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>
| |
|}

Latest revision as of 14:22, 5 May 2025

↖ 6L 1s⟨5/2⟩ ↑ 7L 1s⟨5/2⟩ 8L 1s⟨5/2⟩ ↗
← 6L 2s⟨5/2⟩ 7L 2s (5/2-equivalent) 8L 2s⟨5/2⟩ →
↙ 6L 3s⟨5/2⟩ ↓ 7L 3s⟨5/2⟩ 8L 3s⟨5/2⟩ ↘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 5/2 (1586.3 ¢)
Period 5/2 (1586.3 ¢)
Generator size(ed5/2)
Bright 5\9 to 4\7 (881.3 ¢ to 906.5 ¢)
Dark 3\7 to 4\9 (679.8 ¢ to 705.0 ¢)
Related MOS scales
Parent 2L 5s⟨5/2⟩
Sister 2L 7s⟨5/2⟩
Daughters 9L 7s⟨5/2⟩, 7L 9s⟨5/2⟩
Neutralized 5L 4s⟨5/2⟩
2-Flought 16L 2s⟨5/2⟩, 7L 11s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1) 5\9 (881.3 ¢)
Supersoft (L:s = 4:3) 19\34 (886.5 ¢)
Soft (L:s = 3:2) 14\25 (888.3 ¢)
Semisoft (L:s = 5:3) 23\41 (889.9 ¢)
Basic (L:s = 2:1) 9\16 (892.3 ¢)
Semihard (L:s = 5:2) 22\39 (894.8 ¢)
Hard (L:s = 3:1) 13\23 (896.6 ¢)
Superhard (L:s = 4:1) 17\30 (898.9 ¢)
Collapsed (L:s = 1:0) 4\7 (906.5 ¢)
View • Talk • Edit

7L 2s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every interval of 5/2 (1586.3 ¢). Generators that produce this scale range from 881.3 ¢ to 906.5 ¢, or from 679.8 ¢ to 705 ¢. 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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 7L 2s⟨5/2⟩
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 176.3 ¢
Major 1-mosstep M1ms L 176.3 ¢ to 226.6 ¢
2-mosstep Minor 2-mosstep m2ms L + s 226.6 ¢ to 352.5 ¢
Major 2-mosstep M2ms 2L 352.5 ¢ to 453.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 453.2 ¢ to 528.8 ¢
Major 3-mosstep M3ms 3L 528.8 ¢ to 679.8 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 679.8 ¢ to 705.0 ¢
Augmented 4-mosstep A4ms 4L 705.0 ¢ to 906.5 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 679.8 ¢ to 881.3 ¢
Perfect 5-mosstep P5ms 4L + s 881.3 ¢ to 906.5 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 906.5 ¢ to 1057.5 ¢
Major 6-mosstep M6ms 5L + s 1057.5 ¢ to 1133.1 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 1133.1 ¢ to 1233.8 ¢
Major 7-mosstep M7ms 6L + s 1233.8 ¢ to 1359.7 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1359.7 ¢ to 1410.1 ¢
Major 8-mosstep M8ms 7L + s 1410.1 ¢ to 1586.3 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 1586.3 ¢

Generator chain

Generator chain of 7L 2s⟨5/2⟩
Bright gens Scale degree Abbrev.
15 Augmented 3-mosdegree A3md
14 Augmented 7-mosdegree A7md
13 Augmented 2-mosdegree A2md
12 Augmented 6-mosdegree A6md
11 Augmented 1-mosdegree A1md
10 Augmented 5-mosdegree A5md
9 Augmented 0-mosdegree A0md
8 Augmented 4-mosdegree A4md
7 Major 8-mosdegree M8md
6 Major 3-mosdegree M3md
5 Major 7-mosdegree M7md
4 Major 2-mosdegree M2md
3 Major 6-mosdegree M6md
2 Major 1-mosdegree M1md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 9-mosdegree		 P0md
P9md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 3-mosdegree m3md
−4 Minor 7-mosdegree m7md
−5 Minor 2-mosdegree m2md
−6 Minor 6-mosdegree m6md
−7 Minor 1-mosdegree m1md
−8 Diminished 5-mosdegree d5md
−9 Diminished 9-mosdegree d9md
−10 Diminished 4-mosdegree d4md
−11 Diminished 8-mosdegree d8md
−12 Diminished 3-mosdegree d3md
−13 Diminished 7-mosdegree d7md
−14 Diminished 2-mosdegree d2md
−15 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 7L 2s⟨5/2⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLsLLLs Perf. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Perf.
7|1 6 LLLsLLLLs Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
6|2 2 LLLsLLLsL Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Min. Perf.
5|3 7 LLsLLLLsL Perf. Maj. Maj. Min. Perf. Perf. Maj. Maj. Min. Perf.
4|4 3 LLsLLLsLL Perf. Maj. Maj. Min. Perf. Perf. Maj. Min. Min. Perf.
3|5 8 LsLLLLsLL Perf. Maj. Min. Min. Perf. Perf. Maj. Min. Min. Perf.
2|6 4 LsLLLsLLL Perf. Maj. Min. Min. Perf. Perf. Min. Min. Min. Perf.
1|7 9 sLLLLsLLL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|8 5 sLLLsLLLL Perf. Min. Min. Min. Perf. Dim. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 2s⟨5/2⟩
Generator(ed5/2) Cents Step ratio Comments
Bright Dark L:s Hardness
5\9 881.285 705.028 1:1 1.000 Equalized 7L 2s⟨5/2⟩
29\52 884.675 701.639 6:5 1.200
24\43 885.384 700.929 5:4 1.250
43\77 885.864 700.450 9:7 1.286
19\34 886.469 699.844 4:3 1.333 Supersoft 7L 2s⟨5/2⟩
52\93 886.971 699.343 11:8 1.375
33\59 887.260 699.054 7:5 1.400
47\84 887.580 698.733 10:7 1.429
14\25 888.336 697.978 3:2 1.500 Soft 7L 2s⟨5/2⟩
51\91 889.033 697.281 11:7 1.571
37\66 889.297 697.017 8:5 1.600
60\107 889.522 696.792 13:8 1.625
23\41 889.883 696.430 5:3 1.667 Semisoft 7L 2s⟨5/2⟩
55\98 890.278 696.036 12:7 1.714
32\57 890.562 695.752 7:4 1.750
41\73 890.943 695.370 9:5 1.800
9\16 892.301 694.012 2:1 2.000 Basic 7L 2s⟨5/2⟩
Scales with tunings softer than this are proper
40\71 893.698 692.616 9:4 2.250
31\55 894.104 692.210 7:3 2.333
53\94 894.411 691.903 12:5 2.400
22\39 894.844 691.470 5:2 2.500 Semihard 7L 2s⟨5/2⟩
57\101 895.246 691.067 13:5 2.600
35\62 895.500 690.814 8:3 2.667
48\85 895.801 690.513 11:4 2.750
13\23 896.612 689.702 3:1 3.000 Hard 7L 2s⟨5/2⟩
43\76 897.520 688.794 10:3 3.333
30\53 897.913 688.400 7:2 3.500
47\83 898.274 688.040 11:3 3.667
17\30 898.911 687.403 4:1 4.000 Superhard 7L 2s⟨5/2⟩
38\67 899.700 686.613 9:2 4.500
21\37 900.340 685.973 5:1 5.000
25\44 901.315 684.999 6:1 6.000
4\7 906.465 679.849 1:0 → ∞ Collapsed 7L 2s⟨5/2⟩
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