Nicetone: Difference between revisions

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'''Nicetone''' (also known as the '''Zarlino pattern''' or '''Ptolemaic~~-Auric~~ diatonic''') is a 7-note [[Maximum variety|~~Maximum~~ variety 3]] scale with the step ~~pattern~~ 3L 2m 2s. 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 3L 2m 2s. It's also a subset of the 5L 2m 3s [[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]] diatonic scale and the [[3L 4s]] neutral scale.

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

~~Nicetone can be tuned as a~~ [[~~5-limit]]~~ JI ~~scale or a tempered version thereof~~, ~~where L represents [[9/8]], m represents [[10/9]]~~, and ~~s represents [[16/15~~]].

[[File:Nicetone.svg|900px|thumb|center|Comparison of diatonic scales in JI, Pythagorean tuning, and meantone]]

{| class="wikitable"

{| class="wikitable" style="margin-left: auto; margin-right: auto;"

|+ Comparison with mosh and ~~diatonic~~ in ~~41edo~~

|+ Comparison with mosh and antipentic in 33edo

|-

! Name !! Structure !! Step Sizes !! Graphical Representation

|-

| Mosh || 3L 4s || 7\41, 5\41 || ~~├──────┼────┼────┼──────┼────┼──────┼────┤~~

| Mosh || {{nowrap|3L 4s}} || 7\33, 3\33 || {{step vis| 3 7 3 7 3 3 7 }}

|-

| Nicetone || 3L 2m 2s || 7\41, 6\41, 4\41 || ~~├──────┼─────┼───┼──────┼─────┼──────┼───┤~~

| Nicetone || {{nowrap|3L 2M 2s}} || 7\33, 4\33, 2\33 || {{step vis| 4 7 2 7 4 2 7 }}

|-

| ~~Diatonic~~ || 5L 2s || 7\41, 3\41 || ~~├──────┼──────┼──┼──────┼──────┼──────┼──┤~~

| Antipentic || {{nowrap|3L 2s}} || 7\33, 6\33 || {{step vis| 6 7 7 6 7 }}

|}

~~{| class~~=~~"wikitable"~~

== 5-limit Zarlino scale ==

~~|+ Comparison with mosh and antipentic in 33edo~~

'''[[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.

|-

~~! Name !! Structure !! Step Sizes !! Graphical Representation~~

|-

~~| Mosh || 3L 4s || 7\33, 3\33 || ├──┼──────┼──┼──────┼──┼──┼──────┤~~

|-

~~| Nicetone || 3L 2m 2s || 7\33,~~ 4~~\33~~, ~~2\33 || ├───┼──────┼─┼──────┼───┼─┼──────┤~~

|-

~~| Antipentic || 3L 2s || 7\33~~, ~~6\33~~ |~~| ├─────┼──────╫──────┼─────╫──────┤~~

|}

== 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.

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"

|+ Interval sizes in nicetone

|+ style="font-size: 105%;" | Interval sizes in nicetone

|-

|- style="white-space: nowrap;"

!colspan=2|Interval class

! colspan="2" | Interval class

! Sizes

! 5-limit JI

! [[15edo]] (L:m:s = 3:2:1)

! [[15edo]] (L:M:s = 3:2:1)

! [[41edo]] (L:m:s = 7:6:4)

! [[41edo]] (L:M:s = 7:6:4)

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: #eaeaff;"

!rowspan=3|Second ([[TAMNAMS|1-step]])

! rowspan="3" | Second ([[TAMNAMS|1-step]])

!| ~~small~~

! style="font-size: 0.75em;" | Small

| s

| 16/15, 111.73¢

| 1\15, 80.00¢

| 4\41, 117.07¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| m

| M

| 10/9, 182.40¢

| 2\15, 160.00¢

| 6\41, 175.61¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~large~~

! style="font-size: 0.75em;" | Large

| L

| 9/8, 203.91¢

Line 62:

Line 53:

| 7\41, 204.88¢

|-

!rowspan=3|Third ([[TAMNAMS|2-step]])

! rowspan="3" | Third ([[TAMNAMS|2-step]])

!|~~small~~

! style="font-size: 0.75em;" | Small

| m + s

| {{nowrap|M + s}}

| 32/27, 294.13¢

| 3\15, 240.00¢

| 10\41, 292.68¢

|-

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| L + s

| {{nowrap|L + s}}

| 6/5, 315.64¢

| 4\15, 320.00¢

| 11\41, 321.95¢

|-

!|~~large~~

! style="font-size: 0.75em;" | Large

| L + m

| {{nowrap|L + M}}

| 5/4, 386.31¢

| 5\15, 400.00¢

| 13\41, 380.49¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!rowspan=3|Fourth ([[TAMNAMS|3-step]])

! rowspan="3" | Fourth ([[TAMNAMS|3-step]])

!|~~small~~

! style="font-size: 0.75em;" | Small

| L + m + s

| {{nowrap|L + M + s}}

| 4/3, 498.04¢

| 6\15, 480.00¢

| 17\41, 497.56¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| 2L + s

| {{nowrap|2L + s}}

| 27/20, 519.55¢

| 7\15, 560.00¢

| 18\41, 526.83¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~large~~

! style="font-size: 0.75em;" | Large

| 2L + m

| {{nowrap|2L + M}}

| 45/32, 590.22¢

| 8\15, 640.00¢

| 20\41, 585.37¢

|-

!rowspan=3|Fifth ([[TAMNAMS|4-step]])

! rowspan="3" | Fifth ([[TAMNAMS|4-step]])

!|~~small~~

! style="font-size: 0.75em;" | Small

| L + m + 2s

| {{nowrap|L + M + 2s}}

| 64/45, 609.78¢

| 7\15, 560.00¢

| 21\41, 614.63¢

|-

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| L + 2m + s

| {{nowrap|L + 2M + s}}

| 40/27, 680.45¢

| 8\15, 640.00¢

| 23\41, 673.17¢

|-

!|~~large~~

! style="font-size: 0.75em;" | Large

| 2L + m + s

| {{nowrap|2L + M + s}}

| 3/2, 701.96¢

| 9\15, 720.00¢

| 24\41, 702.44¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!rowspan=3|Sixth ([[TAMNAMS|5-step]])

! rowspan="3" | Sixth ([[TAMNAMS|5-step]])

!|~~small~~

! style="font-size: 0.75em;" | Small

| 2L + m + 2s

| {{nowrap|2L + M + 2s}}

| 8/5, 813.69¢

| 10\15, 800.00¢

| 28\41, 819.51¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| 2L + 2m + s

| {{nowrap|2L + 2M + s}}

| 5/3, 884.36¢

| 11\15, 880.00¢

| 30\41, 878.05¢

|- ~~bgcolor~~="#eaeaff"

|- style="background-color: "#eaeaff;"

!|~~large~~

! style="font-size: 0.75em;" | Large

| 3L + m + s

| {{nowrap|3L + M + s}}

| 27/16, 905.87¢

| 12\15, 960.00¢

| 31\41, 907.32¢

|-

!rowspan=3|Seventh ([[TAMNAMS|6-step]])

! rowspan="3" | Seventh ([[TAMNAMS|6-step]])

!| ~~small~~

! style="font-size: 0.75em;" | Small

| 2L + 2m + 2s

| {{nowrap|2L + 2M + 2s}}

| 16/9, 996.09¢

| 12\15, 960.00¢

| 34\41, 995.12¢

|-

!|~~medium~~

! style="font-size: 0.75em;" | Medium

| 3L + m + 2s

| {{nowrap|3L + M + 2s}}

| 9/5, 1017.60¢

| 13\15, 1040.00¢

| 35\41, 1024.39¢

|-

!|~~large~~

! style="font-size: 0.75em;" | Large

| 3L + 2m + s

| {{nowrap|3L + 2M + s}}

| 15/8, 1088.27¢

| 14\15, 1120.00¢

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The modes are arranged by brightest to darkest.

{| class="wikitable"

|+Nicetone modes

|+ style="font-size: 105%;" | Nicetone modes

~~!Left handed~~

~~!Right handed~~

|-

~~|LmLsmLs LH Nice-Lydian~~

! Left handed !! Right handed

~~|LmLsLms RH Nice-Lydian~~

|-

|~~mLsLmLs~~ LH Nice-~~Ionian~~

| LMLsMLs LH Nice-Lydian

|~~LmsLmLs~~ RH Nice-~~Ionian~~

| LMLsLMs RH Nice-Lydian

|-

|~~mLsmLsL~~ LH Nice-~~Mixolydian~~

| MLsLMLs LH Nice-Ionian

|~~mLsLmsL~~ RH Nice-~~Mixolydian~~

| LMsLMLs RH Nice-Ionian

|-

|~~LsLmLsm~~ LH Nice-~~Dorian~~

| MLsMLsL LH Nice-Mixolydian

|~~msLmLsL~~ RH Nice-~~Dorian~~

| MLsLMsL RH Nice-Mixolydian

|-

|~~LsmLsLm~~ LH Nice-~~Aeolian~~

| LsLMLsM LH Nice-Dorian

|~~LsLmsLm~~ RH Nice-~~Aeolian~~

| MsLMLsL RH Nice-Dorian

|-

|~~sLmLsmL~~ LH Nice-~~Phrygian~~

| LsMLsLM LH Nice-Aeolian

|~~sLmLsLm~~ RH Nice-~~Phrygian~~

| LsLMsLM RH Nice-Aeolian

|-

|~~smLsLmL~~ LH Nice-Locrian

| sLMLsML LH Nice-Phrygian

|~~sLmsLmL~~ RH Nice-Locrian

| sLMLsLM RH Nice-Phrygian

|-

| sMLsLML LH Nice-Locrian

| sLMsLML RH Nice-Locrian

|}

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{| class="wikitable"

|+Tuning range of nicetone

|+ style="font-size: 105%;" | Tuning range of nicetone

|-

!

! Tuning range (in [[octave]]s)

|-

! Outer generator (''G''1 = 2L + m + s)

! Outer generator ({{nowrap|''G''1 {{=}} 2L + M + s}})

| <math>\displaystyle \frac{4}{7} < G_\text{1} < \frac{2}{3}</math>

| <math>\displaystyle \frac{4}{7} \lt G_\text{1} \lt \frac{2}{3}</math>

|-

! RH inner generator (''G''2R = L + m)

! RH inner generator ({{nowrap|''G''2R {{=}} L + M}})

| <math>\displaystyle \frac{1}{2} G_\text{1} < G_\text{2R} < 4 G_\text{1} - 2 \text{ for } \frac{4}{7} < G_\text{1} ≤ \frac{3}{5}</math> <math>\displaystyle \frac{1}{2} G_\text{1} < G_\text{2R} < 1 - G_\text{1} \text{ for }\frac{3}{5} ≤ G_\text{1} < \frac{2}{3}</math>

| <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> <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>

|-

! LH inner generator (''G''2L = L + s)

! LH inner generator ({{nowrap|''G''2L {{=}} L + s}})

| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < \frac{1}{2} G_\text{1} \text{ for }\frac{4}{7} < G_\text{1} ≤ \frac{3}{5}</math> <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2L} < \frac{1}{2} G_\text{1} \text{ for }\frac{3}{5} ≤ G_\text{1} < \frac{2}{3}</math>

| <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> <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>

|-

! Large step (L = 2''G''1 - 1)

! Large step ({{nowrap|L {{=}} 2''G''1 − 1}})

| <math>\displaystyle \frac{1}{7} < L < \frac{1}{3}</math>

| <math>\displaystyle \frac{1}{7} \lt L \lt \frac{1}{3}</math>

|-

! Middle step (m = 1 - ''G''1 - ''G''2L)

! Middle step ({{nowrap|M {{=}} 1 − ''G''1 − ''G''2L}})

| <math>\displaystyle \frac{1}{4} (1 - 3 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <math>\displaystyle \frac{1}{4} (1 - 3 L) < M < \frac{1}{2} (1 - 3 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{3}</math>

| <math>\displaystyle \frac{1}{4} (1 - 3 L) \lt M \lt L \,\text{ for }\, \frac{1}{7} \lt L \le \frac{1}{5}</math> <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>

|-

! Small step (s = 1 - ''G''1 - ''G''2R)

! Small step ({{nowrap|s {{=}} 1 − ''G''1 − ''G''2R}})

| <math>\displaystyle \frac{1}{2} (1 - 5 L) &lt~~; S &~~lt; \frac{1}{4} (1 - 3 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <math>\displaystyle 0 &lt~~; S &~~lt; \frac{1}{4} (1 - 3 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{3}</math>

| <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> <math>\displaystyle 0 \lt s \lt \frac{1}{4} (1 - 3 L) \,\text{ for }\, \frac{1}{5} \le L \lt \frac{1}{3}</math>

|}

{| class="wikitable"

|+Common Nicetone tunings

|+ style="font-size: 105%;" | Common Nicetone tunings

! rowspan="2" | Tuning

|-

! rowspan="2" | L:m:s

! rowspan="2" | Tuning !! rowspan="2" | L:M:s !! colspan="3" | Size of step (¢) !! colspan="2" | Inner generator !! rowspan="2" | Outer generator ({{nowrap|2L + M + s}}) !! rowspan="2" | Comments

! colspan="3" | Size of step (¢)

! colspan="2" | Inner generator

! rowspan="2" | Outer generator (2L+m+s)

! rowspan="2" | Comments

|-

! L

! L !! M !! s !! LH ({{nowrap|L + s}}) !! RH ({{nowrap|L + M}})

! m

! s

! LH (L+s)

! RH (L+m)

|-

| 5-limit JI || ||203.910||182.404||111.731||315.641||386.314||701.955||L=9/8, m=10/9, s=16/15

| 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}}

|-

|[[15edo]]||3:2:1||240.000||160.000||80.000||320.000||400.000||720.000||5-limit patent val

| [[15edo]] || 3:2:1 || 240.000 || 160.000 || 80.000 || 320.000 || 400.000 || 720.000 || 5-limit patent val

|-

|[[18edo]]||4:2:1||266.667||133.333||66.667||333.333||400.000||733.333||5-limit patent val

| [[18edo]] || 4:2:1 || 266.667 || 133.333 || 66.667 || 333.333 || 400.000 || 733.333 || 5-limit patent val

|-

|[[20edo]]||4:3:1||240.000||180.000||60.000||300.000||420.000||720.000||

| [[20edo]] || 4:3:1 || 240.000 || 180.000 || 60.000 || 300.000 || 420.000 || 720.000 ||

|-

|[[21edo]]||5:2:1||285.714||114.286||57.143||342.857||400.000||742.857||

| [[21edo]] || 5:2:1 || 285.714 || 114.286 || 57.143 || 342.857 || 400.000 || 742.857 ||

|-

|[[22edo]]||4:3:2||218.182||163.636||109.091||327.273||381.818||709.091||5-limit patent val

| [[22edo]] || 4:3:2 || 218.182 || 163.636 || 109.091 || 327.273 || 381.818 || 709.091 || 5-limit patent val

|-

|[[23edo]]||5:3:1||260.870||156.522||52.174||313.043||417.391||730.435||

| [[23edo]] || 5:3:1 || 260.870 || 156.522 || 52.174 || 313.043 || 417.391 || 730.435 ||

|-

|[[24edo]]||6:2:1||300.000||100.000||50.000||350.000||400.000||750.000||

| [[24edo]] || 6:2:1 || 300.000 || 100.000 || 50.000 || 350.000 || 400.000 || 750.000 ||

|-

| rowspan="2" |[[25edo]]||5:3:2||240.000||144.000||96.000||336.000||384.000||720.000||5-limit patent val

| rowspan="2" | [[25edo]] || 5:3:2 || 240.000 || 144.000 || 96.000 || 336.000 || 384.000 || 720.000 || 5-limit patent val

|-

|5:4:1||240.000||192.000||48.000||288.000||432.000||720.000||

| 5:4:1 || 240.000 || 192.000 || 48.000 || 288.000 || 432.000 || 720.000 ||

|-

|[[26edo]]||6:3:1||276.923||138.462||46.154||323.077||415.385||738.462||

| [[26edo]] || 6:3:1 || 276.923 || 138.462 || 46.154 || 323.077 || 415.385 || 738.462 ||

|-

| rowspan="2" |[[27edo]]||5:4:2||222.222||177.778||88.889||311.111||400.000||711.111||5-limit patent val

| rowspan="2" | [[27edo]] || 5:4:2 || 222.222 || 177.778 || 88.889 || 311.111 || 400.000 || 711.111 || 5-limit patent val

|-

|7:2:1||311.111||88.889||44.444||355.556||400.000||755.556||

| 7:2:1 || 311.111 || 88.889 || 44.444 || 355.556 || 400.000 || 755.556 ||

|-

| rowspan="2" |[[28edo]]||6:3:2||257.143||128.571||85.714||342.857||385.714||728.571||

| rowspan="2" | [[28edo]] || 6:3:2 || 257.143 || 128.571 || 85.714 || 342.857 || 385.714 || 728.571 ||

|-

|6:4:1||257.143||171.429||42.857||300.000||428.571||728.571||

| 6:4:1 || 257.143 || 171.429 || 42.857 || 300.000 || 428.571 || 728.571 ||

|-

| rowspan="2" |[[29edo]]||5:4:3||206.897||165.517||124.138||331.034||372.414||703.448||5-limit patent val

| rowspan="2" | [[29edo]] || 5:4:3 || 206.897 || 165.517 || 124.138 || 331.034 || 372.414 || 703.448 || 5-limit patent val

|-

|7:3:1||289.655||124.138||41.379||331.034||413.793||744.828||

| 7:3:1 || 289.655 || 124.138 || 41.379 || 331.034 || 413.793 || 744.828 ||

|-

| rowspan="2" |[[30edo]]||6:5:1||240.000||200.000||40.000||280.000||440.000||720.000||

| rowspan="2" | [[30edo]] || 6:5:1 || 240.000 || 200.000 || 40.000 || 280.000 || 440.000 || 720.000 ||

|-

|8:2:1||320.000||80.000||40.000||360.000||400.000||760.000||

| 8:2:1 || 320.000 || 80.000 || 40.000 || 360.000 || 400.000 || 760.000 ||

|-

| rowspan="2" |[[31edo]]||7:3:2||270.968||116.129||77.419||348.387||387.097||735.484||

| rowspan="2" | [[31edo]] || 7:3:2 || 270.968 || 116.129 || 77.419 || 348.387 || 387.097 || 735.484 ||

|-

|7:4:1||270.968||154.839||38.710||309.677||425.806||735.484||

| 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

| 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||

| 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||

| 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||

| 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||

| 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||

| 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

| 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||

| 8:3:2 || 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||

| 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||

| 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||

| 7:5:2 || 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||

| 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||

| 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||

| 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||

| 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||

| 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

| 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||

| 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||

| 9:3:2 || 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||

| 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||

| 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||

| 8:5:2 || 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||

| 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||

| 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||

| 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

| 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||

| 9:4:2 || 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||

| 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||

| 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||

| 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||

| 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||

| 10:3:2 || 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||

| 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

| 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||

| 9:4:3 || 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||

| 9:5:2 || 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||

| 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||

| 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||

| 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

| 8:6:3 || 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||

| 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||

| 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||

| 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||

| 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||

| 9:5:3 || 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||

| 9:6:2 || 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||

| 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||

| 11:3:2 || 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||

| 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||

| 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||

| 10:4:3 || 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||

| 10:5:2 || 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||

| 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||

| 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||

| 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||

| 9:7:2 || 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||

| 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||

| 11:4:2 || 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||

| 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||

| 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||

| 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

| 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||

| 10:5:3 || 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||

| 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||

| 12:3:2 || 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||

| 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||

| 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||

| 9:7:3 || 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||

| 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||

| 11:4:3 || 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||

| 11:5:2 || 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||

| 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||

| 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

| 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||

| 10:5:4 || 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||

| 10:6:3 || 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||

| 10:7:2 || 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||

| 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||

| 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||

| 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||

| 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

| 9:7:4 || 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||

| 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||

| 11:5:3 || 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||

| 11:6:2 || 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||

| 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||

| 13:3:2 || 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||

| 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||

| 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||

| 10:7:3 || 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||

| 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||

| 12:4:3 || 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||

| 12:5:2 || 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||

| 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||

| 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

| 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||

| 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||

| 11:5:4 || 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||

| 11:6:3 || 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||

| 11:7:2 || 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||

| 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||

| 13:4:2 || 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||

| 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||

| 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||

| 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||

| 10:7:4 || 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||

| 10:8:3 || 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||

| 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||

| 12:5:3 || 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||

| 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||

| 14:3:2 || 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||

| 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||

| 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

| 9:8:5 || 203.774 || 181.132 || 113.208 || 316.981 || 384.906 || 701.887 || 5-limit patent val

|-

|11:6:4||249.057||135.849||90.566||339.623||384.906||724.528||

| 11:6:4 || 249.057 || 135.849 || 90.566 || 339.623 || 384.906 || 724.528 ||

|-

|11:7:3||249.057||158.491||67.925||316.981||407.547||724.528||

| 11:7:3 || 249.057 || 158.491 || 67.925 || 316.981 || 407.547 || 724.528 ||

|-

|11:8:2||249.057||181.132||45.283||294.340||430.189||724.528||

| 11:8:2 || 249.057 || 181.132 || 45.283 || 294.340 || 430.189 || 724.528 ||

|-

|11:9:1||249.057||203.774||22.642||271.698||452.830||724.528||

| 11:9:1 || 249.057 || 203.774 || 22.642 || 271.698 || 452.830 || 724.528 ||

|-

|13:4:3||294.340||90.566||67.925||362.264||384.906||747.170||

| 13:4:3 || 294.340 || 90.566 || 67.925 || 362.264 || 384.906 || 747.170 ||

|-

|13:5:2||294.340||113.208||45.283||339.623||407.547||747.170||

| 13:5:2 || 294.340 || 113.208 || 45.283 || 339.623 || 407.547 || 747.170 ||

|-

|13:6:1||294.340||135.849||22.642||316.981||430.189||747.170||

| 13:6:1 || 294.340 || 135.849 || 22.642 || 316.981 || 430.189 || 747.170 ||

|-

|15:3:1||339.623||67.925||22.642||362.264||407.547||769.811||

| 15:3:1 || 339.623 || 67.925 || 22.642 || 362.264 || 407.547 || 769.811 ||

|-

| rowspan="7" |[[54edo]]||10:7:5||222.222||155.556||111.111||333.333||377.778||711.111||5-limit patent val

| rowspan="7" | [[54edo]] || 10:7:5 || 222.222 || 155.556 || 111.111 || 333.333 || 377.778 || 711.111 || 5-limit patent val

|-

|10:9:3||222.222||200.000||66.667||288.889||422.222||711.111||

| 10:9:3 || 222.222 || 200.000 || 66.667 || 288.889 || 422.222 || 711.111 ||

|-

|12:5:4||266.667||111.111||88.889||355.556||377.778||733.333||

| 12:5:4 || 266.667 || 111.111 || 88.889 || 355.556 || 377.778 || 733.333 ||

|-

|12:7:2||266.667||155.556||44.444||311.111||422.222||733.333||

| 12:7:2 || 266.667 || 155.556 || 44.444 || 311.111 || 422.222 || 733.333 ||

|-

|12:8:1||266.667||177.778||22.222||288.889||444.444||733.333||

| 12:8:1 || 266.667 || 177.778 || 22.222 || 288.889 || 444.444 || 733.333 ||

|-

|14:5:1||311.111||111.111||22.222||333.333||422.222||755.556||

| 14:5:1 || 311.111 || 111.111 || 22.222 || 333.333 || 422.222 || 755.556 ||

|-

|16:2:1||355.556||44.444||22.222||377.778||400.000||777.778||

| 16:2:1 || 355.556 || 44.444 || 22.222 || 377.778 || 400.000 || 777.778 ||

|}

Line 536:

Line 520:

Nicetone has following generator-offset MV3 supersets:

* [[Sephipechroid]]: 13-note 3L 5m 5s scale (~~LmsmLsmsLmsms~~ and ~~LmsmLsmsmLsms~~)

* [[Sephipechroid]]: 13-note 3L 5M 5s scale (LMsMLsMsLMsMs and LMsMLsMsMLsMs)

* [[Interoneichro]]: 13-note 5L 3m 5s scale (~~LmsLsLmsLsmLs~~ and ~~LmsLsmLsLsmLs~~)

* [[Interoneichro]]: 13-note 5L 3M 5s scale (LMsLsLMsLsMLs and LMsLsMLsLsMLs)

* [[Sephimechroid]]: 13-note 5L 5m 3s scale (~~LmLmsLmLsmLms~~ and ~~LmLsmLmLsmLms~~)

* [[Sephimechroid]]: 13-note 5L 5M 3s scale (LMLMsLMLsMLMs and LMLsMLMLsMLMs)

* [[Beatloid]]: 17-note 5L 5m 7s scale (~~LmsLsmLsmsLmsLsms~~ and ~~LmsLsmLsmsLsmLsms~~)

* [[Beatloid]]: 17-note 5L 5M 7s scale (LMsLsMLsMsLMsLsMs and LMsLsMLsMsLsMLsMs)

* [[Enharoid]]: 17-note 5L 7m 5s scale (~~LmsLmsmLmsLmsmLsm~~ and ~~LmsLmsmLsmLmsmLsm~~)

* [[Enharoid]]: 17-note 5L 7M 5s scale (LMsLMsMLMsLMsMLsM and LMsLMsMLsMLMsMLsM)

* [[Moharoid]]: 17-note 7L 5m 5s scale (~~LmLsLmsLmLsmLsLms~~ and ~~LmLsmLsLmLsmLsLms~~)

* [[Moharoid]]: 17-note 7L 5M 5s scale (LMLsLMsLMLsMLsLMs and LMLsMLsLMLsMLsLMs)

Remarkable non-MV3 generator-offset supersets include [[blackdye]] (10-note, LmLsLmLsLs).

== See also ==

* [[Blackdye]] ~~– a~~ 10-note scale that is an extension to nicetone.

* [[Blackdye]] – A 10-note scale that is an extension to nicetone.

* [[~~Zarlino]] – a 5-limit JI scale with the same pattern.~~

* [[Omnidiatonic]] – Sister 2L 3M 2s scale

* [[Interdia]] ~~– sister~~ 2L 3m 2s scale

* [[Antinicetone]] – Sister 2L 2M 3s scale

* [[Antinicetone]] ~~– sister~~ 2L 2m 3s scale

* [[5L 2s]] – LM-equalized version of nicetone

** [[5L 2s Muddles]] – Other diatonic muddles

** [[5L 2s Muddles]] ~~– other~~ diatonic muddles

* [[3L 4s]] – MS-equalized version of nicetone

* [[3L 2s]] – Collapsed version of nicetone

* [[3L 2s]] ~~– collapsed~~ version of nicetone

* [[Nicepent]] – The pentatonic predecessor to nicetone.

* [[Nicechrome]] – A possible chromatic (12-note) extension to nicetone.

* [[Superzarlino]]

* [[Zarlino (Pianoteq)]]

[[Category:Rank-3 scales]]

[[Category:7-tone scales]]

[[Category:GO scales]]

@@ Line 1: / Line 1: @@
-'''Nicetone''' (also known as the '''Zarlino pattern''' or '''Ptolemaic-Auric diatonic''') is a 7-note [[Maximum variety|Maximum variety 3]] scale with the step pattern 3L 2m 2s. 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 3L 2m 2s. It's also a subset of the 5L 2m 3s [[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]] diatonic scale and the [[3L 4s]] neutral scale.
+Nicetone is intermediate between the [[5L&nbsp;2s]] diatonic scale and the [[3L&nbsp;4s]] neutral scale.
-Nicetone can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[9/8]], m represents [[10/9]], and s represents [[16/15]].
+[[File:Nicetone.svg|900px|thumb|center|Comparison of diatonic scales in JI, Pythagorean tuning, and meantone]]
-{| class="wikitable"
+{| class="wikitable" style="margin-left: auto; margin-right: auto;"
-|+ Comparison with mosh and diatonic in 41edo
+|+ Comparison with mosh and antipentic in 33edo
 |-
 ! Name !! Structure !! Step Sizes !! Graphical Representation
 |-
-| Mosh || 3L 4s || 7\41, 5\41 || ├──────┼────┼────┼──────┼────┼──────┼────┤
+| Mosh || {{nowrap|3L 4s}} || 7\33, 3\33 || {{step vis| 3 7 3 7 3 3 7 }}
 |-
-| Nicetone || 3L 2m 2s || 7\41, 6\41, 4\41 || ├──────┼─────┼───┼──────┼─────┼──────┼───┤
+| Nicetone || {{nowrap|3L 2M 2s}} || 7\33, 4\33, 2\33 || {{step vis| 4 7 2 7 4 2 7 }}
 |-
-| Diatonic || 5L 2s || 7\41, 3\41 || ├──────┼──────┼──┼──────┼──────┼──────┼──┤
+| Antipentic || {{nowrap|3L 2s}} || 7\33, 6\33 || {{step vis| 6 7 7 6 7 }}
 |}
-{| class="wikitable"
+== 5-limit Zarlino scale ==
-|+ Comparison with mosh and antipentic in 33edo
+'''[[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.
-|-
-! Name !! Structure !! Step Sizes !! Graphical Representation
-|-
-| Mosh || 3L 4s || 7\33, 3\33 || ├──┼──────┼──┼──────┼──┼──┼──────┤
-|-
-| Nicetone || 3L 2m 2s || 7\33, 4\33, 2\33 || ├───┼──────┼─┼──────┼───┼─┼──────┤
-|-
-| Antipentic || 3L 2s || 7\33, 6\33 || ├─────┼──────╫──────┼─────╫──────┤
-|}
 == 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.
+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"
-|+ Interval sizes in nicetone
+|+ style="font-size: 105%;" | Interval sizes in nicetone
-|-
+|- style="white-space: nowrap;"
-!colspan=2|Interval class
+! colspan="2" | Interval class
 ! Sizes
 ! 5-limit JI
-! [[15edo]] <br>(L:m:s = 3:2:1)
+! [[15edo]]<br />(L:M:s = 3:2:1)
-! [[41edo]] <br>(L:m:s = 7:6:4)
+! [[41edo]]<br />(L:M:s = 7:6:4)
-|- bgcolor="#eaeaff"
+|- style="background-color: #eaeaff;"
-!rowspan=3|Second <br>([[TAMNAMS|1-step]])
+! rowspan="3" | Second<br />([[TAMNAMS|1-step]])
-!| <small>small</small>
+! style="font-size: 0.75em;" | Small
 | s
 | 16/15, 111.73¢
 | 1\15, 80.00¢
 | 4\41, 117.07¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| m
+| M
 | 10/9, 182.40¢
 | 2\15, 160.00¢
 | 6\41, 175.61¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
 | L
 | 9/8, 203.91¢
@@ Line 62: / Line 53: @@
 | 7\41, 204.88¢
 |-
-!rowspan=3|Third <br>([[TAMNAMS|2-step]])
+! rowspan="3" | Third<br />([[TAMNAMS|2-step]])
-!|<small>small</small>
+! style="font-size: 0.75em;" | Small
-| m + s
+| {{nowrap|M + s}}
 | 32/27, 294.13¢
 | 3\15, 240.00¢
 | 10\41, 292.68¢
 |-
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| L + s
+| {{nowrap|L + s}}
 | 6/5, 315.64¢
 | 4\15, 320.00¢
 | 11\41, 321.95¢
 |-
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
-| L + m
+| {{nowrap|L + M}}
 | 5/4, 386.31¢
 | 5\15, 400.00¢
 | 13\41, 380.49¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!rowspan=3|Fourth <br>([[TAMNAMS|3-step]])
+! rowspan="3" | Fourth<br />([[TAMNAMS|3-step]])
-!|<small>small</small>
+! style="font-size: 0.75em;" | Small
-| L + m + s
+| {{nowrap|L + M + s}}
 | 4/3, 498.04¢
 | 6\15, 480.00¢
 | 17\41, 497.56¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| 2L + s
+| {{nowrap|2L + s}}
 | 27/20, 519.55¢
 | 7\15, 560.00¢
 | 18\41, 526.83¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
-| 2L + m
+| {{nowrap|2L + M}}
 | 45/32, 590.22¢
 | 8\15, 640.00¢
 | 20\41, 585.37¢
 |-
-!rowspan=3|Fifth <br>([[TAMNAMS|4-step]])
+! rowspan="3" | Fifth<br />([[TAMNAMS|4-step]])
-!|<small>small</small>
+! style="font-size: 0.75em;" | Small
-| L + m + 2s
+| {{nowrap|L + M + 2s}}
 | 64/45, 609.78¢
 | 7\15, 560.00¢
 | 21\41, 614.63¢
 |-
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| L + 2m + s
+| {{nowrap|L + 2M + s}}
 | 40/27, 680.45¢
 | 8\15, 640.00¢
 | 23\41, 673.17¢
 |-
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
-| 2L + m + s
+| {{nowrap|2L + M + s}}
 | 3/2, 701.96¢
 | 9\15, 720.00¢
 | 24\41, 702.44¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!rowspan=3|Sixth <br>([[TAMNAMS|5-step]])
+! rowspan="3" | Sixth<br />([[TAMNAMS|5-step]])
-!|<small>small</small>
+! style="font-size: 0.75em;" | Small
-| 2L + m + 2s
+| {{nowrap|2L + M + 2s}}
 | 8/5, 813.69¢
 | 10\15, 800.00¢
 | 28\41, 819.51¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| 2L + 2m + s
+| {{nowrap|2L + 2M + s}}
 | 5/3, 884.36¢
 | 11\15, 880.00¢
 | 30\41, 878.05¢
-|- bgcolor="#eaeaff"
+|- style="background-color: "#eaeaff;"
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
-| 3L + m + s
+| {{nowrap|3L + M + s}}
 | 27/16, 905.87¢
 | 12\15, 960.00¢
 | 31\41, 907.32¢
 |-
-!rowspan=3|Seventh <br>([[TAMNAMS|6-step]])
+! rowspan="3" | Seventh<br />([[TAMNAMS|6-step]])
-!| <small>small</small>
+! style="font-size: 0.75em;" | Small
-| 2L + 2m + 2s
+| {{nowrap|2L + 2M + 2s}}
 | 16/9, 996.09¢
 | 12\15, 960.00¢
 | 34\41, 995.12¢
 |-
-!|<small>medium</small>
+! style="font-size: 0.75em;" | Medium
-| 3L + m + 2s
+| {{nowrap|3L + M + 2s}}
 | 9/5, 1017.60¢
 | 13\15, 1040.00¢
 | 35\41, 1024.39¢
 |-
-!|<small>large</small>
+! style="font-size: 0.75em;" | Large
-| 3L + 2m + s
+| {{nowrap|3L + 2M + s}}
 | 15/8, 1088.27¢
 | 14\15, 1120.00¢
@@ Line 163: / Line 154: @@
 The modes are arranged by brightest to darkest.
 {| class="wikitable"
-|+Nicetone modes
+|+ style="font-size: 105%;" | Nicetone modes
-!Left handed
-!Right handed
 |-
-|LmLsmLs <br>LH Nice-Lydian
+! Left handed !! Right handed
-|LmLsLms <br>RH Nice-Lydian
 |-
-|mLsLmLs <br>LH Nice-Ionian
+| LMLsMLs<br />LH Nice-Lydian
-|LmsLmLs <br>RH Nice-Ionian
+| LMLsLMs<br />RH Nice-Lydian
 |-
-|mLsmLsL <br>LH Nice-Mixolydian
+| MLsLMLs<br />LH Nice-Ionian
-|mLsLmsL <br>RH Nice-Mixolydian
+| LMsLMLs<br />RH Nice-Ionian
 |-
-|LsLmLsm <br>LH Nice-Dorian
+| MLsMLsL<br />LH Nice-Mixolydian
-|msLmLsL <br>RH Nice-Dorian
+| MLsLMsL<br />RH Nice-Mixolydian
 |-
-|LsmLsLm <br>LH Nice-Aeolian
+| LsLMLsM<br />LH Nice-Dorian
-|LsLmsLm <br>RH Nice-Aeolian
+| MsLMLsL<br />RH Nice-Dorian
 |-
-|sLmLsmL <br>LH Nice-Phrygian
+| LsMLsLM<br />LH Nice-Aeolian
-|sLmLsLm <br>RH Nice-Phrygian
+| LsLMsLM<br />RH Nice-Aeolian
 |-
-|smLsLmL <br>LH Nice-Locrian
+| sLMLsML<br />LH Nice-Phrygian
-|sLmsLmL <br>RH Nice-Locrian
+| sLMLsLM<br />RH Nice-Phrygian
+|-
+| sMLsLML<br />LH Nice-Locrian
+| sLMsLML<br />RH Nice-Locrian
 |}
@@ Line 193: / Line 184: @@
 {| class="wikitable"
-|+Tuning range of nicetone
+|+ style="font-size: 105%;" | Tuning range of nicetone
+|-
 !
 ! Tuning range (in [[octave]]s)
 |-
-! Outer generator <br>(''G''<sub>1</sub> = 2L + m + s)
+! 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>
+| <math>\displaystyle \frac{4}{7} \lt G_\text{1} \lt \frac{2}{3}</math>
 |-
-! RH inner generator <br>(''G''<sub>2R</sub> = L + m)
+! RH inner generator<br />({{nowrap|''G''<sub>2R</sub> {{=}} L + M}})
-| <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>
+| <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>
 |-
-! LH inner generator <br>(''G''<sub>2L</sub> = L + s)
+! LH inner generator<br />({{nowrap|''G''<sub>2L</sub> {{=}} L + s}})
-| <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>
+| <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>
 |-
-! Large step <br>(L = 2''G''<sub>1</sub> - 1)
+! Large step<br />({{nowrap|L {{=}} 2''G''<sub>1</sub> &minus; 1}})
-| <math>\displaystyle \frac{1}{7} &lt; L &lt; \frac{1}{3}</math>
+| <math>\displaystyle \frac{1}{7} \lt L \lt \frac{1}{3}</math>
 |-
-! Middle step <br>(m = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)
+! Middle step<br />({{nowrap|M {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''G''<sub>2L</sub>}})
-| <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>
+| <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>
 |-
-! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2R</sub>)
+! Small step<br />({{nowrap|s {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''G''<sub>2R</sub>}})
-| <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>
+| <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>
 |}
 {| class="wikitable"
-|+Common Nicetone tunings
+|+ style="font-size: 105%;" | Common Nicetone tunings
-! rowspan="2" | Tuning
+|-
-! rowspan="2" | L:m:s
+! 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
-! colspan="3" | Size of step (¢)
-! colspan="2" | Inner generator
-! rowspan="2" | Outer generator <br>(2L+m+s)
-! rowspan="2" | Comments
 |-
-! L
+! L !! M !! s !! LH ({{nowrap|L + s}}) !! RH ({{nowrap|L + M}})
-! m
-! s
-! LH (L+s)
-! RH (L+m)
 |-
-| 5-limit JI || ||203.910||182.404||111.731||315.641||386.314||701.955||L=9/8, m=10/9, s=16/15
+| 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}}
 |-
-|[[15edo]]||3:2:1||240.000||160.000||80.000||320.000||400.000||720.000||5-limit patent val
+| [[15edo]] || 3:2:1 || 240.000 || 160.000 || 80.000 || 320.000 || 400.000 || 720.000 || 5-limit patent val
 |-
-|[[18edo]]||4:2:1||266.667||133.333||66.667||333.333||400.000||733.333||5-limit patent val
+| [[18edo]] || 4:2:1 || 266.667 || 133.333 || 66.667 || 333.333 || 400.000 || 733.333 || 5-limit patent val
 |-
-|[[20edo]]||4:3:1||240.000||180.000||60.000||300.000||420.000||720.000||
+| [[20edo]] || 4:3:1 || 240.000 || 180.000 || 60.000 || 300.000 || 420.000 || 720.000 ||
 |-
-|[[21edo]]||5:2:1||285.714||114.286||57.143||342.857||400.000||742.857||
+| [[21edo]] || 5:2:1 || 285.714 || 114.286 || 57.143 || 342.857 || 400.000 || 742.857 ||
 |-
-|[[22edo]]||4:3:2||218.182||163.636||109.091||327.273||381.818||709.091||5-limit patent val
+| [[22edo]] || 4:3:2 || 218.182 || 163.636 || 109.091 || 327.273 || 381.818 || 709.091 || 5-limit patent val
 |-
-|[[23edo]]||5:3:1||260.870||156.522||52.174||313.043||417.391||730.435||
+| [[23edo]] || 5:3:1 || 260.870 || 156.522 || 52.174 || 313.043 || 417.391 || 730.435 ||
 |-
-|[[24edo]]||6:2:1||300.000||100.000||50.000||350.000||400.000||750.000||
+| [[24edo]] || 6:2:1 || 300.000 || 100.000 || 50.000 || 350.000 || 400.000 || 750.000 ||
 |-
-| rowspan="2" |[[25edo]]||5:3:2||240.000||144.000||96.000||336.000||384.000||720.000||5-limit patent val
+| rowspan="2" | [[25edo]] || 5:3:2 || 240.000 || 144.000 || 96.000 || 336.000 || 384.000 || 720.000 || 5-limit patent val
 |-
-|5:4:1||240.000||192.000||48.000||288.000||432.000||720.000||
+| 5:4:1 || 240.000 || 192.000 || 48.000 || 288.000 || 432.000 || 720.000 ||
 |-
-|[[26edo]]||6:3:1||276.923||138.462||46.154||323.077||415.385||738.462||
+| [[26edo]] || 6:3:1 || 276.923 || 138.462 || 46.154 || 323.077 || 415.385 || 738.462 ||
 |-
-| rowspan="2" |[[27edo]]||5:4:2||222.222||177.778||88.889||311.111||400.000||711.111||5-limit patent val
+| rowspan="2" | [[27edo]] || 5:4:2 || 222.222 || 177.778 || 88.889 || 311.111 || 400.000 || 711.111 || 5-limit patent val
 |-
-|7:2:1||311.111||88.889||44.444||355.556||400.000||755.556||
+| 7:2:1 || 311.111 || 88.889 || 44.444 || 355.556 || 400.000 || 755.556 ||
 |-
-| rowspan="2" |[[28edo]]||6:3:2||257.143||128.571||85.714||342.857||385.714||728.571||
+| rowspan="2" | [[28edo]] || 6:3:2 || 257.143 || 128.571 || 85.714 || 342.857 || 385.714 || 728.571 ||
 |-
-|6:4:1||257.143||171.429||42.857||300.000||428.571||728.571||
+| 6:4:1 || 257.143 || 171.429 || 42.857 || 300.000 || 428.571 || 728.571 ||
 |-
-| rowspan="2" |[[29edo]]||5:4:3||206.897||165.517||124.138||331.034||372.414||703.448||5-limit patent val
+| rowspan="2" | [[29edo]] || 5:4:3 || 206.897 || 165.517 || 124.138 || 331.034 || 372.414 || 703.448 || 5-limit patent val
 |-
-|7:3:1||289.655||124.138||41.379||331.034||413.793||744.828||
+| 7:3:1 || 289.655 || 124.138 || 41.379 || 331.034 || 413.793 || 744.828 ||
 |-
-| rowspan="2" |[[30edo]]||6:5:1||240.000||200.000||40.000||280.000||440.000||720.000||
+| rowspan="2" | [[30edo]] || 6:5:1 || 240.000 || 200.000 || 40.000 || 280.000 || 440.000 || 720.000 ||
 |-
-|8:2:1||320.000||80.000||40.000||360.000||400.000||760.000||
+| 8:2:1 || 320.000 || 80.000 || 40.000 || 360.000 || 400.000 || 760.000 ||
 |-
-| rowspan="2" |[[31edo]]||7:3:2||270.968||116.129||77.419||348.387||387.097||735.484||
+| rowspan="2" | [[31edo]] || 7:3:2 || 270.968 || 116.129 || 77.419 || 348.387 || 387.097 || 735.484 ||
 |-
-|7:4:1||270.968||154.839||38.710||309.677||425.806||735.484||
+| 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
+| 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||
+| 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||
+| 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||
+| 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||
+| 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||
+| 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
+| 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||
+| 8:3:2 || 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||
+| 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||
+| 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||
+| 7:5:2 || 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||
+| 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||
+| 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||
+| 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||
+| 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||
+| 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
+| 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||
+| 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||
+| 9:3:2 || 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||
+| 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||
+| 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||
+| 8:5:2 || 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||
+| 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||
+| 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||
+| 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
+| 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||
+| 9:4:2 || 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||
+| 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||
+| 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||
+| 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||
+| 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||
+| 10:3:2 || 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||
+| 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
+| 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||
+| 9:4:3 || 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||
+| 9:5:2 || 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||
+| 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||
+| 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||
+| 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
+| 8:6:3 || 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||
+| 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||
+| 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||
+| 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||
+| 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||
+| 9:5:3 || 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||
+| 9:6:2 || 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||
+| 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||
+| 11:3:2 || 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||
+| 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||
+| 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||
+| 10:4:3 || 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||
+| 10:5:2 || 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||
+| 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||
+| 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||
+| 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||
+| 9:7:2 || 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||
+| 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||
+| 11:4:2 || 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||
+| 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||
+| 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||
+| 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
+| 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||
+| 10:5:3 || 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||
+| 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||
+| 12:3:2 || 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||
+| 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||
+| 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||
+| 9:7:3 || 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||
+| 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||
+| 11:4:3 || 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||
+| 11:5:2 || 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||
+| 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||
+| 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
+| 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||
+| 10:5:4 || 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||
+| 10:6:3 || 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||
+| 10:7:2 || 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||
+| 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||
+| 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||
+| 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||
+| 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
+| 9:7:4 || 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||
+| 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||
+| 11:5:3 || 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||
+| 11:6:2 || 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||
+| 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||
+| 13:3:2 || 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||
+| 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||
+| 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||
+| 10:7:3 || 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||
+| 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||
+| 12:4:3 || 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||
+| 12:5:2 || 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||
+| 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||
+| 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
+| 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||
+| 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||
+| 11:5:4 || 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||
+| 11:6:3 || 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||
+| 11:7:2 || 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||
+| 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||
+| 13:4:2 || 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||
+| 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||
+| 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||
+| 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||
+| 10:7:4 || 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||
+| 10:8:3 || 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||
+| 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||
+| 12:5:3 || 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||
+| 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||
+| 14:3:2 || 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||
+| 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||
+| 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
+| 9:8:5 || 203.774 || 181.132 || 113.208 || 316.981 || 384.906 || 701.887 || 5-limit patent val
 |-
-|11:6:4||249.057||135.849||90.566||339.623||384.906||724.528||
+| 11:6:4 || 249.057 || 135.849 || 90.566 || 339.623 || 384.906 || 724.528 ||
 |-
-|11:7:3||249.057||158.491||67.925||316.981||407.547||724.528||
+| 11:7:3 || 249.057 || 158.491 || 67.925 || 316.981 || 407.547 || 724.528 ||
 |-
-|11:8:2||249.057||181.132||45.283||294.340||430.189||724.528||
+| 11:8:2 || 249.057 || 181.132 || 45.283 || 294.340 || 430.189 || 724.528 ||
 |-
-|11:9:1||249.057||203.774||22.642||271.698||452.830||724.528||
+| 11:9:1 || 249.057 || 203.774 || 22.642 || 271.698 || 452.830 || 724.528 ||
 |-
-|13:4:3||294.340||90.566||67.925||362.264||384.906||747.170||
+| 13:4:3 || 294.340 || 90.566 || 67.925 || 362.264 || 384.906 || 747.170 ||
 |-
-|13:5:2||294.340||113.208||45.283||339.623||407.547||747.170||
+| 13:5:2 || 294.340 || 113.208 || 45.283 || 339.623 || 407.547 || 747.170 ||
 |-
-|13:6:1||294.340||135.849||22.642||316.981||430.189||747.170||
+| 13:6:1 || 294.340 || 135.849 || 22.642 || 316.981 || 430.189 || 747.170 ||
 |-
-|15:3:1||339.623||67.925||22.642||362.264||407.547||769.811||
+| 15:3:1 || 339.623 || 67.925 || 22.642 || 362.264 || 407.547 || 769.811 ||
 |-
-| rowspan="7" |[[54edo]]||10:7:5||222.222||155.556||111.111||333.333||377.778||711.111||5-limit patent val
+| rowspan="7" | [[54edo]] || 10:7:5 || 222.222 || 155.556 || 111.111 || 333.333 || 377.778 || 711.111 || 5-limit patent val
 |-
-|10:9:3||222.222||200.000||66.667||288.889||422.222||711.111||
+| 10:9:3 || 222.222 || 200.000 || 66.667 || 288.889 || 422.222 || 711.111 ||
 |-
-|12:5:4||266.667||111.111||88.889||355.556||377.778||733.333||
+| 12:5:4 || 266.667 || 111.111 || 88.889 || 355.556 || 377.778 || 733.333 ||
 |-
-|12:7:2||266.667||155.556||44.444||311.111||422.222||733.333||
+| 12:7:2 || 266.667 || 155.556 || 44.444 || 311.111 || 422.222 || 733.333 ||
 |-
-|12:8:1||266.667||177.778||22.222||288.889||444.444||733.333||
+| 12:8:1 || 266.667 || 177.778 || 22.222 || 288.889 || 444.444 || 733.333 ||
 |-
-|14:5:1||311.111||111.111||22.222||333.333||422.222||755.556||
+| 14:5:1 || 311.111 || 111.111 || 22.222 || 333.333 || 422.222 || 755.556 ||
 |-
-|16:2:1||355.556||44.444||22.222||377.778||400.000||777.778||
+| 16:2:1 || 355.556 || 44.444 || 22.222 || 377.778 || 400.000 || 777.778 ||
 |}
@@ Line 536: / Line 520: @@
 Nicetone has following generator-offset MV3 supersets:
-* [[Sephipechroid]]: 13-note 3L 5m 5s scale (LmsmLsmsLmsms and LmsmLsmsmLsms)
+* [[Sephipechroid]]: 13-note 3L 5M 5s scale (LMsMLsMsLMsMs and LMsMLsMsMLsMs)
-* [[Interoneichro]]: 13-note 5L 3m 5s scale (LmsLsLmsLsmLs and LmsLsmLsLsmLs)
+* [[Interoneichro]]: 13-note 5L 3M 5s scale (LMsLsLMsLsMLs and LMsLsMLsLsMLs)
-* [[Sephimechroid]]: 13-note 5L 5m 3s scale (LmLmsLmLsmLms and LmLsmLmLsmLms)
+* [[Sephimechroid]]: 13-note 5L 5M 3s scale (LMLMsLMLsMLMs and LMLsMLMLsMLMs)
-* [[Beatloid]]: 17-note 5L 5m 7s scale (LmsLsmLsmsLmsLsms and LmsLsmLsmsLsmLsms)
+* [[Beatloid]]: 17-note 5L 5M 7s scale (LMsLsMLsMsLMsLsMs and LMsLsMLsMsLsMLsMs)
-* [[Enharoid]]: 17-note 5L 7m 5s scale (LmsLmsmLmsLmsmLsm and LmsLmsmLsmLmsmLsm)
+* [[Enharoid]]: 17-note 5L 7M 5s scale (LMsLMsMLMsLMsMLsM and LMsLMsMLsMLMsMLsM)
-* [[Moharoid]]: 17-note 7L 5m 5s scale (LmLsLmsLmLsmLsLms and LmLsmLsLmLsmLsLms)
+* [[Moharoid]]: 17-note 7L 5M 5s scale (LMLsLMsLMLsMLsLMs and LMLsMLsLMLsMLsLMs)
 Remarkable non-MV3 generator-offset supersets include [[blackdye]] (10-note, LmLsLmLsLs).
 == 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.
-* [[Zarlino]] – a 5-limit JI scale with the same pattern.
+* [[Omnidiatonic]] &ndash; Sister 2L 3M 2s scale
-* [[Interdia]] – sister 2L 3m 2s scale
+* [[Antinicetone]] &ndash; Sister 2L 2M 3s scale
-* [[Antinicetone]] – sister 2L 2m 3s scale
+* [[5L 2s]] &ndash; LM-equalized version of nicetone
-* [[5L 2s]] – LM-equalized version of nicetone
+** [[5L 2s Muddles]] &ndash; Other diatonic muddles
-** [[5L 2s Muddles]] – other diatonic muddles
+* [[3L 4s]] &ndash; MS-equalized version of nicetone
-* [[3L 4s]] – MS-equalized version of nicetone
+* [[3L 2s]] &ndash; Collapsed version of nicetone
-* [[3L 2s]] – collapsed version of nicetone
+* [[Nicepent]] &ndash; The pentatonic predecessor to nicetone.
+* [[Nicechrome]] &ndash; A possible chromatic (12-note) extension to nicetone.
+* [[Superzarlino]]
+* [[Zarlino (Pianoteq)]]
 [[Category:Rank-3 scales]]
 [[Category:7-tone scales]]
 [[Category:GO scales]]