|
|<u>929.032…</u>
|''907.086…''
|<nowiki>17 17|17 4</nowiki>
|
|-
|
|89\157
|
|<u>928.695…</u>
|''907.006…''
|<nowiki>21 21|21 5</nowiki>
|
|-
| |17\30
| |
| |
| |<u>927.{{Overline|27}}</u>
|''906.{{Overline|6}}''
| |<nowiki>4 4|4 1</nowiki>
| |L/s = 4
|-
|
|115\203
|
|<u>926.174…</u>
|''906.403…''
|<nowiki>27 27|27 7</nowiki>
|
|-
|
|98\173
|
|<u>925.984…</u>
|''906.358…''
|<nowiki>23 23|23 6</nowiki>
|
|-
|
|81\143
|
|<u>925.714…</u>
|''906.293…''
|<nowiki>19 19|19 5</nowiki>
|
|-
|
|64\113
|
|<u>925.301…</u>
|''906.194…''
|<nowiki>15 15|15 4</nowiki>
|
|-
|
|47\83
|
|<u>924.591…</u>
|''906.024…''
|<nowiki>11 11|11 3</nowiki>
|
|-
| |
| |30\53
| |
| |<u>923.076…</u>
|''905.660…''
| |<nowiki>7 7|7 2</nowiki>
| |
|-
|
|
|73\129
|<u>922.105…</u>
|''905.426…''
|<nowiki>17 17|17 5</nowiki>
|
|-
| |
| |43\76
| |
| |<u>921.428…</u>
|''905.263…''
| |<nowiki>10 10|10 3</nowiki>
| |
|-
| |
| |56\99
| |
| |<u>920.547…</u>
|''905.{{Overline|05}}''
| |<nowiki>13 13|13 4</nowiki>
| |
|-
| |
| |69\122
| |
| |<u>920</u>
|''904.918…''
| |<nowiki>16 16|16 5</nowiki>
| |
|-
| |
| |82\145
| |
| |<u>919.626…</u>
|''904.827…''
| |<nowiki>19 19|19 6</nowiki>
| |
|-
| |
| |95\168
| |
| |<u>919.354…</u>
|''904.761…''
| |<nowiki>22 22|22 7</nowiki>
| |
|-
| |
| |
| |
| |<u>919.340…</u>
|''904.758…''
| |<nowiki>π π|π 1</nowiki>
| |L/s = π
|-
| |
| |108\191
| |
| |<u>919.148…</u>
|''904.712…''
| |<nowiki>25 25|25 8</nowiki>
| |
|-
| |
| |121\214
| |
| |<u>918.987…</u>
|''904.672…''
| |<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
| |
| |
| |<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
| |
| |<u>916.030…</u>
|''903.954…''
| |<nowiki>23 23|23 8</nowiki>
| |
|-
| |
| |87\154
| |
| |<u>915.789…</u>
|''903.896…''
| |<nowiki>20 20|20 7</nowiki>
| |
|-
| |
| |74\131
| |
| |<u>915.463…</u>
|''903.816…''
| |<nowiki>17 17|17 6</nowiki>
| |Terra Rubra 1/17-tone
|-
| |
| |61\108
| |
| |<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
| |
| |<u>914.286…</u>
|''903.529…''
| |<nowiki>11 11|11 4</nowiki>
| |Terra Rubra 1/11-tone
|-
| |
| |
| |
| |<u>913.820…</u>
|''903.415…''
| |<nowiki>e e|e 1</nowiki>
| |L/s = e
|-
| |
| |35\62
| |
| |<u>913.043…</u>
|''903.225…''
| |<nowiki>8 8|8 3</nowiki>
| |Terra Rubra 1/8-tone
|-
| |
| |
| |92\163
| |<u>912.396…</u>
|''903.067…''
| |<nowiki>21 21|21 8</nowiki>
| |21;8 Superdiatonic 1/21-tone
|-
| |
| |
| |
| |<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
|<u>911.538…</u>
|''902.857…''
|<nowiki>18 18|18 7</nowiki>
|
|-
| |
| |22\39
| |
| |<u>910.344…</u>
|''902.564…''
| |<nowiki>5 5|5 2</nowiki>
| |Terra Rubra 1/5-tone
|-
| |
| |
| |75\133
| |<u>909.0̄9̄</u>
|''902.255…''
| |<nowiki>17 17|17 7</nowiki>
| |17;7 Superdiatonic 1/17-tone
|-
| |
| |
| |53\94
| |<u>908.571…</u>
|''902.127…''
| |<nowiki>12 12|12 5</nowiki>
| |
|-
| |
| |31\55
| |
| |<u>907.317…</u>
|''901.{{Overline|81}}''
| |<nowiki>7 7|7 3</nowiki>
| |7;3 Superdiatonic 1/7-tone
|-
|
|
|71\126
|<u>906.382…</u>
|''901.587…''
|<nowiki>16 16|16 7</nowiki>
|
|-
| |
| |40\71
| |
| |<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>
|
|-
|
|85\151
|
|<u>902.654…</u>
|''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
| |
| |
| |<u>900</u>
|''900''
| |<nowiki>2 2|2 1</nowiki>
| |<span style="display: block; text-align: left;">'''[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]'''</span>
|-
|
|230\409
|
|<u>899.022…</u>
|''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
| |
| |<u>894.5̄4̄</u>
|''898.630…''
| |<nowiki>9 9|9 5</nowiki>
| |Terra Rubra 1/9-tone
|-
| |
| |32\57
| |
| |<u>893.023…</u>
|''898.245…''
| |<nowiki>7 7|7 4</nowiki>
| |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>
|''898.102…''
| |<span style="background-color: #ffffff;"><nowiki>√3 √3|√3 1</nowiki></span>
| |
|-
| |
| |
| |55\98
| |<u>891.{{Overline|891}}</u>
|''897.959…''
| |<nowiki>12 12|12 7</nowiki>
| |
|-
| |
| |
| |78\139
| |<u>891.428…</u>
|''897.841…''
| |<nowiki>17 17|17 10</nowiki>
| |Terra Rubra 1/17-tone
|-
| |
| |23\41
| |
| |<u>890.323…</u>
|''897.560…''
| |<nowiki>5 5|5 3</nowiki>
| |5;3 Golden Terra Rubra 1/5-tone
|-
|
|
|83\148
|<u>889.285…</u>
|''897.{{Overline|297}}''
|<nowiki>18 18|18 11</nowiki>
|
|-
| |
| |
| |60\107
| |<u>888.{{Overline|8}}</u>
|''897.196…''
| |<nowiki>13 13|13 8</nowiki>
| |13;8 Golden Terra Rubra 1/13-tone
|-
| |
| |
| |
| |<u>888.643…</u>
|''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>
|-
| |
| |
| |97\173
| |<u>888.549…</u>
|''897.109…''
| |<nowiki>21 21|21 13</nowiki>
| |21;13 Golden Terra Rubra 1/21-tone
|-
| |
| |37\66
| |
| |<u>888</u>
|''896.{{Overline|96}}''
| |<nowiki>8 8|8 5</nowiki>
| |8;5 Golden Terra Rubra 1/8-tone
|-
|
|
|88\157
|<u>887.394…</u>
|''896.815…''
|<nowiki>19 19|19 12</nowiki>
|
|-
| |
| |51\91
| |
| |<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
| |
| |<u>886.{{Overline|36}}</u>
|''896.551…''
| |<nowiki>14 14|14 9</nowiki>
| |14;9 Superdiatonic 1/14-tone
|-
| |
| |79\141
| |
| |<u>885.981…</u>
|''896.453…''
| |<nowiki>17 17|17 11</nowiki>
| |17;11 Superdiatonic 1/17-tone
|-
| |
| |93\166
| |
| |<u>885.714…</u>
|''896.385…''
| |<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
| |
| |
| |<u>884.210…</u>
|''896''
| |<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
| |
| |<u>883.018…</u>
|''895.693…''
| |<nowiki>25 25|25 17</nowiki>
| |
|-
| |
| |103\184
| |
| |<u>882.857…</u>
|''895.652…''
| |<nowiki>22 22|22 15</nowiki>
| |
|-
| |
| |89\159
| |
| |<u>882.644…</u>
|''895.579…''
| |<nowiki>19 19|19 13</nowiki>
| |
|-
| |
| |75\134
| |
| |<u>882.353…</u>
|''895.522…''
| |<nowiki>16 16|16 11</nowiki>
| |
|-
| |
| |61\109
| |
| |<u>881.927…</u>
|''895.412…''
| |<nowiki>13 13|13 9</nowiki>
| |
|-
| |
| |47\84
| |
| |<u>881.25</u>
|''895.238…''
| |<nowiki>10 10|10 7</nowiki>
| |
|-
|
|
|80\143
|<u>880.733…</u>
|''895.104…''
|<nowiki>17 17|17 12</nowiki>
|
|-
| |
| |33\59
| |
| |<u>880</u>
|''894.915…''
| |<nowiki>7 7|7 5</nowiki>
| |
|-
|
|
|85\152
|<u>879.310…</u>
|''894.736…''
|<nowiki>18 18|18 13</nowiki>
|
|-
|
|52\93
|
|<u>878.873…</u>
|''894.623…''
|<nowiki>11 11|11 8</nowiki>
|
|-
|
|71\127
|
|<u>878.350…</u>
|''894.488…''
|<nowiki>15 15|15 8</nowiki>
|
|-
| |19\34
| |
| |
| |<u>876.923…</u>
|''894.117…''
| |<nowiki>4 4|4 3</nowiki>
| |
|-
|
|62\111
|
|<u>875.294…</u>
|''893.{{Overline|693}}''
|<nowiki>13 13|13 10</nowiki>
|
|-
|
|43\77
|
|<u>874.576…</u>
|''893.506…''
|<nowiki>9 9|9 7</nowiki>
|
|-
|
|67\120
|
|<u>873.913…</u>
|''893.{{Overline|3}}''
|<nowiki>14 14|14 11</nowiki>
|
|-
|24\43
|
|
|<u>872.{{Overline|72}}</u>
|''893.023…''
|<nowiki>5 5|5 4</nowiki>
|
|-
|
|53\95
|
|<u>871.232…</u>
|''892.631…''
|<nowiki>11 11|11 9</nowiki>
|
|-
|29\52
|
|
|<u>870</u>
|''892.307…''
|<nowiki>6 6|6 5</nowiki>
|
|-
| |5\[[9edo|9]]
| |
| |
| |<u>857.142…</u>
|''888.{{Overline|8}}''
| |<nowiki>1 1|1 1</nowiki>
| |
|}
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