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Nicetone (also known as the Zarlino pattern) is a 7-note [[Maximum variety|Maximum variety 3]] scale with the step pattern 3L2M2S. Nicetone is a [[Chirality|chiral]] scale with left-handed (LmLsmLs) and right-handed (LmLsLms) variants that are rotationally non-equivalent. [[15edo]] is the first equal division that supports nicetone.
'''Nicetone''' (also known as the '''Zarlino pattern''', simply '''Zarlino''', or '''Ptolemaic diatonic''') is a 7-note [[Maximum variety|maximum-variety-3]] scale with the [[step signature]] {{nowrap|3L 2M 2s}}. Nicetone is a [[chiral]] scale with left-handed (LH, step pattern LMLsMLs) and right-handed (RH, step pattern LMLsLMs) variants that are rotationally non-equivalent. [[15edo]] is the first equal division that supports nicetone. This pattern is a variety of diatonic, distinct from the [[mos]] pattern [[5L 2s]] officially called diatonic and found as such in fifth-generated tunings.


Nicetone has the same pattern of the [[5-limit]] [[Zarlino]] scale, though it encompasses the whole range of 3L2M2S. It's also a subset of the 5L2M2S [[blackdye]] scale.
Nicetone has the same pattern of the [[#5-limit Zarlino scale|5-limit Zarlino]] scale, where L represents [[9/8]], M represents [[10/9]], and s represents [[16/15]], though it encompasses the whole range of {{nowrap|3L 2M 2s}}. It's also a subset of the {{nowrap|5L 2m 3s}} [[blackdye]] scale. Note that "Zarlino" by itself can refer to both the JI scale and the scale pattern.


Nicetone is intermediate between the [[5L 2s|5L2s]] diatonic scale and the [[3L 4s|3L4s]] Neutral scale.
Nicetone is intermediate between the [[5L 2s]] diatonic scale and the [[3L 4s]] neutral scale.


__TOC__
[[File:Nicetone.svg|900px|thumb|center|Comparison of diatonic scales in JI, Pythagorean tuning, and meantone]]
 
{| class="wikitable" style="margin-left: auto; margin-right: auto;"
|+ Comparison with mosh and antipentic in 33edo
|-
! Name !! Structure !! Step Sizes !! Graphical Representation
|-
| Mosh || {{nowrap|3L 4s}} || 7\33, 3\33 || {{step vis| 3 7 3 7 3 3 7 }}
|-
| Nicetone || {{nowrap|3L 2M 2s}} || 7\33, 4\33, 2\33 || {{step vis| 4 7 2 7 4 2 7 }}
|-
| Antipentic || {{nowrap|3L 2s}} || 7\33, 6\33 || {{step vis| 6 7 7 6 7 }}
|}
 
== 5-limit Zarlino scale ==
'''[[Ptolemy's intense diatonic]]''', '''5-limit Zarlino''' or sometimes '''Zarlino''' for short is a [[heptatonic]] [[5-limit]] [[JI]] [[scale]] with the [[nicetone]] step pattern. It consists of the intervals [[1/1]]–9/8–[[5/4]]–[[4/3]]–[[3/2]]–[[5/3]]–[[15/8]]–[[2/1]]. It corresponds to the case where L represents [[9/8]], M represents [[10/9]], and s represents [[16/15]]. See the [[Ptolemy's intense diatonic|dedicated page]] for Scala files and Fokker blocks information.
 
== Intervals ==
The following is a table of nicetone intervals and their abstract sizes in terms of L, M, and s. Given concrete sizes of L, M, and s in EDO steps or cents, you can compute the concrete size of any interval in nicetone using the following expressions.
 
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
|+ style="font-size: 105%;" | Interval sizes in nicetone
|- style="white-space: nowrap;"
! colspan="2" | Interval class
! Sizes
! 5-limit JI
! [[15edo]]<br />(L:M:s = 3:2:1)
! [[41edo]]<br />(L:M:s = 7:6:4)
|- style="background-color: #eaeaff;"
! rowspan="3" | Second<br />([[TAMNAMS|1-step]])
! style="font-size: 0.75em;" | Small
| s
| 16/15, 111.73¢
| 1\15, 80.00¢
| 4\41, 117.07¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Medium
| M
| 10/9, 182.40¢
| 2\15, 160.00¢
| 6\41, 175.61¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Large
| L
| 9/8, 203.91¢
| 3\15, 240.00¢
| 7\41, 204.88¢
|-
! rowspan="3" | Third<br />([[TAMNAMS|2-step]])
! style="font-size: 0.75em;" | Small
| {{nowrap|M + s}}
| 32/27, 294.13¢
| 3\15, 240.00¢
| 10\41, 292.68¢
|-
! style="font-size: 0.75em;" | Medium
| {{nowrap|L + s}}
| 6/5, 315.64¢
| 4\15, 320.00¢
| 11\41, 321.95¢
|-
! style="font-size: 0.75em;" | Large
| {{nowrap|L + M}}
| 5/4, 386.31¢
| 5\15, 400.00¢
| 13\41, 380.49¢
|- style="background-color: "#eaeaff;"
! rowspan="3" | Fourth<br />([[TAMNAMS|3-step]])
! style="font-size: 0.75em;" | Small
| {{nowrap|L + M + s}}
| 4/3, 498.04¢
| 6\15, 480.00¢
| 17\41, 497.56¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Medium
| {{nowrap|2L + s}}
| 27/20, 519.55¢
| 7\15, 560.00¢
| 18\41, 526.83¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Large
| {{nowrap|2L + M}}
| 45/32, 590.22¢
| 8\15, 640.00¢
| 20\41, 585.37¢
|-
! rowspan="3" | Fifth<br />([[TAMNAMS|4-step]])
! style="font-size: 0.75em;" | Small
| {{nowrap|L + M + 2s}}
| 64/45, 609.78¢
| 7\15, 560.00¢
| 21\41, 614.63¢
|-
! style="font-size: 0.75em;" | Medium
| {{nowrap|L + 2M + s}}
| 40/27, 680.45¢
| 8\15, 640.00¢
| 23\41, 673.17¢
|-
! style="font-size: 0.75em;" | Large
| {{nowrap|2L + M + s}}
| 3/2, 701.96¢
| 9\15, 720.00¢
| 24\41, 702.44¢
|- style="background-color: "#eaeaff;"
! rowspan="3" | Sixth<br />([[TAMNAMS|5-step]])
! style="font-size: 0.75em;" | Small
| {{nowrap|2L + M + 2s}}
| 8/5, 813.69¢
| 10\15, 800.00¢
| 28\41, 819.51¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Medium
| {{nowrap|2L + 2M + s}}
| 5/3, 884.36¢
| 11\15, 880.00¢
| 30\41, 878.05¢
|- style="background-color: "#eaeaff;"
! style="font-size: 0.75em;" | Large
| {{nowrap|3L + M + s}}
| 27/16, 905.87¢
| 12\15, 960.00¢
| 31\41, 907.32¢
|-
! rowspan="3" | Seventh<br />([[TAMNAMS|6-step]])
! style="font-size: 0.75em;" | Small
| {{nowrap|2L + 2M + 2s}}
| 16/9, 996.09¢
| 12\15, 960.00¢
| 34\41, 995.12¢
|-
! style="font-size: 0.75em;" | Medium
| {{nowrap|3L + M + 2s}}
| 9/5, 1017.60¢
| 13\15, 1040.00¢
| 35\41, 1024.39¢
|-
! style="font-size: 0.75em;" | Large
| {{nowrap|3L + 2M + s}}
| 15/8, 1088.27¢
| 14\15, 1120.00¢
| 37\41, 1082.93¢
|}


== Modes ==
== Modes ==
Nicetone has 14 modes total, with 7 LH and 7 RH modes. The names are based on their diatonic (5L2s) counterparts.
Nicetone has 14 modes total, with 7 LH and 7 RH modes. The names are based on their diatonic (5L 2s) counterparts.


The modes are arranged by brightest to darkest.
The modes are arranged by brightest to darkest.
{| class="wikitable"
{| class="wikitable"
|+Nicetone modes
|+ style="font-size: 105%;" | Nicetone modes
!Left handed
!Right handed
|-
|-
|LMLSMLS
! Left handed !! Right handed
LH NiceLydian
|LMLSLMS
RH NiceLydian
|-
|-
|MLSLMLS
| LMLsMLs<br />LH Nice-Lydian
LH NiceIonian
| LMLsLMs<br />RH Nice-Lydian
|LMSLMLS
RH NiceIonian
|-
|-
|MLSMLSL
| MLsLMLs<br />LH Nice-Ionian
LH NiceMixo
| LMsLMLs<br />RH Nice-Ionian
|MLSLMSL
RH NiceMixo
|-
|-
|LSLMLSM
| MLsMLsL<br />LH Nice-Mixolydian
LH NiceDorian
| MLsLMsL<br />RH Nice-Mixolydian
|MSLMLSL
RH NiceDorian
|-
|-
|LSMLSLM
| LsLMLsM<br />LH Nice-Dorian
LH NiceAolian
| MsLMLsL<br />RH Nice-Dorian
|LSLMSLM
RH NiceAolian
|-
|-
|SLMLSML
| LsMLsLM<br />LH Nice-Aeolian
LH NicePhrygian
| LsLMsLM<br />RH Nice-Aeolian
|SLMLSLM
RH NicePhrygian
|-
|-
|SMLSLML
| sLMLsML<br />LH Nice-Phrygian
LH NiceLocrian
| sLMLsLM<br />RH Nice-Phrygian
|SLMSLML
|-
RH NiceLocrian
| sMLsLML<br />LH Nice-Locrian
| sLMsLML<br />RH Nice-Locrian
|}
|}


== Tunings ==
== Tunings ==
[[File:3L2m2s GO scale region.png]]
{| class="wikitable"
{| class="wikitable"
|+Common Nicetone tunings
|+ style="font-size: 105%;" | Tuning range of nicetone
! rowspan="2" |Tuning
! rowspan="2" |L:m:s
! rowspan="2" |Good Just Approximations
! rowspan="2" |Other comments
! colspan="6" |Degrees
|-
|-
!D
!  
!vE
! Tuning range (in [[octave]]s)
!F
!G
!vA
!vB
|-
|-
|
! Outer generator<br />({{nowrap|''G''<sub>1</sub> {{=}} 2L + M + s}})
|
| <math>\displaystyle \frac{4}{7} \lt G_\text{1} \lt \frac{2}{3}</math>
|
|
|9/8
|5/4
|4/3
|3/2
|5/3
|15/8
|-
|-
|Just
! RH inner generator<br />({{nowrap|''G''<sub>2R</sub> {{=}} L + M}})
|1.825:1.6325:1
| <math>\displaystyle \frac{1}{2} G_\text{1} \lt G_\text{2R} \lt 4 G_\text{1} - 2 \,\text{ for }\, \frac{4}{7} \lt G_\text{1} \le \frac{3}{5}</math> <br><math>\displaystyle \frac{1}{2} G_\text{1} \lt G_\text{2R} \lt 1 - G_\text{1} \,\text{ for }\,\frac{3}{5} \le G_\text{1} \lt \frac{2}{3}</math>
|Just 9/8, 5/4 and 4/3
|
|203.91
|386.314
|498.045
|701.955
|884.359
|1088.269
|-
|-
|15edo
! LH inner generator<br />({{nowrap|''G''<sub>2L</sub> {{=}} L + s}})
|3:2:1
| <math>\displaystyle 2 - 3 G_\text{1} \lt G_\text{2L} \lt \frac{1}{2} G_\text{1} \,\text{ for }\,\frac{4}{7} \lt G_\text{1} \le \frac{3}{5}</math> <br><math>\displaystyle 2 G_\text{1} - 1 \lt G_\text{2L} \lt \frac{1}{2} G_\text{1} \,\text{ for }\,\frac{3}{5} \le G_\text{1} \lt \frac{2}{3}</math>
|
|
|240
| rowspan="2" |400
|480
|720
|880
|1120
|-
|-
|18edo
! Large step<br />({{nowrap|L {{=}} 2''G''<sub>1</sub> &minus; 1}})
|4:2:1
| <math>\displaystyle \frac{1}{7} \lt L \lt \frac{1}{3}</math>
|
|Wolf fourth and fifth
|266.667
|466.667
|733.333
|866.667
|1133.333
|-
|-
|20edo
! Middle step<br />({{nowrap|M {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''G''<sub>2L</sub>}})
|4:3:1
| <math>\displaystyle \frac{1}{4} (1 - 3 L) \lt M \lt L \,\text{ for }\, \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{4} (1 - 3 L) \lt M \lt \frac{1}{2} (1 - 3 L) \,\text{ for }\, \frac{1}{5} \le L \lt \frac{1}{3}</math>
|
|
|240
|420
|480
|720
|900
|1140
|-
|-
|21edo
! Small step<br />({{nowrap|s {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''G''<sub>2R</sub>}})
|5:2:1
| <math>\displaystyle \frac{1}{2} (1 - 5 L) \lt s \lt \frac{1}{4} (1 - 3 L) \,\text{ for }\, \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle 0 \lt s \lt \frac{1}{4} (1 - 3 L) \,\text{ for }\, \frac{1}{5} \le L \lt \frac{1}{3}</math>
|
|}
|Wolf fourth and fifth
 
|285.714
{| class="wikitable"
|400
|+ style="font-size: 105%;" | Common Nicetone tunings
|457.143
|-
|742.857
! rowspan="2" | Tuning !! rowspan="2" | L:M:s !! colspan="3" | Size of step (¢) !! colspan="2" | Inner generator !! rowspan="2" | Outer generator<br />({{nowrap|2L + M + s}}) !! rowspan="2" | Comments
|857.143
|-
|1142.857
! L !! M !! s !! LH ({{nowrap|L + s}}) !! RH ({{nowrap|L + M}})
|-
|-
|22edo
| 5-limit JI  || || 203.910 || 182.404 || 111.731 || 315.641 || 386.314 || 701.955 || {{nowrap|L {{=}} 9/8}}, {{nowrap|M {{=}} 10/9}}, {{nowrap|s {{=}} 16/15}}
|4:3:2
|
|Also has diatonic MOS
|218.182
|381.182
|490.909
|709.091
|872.727
|1090.909
|-
|-
|23edo
| [[15edo]] || 3:2:1 || 240.000 || 160.000 || 80.000 || 320.000 || 400.000 || 720.000 || 5-limit patent val
|5:3:1
|14/11
|Wolf fourth and fifth
|260.87
|417.391
|469.565
|730.435
|886.9565
|1147.826
|-
|-
|24edo
| [[18edo]] || 4:2:1 || 266.667 || 133.333 || 66.667 || 333.333 || 400.000 || 733.333 || 5-limit patent val
|6:2:1
|
|Also has neutral diatonic MOS
|300
|400
|450
|750
|850
|1050
|-
|-
|25edo
| [[20edo]] || 4:3:1 || 240.000 || 180.000 || 60.000 || 300.000 || 420.000 || 720.000 ||
|5:3:2
5:4:1
|
|
|240
|384
432
|480
|720
|864
912
|1104
|-
|-
|26edo
| [[21edo]] || 5:2:1 || 285.714 || 114.286 || 57.143 || 342.857 || 400.000 || 742.857 ||
|6:3:1
|
|Also has diatonic MOS
|276.923
|415.385
|461.5385
|738.4615
|876.923
|1153.846
|-
|-
|27edo
| [[22edo]] || 4:3:2 || 218.182 || 163.636 || 109.091 || 327.273 || 381.818 || 709.091 || 5-limit patent val
|5:4:2
7:2:1
|
|Also has diatonic MOS
|222.222
311.111
|400
|488.889
444.444
|711.111
755.556
|888.889
844.444
|1111.111
1155.556
|-
|-
|28edo
| [[23edo]] || 5:3:1 || 260.870 || 156.522 || 52.174 || 313.043 || 417.391 || 730.435 ||
|6:3:2
6:4:1
|
|
|257.143
|385.714
428.571
|471.429
|728.571
|857.143
900
|1114.286
1157.143
|-
|-
|29edo
| [[24edo]] || 6:2:1 || 300.000 || 100.000 || 50.000 || 350.000 || 400.000 || 750.000 ||
|5:4:3
7:3:1
|
|Gentle fifth
Also has diatonic MOS
|206.897
289.655
|372.414
413.793
|496.551
455.172
|703.449
745.828
|868.9655
|1075.862
1158.721
|-
|-
|30edo
| rowspan="2" | [[25edo]] || 5:3:2 || 240.000 || 144.000 || 96.000 || 336.000 || 384.000 || 720.000 || 5-limit patent val
|6:5:1
8:2:1
|
|
|240
320
|440
400
|480
440
|720
760
|920
840
|1160
|-
|-
|31edo
| 5:4:1 || 240.000 || 192.000 || 48.000 || 288.000 || 432.000 || 720.000 ||
|7:3:2
7:4:1
|
|Also has diatonic MOS
|270.968
|386.314
425.8065
|464.516
|735.484
|851.613
890.323
|1122.581
1161.29
|-
|-
|32edo
| [[26edo]] || 6:3:1 || 276.923 || 138.462 || 46.154 || 323.077 || 415.385 || 738.462 ||
|6:4:3
|-
6:5:2
| rowspan="2" | [[27edo]] || 5:4:2 || 222.222 || 177.778 || 88.889 || 311.111 || 400.000 || 711.111 || 5-limit patent val
 
|-
8:3:1
| 7:2:1 || 311.111 || 88.889 || 44.444 || 355.556 || 400.000 || 755.556 ||
|
|-
|Also has diatonic MOS
| rowspan="2" | [[28edo]] || 6:3:2 || 257.143 || 128.571 || 85.714 || 342.857 || 385.714 || 728.571 ||
|225
|-
300
| 6:4:1 || 257.143 || 171.429 || 42.857 || 300.000 || 428.571 || 728.571 ||
|375
|-
412.5
| rowspan="2" | [[29edo]] || 5:4:3 || 206.897 || 165.517 || 124.138 || 331.034 || 372.414 || 703.448 || 5-limit patent val
|487.5
|-
450
| 7:3:1 || 289.655 || 124.138 || 41.379 || 331.034 || 413.793 || 744.828 ||
|712.5
|-
750
| rowspan="2" | [[30edo]] || 6:5:1 || 240.000 || 200.000 || 40.000 || 280.000 || 440.000 || 720.000 ||
|862.5
|-
900
| 8:2:1 || 320.000 || 80.000 || 40.000 || 360.000 || 400.000 || 760.000 ||
|1087.5
|-
1125
| rowspan="2" | [[31edo]] || 7:3:2 || 270.968 || 116.129 || 77.419 || 348.387 || 387.097 || 735.484 ||
 
|-
1162.5
| 7:4:1 || 270.968 || 154.839 || 38.710 || 309.677 || 425.806 || 735.484 ||
|-
| rowspan="3" | [[32edo]] || 6:4:3 || 225.000 || 150.000 || 112.500 || 337.500 || 375.000 || 712.500 || 5-limit patent val
|-
| 6:5:2 || 225.000 || 187.500 || 75.000 || 300.000 || 412.500 || 712.500 ||
|-
| 8:3:1 || 300.000 || 112.500 || 37.500 || 337.500 || 412.500 || 750.000 ||
|-
| rowspan="3" | [[33edo]] || 7:4:2 || 254.545 || 145.455 || 72.727 || 327.273 || 400.000 || 727.273 ||
|-
| 7:5:1 || 254.545 || 181.818 || 36.364 || 290.909 || 436.364 || 727.273 ||
|-
| 9:2:1 || 327.273 || 72.727 || 36.364 || 363.636 || 400.000 || 763.636 ||
|-
| rowspan="3" | [[34edo]] || 6:5:3 || 211.765 || 176.471 || 105.882 || 317.647 || 388.235 || 705.882 || 5-limit patent val
|-
| 8:3:2 || 282.353 || 105.882 || 70.588 || 352.941 || 388.235 || 741.176 ||
|-
| 8:4:1 || 282.353 || 141.176 || 35.294 || 317.647 || 423.529 || 741.176 ||
|-
| rowspan="4" | [[35edo]] || 7:4:3 || 240.000 || 137.143 || 102.857 || 342.857 || 377.143 || 720.000 ||
|-
| 7:5:2 || 240.000 || 171.429 || 68.571 || 308.571 || 411.429 || 720.000 ||
|-
| 7:6:1 || 240.000 || 205.714 || 34.286 || 274.286 || 445.714 || 720.000 ||
|-
| 9:3:1 || 308.571 || 102.857 || 34.286 || 342.857 || 411.429 || 754.286 ||
|-
| rowspan="3" | [[36edo]] || 6:5:4 || 200.000 || 166.667 || 133.333 || 333.333 || 366.667 || 700.000 ||
|-
| 8:5:1 || 266.667 || 166.667 || 33.333 || 300.000 || 433.333 || 733.333 ||
|-
| 10:2:1 || 333.333 || 66.667 || 33.333 || 366.667 || 400.000 || 766.667 ||
|-
| rowspan="4" | [[37edo]] || 7:5:3 || 227.027 || 162.162 || 97.297 || 324.324 || 389.189 || 713.514 || 5-limit patent val
|-
| 7:6:2 || 227.027 || 194.595 || 64.865 || 291.892 || 421.622 || 713.514 ||
|-
| 9:3:2 || 291.892 || 97.297 || 64.865 || 356.757 || 389.189 || 745.946 ||
|-
| 9:4:1 || 291.892 || 129.730 || 32.432 || 324.324 || 421.622 || 745.946 ||
|-
| rowspan="4" | [[38edo]] || 8:4:3 || 252.632 || 126.316 || 94.737 || 347.368 || 378.947 || 726.316 ||
|-
| 8:5:2 || 252.632 || 157.895 || 63.158 || 315.789 || 410.526 || 726.316 ||
|-
| 8:6:1 || 252.632 || 189.474 || 31.579 || 284.211 || 442.105 || 726.316 ||
|-
| 10:3:1 || 315.789 || 94.737 || 31.579 || 347.368 || 410.526 || 757.895 ||
|-
| rowspan="5" | [[39edo]] || 7:5:4 || 215.385 || 153.846 || 123.077 || 338.462 || 369.231 || 707.692 ||
|-
| 7:6:3 || 215.385 || 184.615 || 92.308 || 307.692 || 400.000 || 707.692 || 5-limit patent val
|-
| 9:4:2 || 276.923 || 123.077 || 61.538 || 338.462 || 400.000 || 738.462 ||
|-
| 9:5:1 || 276.923 || 153.846 || 30.769 || 307.692 || 430.769 || 738.462 ||
|-
| 11:2:1 || 338.462 || 61.538 || 30.769 || 369.231 || 400.000 || 769.231 ||
|-
| rowspan="4" | [[40edo]] || 8:5:3 || 240.000 || 150.000 || 90.000 || 330.000 || 390.000 || 720.000 ||
|-
| 8:7:1 || 240.000 || 210.000 || 30.000 || 270.000 || 450.000 || 720.000 ||
|-
| 10:3:2 || 300.000 || 90.000 || 60.000 || 360.000 || 390.000 || 750.000 ||
|-
| 10:4:1 || 300.000 || 120.000 || 30.000 || 330.000 || 420.000 || 750.000 ||
|-
| rowspan="5" | [[41edo]] || 7:6:4 || 204.878 || 175.610 || 117.073 || 321.951 || 380.488 || 702.439 || 5-limit patent val
|-
| 9:4:3 || 263.415 || 117.073 || 87.805 || 351.220 || 380.488 || 731.707 ||
|-
| 9:5:2 || 263.415 || 146.341 || 58.537 || 321.951 || 409.756 || 731.707 ||
|-
| 9:6:1 || 263.415 || 175.610 || 29.268 || 292.683 || 439.024 || 731.707 ||
|-
| 11:3:1 || 321.951 || 87.805 || 29.268 || 351.220 || 409.756 || 760.976 ||
|-
| rowspan="5" | [[42edo]] || 8:5:4 || 228.571 || 142.857 || 114.286 || 342.857 || 371.429 || 714.286 ||
|-
| 8:6:3 || 228.571 || 171.429 || 85.714 || 314.286 || 400.000 || 714.286 || 5-limit patent val
|-
| 8:7:2 || 228.571 || 200.000 || 57.143 || 285.714 || 428.571 || 714.286 ||
|-
| 10:5:1 || 285.714 || 142.857 || 28.571 || 314.286 || 428.571 || 742.857 ||
|-
| 12:2:1 || 342.857 || 57.143 || 28.571 || 371.429 || 400.000 || 771.429 ||
|-
| rowspan="6" | [[43edo]] || 7:6:5 || 195.349 || 167.442 || 139.535 || 334.884 || 362.791 || 697.674 ||
|-
| 9:5:3 || 251.163 || 139.535 || 83.721 || 334.884 || 390.698 || 725.581 ||
|-
| 9:6:2 || 251.163 || 167.442 || 55.814 || 306.977 || 418.605 || 725.581 ||
|-
| 9:7:1 || 251.163 || 195.349 || 27.907 || 279.070 || 446.512 || 725.581 ||
|-
| 11:3:2 || 306.977 || 83.721 || 55.814 || 362.791 || 390.698 || 753.488 ||
|-
| 11:4:1 || 306.977 || 111.628 || 27.907 || 334.884 || 418.605 || 753.488 ||
|-
| rowspan="5" | [[44edo]] || 8:7:3 || 218.182 || 190.909 || 81.818 || 300.000 || 409.091 || 709.091 ||
|-
| 10:4:3 || 272.727 || 109.091 || 81.818 || 354.545 || 381.818 || 736.364 ||
|-
| 10:5:2 || 272.727 || 136.364 || 54.545 || 327.273 || 409.091 || 736.364 ||
|-
| 10:6:1 || 272.727 || 163.636 || 27.273 || 300.000 || 436.364 || 736.364 ||
|-
| 12:3:1 || 327.273 || 81.818 || 27.273 || 354.545 || 409.091 || 763.636 ||
|-
| rowspan="6" | [[45edo]] || 9:5:4 || 240.000 || 133.333 || 106.667 || 346.667 || 373.333 || 720.000 ||
|-
| 9:7:2 || 240.000 || 186.667 || 53.333 || 293.333 || 426.667 || 720.000 ||
|-
| 9:8:1 || 240.000 || 213.333 || 26.667 || 266.667 || 453.333 || 720.000 ||
|-
| 11:4:2 || 293.333 || 106.667 || 53.333 || 346.667 || 400.000 || 746.667 ||
|-
| 11:5:1 || 293.333 || 133.333 || 26.667 || 320.000 || 426.667 || 746.667 ||
|-
| 13:2:1 || 346.667 || 53.333 || 26.667 || 373.333 || 400.000 || 773.333 ||
|-
| rowspan="6" | [[46edo]] || 8:6:5 || 208.696 || 156.522 || 130.435 || 339.130 || 365.217 || 704.348 ||
|-
| 8:7:4 || 208.696 || 182.609 || 104.348 || 313.043 || 391.304 || 704.348 || 5-limit patent val
|-
| 10:5:3 || 260.870 || 130.435 || 78.261 || 339.130 || 391.304 || 730.435 ||
|-
| 10:7:1 || 260.870 || 182.609 || 26.087 || 286.957 || 443.478 || 730.435 ||
|-
| 12:3:2 || 313.043 || 78.261 || 52.174 || 365.217 || 391.304 || 756.522 ||
|-
| 12:4:1 || 313.043 || 104.348 || 26.087 || 339.130 || 417.391 || 756.522 ||
|-
| rowspan="7" | [[47edo]] || 9:6:4 || 229.787 || 153.191 || 102.128 || 331.915 || 382.979 || 714.894 ||
|-
| 9:7:3 || 229.787 || 178.723 || 76.596 || 306.383 || 408.511 || 714.894 ||
|-
| 9:8:2 || 229.787 || 204.255 || 51.064 || 280.851 || 434.043 || 714.894 ||
|-
| 11:4:3 || 280.851 || 102.128 || 76.596 || 357.447 || 382.979 || 740.426 ||
|-
| 11:5:2 || 280.851 || 127.660 || 51.064 || 331.915 || 408.511 || 740.426 ||
|-
| 11:6:1 || 280.851 || 153.191 || 25.532 || 306.383 || 434.043 || 740.426 ||
|-
| 13:3:1 || 331.915 || 76.596 || 25.532 || 357.447 || 408.511 || 765.957 ||
|-
| rowspan="7" | [[48edo]] || 8:7:5 || 200.000 || 175.000 || 125.000 || 325.000 || 375.000 || 700.000 || 5-limit patent val
|-
| 10:5:4 || 250.000 || 125.000 || 100.000 || 350.000 || 375.000 || 725.000 ||
|-
| 10:6:3 || 250.000 || 150.000 || 75.000 || 325.000 || 400.000 || 725.000 ||
|-
| 10:7:2 || 250.000 || 175.000 || 50.000 || 300.000 || 425.000 || 725.000 ||
|-
| 10:8:1 || 250.000 || 200.000 || 25.000 || 275.000 || 450.000 || 725.000 ||
|-
| 12:5:1 || 300.000 || 125.000 || 25.000 || 325.000 || 425.000 || 750.000 ||
|-
| 14:2:1 || 350.000 || 50.000 || 25.000 || 375.000 || 400.000 || 775.000 ||
|-
| rowspan="8" | [[49edo]] || 9:6:5 || 220.408 || 146.939 || 122.449 || 342.857 || 367.347 || 710.204 ||
|-
| 9:7:4 || 220.408 || 171.429 || 97.959 || 318.367 || 391.837 || 710.204 || 5-limit patent val
|-
| 9:8:3 || 220.408 || 195.918 || 73.469 || 293.878 || 416.327 || 710.204 ||
|-
| 11:5:3 || 269.388 || 122.449 || 73.469 || 342.857 || 391.837 || 734.694 ||
|-
| 11:6:2 || 269.388 || 146.939 || 48.980 || 318.367 || 416.327 || 734.694 ||
|-
| 11:7:1 || 269.388 || 171.429 || 24.490 || 293.878 || 440.816 || 734.694 ||
|-
| 13:3:2 || 318.367 || 73.469 || 48.980 || 367.347 || 391.837 || 759.184 ||
|-
| 13:4:1 || 318.367 || 97.959 || 24.490 || 342.857 || 416.327 || 759.184 ||
|-
| rowspan="7" | [[50edo]] || 8:7:6 || 192.000 || 168.000 || 144.000 || 336.000 || 360.000 || 696.000 ||
|-
| 10:7:3 || 240.000 || 168.000 || 72.000 || 312.000 || 408.000 || 720.000 ||
|-
| 10:9:1 || 240.000 || 216.000 || 24.000 || 264.000 || 456.000 || 720.000 ||
|-
| 12:4:3 || 288.000 || 96.000 || 72.000 || 360.000 || 384.000 || 744.000 ||
|-
| 12:5:2 || 288.000 || 120.000 || 48.000 || 336.000 || 408.000 || 744.000 ||
|-
| 12:6:1 || 288.000 || 144.000 || 24.000 || 312.000 || 432.000 || 744.000 ||
|-
| 14:3:1 || 336.000 || 72.000 || 24.000 || 360.000 || 408.000 || 768.000 ||
|-
| rowspan="9" | [[51edo]] || 9:7:5 || 211.765 || 164.706 || 117.647 || 329.412 || 376.471 || 705.882 || 5-limit patent val
|-
| 9:8:4 || 211.765 || 188.235 || 94.118 || 305.882 || 400.000 || 705.882 ||
|-
| 11:5:4 || 258.824 || 117.647 || 94.118 || 352.941 || 376.471 || 729.412 ||
|-
| 11:6:3 || 258.824 || 141.176 || 70.588 || 329.412 || 400.000 || 729.412 ||
|-
| 11:7:2 || 258.824 || 164.706 || 47.059 || 305.882 || 423.529 || 729.412 ||
|-
| 11:8:1 || 258.824 || 188.235 || 23.529 || 282.353 || 447.059 || 729.412 ||
|-
| 13:4:2 || 305.882 || 94.118 || 47.059 || 352.941 || 400.000 || 752.941 ||
|-
| 13:5:1 || 305.882 || 117.647 || 23.529 || 329.412 || 423.529 || 752.941 ||
|-
| 15:2:1 || 352.941 || 47.059 || 23.529 || 376.471 || 400.000 || 776.471 ||
|-
| rowspan="8" | [[52edo]] || 10:6:5 || 230.769 || 138.462 || 115.385 || 346.154 || 369.231 || 715.385 ||
|-
| 10:7:4 || 230.769 || 161.538 || 92.308 || 323.077 || 392.308 || 715.385 ||
|-
| 10:8:3 || 230.769 || 184.615 || 69.231 || 300.000 || 415.385 || 715.385 ||
|-
| 10:9:2 || 230.769 || 207.692 || 46.154 || 276.923 || 438.462 || 715.385 ||
|-
| 12:5:3 || 276.923 || 115.385 || 69.231 || 346.154 || 392.308 || 738.462 ||
|-
| 12:7:1 || 276.923 || 161.538 || 23.077 || 300.000 || 438.462 || 738.462 ||
|-
| 14:3:2 || 323.077 || 69.231 || 46.154 || 369.231 || 392.308 || 761.538 ||
|-
| 14:4:1 || 323.077 || 92.308 || 23.077 || 346.154 || 415.385 || 761.538 ||
|-
| rowspan="10" | [[53edo]] || 9:7:6 || 203.774 || 158.491 || 135.849 || 339.623 || 362.264 || 701.887 ||
|-
| 9:8:5 || 203.774 || 181.132 || 113.208 || 316.981 || 384.906 || 701.887 || 5-limit patent val
|-
|-
|33edo
| 11:6:4 || 249.057 || 135.849 || 90.566 || 339.623 || 384.906 || 724.528 ||
|7:4:2
7:5:1
|13/11
|Also has diatonic MOS
|254.5455
|400
436.364
|472.727
|727.272
|872.727
909.091
|1127.273
1163.636
|-
|-
|34edo
| 11:7:3 || 249.057 || 158.491 || 67.925 || 316.981 || 407.547 || 724.528 ||
|6:5:3
8:3:2
 
8:4:1
|25/24
50/49
|Gentle fifth
Also has neutral diatonic MOS
|211.765
282.353
|388.235
423.529
|494.118
458.8235
|705.882
741.1765
|882.353
847.059
|1094.118
1129.412
 
1164.706
|-
|-
|35edo
| 11:8:2 || 249.057 || 181.132 || 45.283 || 294.340 || 430.189 || 724.528 ||
|7:4:3
7:5:2
 
7:6:1
|33/26
|
|240
|377.143
411.429
 
445.714
|480
|720
|857.143
891.429
 
925.714
|1097.143
1131.429
 
1165.714
|-
|-
|36edo
| 11:9:1 || 249.057 || 203.774 || 22.642 || 271.698 || 452.830 || 724.528 ||
|6:5:4
|27/25
|Also has Porcupine MOS
|200
|366.667
|500
|700
|866.667
|1066.667
|-
|-
|37edo
| 13:4:3 || 294.340 || 90.566 || 67.925 || 362.264 || 384.906 || 747.170 ||
|7:5:3
7:6:2
|
|Has 37edo just major triad
|227.027
|389.189
|486.4865
|713.5135
|875.676
|1102.703
|-
|-
|38edo
| 13:5:2 || 294.340 || 113.208 || 45.283 || 339.623 || 407.547 || 747.170 ||
|8:4:3
8:5:2
 
8:6:1
|6/5, 33/26 and 14/13 or 28/27
|Has wolf major and minor triads
Also has neutral diatonic MOS
|252.632
|378.947
410.526
 
442.105
|473.684
|726.318
|852.632
884.2105
 
915.7895
|1105.263
1136.842
 
1168.421
|-
|-
|39edo
| 13:6:1 || 294.340 || 135.849 || 22.642 || 316.981 || 430.189 || 747.170 ||
|7:5:4
7:6:3
|
|Also has diatonic MOS
|215.385
|369.231
400
|492.308
|707.692
|861.5385
892.308
|1076.923
1107.
|-
|-
|40edo
| 15:3:1 || 339.623 || 67.925 || 22.642 || 362.264 || 407.547 || 769.811 ||
|8:5:3
8:7:1
|
|Golden Nicetone
Also has diatonic MOS
|240
|390
450
|480
|720
|870
930
|1110
1170
|-
|-
|41edo
| rowspan="7" | [[54edo]] || 10:7:5 || 222.222 || 155.556 || 111.111 || 333.333 || 377.778 || 711.111 || 5-limit patent val
|7:6:4
|
|Also has diatonic MOS
|204.878
|380.488
|497.561
|702.439
|878.049
|1082.927
|-
|-
|42edo
| 10:9:3 || 222.222 || 200.000 || 66.667 || 288.889 || 422.222 || 711.111 ||
|8:5:4
8:6:3
 
8:7:2
|6/5
|Also has diatonic MOS
|228.571
|371.429
400
 
428.571
|485.714
|714.286
|857.143
885.714
 
914.286
|1085.714
1114.286
 
1142.857
|-
|-
|43edo
| 12:5:4 || 266.667 || 111.111 || 88.889 || 355.556 || 377.778 || 733.333 ||
|7:6:5
|
|Also has diatonic MOS
|195.349
|362.791
|502.326
|697.674
|865.116
|1060.465
|-
|-
|44edo
| 12:7:2 || 266.667 || 155.556 || 44.444 || 311.111 || 422.222 || 733.333 ||
|8:7:3
|
|Also has neutral diatonic MOS
|218.182
|409.091
|490.909
|709.091
|900
|1118.182
|-
|-
|46edo
| 12:8:1 || 266.667 || 177.778 || 22.222 || 288.889 || 444.444 || 733.333 ||
|8:6:5
8:7:4
|10/9
|Gentle fifth
Also has diatonic MOS
|208.696
|365.217
391.304
|495.652
|704.348
|860.87
886.9565
|1069.565
1095.652
|-
|-
|48edo
| 14:5:1 || 311.111 || 111.111 || 22.222 || 333.333 || 422.222 || 755.556 ||
|8:7:5
|
|
|200
|375
|500
|700
|875
|1075
|-
|-
|50edo
| 16:2:1 || 355.556 || 44.444 || 22.222 || 377.778 || 400.000 || 777.778 ||  
|8:7:6
|
|Also has diatonic MOS
|192
|360
|504
|696
|864
|1056
|}
|}
== Supersets ==
[[File:Regions of MV3 supersets of 3L2m2s.png]]
Nicetone has following generator-offset MV3 supersets:
* [[Sephipechroid]]: 13-note 3L 5M 5s scale (LMsMLsMsLMsMs and LMsMLsMsMLsMs)
* [[Interoneichro]]: 13-note 5L 3M 5s scale (LMsLsLMsLsMLs and LMsLsMLsLsMLs)
* [[Sephimechroid]]: 13-note 5L 5M 3s scale (LMLMsLMLsMLMs and LMLsMLMLsMLMs)
* [[Beatloid]]: 17-note 5L 5M 7s scale (LMsLsMLsMsLMsLsMs and LMsLsMLsMsLsMLsMs)
* [[Enharoid]]: 17-note 5L 7M 5s scale (LMsLMsMLMsLMsMLsM and LMsLMsMLsMLMsMLsM)
* [[Moharoid]]: 17-note 7L 5M 5s scale (LMLsLMsLMLsMLsLMs and LMLsMLsLMLsMLsLMs)
Remarkable non-MV3 generator-offset supersets include [[blackdye]] (10-note, LmLsLmLsLs).


== See also ==
== See also ==
[[Blackdye]], a 10-note scale that is an extension to nicetone.
* [[Blackdye]] &ndash; A 10-note scale that is an extension to nicetone.
* [[Omnidiatonic]]­­ ­&ndash; Sister 2L 3M 2s scale
* [[Antinicetone]] &ndash; Sister 2L 2M 3s scale
* [[5L 2s]] &ndash; LM-equalized version of nicetone
** [[5L 2s Muddles]] &ndash; Other diatonic muddles
* [[3L 4s]] &ndash; MS-equalized version of nicetone
* [[3L 2s]] &ndash; Collapsed version of nicetone
* [[Nicepent]] &ndash; The pentatonic predecessor to nicetone.
* [[Nicechrome]] &ndash; A possible chromatic (12-note) extension to nicetone.
* [[Superzarlino]]
* [[Zarlino (Pianoteq)]]


[[Zarlino]], a 5-limit JI scale with the same pattern.
[[Category:Rank-3 scales]]
[[Category:7-tone scales]]
[[Category:GO scales]]
Retrieved from "https://en.xen.wiki/w/Nicetone"