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]]

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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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|-

! 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]]
@@ 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 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]]