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7L 2s (5/2-equivalent): Difference between revisions

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This page is about a [[MOSScales|MOSScale]] with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).
{{Infobox MOS}}
{{MOS intro}} It is significant due to being generated by fifths, like diatonic, and also having a similar structure to diatonic. With a tempered period, 19edo makes for a good tuning.  


{{Infobox MOS|Equave=5/2|Pattern=LLLsLLLLs|nLargeSteps=7|nSmallSteps=2|Collapsed=4|Equalized=5}}
== Scale properties ==
{{TAMNAMS use}}


==Name==
=== Intervals ===
The name '''superdiatonic''' has been established by [[Armodue]] theorists, and so [[TAMNAMS]] adopts it as well.
{{MOS intervals}}
==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'.
=== Generator chain ===
==Scale tree==
{{MOS genchain}}
{| class="wikitable"
 
|-
=== Modes ===
! colspan="3" |Generator
{{MOS mode degrees}}
! |<span style="display: block; text-align: center;">'''Generator size (normalized)'''</span>
 
!<span style="display: block; text-align: center;">'''Generator size (ed16\12 [→ed4\3])'''</span>
== Scale tree ==
! |Pentachord steps
{{MOS tuning spectrum}}
! |Comments
 
|-
{{stub}}
| |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.{{Overline|09}}</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>
|''899.755…''
|<nowiki>51 51|51 26</nowiki>
|
|-
|
|221\393
|
|<u>898.983…</u>
|''899.745…''
|<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.{{Overline|54}}</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 11</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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