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* SV3: [[Strict variety]] 3.
* SV3: [[Strict variety]] 3.
* HSA5: Harmonic Segments Along Fifths: Made up concept; a mix of diatonoid structures and harmonic segments, where a given arithmetic division of the 4/3 or 3/2 is repeated *3/2 to end up at the octave.
* HSA5: [[User:Eufalesio/Harmonic Segments Along Fifths|Harmonic Segments Along Fifths]]: Made up concept; a mix of diatonoid structures and harmonic segments, where a given arithmetic division of the 4/3 or 3/2 is repeated *3/2 to end up at the octave.
* SP: [[Strictly proper]]. Because I'm cataloging JI scales, they can only be strictly proper or not proper.
* SP: [[Strictly proper]]. Because I'm cataloging JI scales, they can only be strictly proper or not proper.
* SYM: Symmetric. That is, not [[chiral]].
* SYM: Symmetric. That is, not [[chiral]].
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=== Úuñmulu - Íegmul [HSA5, CS, SP] ===
=== HSA5 3; Úuñmulu - Íegmul [HSA5, CS, SP] ===
The simples 7et detempers that are easy to use and have delectable sonorities, based on the 10::12 trichord and 9::12 tetrachord respectively. I prefer LH but RH has its uses.
The simples 7et detempers that are easy to use and have delectable sonorities, based on the 10::12 trichord and 9::12 tetrachord respectively. I prefer LH but RH has its uses.
{| class="wikitable"
{| class="wikitable"
Line 739: Line 739:


=== A general Diatonoid [SV3, CS, SP] ===
=== A general Diatonoid [SV3, CS, SP] ===
A generalization of the general 2.3.p thing that makes all of the scales I've shown before so great, baked into a general scale. This means that Zarlino is a Diatonoid, Ghyef is a Diatonoid, Archylino is a Diatonoid, etc... Just like with Skirmishes, apply 9/8 < C < sqrt(3/2) beget L modes, sqrt(3/2) < C < 4/3 beget R modes.
A generalization of the general 2.3.p thing that makes all of the scales I've shown before so great, baked into a general scale. This means that Zarlino is a Diatonoid, Ghyef is a Diatonoid, Archylino is a Diatonoid, etc... Just like with Skirmishes, apply 9/8 < C < sqrt(3/2) beget L modes and sqrt(3/2) < C < 4/3 beget R modes.
{| class="wikitable"
{| class="wikitable"
|-
|-
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== 10-form ==
== 10-form ==


=== Ngwóoghe - Góqäi [HSA5, CS, SP] ===
=== heHSA5 4; Ngwóoghe - Góqäi [HSA5, CS, SP] ===
24:26:28:30:32:''34'':36:39:42:45:48. 12::18 repeated and cut at the octave, or alternatively, two 12::16 pentachords, with another a fifth up and with the addition of 17/12 to fill out the scale into a proper 10-form. I personally don't use the 17/ intervals as much, instead I change between the modes to pick what I need, but 17 is undoubtedly the most natural rendition of the 5-step of the scale.
24:26:28:30:32:''34'':36:39:42:45:48. 12::18 repeated and cut at the octave, or alternatively, two 12::16 pentachords, with another a fifth up and with the addition of 17/12 to fill out the scale into a proper 10-form. I personally don't use the 17/ intervals as much, instead I change between the modes to pick what I need, but 17 is undoubtedly the most natural rendition of the 5-step of the scale.


Line 1,550: Line 1,550:
|<small>9/5</small>
|<small>9/5</small>
|<small>28/15</small>
|<small>28/15</small>
|}
== Other octave-periodic scales ==
=== heHSA5 8; Veljeuwof [HSA5] ===
A massive scale that includes all of 8afdo, Ngwóoghe, Didymus, and Zontatonic as subsets. Named Veljeuwof by Lawitalawitaluna, it's a scale she and I hold in high regard. It also introduces 29 and 31 featuring mild superminor and subperfect qualities within an otonal context, which I think is quite neat. Much like Ngwóoghe, it features extensions between 4/3 and 3/2 that may or may not be used, and though 11/8 is one of the best interval additions and 35/24 is part of the subgroup already, 17/12 is still a slight misfit.
Great melodic movements include 1 9/8 29/24 4/3, 1 13/12 29/24 31/24 and in the 4/3 mode, 1 9/8 39/32 87/64.
{| class="wikitable"
! colspan="20" |Scale degrees
|-
!25/24
!13/12
!9/8
!7/6
!29/24
!5/4
!31/24
!4/3
!11/8
!17/12
!35/24
!3/2
!25/16
!13/8
!27/16
!7/4
!29/16
!15/8
!31/16
| rowspan="20" |2
|-
|<small>26/25</small>
|<small>27/25</small>
|<small>28/25</small>
|<small>29/25</small>
|<small>6/5</small>
|<small>31/25</small>
|<small>32/25</small>
|<small>33/25</small>
|<small>34/25</small>
|<small>7/5</small>
|<small>36/25</small>
|<small>3/2</small>
|<small>39/25</small>
|<small>81/50</small>
|<small>42/25</small>
|<small>87/50</small>
|<small>9/5</small>
|<small>93/50</small>
|<small>48/25</small>
|-
|<small>27/26</small>
|<small>14/13</small>
|<small>29/26</small>
|<small>15/13</small>
|<small>31/26</small>
|<small>16/13</small>
|<small>33/26</small>
|<small>17/13</small>
|<small>35/26</small>
|<small>18/13</small>
|<small>75/52</small>
|<small>3/2</small>
|<small>81/52</small>
|<small>21/13</small>
|<small>87/52</small>
|<small>45/26</small>
|<small>93/52</small>
|<small>24/13</small>
|<small>25/13</small>
|-
|<small>28/27</small>
|<small>29/27</small>
|<small>10/9</small>
|<small>31/27</small>
|<small>32/27</small>
|<small>11/9</small>
|<small>34/27</small>
|<small>35/27</small>
|<small>4/3</small>
|<small>25/18</small>
|<small>13/9</small>
|<small>3/2</small>
|<small>14/9</small>
|<small>29/18</small>
|<small>5/3</small>
|<small>31/18</small>
|<small>16/9</small>
|<small>50/27</small>
|<small>52/27</small>
|-
|<small>29/28</small>
|<small>15/14</small>
|<small>31/28</small>
|<small>8/7</small>
|<small>33/28</small>
|<small>17/14</small>
|<small>5/4</small>
|<small>9/7</small>
|<small>75/56</small>
|<small>39/28</small>
|<small>81/56</small>
|<small>3/2</small>
|<small>87/56</small>
|<small>45/28</small>
|<small>93/56</small>
|<small>12/7</small>
|<small>25/14</small>
|<small>13/7</small>
|<small>27/14</small>
|-
|<small>30/29</small>
|<small>31/29</small>
|<small>32/29</small>
|<small>33/29</small>
|<small>34/29</small>
|<small>35/29</small>
|<small>36/29</small>
|<small>75/58</small>
|<small>39/29</small>
|<small>81/58</small>
|<small>42/29</small>
|<small>3/2</small>
|<small>45/29</small>
|<small>93/58</small>
|<small>48/29</small>
|<small>50/29</small>
|<small>52/29</small>
|<small>54/29</small>
|<small>56/29</small>
|-
|<small>31/30</small>
|<small>16/15</small>
|<small>11/10</small>
|<small>17/15</small>
|<small>7/6</small>
|<small>6/5</small>
|<small>5/4</small>
|<small>13/10</small>
|<small>27/20</small>
|<small>7/5</small>
|<small>29/20</small>
|<small>3/2</small>
|<small>31/20</small>
|<small>8/5</small>
|<small>5/3</small>
|<small>26/15</small>
|<small>9/5</small>
|<small>28/15</small>
|<small>29/15</small>
|-
|<small>32/31</small>
|<small>33/31</small>
|<small>34/31</small>
|<small>35/31</small>
|<small>36/31</small>
|<small>75/62</small>
|<small>39/31</small>
|<small>81/62</small>
|<small>42/31</small>
|<small>87/62</small>
|<small>45/31</small>
|<small>3/2</small>
|<small>48/31</small>
|<small>50/31</small>
|<small>52/31</small>
|<small>54/31</small>
|<small>56/31</small>
|<small>58/31</small>
|<small>60/31</small>
|-
|<small>33/32</small>
|<small>17/16</small>
|<small>35/32</small>
|<small>9/8</small>
|<small>75/64</small>
|<small>39/32</small>
|<small>81/64</small>
|<small>21/16</small>
|<small>87/64</small>
|<small>45/32</small>
|<small>93/64</small>
|<small>3/2</small>
|<small>25/16</small>
|<small>13/8</small>
|<small>27/16</small>
|<small>7/4</small>
|<small>29/16</small>
|<small>15/8</small>
|<small>31/16</small>
|-
|<small>34/33</small>
|<small>35/33</small>
|<small>12/11</small>
|<small>25/22</small>
|<small>13/11</small>
|<small>27/22</small>
|<small>14/11</small>
|<small>29/22</small>
|<small>15/11</small>
|<small>31/22</small>
|<small>16/11</small>
|<small>50/33</small>
|<small>52/33</small>
|<small>18/11</small>
|<small>56/33</small>
|<small>58/33</small>
|<small>20/11</small>
|<small>62/33</small>
|<small>64/33</small>
|-
|<small>35/34</small>
|<small>18/17</small>
|<small>75/68</small>
|<small>39/34</small>
|<small>81/68</small>
|<small>21/17</small>
|<small>87/68</small>
|<small>45/34</small>
|<small>93/68</small>
|<small>24/17</small>
|<small>25/17</small>
|<small>26/17</small>
|<small>27/17</small>
|<small>28/17</small>
|<small>29/17</small>
|<small>30/17</small>
|<small>31/17</small>
|<small>32/17</small>
|<small>33/17</small>
|-
|<small>36/35</small>
|<small>15/14</small>
|<small>39/35</small>
|<small>81/70</small>
|<small>6/5</small>
|<small>87/70</small>
|<small>9/7</small>
|<small>93/70</small>
|<small>48/35</small>
|<small>10/7</small>
|<small>52/35</small>
|<small>54/35</small>
|<small>8/5</small>
|<small>58/35</small>
|<small>12/7</small>
|<small>62/35</small>
|<small>64/35</small>
|<small>66/35</small>
|<small>68/35</small>
|-
|<small>25/24</small>
|<small>13/12</small>
|<small>9/8</small>
|<small>7/6</small>
|<small>29/24</small>
|<small>5/4</small>
|<small>31/24</small>
|<small>4/3</small>
|<small>25/18</small>
|<small>13/9</small>
|<small>3/2</small>
|<small>14/9</small>
|<small>29/18</small>
|<small>5/3</small>
|<small>31/18</small>
|<small>16/9</small>
|<small>11/6</small>
|<small>17/9</small>
|<small>35/18</small>
|-
|<small>26/25</small>
|<small>27/25</small>
|<small>28/25</small>
|<small>29/25</small>
|<small>6/5</small>
|<small>31/25</small>
|<small>32/25</small>
|<small>4/3</small>
|<small>104/75</small>
|<small>36/25</small>
|<small>112/75</small>
|<small>116/75</small>
|<small>8/5</small>
|<small>124/75</small>
|<small>128/75</small>
|<small>44/25</small>
|<small>136/75</small>
|<small>28/15</small>
|<small>48/25</small>
|-
|<small>27/26</small>
|<small>14/13</small>
|<small>29/26</small>
|<small>15/13</small>
|<small>31/26</small>
|<small>16/13</small>
|<small>50/39</small>
|<small>4/3</small>
|<small>18/13</small>
|<small>56/39</small>
|<small>58/39</small>
|<small>20/13</small>
|<small>62/39</small>
|<small>64/39</small>
|<small>22/13</small>
|<small>68/39</small>
|<small>70/39</small>
|<small>24/13</small>
|<small>25/13</small>
|-
|<small>28/27</small>
|<small>29/27</small>
|<small>10/9</small>
|<small>31/27</small>
|<small>32/27</small>
|<small>100/81</small>
|<small>104/81</small>
|<small>4/3</small>
|<small>112/81</small>
|<small>116/81</small>
|<small>40/27</small>
|<small>124/81</small>
|<small>128/81</small>
|<small>44/27</small>
|<small>136/81</small>
|<small>140/81</small>
|<small>16/9</small>
|<small>50/27</small>
|<small>52/27</small>
|-
|<small>29/28</small>
|<small>15/14</small>
|<small>31/28</small>
|<small>8/7</small>
|<small>25/21</small>
|<small>26/21</small>
|<small>9/7</small>
|<small>4/3</small>
|<small>29/21</small>
|<small>10/7</small>
|<small>31/21</small>
|<small>32/21</small>
|<small>11/7</small>
|<small>34/21</small>
|<small>5/3</small>
|<small>12/7</small>
|<small>25/14</small>
|<small>13/7</small>
|<small>27/14</small>
|-
|<small>30/29</small>
|<small>31/29</small>
|<small>32/29</small>
|<small>100/87</small>
|<small>104/87</small>
|<small>36/29</small>
|<small>112/87</small>
|<small>4/3</small>
|<small>40/29</small>
|<small>124/87</small>
|<small>128/87</small>
|<small>44/29</small>
|<small>136/87</small>
|<small>140/87</small>
|<small>48/29</small>
|<small>50/29</small>
|<small>52/29</small>
|<small>54/29</small>
|<small>56/29</small>
|-
|<small>31/30</small>
|<small>16/15</small>
|<small>10/9</small>
|<small>52/45</small>
|<small>6/5</small>
|<small>56/45</small>
|<small>58/45</small>
|<small>4/3</small>
|<small>62/45</small>
|<small>64/45</small>
|<small>22/15</small>
|<small>68/45</small>
|<small>14/9</small>
|<small>8/5</small>
|<small>5/3</small>
|<small>26/15</small>
|<small>9/5</small>
|<small>28/15</small>
|<small>29/15</small>
|-
|<small>32/31</small>
|<small>100/93</small>
|<small>104/93</small>
|<small>36/31</small>
|<small>112/93</small>
|<small>116/93</small>
|<small>40/31</small>
|<small>4/3</small>
|<small>128/93</small>
|<small>44/31</small>
|<small>136/93</small>
|<small>140/93</small>
|<small>48/31</small>
|<small>50/31</small>
|<small>52/31</small>
|<small>54/31</small>
|<small>56/31</small>
|<small>58/31</small>
|<small>60/31</small>
|}
|}


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