User:BudjarnLambeth/101afdo: Difference between revisions
m Replaced content with "See 101afdo." Tag: Replaced |
mNo edit summary |
||
| Line 1: | Line 1: | ||
{{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]] 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]]. | |||
== Lowest-error neji approximations == | |||
The Dalmatian scale 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) | |||
* [[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) | |||
* [[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:<small> | |||
* [[5edo]] (101:116:133:153:176:202) | |||
* [[12edo]] (101:107:113:120:127:135:143:151:160:170:180:191:202) | |||
* [[14edo]] (101:106:112:117:123:129:136:143:150:158:166:174:183:192:202) | |||
* [[22edo]] (101:104:108:111:115:118:122:126:130:134:138:143:147:152:157:162:167:173:178:184:190:196:202) | |||
* [[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) | |||
* [[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 == | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ Intervals of mode 101 of the harmonic series | |||
|- | |||
! <small>Step</small> | |||
! <small>Harmonic</small> | |||
! <small>Just ratio</small> | |||
! <small>[[Cent]]s value</small> | |||
|- | |||
! <small>1</small> | |||
| <small>102nd</small> | |||
| <small>102/101</small> | |||
| <small>17.057</small> | |||
|- | |||
! <small>2</small> | |||
| <small>103rd</small> | |||
| <small>103/101</small> | |||
| <small>33.947</small> | |||
|- | |||
! <small>3</small> | |||
| <small>104th</small> | |||
| <small>104/101</small> | |||
| <small>50.674</small> | |||
|- | |||
! <small>4</small> | |||
| <small>105th</small> | |||
| <small>105/101</small> | |||
| <small>67.241</small> | |||
|- | |||
! <small>5</small> | |||
| <small>106th</small> | |||
| <small>106/101</small> | |||
| <small>83.651</small> | |||
|- | |||
! <small>6</small> | |||
| <small>107th</small> | |||
| <small>107/101</small> | |||
| <small>99.907</small> | |||
|- | |||
! <small>7</small> | |||
| <small>108th</small> | |||
| <small>108/101</small> | |||
| <small>116.011</small> | |||
|- | |||
! <small>8</small> | |||
| <small>109th</small> | |||
| <small>109/101</small> | |||
| <small>131.967</small> | |||
|- | |||
! <small>9</small> | |||
| <small>110th</small> | |||
| <small>110/101</small> | |||
| <small>147.778</small> | |||
|- | |||
! <small>10</small> | |||
| <small>111th</small> | |||
| <small>111/101</small> | |||
| <small>163.445</small> | |||
|- | |||
! <small>11</small> | |||
| <small>112th</small> | |||
| <small>112/101</small> | |||
| <small>178.972</small> | |||
|- | |||
! <small>12</small> | |||
| <small>113th</small> | |||
| <small>113/101</small> | |||
| <small>194.361</small> | |||
|- | |||
! <small>13</small> | |||
| <small>114th</small> | |||
| <small>114/101</small> | |||
| <small>209.614</small> | |||
|- | |||
! <small>14</small> | |||
| <small>115th</small> | |||
| <small>115/101</small> | |||
| <small>224.734</small> | |||
|- | |||
! <small>15</small> | |||
| <small>116th</small> | |||
| <small>116/101</small> | |||
| <small>239.723</small> | |||
|- | |||
! <small>16</small> | |||
| <small>117th</small> | |||
| <small>117/101</small> | |||
| <small>254.584</small> | |||
|- | |||
! <small>17</small> | |||
| <small>118th</small> | |||
| <small>118/101</small> | |||
| <small>269.318</small> | |||
|- | |||
! <small>18</small> | |||
| <small>119th</small> | |||
| <small>119/101</small> | |||
| <small>283.928</small> | |||
|- | |||
! <small>19</small> | |||
| <small>120th</small> | |||
| <small>120/101</small> | |||
| <small>298.415</small> | |||
|- | |||
! <small>20</small> | |||
| <small>121st</small> | |||
| <small>121/101</small> | |||
| <small>312.782</small> | |||
|- | |||
! <small>21</small> | |||
| <small>122nd</small> | |||
| <small>122/101</small> | |||
| <small>327.031</small> | |||
|- | |||
! <small>22</small> | |||
| <small>123rd</small> | |||
| <small>123/101</small> | |||
| <small>341.164</small> | |||
|- | |||
! <small>23</small> | |||
| <small>124th</small> | |||
| <small>124/101</small> | |||
| <small>355.182</small> | |||
|- | |||
! <small>24</small> | |||
| <small>125th</small> | |||
| <small>125/101</small> | |||
| <small>369.087</small> | |||
|- | |||
! <small>25</small> | |||
| <small>126th</small> | |||
| <small>126/101</small> | |||
| <small>382.882</small> | |||
|- | |||
! <small>26</small> | |||
| <small>127th</small> | |||
| <small>127/101</small> | |||
| <small>396.568</small> | |||
|- | |||
! <small>27</small> | |||
| <small>128th</small> | |||
| <small>128/101</small> | |||
| <small>410.146</small> | |||
|- | |||
! <small>28</small> | |||
| <small>129th</small> | |||
| <small>129/101</small> | |||
| <small>423.619</small> | |||
|- | |||
! <small>29</small> | |||
| <small>130th</small> | |||
| <small>130/101</small> | |||
| <small>436.988</small> | |||
|- | |||
! <small>30</small> | |||
| <small>131st</small> | |||
| <small>131/101</small> | |||
| <small>450.254</small> | |||
|- | |||
! <small>31</small> | |||
| <small>132nd</small> | |||
| <small>132/101</small> | |||
| <small>463.419</small> | |||
|- | |||
! <small>32</small> | |||
| <small>133rd</small> | |||
| <small>133/101</small> | |||
| <small>476.485</small> | |||
|- | |||
! <small>33</small> | |||
| <small>134th</small> | |||
| <small>134/101</small> | |||
| <small>489.453</small> | |||
|- | |||
! <small>34</small> | |||
| <small>135th</small> | |||
| <small>135/101</small> | |||
| <small>502.325</small> | |||
|- | |||
! <small>35</small> | |||
| <small>136th</small> | |||
| <small>136/101</small> | |||
| <small>515.102</small> | |||
|- | |||
! <small>36</small> | |||
| <small>137th</small> | |||
| <small>137/101</small> | |||
| <small>527.785</small> | |||
|- | |||
! <small>37</small> | |||
| <small>138th</small> | |||
| <small>138/101</small> | |||
| <small>540.376</small> | |||
|- | |||
! <small>38</small> | |||
| <small>139th</small> | |||
| <small>139/101</small> | |||
| <small>552.876</small> | |||
|- | |||
! <small>39</small> | |||
| <small>140th</small> | |||
| <small>140/101</small> | |||
| <small>565.286</small> | |||
|- | |||
! <small>40</small> | |||
| <small>141st</small> | |||
| <small>141/101</small> | |||
| <small>577.608</small> | |||
|- | |||
! <small>41</small> | |||
| <small>142nd</small> | |||
| <small>142/101</small> | |||
| <small>589.843</small> | |||
|- | |||
! <small>42</small> | |||
| <small>143rd</small> | |||
| <small>143/101</small> | |||
| <small>601.992</small> | |||
|- | |||
! <small>43</small> | |||
| <small>144th</small> | |||
| <small>144/101</small> | |||
| <small>614.056</small> | |||
|- | |||
! <small>44</small> | |||
| <small>145th</small> | |||
| <small>145/101</small> | |||
| <small>626.037</small> | |||
|- | |||
! <small>45</small> | |||
| <small>146th</small> | |||
| <small>146/101</small> | |||
| <small>637.936</small> | |||
|- | |||
! <small>46</small> | |||
| <small>147th</small> | |||
| <small>147/101</small> | |||
| <small>649.753</small> | |||
|- | |||
! <small>47</small> | |||
| <small>148th</small> | |||
| <small>148/101</small> | |||
| <small>661.490</small> | |||
|- | |||
! <small>48</small> | |||
| <small>149th</small> | |||
| <small>149/101</small> | |||
| <small>673.148</small> | |||
|- | |||
! <small>49</small> | |||
| <small>150th</small> | |||
| <small>150/101</small> | |||
| <small>684.729</small> | |||
|- | |||
! <small>50</small> | |||
| <small>151st</small> | |||
| <small>151/101</small> | |||
| <small>696.232</small> | |||
|- | |||
! <small>51</small> | |||
| <small>152nd</small> | |||
| <small>152/101</small> | |||
| <small>707.659</small> | |||
|- | |||
! <small>52</small> | |||
| <small>153rd</small> | |||
| <small>153/101</small> | |||
| <small>719.012</small> | |||
|- | |||
! <small>53</small> | |||
| <small>154th</small> | |||
| <small>154/101</small> | |||
| <small>730.290</small> | |||
|- | |||
! <small>54</small> | |||
| <small>155th</small> | |||
| <small>155/101</small> | |||
| <small>741.496</small> | |||
|- | |||
! <small>55</small> | |||
| <small>156th</small> | |||
| <small>156/101</small> | |||
| <small>752.629</small> | |||
|- | |||
! <small>56</small> | |||
| <small>157th</small> | |||
| <small>157/101</small> | |||
| <small>763.691</small> | |||
|- | |||
! <small>57</small> | |||
| <small>158th</small> | |||
| <small>158/101</small> | |||
| <small>774.683</small> | |||
|- | |||
! <small>58</small> | |||
| <small>159th</small> | |||
| <small>159/101</small> | |||
| <small>785.606</small> | |||
|- | |||
! <small>59</small> | |||
| <small>160th</small> | |||
| <small>160/101</small> | |||
| <small>796.460</small> | |||
|- | |||
! <small>60</small> | |||
| <small>161st</small> | |||
| <small>161/101</small> | |||
| <small>807.246</small> | |||
|- | |||
! <small>61</small> | |||
| <small>162nd</small> | |||
| <small>162/101</small> | |||
| <small>817.966</small> | |||
|- | |||
! <small>62</small> | |||
| <small>163rd</small> | |||
| <small>163/101</small> | |||
| <small>828.620</small> | |||
|- | |||
! <small>63</small> | |||
| <small>164th</small> | |||
| <small>164/101</small> | |||
| <small>839.209</small> | |||
|- | |||
! <small>64</small> | |||
| <small>165th</small> | |||
| <small>165/101</small> | |||
| <small>849.733</small> | |||
|- | |||
! <small>65</small> | |||
| <small>166th</small> | |||
| <small>166/101</small> | |||
| <small>860.194</small> | |||
|- | |||
! <small>66</small> | |||
| <small>167th</small> | |||
| <small>167/101</small> | |||
| <small>870.591</small> | |||
|- | |||
! <small>67</small> | |||
| <small>168th</small> | |||
| <small>168/101</small> | |||
| <small>880.927</small> | |||
|- | |||
! <small>68</small> | |||
| <small>169th</small> | |||
| <small>169/101</small> | |||
| <small>891.202</small> | |||
|- | |||
! <small>69</small> | |||
| <small>170th</small> | |||
| <small>170/101</small> | |||
| <small>901.415</small> | |||
|- | |||
! <small>70</small> | |||
| <small>171st</small> | |||
| <small>171/101</small> | |||
| <small>911.569</small> | |||
|- | |||
! <small>71</small> | |||
| <small>172nd</small> | |||
| <small>172/101</small> | |||
| <small>921.664</small> | |||
|- | |||
! <small>72</small> | |||
| <small>173rd</small> | |||
| <small>173/101</small> | |||
| <small>931.700</small> | |||
|- | |||
! <small>73</small> | |||
| <small>174th</small> | |||
| <small>174/101</small> | |||
| <small>941.678</small> | |||
|- | |||
! <small>74</small> | |||
| <small>175th</small> | |||
| <small>175/101</small> | |||
| <small>951.600</small> | |||
|- | |||
! <small>75</small> | |||
| <small>176th</small> | |||
| <small>176/101</small> | |||
| <small>961.464</small> | |||
|- | |||
! <small>76</small> | |||
| <small>177th</small> | |||
| <small>177/101</small> | |||
| <small>971.273</small> | |||
|- | |||
! <small>77</small> | |||
| <small>178th</small> | |||
| <small>178/101</small> | |||
| <small>981.026</small> | |||
|- | |||
! <small>78</small> | |||
| <small>179th</small> | |||
| <small>179/101</small> | |||
| <small>990.725</small> | |||
|- | |||
! <small>79</small> | |||
| <small>180th</small> | |||
| <small>180/101</small> | |||
| <small>1000.370</small> | |||
|- | |||
! <small>80</small> | |||
| <small>181st</small> | |||
| <small>181/101</small> | |||
| <small>1009.961</small> | |||
|- | |||
! <small>81</small> | |||
| <small>182nd</small> | |||
| <small>182/101</small> | |||
| <small>1019.500</small> | |||
|- | |||
! <small>82</small> | |||
| <small>183rd</small> | |||
| <small>183/101</small> | |||
| <small>1028.986</small> | |||
|- | |||
! <small>83</small> | |||
| <small>184th</small> | |||
| <small>184/101</small> | |||
| <small>1038.421</small> | |||
|- | |||
! <small>84</small> | |||
| <small>185th</small> | |||
| <small>185/101</small> | |||
| <small>1047.804</small> | |||
|- | |||
! <small>85</small> | |||
| <small>186th</small> | |||
| <small>186/101</small> | |||
| <small>1057.137</small> | |||
|- | |||
! <small>86</small> | |||
| <small>187th</small> | |||
| <small>187/101</small> | |||
| <small>1066.420</small> | |||
|- | |||
! <small>87</small> | |||
| <small>188th</small> | |||
| <small>188/101</small> | |||
| <small>1075.653</small> | |||
|- | |||
! <small>88</small> | |||
| <small>189th</small> | |||
| <small>189/101</small> | |||
| <small>1084.837</small> | |||
|- | |||
! <small>89</small> | |||
| <small>190th</small> | |||
| <small>190/101</small> | |||
| <small>1093.973</small> | |||
|- | |||
! <small>90</small> | |||
| <small>191st</small> | |||
| <small>191/101</small> | |||
| <small>1103.061</small> | |||
|- | |||
! <small>91</small> | |||
| <small>192nd</small> | |||
| <small>192/101</small> | |||
| <small>1112.101</small> | |||
|- | |||
! <small>92</small> | |||
| <small>193rd</small> | |||
| <small>193/101</small> | |||
| <small>1121.095</small> | |||
|- | |||
! <small>93</small> | |||
| <small>194th</small> | |||
| <small>194/101</small> | |||
| <small>1130.042</small> | |||
|- | |||
! <small>94</small> | |||
| <small>195th</small> | |||
| <small>195/101</small> | |||
| <small>1138.943</small> | |||
|- | |||
! <small>95</small> | |||
| <small>196th</small> | |||
| <small>196/101</small> | |||
| <small>1147.798</small> | |||
|- | |||
! <small>96</small> | |||
| <small>197th</small> | |||
| <small>197/101</small> | |||
| <small>1156.608</small> | |||
|- | |||
! <small>97</small> | |||
| <small>198th</small> | |||
| <small>198/101</small> | |||
| <small>1165.374</small> | |||
|- | |||
! <small>98</small> | |||
| <small>199th</small> | |||
| <small>199/101</small> | |||
| <small>1174.096</small> | |||
|- | |||
! <small>99</small> | |||
| <small>200th</small> | |||
| <small>200/101</small> | |||
| <small>1182.774</small> | |||
|- | |||
! <small>100</small> | |||
| <small>201st</small> | |||
| <small>201/101</small> | |||
| <small>1191.408</small> | |||
|- | |||
! <small>101</small> | |||
| <small>202nd</small> | |||
| <small>202/101</small> | |||
| <small>1200.000</small> | |||
|} | |||
== Scales == | |||
{{Idiosyncratic terms}} | |||
=== Non-neji === | |||
Dante | |||
101:114:120:152:189:202 | |||
Da Vinci | |||
101:113:126:151:178:202 | |||
Dawkins | |||
101:118:135:152:185:202 | |||
Deepak | |||
101:126:135:152:160:202 | |||
Deja Vu | |||
101:121:151:162:182:202 | |||
Delgado | |||
101:107:126:152:177:202 | |||
Dolly | |||
101:127:134:152:177:202 | |||
Dylan | |||
101:135:151:161:180:202 | |||
Fergus | |||
101:121:135:140:151:175:181:202 | |||
Hansel | |||
101:113:126:135:151:169:189:202 | |||
=== Neji 5edo === | |||
Equipentatonic | |||
101:116:133:153:176:202 | |||
=== Neji 6edo === | |||
Liquorice | |||
101:113:127:143:160:180:202 | |||
=== Neji 12edo === | |||
Blues Aeolian Hexatonic | |||
101:120:135:143:151:160:202 | |||
Blues Aeolian Pentatonic I | |||
101:120:135:151:160:202 | |||
Blues Aeolian Pentatonic II | |||
101:120:151:160:180:202 | |||
Blues Bright Double Harmonic | |||
101:107:127:135:151:160:180:191:202 | |||
Blues Dark Double Harmonic | |||
101:113:120:135:143:151:160:191:202 | |||
Blues Dorian Hexatonic | |||
101:120:135:151:170:180:202 | |||
Blues Dorian Pentatonic | |||
101:120:151:170:180:202 | |||
Blues Dorian Septatonic | |||
101:120:135:143:151:170:180:202 | |||
Blues Harmonic Hexatonic | |||
101:113:120:135:151:191:202 | |||
Blues Harmonic Septatonic | |||
101:120:135:143:151:160:191:202 | |||
Blues Leading | |||
101:120:135:143:151:180:191:202 | |||
Blues Minor | |||
101:120:135:143:151:180:202 | |||
Blues Minor Maj7 | |||
101:120:135:143:151:191:202 | |||
Blues Pentachordal | |||
101:113:120:135:143:151:202 | |||
Dominant Pentatonic | |||
101:113:127:151:180:202 | |||
Dorian | |||
101:113:120:135:151:170:180:202 | |||
Double Harmonic | |||
1101:07:127:135:151:160:191:202 | |||
Hirajoshi | |||
101:113:120:151:160:202 | |||
Ionian Pentatonic | |||
101:127:135:151:191:202 | |||
Javanese Pentachordal | |||
101:107:120:143:151:202 | |||
Kokin-Joshi | |||
101:113:120:151:170:202 | |||
Locrian | |||
101:107:120:135:143:160:180:202 | |||
Lydian | |||
101:113:127:143:151:170:191:202 | |||
Major | |||
101:113:127:135:151:170:191:202 | |||
Major Pentatonic | |||
101:113:127:151:170:202 | |||
Minor | |||
101:113:120:135:151:160:180:202 | |||
Minor Harmonic | |||
101:113:120:135:151:160:191:202 | |||
Minor Harmonic Pentatonic | |||
101:113:120:151:191:202 | |||
Minor Hexatonic | |||
101:113:120:135:151:180:202 | |||
Minor Melodic | |||
101:113:120:135:151:170:191:202 | |||
Minor Pentatonic | |||
101:120:135:151:180:202 | |||
Mixolydian | |||
101:113:127:135:151:170:180:202 | |||
Mixolydian Harmonic | |||
101:127:135:151:160:180:202 | |||
Mixolydian Pentatonic | |||
101:127:135:151:180:202 | |||
Phrygian | |||
101:107:120:135:151:160:180:202 | |||
Phrygian Dominant | |||
101:107:127:135:151:160:180:202 | |||
Phrygian Dominant Hexatonic | |||
101:107:127:135:151:180:202 | |||
Phrygian Dominant Pentatonic | |||
101:127:135:151:160:202 | |||
Phrygian Pentatonic | |||
101:107:120:151:160:202 | |||
Picardy Hexatonic | |||
101:113:127:135:151:160:202 | |||
Picardy Pentatonic | |||
101:113:127:151:160:202 | |||
Liquorice (Whole Tone) | |||
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. }} | |||
[[Category:Neji]] | |||
[[Category:Primodality]] | |||
[[Category:Harmonic series]] | |||
[[Category:Just intonation scales]] | |||
[[Category:Pages with mostly numerical content]] | |||