22edo: Difference between revisions
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22-et is very close to an extended "quarter-comma superpyth", a tuning analogous to quarter-comma meantone except that it tempers out the septimal comma 64:63 instead of the syntonic comma 81:80. Because of this it has nearly pure septimal major thirds (9:7). | 22-et is very close to an extended "quarter-comma superpyth", a tuning analogous to quarter-comma meantone except that it tempers out the septimal comma 64:63 instead of the syntonic comma 81:80. Because of this it has nearly pure septimal major thirds (9:7). | ||
=== Differences between distributionally-even scales and smaller edos=== | |||
{| class="wikitable" | |||
|+ | |||
!N | |||
!L-Nedo | |||
!s-Nedo | |||
|- | |||
|3 | |||
|36.364¢ | |||
| -18.182¢ | |||
|- | |||
|4 | |||
|27.273¢ | |||
| -27.273¢ | |||
|- | |||
|5 | |||
|32.727¢ | |||
| -21.818¢ | |||
|- | |||
|6 | |||
|18.182¢ | |||
| -36.364¢ | |||
|- | |||
|7 | |||
|46.753¢ | |||
| -7.792¢ | |||
|- | |||
| 8 | |||
|13.636¢ | |||
| -41.909¢ | |||
|- | |||
|9 | |||
| 30.303¢ | |||
| -24.242¢ | |||
|- | |||
|10 | |||
|43.4545¢ | |||
| -10.909¢ | |||
|- | |||
|12 | |||
|9.091¢ | |||
| -45.4545¢ | |||
|- | |||
|13 | |||
|16.783¢ | |||
| -37.762¢ | |||
|- | |||
|14 | |||
|23.377¢ | |||
| -32.169¢ | |||
|- | |||
| 15 | |||
|29.091¢ | |||
| -25.4545¢ | |||
|- | |||
|16 | |||
|34.091¢ | |||
| -20.4545¢ | |||
|- | |||
| 17 | |||
|38.503¢ | |||
| -16.043¢ | |||
|- | |||
|18 | |||
|42.424¢ | |||
| -12.121¢ | |||
|- | |||
|19 | |||
|45.933¢ | |||
| -8.621¢ | |||
|- | |||
|20 | |||
|49.091¢ | |||
| -5.4545¢ | |||
|} | |||
== Properties of 22 equal temperament == | == Properties of 22 equal temperament == | ||
| Line 1,146: | Line 1,221: | ||
* Porcupine[7] - 3334333 | * Porcupine[7] - 3334333 | ||
* Porcupine[8] - 33333331 | * Porcupine[8] - 33333331 | ||
* Porcupine[15] - 121212121212121 | * Porcupine[15] - [[Tel:121212121212121|121212121212121]] | ||
* Orwell[5] - 55255 | * Orwell[5] - 55255 | ||
* Orwell[9] - 232323232 | * Orwell[9] - 232323232 | ||
* Orwell[13] - 2122122212212 | * Orwell[13] - [[Tel:2122122212212|2122122212212]] | ||
* Magic[7] - 1616161 | * Magic[7] - [[Tel:1616161|1616161]] | ||
* Magic[10] - 5115115111 | * Magic[10] - [[Tel:5115115111|5115115111]] | ||
* Magic[13] - 1141114111411 | * Magic[13] - [[Tel:1141114111411|1141114111411]] | ||
* Magic[16] - 3111131111311111 | * Magic[16] - [[Tel:3111131111311111|3111131111311111]] | ||
* Magic[19] - 1112111112111112111 | * Magic[19] - 1112111112111112111 | ||
* Superpyth[5] - pentatonic - 45454 | * Superpyth[5] - pentatonic - 45454 | ||
* Superpyth[7] - diatonic - 4144414 | * Superpyth[7] - diatonic - 4144414 | ||
* Superpyth[12] - chromatic - 313131131311 | * Superpyth[12] - chromatic - [[Tel:313131131311|313131131311]] | ||
* Superpyth[17] - hyperchromatic - 12111211211211121 | * Superpyth[17] - hyperchromatic - [[Tel:12111211211211121|12111211211211121]] | ||
* Pajara[10] - symmetric decatonic - 2232222322 | * Pajara[10] - symmetric decatonic - [[Tel:2232222322|2232222322]] | ||
* Pajara[12] - 222221222221 | * Pajara[12] - [[Tel:222221222221|222221222221]] | ||
* Hedgehog[6] - 353353 | * Hedgehog[6] - 353353 | ||
* Hedgehog[8] - 33323332 | * Hedgehog[8] - 33323332 | ||
* Hedgehog[14] - 21212122121212 | * Hedgehog[14] - [[Tel:21212122121212|21212122121212]] | ||
* Astrology[6] - 434434 | * Astrology[6] - 434434 | ||
* Astrology[10] - 3131331313 | * Astrology[10] - [[Tel:3131331313|3131331313]] | ||
* Astrology[16] - 2121121121211211 | * Astrology[16] - [[Tel:2121121121211211|2121121121211211]] | ||
* Doublewide[4] - 5656 | * Doublewide[4] - 5656 | ||
* Doublewide[6] - 551551 | * Doublewide[6] - 551551 | ||
* Doublewide[10] - 4141141411 | * Doublewide[10] - [[Tel:4141141411|4141141411]] | ||
* Doublewide[14] - 31131113113111 | * Doublewide[14] - [[Tel:31131113113111|31131113113111]] | ||
* Doublewide[18] - 211121111211121111 | * Doublewide[18] - 211121111211121111 | ||
=== Other scales === | === Other scales === | ||
* Pentachordal decatonic - Pajara[10] 4|4(2) #8 - 2232223222 | * Pentachordal decatonic - Pajara[10] 4|4(2) #8 - [[Tel:2232223222|2232223222]] | ||
* Zarlino/Ptolemy diatonic, "just" major, Ma grama - 4324342 | * Zarlino/Ptolemy diatonic, "just" major, Ma grama - 4324342 | ||
* inverse of Zarlino/Ptolemy diatonic, natural minor - 4234243 | * inverse of Zarlino/Ptolemy diatonic, natural minor - 4234243 | ||
| Line 1,188: | Line 1,263: | ||
* Superpyth harmonic major - Superpyth[7] 5|1 b6 - 4414171 (inverse of harmonic minor) | * Superpyth harmonic major - Superpyth[7] 5|1 b6 - 4414171 (inverse of harmonic minor) | ||
* Superpyth melodic minor - Superpyth[7] 5|1 b3 - 4144441 | * Superpyth melodic minor - Superpyth[7] 5|1 b3 - 4144441 | ||
* Superpyth double harmonic - Superpyth[7] 5|1 b2 b6 - 1714171 | * Superpyth double harmonic - Superpyth[7] 5|1 b2 b6 - [[Tel:1714171|1714171]] | ||
* "just" harmonic minor - 4234252 | * "just" harmonic minor - 4234252 | ||
* "just" harmonic major - 4324252 | * "just" harmonic major - 4324252 | ||