Nicetone: Difference between revisions

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'''Nicetone''' (also known as the '''Zarlino pattern''' 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.

'''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 {{nowrap|3L 2M 2s}}. It's also a subset of the {{nowrap|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 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]]

[[File:Nicetone.svg|~~800px~~|thumb|center|Comparison of diatonic scales in JI, Pythagorean tuning, and meantone]]

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

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| 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 ==

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{| 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]] (~~{{nowrap|~~L:M:s {{=}} 3:2:1}})

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

! [[41edo]] (~~{{nowrap|~~L:M:s {{=}} 7:6:4}})

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

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

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

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

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

| M + s

| {{nowrap|M + s}}

| 32/27, 294.13¢

| 3\15, 240.00¢

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|-

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

| L + s

| {{nowrap|L + s}}

| 6/5, 315.64¢

| 4\15, 320.00¢

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|-

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

| L + M

| {{nowrap|L + M}}

| 5/4, 386.31¢

| 5\15, 400.00¢

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

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

| L + M + s

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

| 4/3, 498.04¢

| 6\15, 480.00¢

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

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

| 2L + s

| {{nowrap|2L + s}}

| 27/20, 519.55¢

| 7\15, 560.00¢

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

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

| 2L + M

| {{nowrap|2L + M}}

| 45/32, 590.22¢

| 8\15, 640.00¢

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

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

| L + M + 2s

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

| 64/45, 609.78¢

| 7\15, 560.00¢

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|-

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

| L + 2M + s

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

| 40/27, 680.45¢

| 8\15, 640.00¢

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|-

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

| 2L + M + s

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

| 3/2, 701.96¢

| 9\15, 720.00¢

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

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

| 2L + M + 2s

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

| 8/5, 813.69¢

| 10\15, 800.00¢

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

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

| 2L + 2M + s

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

| 5/3, 884.36¢

| 11\15, 880.00¢

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

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

| 3L + M + s

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

| 27/16, 905.87¢

| 12\15, 960.00¢

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

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

| 2L + 2M + 2s

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

| 16/9, 996.09¢

| 12\15, 960.00¢

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|-

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

| 3L + M + 2s

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

| 9/5, 1017.60¢

| 13\15, 1040.00¢

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|-

! 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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|-

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

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

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

|}

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

|-

! 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

! 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

|-

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

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== See also ==

* [[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

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

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* [[3L 4s]] – MS-equalized 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 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.
+'''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 {{nowrap|3L 2M 2s}}. It's also a subset of the {{nowrap|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&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]]
-[[File:Nicetone.svg|800px|thumb|center|Comparison of diatonic scales in JI, Pythagorean tuning, and meantone]]
 {| class="wikitable" style="margin-left: auto; margin-right: auto;"
@@ Line 21: / Line 18: @@
 | 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 ==
@@ Line 27: / Line 27: @@
 {| 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 />({{nowrap|L:M:s {{=}} 3:2:1}})
+! [[15edo]]<br />(L:M:s = 3:2:1)
-! [[41edo]]<br />({{nowrap|L:M:s {{=}} 7:6:4}})
+! [[41edo]]<br />(L:M:s = 7:6:4)
 |- style="background-color: #eaeaff;"
 ! rowspan="3" | Second<br />([[TAMNAMS|1-step]])
@@ Line 55: / Line 55: @@
 ! rowspan="3" | Third<br />([[TAMNAMS|2-step]])
 ! style="font-size: 0.75em;" | Small
-| M + s
+| {{nowrap|M + s}}
 | 32/27, 294.13¢
 | 3\15, 240.00¢
@@ Line 61: / Line 61: @@
 |-
 ! style="font-size: 0.75em;" | Medium
-| L + s
+| {{nowrap|L + s}}
 | 6/5, 315.64¢
 | 4\15, 320.00¢
@@ Line 67: / Line 67: @@
 |-
 ! style="font-size: 0.75em;" | Large
-| L + M
+| {{nowrap|L + M}}
 | 5/4, 386.31¢
 | 5\15, 400.00¢
@@ Line 74: / Line 74: @@
 ! rowspan="3" | Fourth<br />([[TAMNAMS|3-step]])
 ! style="font-size: 0.75em;" | Small
-| L + M + s
+| {{nowrap|L + M + s}}
 | 4/3, 498.04¢
 | 6\15, 480.00¢
@@ Line 80: / Line 80: @@
 |- style="background-color: "#eaeaff;"
 ! style="font-size: 0.75em;" | Medium
-| 2L + s
+| {{nowrap|2L + s}}
 | 27/20, 519.55¢
 | 7\15, 560.00¢
@@ Line 86: / Line 86: @@
 |- style="background-color: "#eaeaff;"
 ! style="font-size: 0.75em;" | Large
-| 2L + M
+| {{nowrap|2L + M}}
 | 45/32, 590.22¢
 | 8\15, 640.00¢
@@ Line 93: / Line 93: @@
 ! rowspan="3" | Fifth<br />([[TAMNAMS|4-step]])
 ! style="font-size: 0.75em;" | Small
-| L + M + 2s
+| {{nowrap|L + M + 2s}}
 | 64/45, 609.78¢
 | 7\15, 560.00¢
@@ Line 99: / Line 99: @@
 |-
 ! style="font-size: 0.75em;" | Medium
-| L + 2M + s
+| {{nowrap|L + 2M + s}}
 | 40/27, 680.45¢
 | 8\15, 640.00¢
@@ Line 105: / Line 105: @@
 |-
 ! style="font-size: 0.75em;" | Large
-| 2L + M + s
+| {{nowrap|2L + M + s}}
 | 3/2, 701.96¢
 | 9\15, 720.00¢
@@ Line 112: / Line 112: @@
 ! rowspan="3" | Sixth<br />([[TAMNAMS|5-step]])
 ! style="font-size: 0.75em;" | Small
-| 2L + M + 2s
+| {{nowrap|2L + M + 2s}}
 | 8/5, 813.69¢
 | 10\15, 800.00¢
@@ Line 118: / Line 118: @@
 |- style="background-color: "#eaeaff;"
 ! style="font-size: 0.75em;" | Medium
-| 2L + 2M + s
+| {{nowrap|2L + 2M + s}}
 | 5/3, 884.36¢
 | 11\15, 880.00¢
@@ Line 124: / Line 124: @@
 |- style="background-color: "#eaeaff;"
 ! style="font-size: 0.75em;" | Large
-| 3L + M + s
+| {{nowrap|3L + M + s}}
 | 27/16, 905.87¢
 | 12\15, 960.00¢
@@ Line 131: / Line 131: @@
 ! rowspan="3" | Seventh<br />([[TAMNAMS|6-step]])
 ! style="font-size: 0.75em;" | Small
-| 2L + 2M + 2s
+| {{nowrap|2L + 2M + 2s}}
 | 16/9, 996.09¢
 | 12\15, 960.00¢
@@ Line 137: / Line 137: @@
 |-
 ! style="font-size: 0.75em;" | Medium
-| 3L + M + 2s
+| {{nowrap|3L + M + 2s}}
 | 9/5, 1017.60¢
 | 13\15, 1040.00¢
@@ Line 143: / Line 143: @@
 |-
 ! style="font-size: 0.75em;" | Large
-| 3L + 2M + s
+| {{nowrap|3L + 2M + s}}
 | 15/8, 1088.27¢
 | 14\15, 1120.00¢
@@ Line 190: / Line 190: @@
 |-
 ! 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 />({{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 />({{nowrap|''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 />({{nowrap|L {{=}} 2''G''<sub>1</sub> &minus; 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 />({{nowrap|M {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''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 />({{nowrap|s {{=}} 1 &minus; ''G''<sub>1</sub> &minus; ''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>
 |}
@@ Line 211: / Line 211: @@
 |+ style="font-size: 105%;" | Common Nicetone tunings
 |-
-! 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
+! 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
 |-
 ! L !! M !! s !! LH ({{nowrap|L + s}}) !! RH ({{nowrap|L + M}})
@@ Line 531: / Line 531: @@
 == See also ==
 * [[Blackdye]] &ndash; A 10-note scale that is an extension to nicetone.
-* [[Zarlino]] &ndash; A 5-limit JI scale with the same pattern.
 * [[Omnidiatonic]] &ndash; Sister 2L 3M 2s scale
 * [[Antinicetone]] &ndash; Sister 2L 2M 3s scale
@@ Line 538: / Line 537: @@
 * [[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)]]
 [[Category:Rank-3 scales]]
 [[Category:7-tone scales]]
 [[Category:GO scales]]