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{{Infobox AFDO|steps=101}}
{{Infobox AFDO|steps=101}}


'''101afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''101odo''' ([[otonal division]] of the octave), divides the octave into 101 parts of 1/101 each. It is a superset of [[100afdo]] and a subset of [[102afdo]]. As a scale it may be known as [[harmonic mode|mode 101 of the harmonic series]], the [[overtone scale #Over-n scales|Over-101]] scale, or the '''Dalmatian scale''' {{idiosyncratic}}. This view is equivalent to 101afdo except that it has a fixed root and cannot be rotated.
'''101afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''101odo''' ([[otonal division]] of the octave), divides the octave into 101 parts of 1/101 each. It is a superset of [[100afdo]] and a subset of [[102afdo]]. As a scale it may be known as [[harmonic mode|mode 101 of the harmonic series]] or the [[overtone scale #Over-n scales|Over-101]] scale. This view is equivalent to 101afdo except that it has a fixed root and cannot be rotated.


It is a large [[primodality|primodal]] scale which is suited for use as a [[neji]] tuning. It is the 26th [[prime harmonic series|prime mode of the harmonic series]]. Its name is a reference to the animated TV series {{w|101 Dalmatian Street|''101 Dalmatian Street'' (2019)}}.
It is a large [[primodality|primodal]] scale which is suited for use as a [[neji]] tuning. It is the 26th [[prime harmonic series|prime mode of the harmonic series]].


== Lowest-error neji approximations ==
== Theory ==
The Dalmatian scale approximates four [[edo]]s, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:
=== Lowest-error neji approximations ===
101afdo approximates five [[edo]]s, including two [[zeta peak edo]]s, with lower [[NEJI Tables/Greatest Error|maximum error]] than any smaller mode of the harmonic series:<small>
* [[8edo]] (101:110:120:131:143:156:170:185:202)
* [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
* [[19edo]] (101:105:109:113:117:121:126:130:135:140:145:151:156:162:168:175:181:188:195:202)
* [[24edo]] (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
* [[24edo]] (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
* [[25edo]] (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
* [[25edo]] (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
* [[27edo]] (101:104:106:109:112:115:118:121:124:127:131:134:137:141:145:148:152:156:160:164:169:173:178:182:187:192:197:202)
* [[27edo]] (101:104:106:109:112:115:118:121:124:127:131:134:137:141:145:148:152:156:160:164:169:173:178:182:187:192:197:202)</small>


It approximates ''seven'' edos, including ''three'' zeta peak edos, with lower [[NEJI Tables/Average Error|average error]] than any smaller mode of the harmonic series:
It approximates seven edos, including three zeta peak edos, with lower [[NEJI Tables/Average Error|average error]] than any smaller mode of the harmonic series:<small>
* [[5edo]] (101:116:133:153:176:202)
* [[5edo]] (101:116:133:153:176:202)
* [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202)
* [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202)
Line 19: Line 21:
* [[24edo]] (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
* [[24edo]] (101:104:107:110:113:117:120:124:127:131:135:139:143:147:151:156:160:165:170:175:180:185:191:196:202)
* [[25edo]] (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
* [[25edo]] (101:104:107:110:113:116:119:123:126:130:133:137:141:145:149:153:157:162:166:171:176:181:186:191:196:202)
* [[34edo]] (101:103:105:107:110:112:114:116:119:121:124:126:129:132:134:137:140:143:146:149:152:155:158:161:165:168:172:175:179:182:186:190:194:198:202)
* [[34edo]] (<small>101:103:105:107:110:112:114:116:119:121:124:126:129:132:134:137:140:143:146:149:152:155:158:161:165:168:172:175:179:182:186:190:194:198:202</small>)</small>
 
Best-approximating this many edos in general, and this many zeta peak edos specifically, is more than average for an afdo of this size, but it's not that unusual. [[104afdo]], for example, best-approximates similar numbers of both.


== Table of intervals ==
== Table of intervals ==
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible mw-collapsed"
|+ Intervals of mode 101 of the harmonic series
|+ Intervals of mode 101 of the harmonic series
|-
|-
! Step
! <small>Step</small>
! Harmonic
! <small>Harmonic</small>
! Just ratio
! <small>Just ratio</small>
! [[Cent]]s value
! <small>[[Cent]]s value</small>
|-
|-
| 1
! <small>1</small>
| 102nd
| <small>102nd</small>
| 102/101
| <small>102/101</small>
| 17.057
| <small>17.057</small>
|-
|-
| 2
! <small>2</small>
| 103rd
| <small>103rd</small>
| 103/101
| <small>103/101</small>
| 33.947
| <small>33.947</small>
|-
|-
| 3
! <small>3</small>
| 104th
| <small>104th</small>
| 104/101
| <small>104/101</small>
| 50.674
| <small>50.674</small>
|-
|-
| 4
! <small>4</small>
| 105th
| <small>105th</small>
| 105/101
| <small>105/101</small>
| 67.241
| <small>67.241</small>
|-
|-
| 5
! <small>5</small>
| 106th
| <small>106th</small>
| 106/101
| <small>106/101</small>
| 83.651
| <small>83.651</small>
|-
|-
| 6
! <small>6</small>
| 107th
| <small>107th</small>
| 107/101
| <small>107/101</small>
| 99.907
| <small>99.907</small>
|-
|-
| 7
! <small>7</small>
| 108th
| <small>108th</small>
| 108/101
| <small>108/101</small>
| 116.011
| <small>116.011</small>
|-
|-
| 8
! <small>8</small>
| 109th
| <small>109th</small>
| 109/101
| <small>109/101</small>
| 131.967
| <small>131.967</small>
|-
|-
| 9
! <small>9</small>
| 110th
| <small>110th</small>
| 110/101
| <small>110/101</small>
| 147.778
| <small>147.778</small>
|-
|-
| 10
! <small>10</small>
| 111th
| <small>111th</small>
| 111/101
| <small>111/101</small>
| 163.445
| <small>163.445</small>
|-
|-
| 11
! <small>11</small>
| 112th
| <small>112th</small>
| 112/101
| <small>112/101</small>
| 178.972
| <small>178.972</small>
|-
|-
| 12
! <small>12</small>
| 113th
| <small>113th</small>
| 113/101
| <small>113/101</small>
| 194.361
| <small>194.361</small>
|-
|-
| 13
! <small>13</small>
| 114th
| <small>114th</small>
| 114/101
| <small>114/101</small>
| 209.614
| <small>209.614</small>
|-
|-
| 14
! <small>14</small>
| 115th
| <small>115th</small>
| 115/101
| <small>115/101</small>
| 224.734
| <small>224.734</small>
|-
|-
| 15
! <small>15</small>
| 116th
| <small>116th</small>
| 116/101
| <small>116/101</small>
| 239.723
| <small>239.723</small>
|-
|-
| 16
! <small>16</small>
| 117th
| <small>117th</small>
| 117/101
| <small>117/101</small>
| 254.584
| <small>254.584</small>
|-
|-
| 17
! <small>17</small>
| 118th
| <small>118th</small>
| 118/101
| <small>118/101</small>
| 269.318
| <small>269.318</small>
|-
|-
| 18
! <small>18</small>
| 119th
| <small>119th</small>
| 119/101
| <small>119/101</small>
| 283.928
| <small>283.928</small>
|-
|-
| 19
! <small>19</small>
| 120th
| <small>120th</small>
| 120/101
| <small>120/101</small>
| 298.415
| <small>298.415</small>
|-
|-
| 20
! <small>20</small>
| 121st
| <small>121st</small>
| 121/101
| <small>121/101</small>
| 312.782
| <small>312.782</small>
|-
|-
| 21
! <small>21</small>
| 122nd
| <small>122nd</small>
| 122/101
| <small>122/101</small>
| 327.031
| <small>327.031</small>
|-
|-
| 22
! <small>22</small>
| 123rd
| <small>123rd</small>
| 123/101
| <small>123/101</small>
| 341.164
| <small>341.164</small>
|-
|-
| 23
! <small>23</small>
| 124th
| <small>124th</small>
| 124/101
| <small>124/101</small>
| 355.182
| <small>355.182</small>
|-
|-
| 24
! <small>24</small>
| 125th
| <small>125th</small>
| 125/101
| <small>125/101</small>
| 369.087
| <small>369.087</small>
|-
|-
| 25
! <small>25</small>
| 126th
| <small>126th</small>
| 126/101
| <small>126/101</small>
| 382.882
| <small>382.882</small>
|-
|-
| 26
! <small>26</small>
| 127th
| <small>127th</small>
| 127/101
| <small>127/101</small>
| 396.568
| <small>396.568</small>
|-
|-
| 27
! <small>27</small>
| 128th
| <small>128th</small>
| 128/101
| <small>128/101</small>
| 410.146
| <small>410.146</small>
|-
|-
| 28
! <small>28</small>
| 129th
| <small>129th</small>
| 129/101
| <small>129/101</small>
| 423.619
| <small>423.619</small>
|-
|-
| 29
! <small>29</small>
| 130th
| <small>130th</small>
| 130/101
| <small>130/101</small>
| 436.988
| <small>436.988</small>
|-
|-
| 30
! <small>30</small>
| 131st
| <small>131st</small>
| 131/101
| <small>131/101</small>
| 450.254
| <small>450.254</small>
|-
|-
| 31
! <small>31</small>
| 132nd
| <small>132nd</small>
| 132/101
| <small>132/101</small>
| 463.419
| <small>463.419</small>
|-
|-
| 32
! <small>32</small>
| 133rd
| <small>133rd</small>
| 133/101
| <small>133/101</small>
| 476.485
| <small>476.485</small>
|-
|-
| 33
! <small>33</small>
| 134th
| <small>134th</small>
| 134/101
| <small>134/101</small>
| 489.453
| <small>489.453</small>
|-
|-
| 34
! <small>34</small>
| 135th
| <small>135th</small>
| 135/101
| <small>135/101</small>
| 502.325
| <small>502.325</small>
|-
|-
| 35
! <small>35</small>
| 136th
| <small>136th</small>
| 136/101
| <small>136/101</small>
| 515.102
| <small>515.102</small>
|-
|-
| 36
! <small>36</small>
| 137th
| <small>137th</small>
| 137/101
| <small>137/101</small>
| 527.785
| <small>527.785</small>
|-
|-
| 37
! <small>37</small>
| 138th
| <small>138th</small>
| 138/101
| <small>138/101</small>
| 540.376
| <small>540.376</small>
|-
|-
| 38
! <small>38</small>
| 139th
| <small>139th</small>
| 139/101
| <small>139/101</small>
| 552.876
| <small>552.876</small>
|-
|-
| 39
! <small>39</small>
| 140th
| <small>140th</small>
| 140/101
| <small>140/101</small>
| 565.286
| <small>565.286</small>
|-
|-
| 40
! <small>40</small>
| 141st
| <small>141st</small>
| 141/101
| <small>141/101</small>
| 577.608
| <small>577.608</small>
|-
|-
| 41
! <small>41</small>
| 142nd
| <small>142nd</small>
| 142/101
| <small>142/101</small>
| 589.843
| <small>589.843</small>
|-
|-
| 42
! <small>42</small>
| 143rd
| <small>143rd</small>
| 143/101
| <small>143/101</small>
| 601.992
| <small>601.992</small>
|-
|-
| 43
! <small>43</small>
| 144th
| <small>144th</small>
| 144/101
| <small>144/101</small>
| 614.056
| <small>614.056</small>
|-
|-
| 44
! <small>44</small>
| 145th
| <small>145th</small>
| 145/101
| <small>145/101</small>
| 626.037
| <small>626.037</small>
|-
|-
| 45
! <small>45</small>
| 146th
| <small>146th</small>
| 146/101
| <small>146/101</small>
| 637.936
| <small>637.936</small>
|-
|-
| 46
! <small>46</small>
| 147th
| <small>147th</small>
| 147/101
| <small>147/101</small>
| 649.753
| <small>649.753</small>
|-
|-
| 47
! <small>47</small>
| 148th
| <small>148th</small>
| 148/101
| <small>148/101</small>
| 661.490
| <small>661.490</small>
|-
|-
| 48
! <small>48</small>
| 149th
| <small>149th</small>
| 149/101
| <small>149/101</small>
| 673.148
| <small>673.148</small>
|-
|-
| 49
! <small>49</small>
| 150th
| <small>150th</small>
| 150/101
| <small>150/101</small>
| 684.729
| <small>684.729</small>
|-
|-
| 50
! <small>50</small>
| 151st
| <small>151st</small>
| 151/101
| <small>151/101</small>
| 696.232
| <small>696.232</small>
|-
|-
| 51
! <small>51</small>
| 152nd
| <small>152nd</small>
| 152/101
| <small>152/101</small>
| 707.659
| <small>707.659</small>
|-
|-
| 52
! <small>52</small>
| 153rd
| <small>153rd</small>
| 153/101
| <small>153/101</small>
| 719.012
| <small>719.012</small>
|-
|-
| 53
! <small>53</small>
| 154th
| <small>154th</small>
| 154/101
| <small>154/101</small>
| 730.290
| <small>730.290</small>
|-
|-
| 54
! <small>54</small>
| 155th
| <small>155th</small>
| 155/101
| <small>155/101</small>
| 741.496
| <small>741.496</small>
|-
|-
| 55
! <small>55</small>
| 156th
| <small>156th</small>
| 156/101
| <small>156/101</small>
| 752.629
| <small>752.629</small>
|-
|-
| 56
! <small>56</small>
| 157th
| <small>157th</small>
| 157/101
| <small>157/101</small>
| 763.691
| <small>763.691</small>
|-
|-
| 57
! <small>57</small>
| 158th
| <small>158th</small>
| 158/101
| <small>158/101</small>
| 774.683
| <small>774.683</small>
|-
|-
| 58
! <small>58</small>
| 159th
| <small>159th</small>
| 159/101
| <small>159/101</small>
| 785.606
| <small>785.606</small>
|-
|-
| 59
! <small>59</small>
| 160th
| <small>160th</small>
| 160/101
| <small>160/101</small>
| 796.460
| <small>796.460</small>
|-
|-
| 60
! <small>60</small>
| 161st
| <small>161st</small>
| 161/101
| <small>161/101</small>
| 807.246
| <small>807.246</small>
|-
|-
| 61
! <small>61</small>
| 162nd
| <small>162nd</small>
| 162/101
| <small>162/101</small>
| 817.966
| <small>817.966</small>
|-
|-
| 62
! <small>62</small>
| 163rd
| <small>163rd</small>
| 163/101
| <small>163/101</small>
| 828.620
| <small>828.620</small>
|-
|-
| 63
! <small>63</small>
| 164th
| <small>164th</small>
| 164/101
| <small>164/101</small>
| 839.209
| <small>839.209</small>
|-
|-
| 64
! <small>64</small>
| 165th
| <small>165th</small>
| 165/101
| <small>165/101</small>
| 849.733
| <small>849.733</small>
|-
|-
| 65
! <small>65</small>
| 166th
| <small>166th</small>
| 166/101
| <small>166/101</small>
| 860.194
| <small>860.194</small>
|-
|-
| 66
! <small>66</small>
| 167th
| <small>167th</small>
| 167/101
| <small>167/101</small>
| 870.591
| <small>870.591</small>
|-
|-
| 67
! <small>67</small>
| 168th
| <small>168th</small>
| 168/101
| <small>168/101</small>
| 880.927
| <small>880.927</small>
|-
|-
| 68
! <small>68</small>
| 169th
| <small>169th</small>
| 169/101
| <small>169/101</small>
| 891.202
| <small>891.202</small>
|-
|-
| 69
! <small>69</small>
| 170th
| <small>170th</small>
| 170/101
| <small>170/101</small>
| 901.415
| <small>901.415</small>
|-
|-
| 70
! <small>70</small>
| 171st
| <small>171st</small>
| 171/101
| <small>171/101</small>
| 911.569
| <small>911.569</small>
|-
|-
| 71
! <small>71</small>
| 172nd
| <small>172nd</small>
| 172/101
| <small>172/101</small>
| 921.664
| <small>921.664</small>
|-
|-
| 72
! <small>72</small>
| 173rd
| <small>173rd</small>
| 173/101
| <small>173/101</small>
| 931.700
| <small>931.700</small>
|-
|-
| 73
! <small>73</small>
| 174th
| <small>174th</small>
| 174/101
| <small>174/101</small>
| 941.678
| <small>941.678</small>
|-
|-
| 74
! <small>74</small>
| 175th
| <small>175th</small>
| 175/101
| <small>175/101</small>
| 951.600
| <small>951.600</small>
|-
|-
| 75
! <small>75</small>
| 176th
| <small>176th</small>
| 176/101
| <small>176/101</small>
| 961.464
| <small>961.464</small>
|-
|-
| 76
! <small>76</small>
| 177th
| <small>177th</small>
| 177/101
| <small>177/101</small>
| 971.273
| <small>971.273</small>
|-
|-
| 77
! <small>77</small>
| 178th
| <small>178th</small>
| 178/101
| <small>178/101</small>
| 981.026
| <small>981.026</small>
|-
|-
| 78
! <small>78</small>
| 179th
| <small>179th</small>
| 179/101
| <small>179/101</small>
| 990.725
| <small>990.725</small>
|-
|-
| 79
! <small>79</small>
| 180th
| <small>180th</small>
| 180/101
| <small>180/101</small>
| 1000.370
| <small>1000.370</small>
|-
|-
| 80
! <small>80</small>
| 181st
| <small>181st</small>
| 181/101
| <small>181/101</small>
| 1009.961
| <small>1009.961</small>
|-
|-
| 81
! <small>81</small>
| 182nd
| <small>182nd</small>
| 182/101
| <small>182/101</small>
| 1019.500
| <small>1019.500</small>
|-
|-
| 82
! <small>82</small>
| 183rd
| <small>183rd</small>
| 183/101
| <small>183/101</small>
| 1028.986
| <small>1028.986</small>
|-
|-
| 83
! <small>83</small>
| 184th
| <small>184th</small>
| 184/101
| <small>184/101</small>
| 1038.421
| <small>1038.421</small>
|-
|-
| 84
! <small>84</small>
| 185th
| <small>185th</small>
| 185/101
| <small>185/101</small>
| 1047.804
| <small>1047.804</small>
|-
|-
| 85
! <small>85</small>
| 186th
| <small>186th</small>
| 186/101
| <small>186/101</small>
| 1057.137
| <small>1057.137</small>
|-
|-
| 86
! <small>86</small>
| 187th
| <small>187th</small>
| 187/101
| <small>187/101</small>
| 1066.420
| <small>1066.420</small>
|-
|-
| 87
! <small>87</small>
| 188th
| <small>188th</small>
| 188/101
| <small>188/101</small>
| 1075.653
| <small>1075.653</small>
|-
|-
| 88
! <small>88</small>
| 189th
| <small>189th</small>
| 189/101
| <small>189/101</small>
| 1084.837
| <small>1084.837</small>
|-
|-
| 89
! <small>89</small>
| 190th
| <small>190th</small>
| 190/101
| <small>190/101</small>
| 1093.973
| <small>1093.973</small>
|-
|-
| 90
! <small>90</small>
| 191st
| <small>191st</small>
| 191/101
| <small>191/101</small>
| 1103.061
| <small>1103.061</small>
|-
|-
| 91
! <small>91</small>
| 192nd
| <small>192nd</small>
| 192/101
| <small>192/101</small>
| 1112.101
| <small>1112.101</small>
|-
|-
| 92
! <small>92</small>
| 193rd
| <small>193rd</small>
| 193/101
| <small>193/101</small>
| 1121.095
| <small>1121.095</small>
|-
|-
| 93
! <small>93</small>
| 194th
| <small>194th</small>
| 194/101
| <small>194/101</small>
| 1130.042
| <small>1130.042</small>
|-
|-
| 94
! <small>94</small>
| 195th
| <small>195th</small>
| 195/101
| <small>195/101</small>
| 1138.943
| <small>1138.943</small>
|-
|-
| 95
! <small>95</small>
| 196th
| <small>196th</small>
| 196/101
| <small>196/101</small>
| 1147.798
| <small>1147.798</small>
|-
|-
| 96
! <small>96</small>
| 197th
| <small>197th</small>
| 197/101
| <small>197/101</small>
| 1156.608
| <small>1156.608</small>
|-
|-
| 97
! <small>97</small>
| 198th
| <small>198th</small>
| 198/101
| <small>198/101</small>
| 1165.374
| <small>1165.374</small>
|-
|-
| 98
! <small>98</small>
| 199th
| <small>199th</small>
| 199/101
| <small>199/101</small>
| 1174.096
| <small>1174.096</small>
|-
|-
| 99
! <small>99</small>
| 200th
| <small>200th</small>
| 200/101
| <small>200/101</small>
| 1182.774
| <small>1182.774</small>
|-
|-
| 100
! <small>100</small>
| 201st
| <small>201st</small>
| 201/101
| <small>201/101</small>
| 1191.408
| <small>1191.408</small>
|-
|-
| 101
! <small>101</small>
| 202nd
| <small>202nd</small>
| 202/101
| <small>202/101</small>
| 1200.000
| <small>1200.000</small>
|}
|}


== Scales ==
== Scales ==
{{Idiosyncratic terms}}
=== Non-neji ===
=== Non-neji ===
Dante
Dante
Line 810: Line 816:


101:113:127:143:160:180:202
101:113:127:143:160:180:202
=== Explanation of idiosyncratic names ===
[[Budjarn Lambeth]] named 101afdo the '''Dalmatian scale''' {{idiosyncratic}} but no one else has been recorded using that name. That name is a reference to the animated TV series {{w|101 Dalmatian Street|''101 Dalmatian Street'' (2019)}}. He named some of its subsets after characters from that series based on the 'mood' evoked by the scales resembling those characters' personalities.


{{Todo|cleanup|comment=write these scales more compactly. }}
{{Todo|cleanup|comment=write these scales more compactly. }}
[[Category:Neji]]
[[Category:Neji]]
[[Category:Primodality]]
[[Category:Primodality]]
[[Category:AFDO]]
[[Category:Harmonic series]]
[[Category:Harmonic series]]
[[Category:Just intonation scales]]
[[Category:Just intonation scales]]
[[Category:Pages with mostly numerical content]]
Retrieved from "https://en.xen.wiki/w/101afdo"