User:BudjarnLambeth/101afdo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled
18,202 edits
mNo edit summary
BudjarnLambeth (talk | contribs)
autopatrolled
18,202 edits
m Redirected page to 101afdo
Tag: New redirect
 
Line 1: Line 1:
{{Infobox AFDO|steps=101}}
#redirect [[101afdo]]
 
'''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]]

Latest revision as of 04:34, 30 July 2025

Redirect to:

Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/101afdo&oldid=205411"