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== Theory ==
== Theory ==
''It is recommended to read the page [[regular temperament]] first to understand this section.''
84edo shares the [[3/2|perfect fifth]] with [[12edo]], [[tempering out]] the [[Pythagorean comma]] in its [[patent val]]. In the [[5-limit]] it tempers out the [[sensipent comma]]; in the [[7-limit]] [[225/224]], [[1728/1715]], [[2430/2401]], [[6144/6125]], [[support]]ing [[orwell]], [[compton]], and [[sensei]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].  
84edo shares the [[3/2|perfect fifth]] with [[12edo]], [[tempering out]] the [[Pythagorean comma]] in its [[patent val]]. In the [[5-limit]] it tempers out the [[sensipent comma]]; in the [[7-limit]] [[225/224]], [[1728/1715]], [[2430/2401]], [[6144/6125]], [[support]]ing [[orwell]], [[compton]], and [[sensei]]. In the [[13-limit]] it is the [[optimal patent val]] for the rank-5 temperament tempering out [[144/143]].  


84edo is where the orwell temperament takes its name from, since the generator of [[7/6]] is equal to 19 steps of the edo, referencing the [[Wikipedia: Nineteen Eighty-Four|book 1984]]. Orwell in 84edo comes in two varieties—the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the original orwell, and its [[patent val]] {{val| 84 133 195 236 '''291''' }} supporting [[newspeak]]. 84edo orwell offers [[mos scale]]s of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.
84edo is where the orwell temperament takes its name from, since the generator of [[7/6]] is equal to 19 steps of the edo, referencing the [[Wikipedia: Nineteen Eighty-Four|book 1984]]. Orwell in 84edo comes in two varieties—the 84e val {{val| 84 133 195 236 '''290''' }}, supporting the original orwell, and its [[patent val]] {{val| 84 133 195 236 '''291''' }} supporting [[newspeak]]. 84edo orwell offers [[mos scale]]s of size 9, 13, 22, and 31, of which the 31-note scale is the [[maximal evenness]] scale.
=== High limit consistency and coverage ===
It has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], [[31/1|31]], 41, 43, 53, 59, 61, 73 and 89, so that it is for its size very performant for much of the 61-limit (with more off primes usually being sharp so that they can cancel opportunistically with other sharp harmonics). In fact, if we avoid all intervals of 11 and 17 as well as the complex compound prime powers [[27/1|27]] and [[49/1|49]], it is completely [[consistent]] in the no-37's no-47's 65-odd-limit excepting only 1 inconsistent pair, 45/43 and 86/45, which are inconsistent by ~1.3{{cent}} (off by ~7.3{{cent}}), offering a truly vast inventory of harmony to draw from that has mostly been unexplored. This is especially true because its approximation powers do not end there: prime 11, due to its simplicity (and thus lesser tuning fidelity), is certainly usable (just causes some inconsistencies), and there are higher primes that are reasonably in-tune too (when supported by context). Except 17, the only missing primes are thus [[37/32|37]], [[47/32|47]], [[67/64|67]], [[71/64|71]], [[79/64|79]] and [[83/64|83]], which coincidentally are all about 6 cents sharp, similar to the sharpness of prime 11, so that it somewhat makes up for these omissions by having a very accurate 22:37:47:67:71:79:83 chord, to which various additions are possible (though usually increasing the error as a result).


=== Prime harmonics ===
=== Prime harmonics ===
Line 29: Line 24:
| 0
| 0
| 0.0
| 0.0
| 1/1
| [[1/1]]
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 36: Line 31:
| 1
| 1
| 14.3
| 14.3
| ''81/80'', 105/104, 126/125, 169/168, 196/195
| ''[[81/80]]'', [[105/104]], [[126/125]], [[169/168]], [[196/195]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 43: Line 38:
| 2
| 2
| 28.6
| 28.6
| 50/49, 64/63, 65/64, ''91/90''
| [[50/49]], [[64/63]], [[65/64]], ''[[91/90]]''
| Dup 1sn
| Dup 1sn
| ^^1
| ^^1
Line 50: Line 45:
| 3
| 3
| 42.9
| 42.9
| 36/35, 40/39, 46/45, 49/48
| [[36/35]], [[40/39]], [[46/45]], [[49/48]]
| Trup 1sn
| Trup 1sn
| ^^^1
| ^^^1
Line 57: Line 52:
| 4
| 4
| 57.1
| 57.1
| ''27/26''
| ''[[27/26]]''
| Trudminor 2nd
| Trudminor 2nd
| vvvm2
| vvvm2
Line 64: Line 59:
| 5
| 5
| 71.4
| 71.4
| 24/23, 25/24, 26/25, ''28/27''
| [[24/23]], [[25/24]], [[26/25]], ''[[28/27]]''
| Dudminor 2nd
| Dudminor 2nd
| vvm2
| vvm2
Line 71: Line 66:
| 6
| 6
| 85.7
| 85.7
| 20/19, 21/20
| [[20/19]], [[21/20]]
| Downminor 2nd
| Downminor 2nd
| vm2
| vm2
Line 78: Line 73:
| 7
| 7
| 100.0
| 100.0
| 19/18
| [[19/18]]
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 85: Line 80:
| 8
| 8
| 114.3
| 114.3
| 15/14, 16/15
| [[15/14]], [[16/15]]
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 92: Line 87:
| 9
| 9
| 128.6
| 128.6
| 14/13
| [[14/13]]
| Dupminor 2nd
| Dupminor 2nd
| ^^m2
| ^^m2
Line 99: Line 94:
| 10
| 10
| 142.9
| 142.9
| 13/12
| [[13/12]]
| Trupminor 2nd
| Trupminor 2nd
| ^^^m2
| ^^^m2
Line 106: Line 101:
| 11
| 11
| 157.1
| 157.1
| 23/21
| [[23/21]]
| Trudmajor 2nd
| Trudmajor 2nd
| vvvM2
| vvvM2
Line 113: Line 108:
| 12
| 12
| 171.4
| 171.4
| 21/19
| [[21/19]]
| Dudmajor 2nd
| Dudmajor 2nd
| vvM2
| vvM2
Line 120: Line 115:
| 13
| 13
| 185.7
| 185.7
| 10/9
| [[10/9]]
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 127: Line 122:
| 14
| 14
| 200.0
| 200.0
| 9/8
| [[9/8]]
| Major 2nd
| Major 2nd
| M2
| M2
Line 134: Line 129:
| 15
| 15
| 214.3
| 214.3
| 26/23
| [[26/23]]
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 141: Line 136:
| 16
| 16
| 228.6
| 228.6
| 8/7
| [[8/7]]
| Dupmajor 2nd
| Dupmajor 2nd
| ^^M2
| ^^M2
Line 148: Line 143:
| 17
| 17
| 242.9
| 242.9
| 15/13, 23/20
| [[15/13]], [[23/20]]
| Trupmajor 2nd
| Trupmajor 2nd
| ^^^M2
| ^^^M2
Line 155: Line 150:
| 18
| 18
| 257.1
| 257.1
| 52/45
| [[52/45]]
| Trudminor 3rd
| Trudminor 3rd
| vvvm3
| vvvm3
Line 162: Line 157:
| 19
| 19
| 271.4
| 271.4
| 7/6
| [[7/6]]
| Dudminor 3rd
| Dudminor 3rd
| vvm2
| vvm2
Line 169: Line 164:
| 20
| 20
| 285.7
| 285.7
| 45/38, 46/39
| [[45/38]], [[46/39]]
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 176: Line 171:
| 21
| 21
| 300.0
| 300.0
| 19/16, 25/21, 32/27
| [[19/16]], [[25/21]], [[32/27]]
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 183: Line 178:
| 22
| 22
| 314.3
| 314.3
| 6/5
| [[6/5]]
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 190: Line 185:
| 23
| 23
| 328.6
| 328.6
| 23/19
| [[23/19]]
| Dupminor 3rd
| Dupminor 3rd
| ^^m3
| ^^m3
Line 197: Line 192:
| 24
| 24
| 342.9
| 342.9
| 28/23, 39/32
| [[28/23]], [[39/32]]
| Trupminor 3rd
| Trupminor 3rd
| ^^^m3
| ^^^m3
Line 204: Line 199:
| 25
| 25
| 357.1
| 357.1
| 16/13
| [[16/13]]
| Trudmajor 3rd
| Trudmajor 3rd
| vvvM3
| vvvM3
Line 211: Line 206:
| 26
| 26
| 371.4
| 371.4
| 26/21
| [[26/21]]
| Dudmajor 3rd
| Dudmajor 3rd
| vvM3
| vvM3
Line 218: Line 213:
| 27
| 27
| 385.7
| 385.7
| 5/4
| [[5/4]]
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 225: Line 220:
| 28
| 28
| 400.0
| 400.0
| 24/19
| [[24/19]]
| Major 3rd
| Major 3rd
| M3
| M3
Line 232: Line 227:
| 29
| 29
| 414.3
| 414.3
| 19/15
| [[19/15]]
| Upmajor 3rd
| Upmajor 3rd
| ^M3
| ^M3
Line 239: Line 234:
| 30
| 30
| 428.6
| 428.6
| 9/7, 23/18, 32/25
| [[9/7]], [[23/18]], [[32/25]]
| Dupmajor 3rd
| Dupmajor 3rd
| ^^M3
| ^^M3
Line 246: Line 241:
| 31
| 31
| 442.9
| 442.9
| 84/65
| [[84/65]]
| Trupmajor 3rd
| Trupmajor 3rd
| ^^^M3
| ^^^M3
Line 253: Line 248:
| 32
| 32
| 457.1
| 457.1
| 13/10, 30/23
| [[13/10]], [[30/23]]
| Trud 4th
| Trud 4th
| vvv4
| vvv4
Line 260: Line 255:
| 33
| 33
| 471.4
| 471.4
| 21/16
| [[21/16]]
| Dud 4th
| Dud 4th
| vv4
| vv4
Line 267: Line 262:
| 34
| 34
| 485.7
| 485.7
| 65/49
| [[65/49]]
| Down 4th
| Down 4th
| v4
| v4
Line 274: Line 269:
| 35
| 35
| 500.0
| 500.0
| 4/3
| [[4/3]]
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 281: Line 276:
| 36
| 36
| 514.3
| 514.3
| 27/20
| [[27/20]]
| Up 4th
| Up 4th
| ^4
| ^4
Line 288: Line 283:
| 37
| 37
| 528.6
| 528.6
| 19/14
| [[19/14]]
| Dup 4th
| Dup 4th
| ^^4
| ^^4
Line 295: Line 290:
| 38
| 38
| 542.9
| 542.9
| 26/19
| [[26/19]]
| Trup 4th
| Trup 4th
| ^^^4
| ^^^4
Line 302: Line 297:
| 39
| 39
| 557.1
| 557.1
| 18/13
| [[18/13]]
| Trudaug 4th
| Trudaug 4th
| vvvA4
| vvvA4
Line 309: Line 304:
| 40
| 40
| 571.4
| 571.4
| 25/18, 32/23
| [[25/18]], [[32/23]]
| Dudaug 4th
| Dudaug 4th
| vvA4
| vvA4
Line 316: Line 311:
| 41
| 41
| 585.7
| 585.7
| 7/5
| [[7/5]]
| Downaug 4th
| Downaug 4th
| vA4
| vA4
Line 323: Line 318:
| 42
| 42
| 600.0
| 600.0
| 27/19, 38/27
| [[27/19]], [[38/27]]
| Aug 4th, Dim 5th
| Aug 4th, Dim 5th
| A4, d5
| A4, d5
Line 330: Line 325:
| 43
| 43
| 614.3
| 614.3
| 10/7
| [[10/7]]
| Updim 5th
| Updim 5th
| ^d5
| ^d5
Line 337: Line 332:
| 44
| 44
| 628.6
| 628.6
| 23/16, 36/25
| [[23/16]], [[36/25]]
| Dupdim 5th
| Dupdim 5th
| ^^d5
| ^^d5
Line 344: Line 339:
| 45
| 45
| 642.9
| 642.9
| 13/9
| [[13/9]]
| Trupdim 5th
| Trupdim 5th
| ^^^d5
| ^^^d5
Line 351: Line 346:
| 46
| 46
| 657.1
| 657.1
| 19/13
| [[19/13]]
| Trud 5th
| Trud 5th
| vvv5
| vvv5
Line 358: Line 353:
| 47
| 47
| 671.4
| 671.4
| 28/19
| [[28/19]]
| Dud 5th
| Dud 5th
| vv5
| vv5
Line 365: Line 360:
| 48
| 48
| 685.7
| 685.7
| 40/27
| [[40/27]]
| Down 5th
| Down 5th
| v5
| v5
Line 372: Line 367:
| 49
| 49
| 700.0
| 700.0
| 3/2
| [[3/2]]
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 379: Line 374:
| 50
| 50
| 714.3
| 714.3
| 98/65
| [[98/65]]
| Up 5th
| Up 5th
| ^5
| ^5
Line 386: Line 381:
| 51
| 51
| 728.6
| 728.6
| 32/21
| [[32/21]]
| Dup 5th
| Dup 5th
| ^^5
| ^^5
Line 393: Line 388:
| 52
| 52
| 742.9
| 742.9
| 20/13, 23/15
| [[20/13]], [[23/15]]
| Trup 5th
| Trup 5th
| ^^^5
| ^^^5
Line 400: Line 395:
| 53
| 53
| 757.1
| 757.1
| 65/42
| [[65/42]]
| Trudminor 6th
| Trudminor 6th
| vvvm6
| vvvm6
Line 407: Line 402:
| 54
| 54
| 771.4
| 771.4
| 14/9, 25/16, 36/23
| [[14/9]], [[25/16]], [[36/23]]
| Dudminor 6th
| Dudminor 6th
| vvm6
| vvm6
Line 414: Line 409:
| 55
| 55
| 785.7
| 785.7
| 30/19
| [[30/19]]
| Downminor 6th
| Downminor 6th
| vm6
| vm6
Line 421: Line 416:
| 56
| 56
| 800.0
| 800.0
| 19/12
| [[19/12]]
| Minor 6th
| Minor 6th
| m6
| m6
Line 428: Line 423:
| 57
| 57
| 814.3
| 814.3
| 8/5
| [[8/5]]
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 435: Line 430:
| 58
| 58
| 828.6
| 828.6
| 21/13
| [[21/13]]
| Dupminor 6th
| Dupminor 6th
| ^^m6
| ^^m6
Line 442: Line 437:
| 59
| 59
| 842.9
| 842.9
| 13/8
| [[13/8]]
| Trupminor 6th
| Trupminor 6th
| ^^^m6
| ^^^m6
Line 449: Line 444:
| 60
| 60
| 857.1
| 857.1
| 23/14, 64/39
| [[23/14]], [[64/39]]
| Trudmajor 6th
| Trudmajor 6th
| vvvM6
| vvvM6
Line 456: Line 451:
| 61
| 61
| 871.4
| 871.4
| 38/23
| [[38/23]]
| Dudmajor 6th
| Dudmajor 6th
| vvM6
| vvM6
Line 463: Line 458:
| 62
| 62
| 885.7
| 885.7
| 5/3
| [[5/3]]
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 470: Line 465:
| 63
| 63
| 900.0
| 900.0
| 32/19, 27/16, 42/25
| [[32/19]], [[27/16]], [[42/25]]
| Major 6th
| Major 6th
| M6
| M6
Line 477: Line 472:
| 64
| 64
| 914.3
| 914.3
| 39/23, 76/45
| [[39/23]], [[76/45]]
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 484: Line 479:
| 65
| 65
| 928.6
| 928.6
| 12/7
| [[12/7]]
| Dupmajor 6th
| Dupmajor 6th
| ^^M6
| ^^M6
Line 491: Line 486:
| 66
| 66
| 942.9
| 942.9
| 45/26
| [[45/26]]
| Trupmajor 6th
| Trupmajor 6th
| ^^^M6
| ^^^M6
Line 498: Line 493:
| 67
| 67
| 957.1
| 957.1
| 26/15, 40/23
| [[26/15]], [[40/23]]
| Trudminor 7th
| Trudminor 7th
| vvvm7
| vvvm7
Line 505: Line 500:
| 68
| 68
| 971.4
| 971.4
| 7/4
| [[7/4]]
| Dudminor 7th
| Dudminor 7th
| vvm7
| vvm7
Line 512: Line 507:
| 69
| 69
| 985.7
| 985.7
| 23/13
| [[23/13]]
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 519: Line 514:
| 70
| 70
| 1000.0
| 1000.0
| 16/9
| [[16/9]]
| Minor 7th
| Minor 7th
| m7
| m7
Line 526: Line 521:
| 71
| 71
| 1014.3
| 1014.3
| 9/5
| [[9/5]]
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 533: Line 528:
| 72
| 72
| 1028.6
| 1028.6
| 38/21
| [[38/21]]
| Dupminor 7th
| Dupminor 7th
| ^^m7
| ^^m7
Line 540: Line 535:
| 73
| 73
| 1042.9
| 1042.9
| 42/23
| [[42/23]]
| Trupminor 7th
| Trupminor 7th
| ^^^m7
| ^^^m7
Line 547: Line 542:
| 74
| 74
| 1057.1
| 1057.1
| 24/13
| [[24/13]]
| Trudmajor 7th
| Trudmajor 7th
| vvvM7
| vvvM7
Line 554: Line 549:
| 75
| 75
| 1071.4
| 1071.4
| 13/7
| [[13/7]]
| Dudmajor 7th
| Dudmajor 7th
| vvM7
| vvM7
Line 561: Line 556:
| 76
| 76
| 1085.7
| 1085.7
| 15/8, 28/15
| [[15/8]], [[28/15]]
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 568: Line 563:
| 77
| 77
| 1100.0
| 1100.0
| 36/19
| [[36/19]]
| Major 7th
| Major 7th
| M7
| M7
Line 575: Line 570:
| 78
| 78
| 1114.3
| 1114.3
| 19/10, 40/21
| [[19/10]], [[40/21]]
| Upmajor 7th
| Upmajor 7th
| ^M7
| ^M7
Line 582: Line 577:
| 79
| 79
| 1128.6
| 1128.6
| 23/12, 25/13, ''27/14'', 48/25
| [[23/12]], [[25/13]], ''[[27/14]]'', [[48/25]]
| Dupmajor 7th
| Dupmajor 7th
| ^^M7
| ^^M7
Line 589: Line 584:
| 80
| 80
| 1142.9
| 1142.9
| ''52/27''
| ''[[52/27]]''
| Trupmajor 7th
| Trupmajor 7th
| ^^^M7
| ^^^M7
Line 596: Line 591:
| 81
| 81
| 1157.1
| 1157.1
| 35/18, 39/20, 96/49
| [[35/18]], [[39/20]], [[96/49]]
| Trud 8ve
| Trud 8ve
| vvv8
| vvv8
Line 603: Line 598:
| 82
| 82
| 1171.4
| 1171.4
| 45/23, 49/25, 63/32, 128/65, ''180/91''
| [[45/23]], [[49/25]], [[63/32]], [[128/65]], ''[[180/91]]''
| Dud 8ve
| Dud 8ve
| vv8
| vv8
Line 610: Line 605:
| 83
| 83
| 1185.7
| 1185.7
| 125/63, ''160/81'', 195/98, 336/169
| [[125/63]], ''[[160/81]]'', [[195/98]], [[336/169]]
| Down 8ve
| Down 8ve
| v8
| v8
Line 617: Line 612:
| 84
| 84
| 1200.0
| 1200.0
| 2/1
| [[2/1]]
| Perfect 8ve
| Perfect 8ve
| P8
| P8
Line 625: Line 620:


== Notation ==
== Notation ==
=== Ups and downs notation ===
=== Ups and downs notation ===


84edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
84edo can be notated using [[ups and downs notation|ups and downs]]. Trup is equivalent to quudsharp, trudsharp is equivalent to quup, etc.
{{Sharpness-sharp7a|84}}
{{Ups and downs sharpness|84}}


Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used:
Line 756: Line 749:


== Approximation to JI ==
== Approximation to JI ==
=== Zeta peak index ===
=== 15-odd-limit intervals ===
{{ZPI
{{Q-odd-limit intervals|84}}
| zpi = 462
 
| steps = 83.9972142607288
=== Higher-limit JI ===
| step size = 14.2861880666087
84edo has fairly good approximation to higher [[prime harmonic]]s such as [[13/1|13]], [[19/1|19]], [[23/1|23]], [[29/1|29]], [[31/1|31]], 41, 43, 53, 59, 61, 73 and 89, so that it is for its size very performant for much of the 61-limit, with more off primes usually being sharp so that they can cancel opportunistically with other sharp harmonics. In fact, it is [[consistent]] in the no-11 no-17 no-27 no-37 no-47 no-49 no-51 no-55 65-odd-limit excepting only 1 inconsistent pair, 45/43 and 86/45, which are inconsistent by ~0.13{{cent}} (off by ~7.3{{cent}}), offering a truly vast inventory of harmony to draw from that has mostly been unexplored. This is especially true because its approximation powers do not end there: prime 11, due to its simplicity (and thus lesser tuning fidelity), is certainly usable (just causes some inconsistencies), and there are higher primes that are reasonably in-tune too when supported by context. The only missing primes are thus 17, 37, 47, 67, 71, 79 and 83, which except for 17 are all about 6 cents sharp, similar to the sharpness of prime 11, so that it somewhat makes up for these omissions by having a very accurate 22:37:47:67:71:79:83 chord, to which various additions are possible (though usually increasing the error as a result).
| tempered height = 8.020965
| pure height = 8.014953
| integral = 1.241945
| gap = 16.733121
| octave = 1200.03979759513
| consistent = 10
| distinct = 10
}}


== Regular temperament properties ==
== Regular temperament properties ==
Line 784: Line 769:
| 2.3.5
| 2.3.5
| 78732/78125, 531441/524288
| 78732/78125, 531441/524288
| {{mapping| 84 133 195 }}
| {{Mapping| 84 133 195 }}
| +0.498
| +0.498
| 0.531
| 0.531
Line 791: Line 776:
| 2.3.5.7
| 2.3.5.7
| 225/224, 1728/1715, 78732/78125
| 225/224, 1728/1715, 78732/78125
| {{mapping| 84 133 195 236 }}
| {{Mapping| 84 133 195 236 }}
| +0.141
| +0.141
| 0.769
| 0.769
Line 798: Line 783:
| 2.3.5.7.13
| 2.3.5.7.13
| 225/224, 351/350, 640/637, 1701/1690
| 225/224, 351/350, 640/637, 1701/1690
| {{mapping| 84 133 195 236 311 }}
| {{Mapping| 84 133 195 236 311 }}
| −0.013
| −0.013
| 0.754
| 0.754
Line 805: Line 790:
| 2.3.5.7.11
| 2.3.5.7.11
| 225/224, 441/440, 1344/1331, 1728/1715
| 225/224, 441/440, 1344/1331, 1728/1715
| {{mapping| 84 133 195 236 291 }} (84)
| {{Mapping| 84 133 195 236 291 }} (84)
| −0.225
| −0.225
| 1.003
| 1.003
Line 812: Line 797:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 144/143, 225/224, 351/350, 441/440, 975/968
| 144/143, 225/224, 351/350, 441/440, 975/968
| {{mapping| 84 133 195 236 291 311 }} (84)
| {{Mapping| 84 133 195 236 291 311 }} (84)
| −0.292
| −0.292
| 0.928
| 0.928
Line 819: Line 804:
| 2.3.5.7.11
| 2.3.5.7.11
| 99/98, 121/120, 176/175, 78732/78125
| 99/98, 121/120, 176/175, 78732/78125
| {{mapping| 84 133 195 236 290 }} (84e)
| {{Mapping| 84 133 195 236 290 }} (84e)
| +0.601
| +0.601
| 1.151
| 1.151
Line 826: Line 811:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 99/98, 121/120, 176/175, 275/273, 1701/1690
| 99/98, 121/120, 176/175, 275/273, 1701/1690
| {{mapping| 84 133 195 236 290 311 }} (84e)
| {{Mapping| 84 133 195 236 290 311 }} (84e)
| +0.396
| +0.396
| 1.146
| 1.146
Line 844: Line 829:
| 1
| 1
| 19\84
| 19\84
| 271.43
| 271.4
| 7/6
| 7/6
| [[Orwell]] (84e) / [[newspeak]] (84)
| [[Orwell]] (84e) / [[newspeak]] (84)
Line 850: Line 835:
| 1
| 1
| 25\84
| 25\84
| 357.14
| 357.1
| 768/625
| 768/625
| [[Dodifo]]
| [[Dodifo]]
Line 856: Line 841:
| 1
| 1
| 27\84
| 27\84
| 385.71
| 385.7
| 5/4
| 5/4
| [[Mutt]]
| [[Mutt]]
Line 862: Line 847:
| 1
| 1
| 31\84
| 31\84
| 442.86
| 442.9
| 125/81
| 162/125
| [[Sensei]]
| [[Sensei]]
|-
|-
| 1
| 1
| 41\84
| 41\84
| 585.71
| 585.7
| 7/5
| 7/5
| [[Merman]]
| [[Merman]]
Line 874: Line 859:
| 2
| 2
| 5\84
| 5\84
| 71.43
| 71.4
| 25/24
| 25/24
| [[Narayana]]
| [[Narayana]]
Line 880: Line 865:
| 2
| 2
| 11\84
| 11\84
| 157.14
| 157.1
| 35/32
| 35/32
| [[Bison]]
| [[Bison]]
Line 886: Line 871:
| 2
| 2
| 13\84
| 13\84
| 185.71
| 185.7
| 10/9
| 10/9
| [[Secant]]
| [[Secant]]
Line 892: Line 877:
| 3
| 3
| 11\84
| 11\84
| 157.14
| 157.1
| 35/32
| 35/32
| [[Nessafof]]
| [[Nessafof]]
|-
| 6
| 5\84
| 71.4
| 25/24
| [[Trivish]]
|-
|-
| 7
| 7
| 5\84
| 5\84
| 500.00<br>(14.29)
| 14.3
| 4/3<br>(81/80)
| 81/80
| [[Absurdity]]
| [[Absurdity]]
|-
|-
| 12
| 12
| 27\84<br>(1\84)
| 1\84
| 385.71<br>(14.29)
| 14.3
| 5/4<br>(126/125)
| 126/125
| [[Compton]]
| [[Compton]]
|-
| 12
| 2\84
| 28.6
| 64/63
| [[Catler]] (84c)
|-
|-
| 21
| 21
| 41\84<br>(1\84)
| 1\84)
| 585.71<br>(14.29)
| 14.3
| 91875/65536<br>(126/125)
| 126/125
| [[Akjayland]]
| [[Akjayland]]
|-
|-
| 28
| 28
| 49\84<br>(1\84)
| 1\84
| 500.00<br>(14.29)
| 14.3
| 4/3<br>(105/104)
| 105/104
| [[Oquatonic]]
| [[Oquatonic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]


== Scales ==
== Scales ==
Line 934: Line 931:
=== Other ===
=== Other ===
* [[5- to 10-tone scales in 84edo]]
* [[5- to 10-tone scales in 84edo]]
* [[Maeve Gutierrez|Gutierrez Moonglade scale]]


== Instruments ==
== Instruments ==
Line 946: Line 944:
* ''Two5'' for tenor trombone and piano (1991) [https://youtu.be/YOtQZIqfY1w Fulkerson &amp; Denyer recording (YouTube)]
* ''Two5'' for tenor trombone and piano (1991) [https://youtu.be/YOtQZIqfY1w Fulkerson &amp; Denyer recording (YouTube)]
* ''Two6'' for violin and piano (1992) [https://youtu.be/XkX37zH6AbU Haar &amp; Snijders recording (YouTube)]
* ''Two6'' for violin and piano (1992) [https://youtu.be/XkX37zH6AbU Haar &amp; Snijders recording (YouTube)]
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/Sqkxrmwggr0 ''microtonal improvisation in 84edo''] (2025)
* [https://www.youtube.com/shorts/Qu6UIA2NmmQ ''84edo groove''] (2026)


; [[Eliora]]
; [[Eliora]]
Retrieved from "https://en.xen.wiki/w/84edo"