Xenharmonic Wiki

User:Moremajorthanmajor/8L 3s (perfect twelfth-equivalent): Difference between revisions

← Older edit
VisualWikitext
 
(5 intermediate revisions by the same user not shown)
Line 36: Line 36:


==Intervals==
==Intervals==
The table of Obikhodic intervals below takes the fifth as the generator. Given the size of the fifth generator ''g'', any Obikhodic interval can easily be found by noting what multiple of ''g'' it is, and multiplying the size by the number ''k'' of generators it takes to reach the interval and reducing mod 1900<ref>For relative cents</ref> if necessary (so you can use "''k''*''g'' % 1900" for search engines, for plugged-in values of ''k'' and ''g''). For example, since the major 3rd is reached by six fifth generators, [[27edt]]'s major 3rd is 6*703.7 mod 1900 = 4222.22 mod 1900 = 422.22r¢.
The table of Obikhodic intervals below takes the fifth as the generator.
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 1,444: Line 1,444:
{| class="wikitable"
{| class="wikitable"
|-
|-
| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" |'''Mode'''
| style="text-align:center;" |'''Mode'''
| style="text-align:center;" |[[Modal UDP Notation|'''UDP''']]
| style="text-align:center;" |'''Name'''
| style="text-align:center;" |'''Name'''
|-
|-
| style="text-align:center;" |<nowiki>10|0</nowiki>
|LLLsLLLsLLs
|LLLsLLLsLLs
| style="text-align:center;" |<nowiki>10|0</nowiki>
|(Great) Lydian #8 (Tanagran)
|(Great) Lydian #8 (Tanagran)
|-
|-
| style="text-align:center;" |<nowiki>9|1</nowiki>
|LLLsLLsLLLs
|LLLsLLsLLLs
| style="text-align:center;" |<nowiki>9|1</nowiki>
|(Great) Lydian
|(Great) Lydian
|-
|-
| style="text-align:center;" |<nowiki>8|2</nowiki>
|LLsLLLsLLLs
|LLsLLLsLLLs
| style="text-align:center;" |<nowiki>8|2</nowiki>
|(Great) Lydian f4, Ionian #11 (Distomian)
|(Great) Lydian f4, Ionian #11 (Distomian)
|-
|-
| style="text-align:center;" |<nowiki>7|3</nowiki>
| |LLsLLLsLLsL
| |LLsLLLsLLsL
| style="text-align:center;" |<nowiki>7|3</nowiki>
| |(Great) Ionian
| |(Great) Ionian
|-
|-
| style="text-align:center;" |<nowiki>6|4</nowiki>
| |LLsLLsLLLsL
| |LLsLLsLLLsL
| style="text-align:center;" |<nowiki>6|4</nowiki>
| |(Great) Mixolydian
| |(Great) Mixolydian
|-
|-
| style="text-align:center;" |<nowiki>5|5</nowiki>
| |LsLLLsLLLsL
| |LsLLLsLLLsL
| style="text-align:center;" |<nowiki>5|5</nowiki>
| |(Great) Mixolydian f3, Dorian #10 (Livadeian)
| |(Great) Mixolydian f3, Dorian #10 (Livadeian)
|-
|-
| style="text-align:center;" |<nowiki>4|6</nowiki>
| |LsLLLsLLsLL
| |LsLLLsLLsLL
| style="text-align:center;" |<nowiki>4|6</nowiki>
| |(Great) Dorian
| |(Great) Dorian
|-
|-
| style="text-align:center;" |<nowiki>3|7</nowiki>
| |LsLLsLLLsLL
| |LsLLsLLLsLL
| style="text-align:center;" |<nowiki>3|7</nowiki>
| |(Great) Aeolian
| |(Great) Aeolian
|-
|-
| style="text-align:center;" |<nowiki>2|8</nowiki>
| |sLLLsLLLsLL
| |sLLLsLLLsLL
| style="text-align:center;" |<nowiki>2|8</nowiki>
| |(Great) Aeolian f2, Phrygian #9 (Theban)
| |(Great) Aeolian f2, Phrygian #9 (Theban)
|-
|-
| style="text-align:center;" |<nowiki>1|9</nowiki>
| |sLLLsLLsLLL
| |sLLLsLLsLLL
| style="text-align:center;" |<nowiki>1|9</nowiki>
| |(Great) Phrygian
| |(Great) Phrygian
|-
|-
| style="text-align:center;" |<nowiki>0|10</nowiki>
| |sLLsLLLsLLL
| |sLLsLLLsLLL
| style="text-align:center;" |<nowiki>0|10</nowiki>
| |(Great) Locrian
| |(Great) Locrian
|}
|}
Line 1,507: Line 1,507:
|(Great) Dorian #3
|(Great) Dorian #3
|-
|-
|LsLLsLLLLsL
|LLsLLsLLLLs
|<nowiki>5|5 b6</nowiki>
|<nowiki>8|2 b7</nowiki>
|<nowiki>3|7 #10</nowiki>
|<nowiki>6|4 #11</nowiki>
|(Great) Mixolydian f3 f6, Dorian f6 #10 (Livadeian f6)
|(Great) Lydian f4 f7, Ionian f7 #11 (Distomian Dominant)
|(Great) Aeolian #10
|(Great) Mixolydian #11
|-
|LLsLLLLsLLs
|<nowiki>10|0 b4</nowiki>
|<nowiki>8|2 #8</nowiki>
|(Great) Lydian f4 #8 (Tanagran f4)
|(Great) Lydian f4 #8, Ionian #8 #11 (Distomian #8)
|-
|-
|sLLLLsLLsLL
|LLLLsLLsLLs
|<nowiki>4|6 b2</nowiki>
|<nowiki>1|9 *b1</nowiki>
|<nowiki>2|8 #6</nowiki>
|<nowiki>10|0 #5</nowiki>
|(Great) Dorian f2
|(Great) Phrygian *f1
|(Great) Aeolian f2 #6, Phrygian #6 #9 (Theban #6)
|(Great) Lydian #5 #8 (Tanagran #5)
|-
|-
|LsLLsLLsLLL
|LsLLsLLsLLL
Line 1,525: Line 1,531:
|(Great) Phrygian #2
|(Great) Phrygian #2
|-
|-
|sLLsLLLLsLL
|LsLLsLLLLsL
|<nowiki>2|8 b5</nowiki>
|<nowiki>5|5 b6</nowiki>
|<nowiki>0|10 #9</nowiki>
|<nowiki>3|7 #10</nowiki>
|(Great) Aeolian f2 f5, Phrygian f5 #9 (Theban f5)
|(Great) Mixolydian f3 f6, Dorian f6 #10 (Livadeian f6)
|(Great) Locrian #9
|(Great) Aeolian #10
|-
|-
|LsLLsLLsLLL
|sLLLLsLLsLL
|<nowiki>1|9 *b1</nowiki>
|<nowiki>7|3 b3</nowiki>
|
|<nowiki>5|5 #7</nowiki>
|(Great) Phrygian *f1
|(Great) Ionian f3
|
|(Great) Mixolydian f3 #7, Dorian #7 #10 (Livadeian #7)
|-
|-
|LLLLsLLsLLs
|LLLsLLsLLsL
|
|<nowiki>9|1 b11</nowiki>
|<nowiki>10|0 #5</nowiki>
|<nowiki>7|3 #4</nowiki>
|
|(Great) Lydian f11
|(Great) Lydian #5 #8 (Tanagran #5)
|(Great) Ionian #4
|-
|-
|sLLsLLsLLLL
|sLLsLLsLLLL
Line 1,549: Line 1,555:
|(Great) Lydian *#1
|(Great) Lydian *#1
|-
|-
|LLsLLLLsLLs
|sLLsLLLLsLL
|<nowiki>10|0 b4</nowiki>
|<nowiki>2|8 b5</nowiki>
|<nowiki>8|2 #8</nowiki>
|<nowiki>0|10 #9</nowiki>
|(Great) Lydian f4 #8 (Tanagran f4)
|(Great) Aeolian f2 f5, Phrygian f5 #9 (Theban f5)
|(Great) Lydian f4 #8, Ionian #8 #11 (Distomian #8)
|(Great) Locrian #9
|-
|-
|LLLsLLsLLsL
|LsLLLLsLLsL
|<nowiki>9|1 b11</nowiki>
|<nowiki>4|6 b2</nowiki>
|<nowiki>7|3 #4</nowiki>
|<nowiki>2|8 #6</nowiki>
|(Great) Lydian f11
|(Great) Dorian f2
|(Great) Ionian #4
|(Great) Aeolian f2 #6, Phrygian #6 #9 (Theban #6)
|-
|LLsLLsLLLLs
|<nowiki>8|2 b7</nowiki>
|<nowiki>6|4 #11</nowiki>
|(Great) Lydian f4 f7, Ionian f7 #11 (Distomian Dominant)
|(Great) Mixolydian #11
|-
|LsLLLLsLLsL
|<nowiki>7|3 b3</nowiki>
|<nowiki>5|5 #7</nowiki>
|(Great) Ionian f3
|(Great) Mixolydian f3 #7, Dorian #7 #10 (Livadeian #7)
|}
|}


Line 1,792: Line 1,786:
|FGHJKLABC#DEF
|FGHJKLABC#DEF
|KLABCDEFG#HJK
|KLABCDEFG#HJK
|sLLsLLsLLLL
|sLLsLLLLsLL
|<nowiki>0|10 #9</nowiki>
|<nowiki>0|10 #9</nowiki>
|(Great) Locrian #9
|(Great) Locrian #9
Line 1,809: Line 1,803:
!Generator
!Generator
!Normalized
!Normalized
!Large step
!Small step
|-
|-
|3\8
|3\8
|<u>720</u>
|<u>720.000</u>
|1\5, <u>240.000</u>
|0
|-
|-
|19\51
|19\51
|<u>712.5</u>
|<u>712.500</u>
|6\51, <u>225.000</u>
|1\51, <u>37.500</u>
|-
|54\145
|<u>712.088</u>
|17\145, <u>224.175</u>
|3\145, <u>39.560</u>
|-
|35\94
|<u>711.864</u>
|11\94, <u>223.729</u>
|2\94, <u>40.678</u>
|-
|-
|16\43
|16\43
|<u>711.111</u>
|<u>711.111</u>
|5\43, <u>222.222</u>
|1\43, <u>44.444</u>
|-
|45\121
|<u>710.526</u>
|14\121, <u>221.053</u>
|3\121, <u>47.368</u>
|-
|-
|29\78
|29\78
|<u>710.204</u>
|<u>710.204</u>
|9\78, <u>220.408</u>
|2\78, <u>48.980</u>
|-
|42\113
|<u>709.859</u>
|13\113, <u>219.718</u>
|3\113, <u>50.704</u>
|-
|-
|13\35
|13\35
|<u>709.091</u>
|<u>709.091</u>
|4\35, <u>218.182</u>
|1\35, <u>54.545</u>
|-
|49\132
|<u>708.434</u>
|15\132, <u>216.867</u>
|4\132, <u>57.831</u>
|-
|-
|36\97
|36\97
|<u>708.197</u>
|<u>708.197</u>
|11\97, <u>216.393</u>
|3\97, <u>59.016</u>
|-
|-
|23\62
|23\62
|<u>707.692</u>
|<u>707.692</u>
|7\62, <u>215.385</u>
|2\62, <u>61.538</u>
|-
|-
|33\89
|33\89
|<u>707.143</u>
|<u>707.143</u>
|10\89, <u>214.286</u>
|3\89, <u>64.286</u>
|-
|-
|43\116
|43\116
|<u>706.849</u>
|<u>706.849</u>
|13\116, <u>213.699</u>
|4\116, <u>65.753</u>
|-
|53\143
|<u>706.667</u>
|16\143, <u>213.333</u>
|5\143, <u>66.667</u>
|-
|63\170
|<u>706.542</u>
|19\170, <u>213.084</u>
|6\170, <u>67.290</u>
|-
|73\197
|<u>706.452</u>
|22\197, <u>212.903</u>
|7\197, <u>67.742</u>
|-
|-
|10\27
|10\27
|<u>705.882</u>
|<u>705.882</u>
|3\27, <u>211.765</u>
|1\27, <u>70.588</u>
|-
|47\127
|<u>705.000</u>
|14\127, <u>210.000</u>
|5\127, <u>75.000</u>
|-
|37\100
|<u>704.762</u>
|11\100, <u>209.524</u>
|4\100, <u>76.190</u>
|-
|-
|27\73
|27\73
|<u>704.348</u>
|<u>704.348</u>
|8\73, <u>208.696</u>
|3\27, <u>78.261</u>
|-
|-
|17\46
|17\46
|<u>703.448</u>
|<u>703.448</u>
|5\46, <u>206.897</u>
|2\46, <u>82.759</u>
|-
|41\111
|<u>702.857</u>
|12\111, <u>205.714</u>
|5\111, <u>85.714</u>
|-
|-
|24\65
|24\65
|<u>702.439</u>
|<u>702.439</u>
|7\65, <u>204.878</u>
|3\65, <u>87.805</u>
|-
|-
|31\84
|31\84
|<u>701.887</u>
|<u>701.887</u>
|9\84, <u>203.774</u>
|4\84, <u>90.566</u>
|-
|…
|…
|…
|…
|-
|59\160
|<u>700.990</u>
|17\160, <u>201.980</u>
|8\160, <u>95.050</u>
|-
|…
|…
|…
|…
|-
|122\331
|<u>700.478</u>
|35\331, <u>200.960</u>
|18\334, <u>97.608</u>
|-
|-
|7\19
|7\19
|<u>700</u>
|<u>700.000</u>
|2\19, <u>200.000</u>
|1\19, <u>100.000</u>
|-
|-
|60\163
|123\334
|<u>699.029</u>
|<u>699.526</u>
|35\334, <u>199.052</u>
|18\334, <u>102.370</u>
|-
|-
|53\144
|…
|<u>698.901</u>
|…
|…
|…
|-
|-
|46\125
|63\163
|<u>698.734</u>
|<u>699.029</u>
|17\163, <u>198.058</u>
|9\163, <u>104.854</u>
|-
|-
|39\106
|…
|<u>698.507</u>
|…
|…
|…
|-
|-
|32\87
|32\87
|<u>698.182</u>
|<u>698.182</u>
|9\87, <u>196.364</u>
|5\87, <u>109.091</u>
|-
|-
|25\68
|25\68
|<u>697.674</u>
|<u>697.674</u>
|7\68, <u>195.349</u>
|4\68, <u>111.628</u>
|-
|43\117
|<u>697.297</u>
|12\117, <u>194.594</u>
|7\117, <u>113.514</u>
|-
|-
|18\49
|18\49
|<u>696.77</u>
|<u>696.774</u>
|5\49, <u>193.548</u>
|3\49, <u>116.129</u>
|-
|-
|29\79
|29\79
|<u>696</u>
|<u>696.000</u>
|8\79, <u>192.000</u>
|5\79, <u>120.000</u>
|-
|-
|40\109
|40\109
|<u>695.652</u>
|<u>695.652</u>
|11\109, <u>191.304</u>
|7\109, <u>121.739</u>
|-
|51\139
|<u>695.455</u>
|14\139, <u>190.909</u>
|9\139, <u>122.727</u>
|-
|-
|11\30
|11\30
|<u>694.737</u>
|<u>694.737</u>
|3\30, <u>189.474</u>
|2\30, <u>126.316</u>
|-
|59\161
|<u>694.118</u>
|16\161, <u>188.235</u>
|11\161, <u>129.412</u>
|-
|48\131
|<u>693.976</u>
|13\131, <u>187.952</u>
|9\131, <u>130.120</u>
|-
|37\101
|<u>693.750</u>
|10\101, <u>187.500</u>
|7\101, <u>131.250</u>
|-
|-
|26\71
|26\71
|<u>693.333</u>
|<u>693.333</u>
|7\71, <u>186.667</u>
|5\71, <u>133.333</u>
|-
|41\112
|<u>692.958</u>
|11\112, <u>185.915</u>
|8\112, <u>135.211</u>
|-
|-
|15\41
|15\41
|<u>692.308</u>
|<u>692.308</u>
|4\41, <u>184.615</u>
|3\41, <u>138.462</u>
|-
|-
|34\93
|34\93
|<u>691.525</u>
|<u>691.525</u>
|9\93, <u>183.051</u>
|7\93, <u>142.373</u>
|-
|53\145
|<u>691.304</u>
|14\145, <u>182.609</u>
|11\145, <u>143.478</u>
|-
|-
|19\52
|19\52
|<u>690.909</u>
|<u>690.909</u>
|5\52, <u>181.818</u>
|4\52, <u>145.455</u>
|-
|-
|23\63
|23\63
|<u>690</u>
|<u>690.000</u>
|6\63, <u>180.000</u>
|5\63, <u>150.000</u>
|-
|-
|4\11
|4\11
|<u>685.714</u>
|<u>685.714</u>
|1\11, <u>171.429</u>
|1\11, <u>171.429</u>
|}
|}


Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/8L_3s_(perfect_twelfth-equivalent)"