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]] 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''' 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 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, 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 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]].

Line 15:

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

|-

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

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

|-

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

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

|-

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

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

|}

== 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"

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! Sizes

! 5-limit JI

! [[15edo]] ({{nowrap|L:M:s {{=}} 3:2:1}})

! [[15edo]] ({{nowrap|L:M:s {{=}} 3:2:1}})

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

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

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

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

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

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

| s

Line 53:

| 7\41, 204.88¢

|-

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

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

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

| M + s

Line 72:

| 13\41, 380.49¢

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

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

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

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

| L + M + s

Line 91:

| 20\41, 585.37¢

|-

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

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

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

| L + M + 2s

Line 110:

| 24\41, 702.44¢

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

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

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

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

| 2L + M + 2s

Line 129:

| 31\41, 907.32¢

|-

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

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

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

| 2L + 2M + 2s

Line 158:

! Left handed !! Right handed

|-

| LMLsMLs LH Nice-Lydian

| LMLsMLs LH Nice-Lydian

| LMLsLMs RH Nice-Lydian

| LMLsLMs RH Nice-Lydian

|-

| MLsLMLs LH Nice-Ionian

| MLsLMLs LH Nice-Ionian

| LMsLMLs RH Nice-Ionian

| LMsLMLs RH Nice-Ionian

|-

| MLsMLsL LH Nice-Mixolydian

| MLsMLsL LH Nice-Mixolydian

| MLsLMsL RH Nice-Mixolydian

| MLsLMsL RH Nice-Mixolydian

|-

| LsLMLsM LH Nice-Dorian

| LsLMLsM LH Nice-Dorian

| MsLMLsL RH Nice-Dorian

| MsLMLsL RH Nice-Dorian

|-

| LsMLsLM LH Nice-Aeolian

| LsMLsLM LH Nice-Aeolian

| LsLMsLM RH Nice-Aeolian

| LsLMsLM RH Nice-Aeolian

|-

| sLMLsML LH Nice-Phrygian

| sLMLsML LH Nice-Phrygian

| sLMLsLM RH Nice-Phrygian

| sLMLsLM RH Nice-Phrygian

|-

| sMLsLML LH Nice-Locrian

| sMLsLML LH Nice-Locrian

| sLMsLML RH Nice-Locrian

| sLMsLML RH Nice-Locrian

|}

Line 189:

! 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>

|-

! 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>

|-

! 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>

|-

! 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>

|-

! 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>

|-

! 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) < 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>

|}

@@ 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]] 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''' 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 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, 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 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]].
@@ Line 15: / Line 15: @@
 ! Name !! Structure !! Step Sizes !! Graphical Representation
 |-
-| Mosh || 3L 4s || 7\33, 3\33 || {{step vis| 3 7 3 7 3 3 7 }}
+| Mosh || {{nowrap|3L 4s}} || 7\33, 3\33 || {{step vis| 3 7 3 7 3 3 7 }}
 |-
-| Nicetone || 3L 2M 2s || 7\33, 4\33, 2\33 || {{step vis| 4 7 2 7 4 2 7 }}
+| Nicetone || {{nowrap|3L 2M 2s}} || 7\33, 4\33, 2\33 || {{step vis| 4 7 2 7 4 2 7 }}
 |-
-| Antipentic || 3L 2s || 7\33, 6\33 || {{step vis| 6 7 7 6 7 }}
+| Antipentic || {{nowrap|3L 2s}} || 7\33, 6\33 || {{step vis| 6 7 7 6 7 }}
 |}
 == 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"
@@ Line 31: / Line 31: @@
 ! Sizes
 ! 5-limit JI
-! [[15edo]] <br />({{nowrap|L:M:s {{=}} 3:2:1}})
+! [[15edo]]<br />({{nowrap|L:M:s {{=}} 3:2:1}})
-! [[41edo]] <br />({{nowrap|L:M:s {{=}} 7:6:4}})
+! [[41edo]]<br />({{nowrap|L:M:s {{=}} 7:6:4}})
 |- style="background-color: #eaeaff;"
-! rowspan="3" | Second <br />([[TAMNAMS|1-step]])
+! rowspan="3" | Second<br />([[TAMNAMS|1-step]])
 ! style="font-size: 0.75em;" | Small
 | s
@@ Line 53: / Line 53: @@
 | 7\41, 204.88¢
 |-
-! rowspan="3" | Third <br />([[TAMNAMS|2-step]])
+! rowspan="3" | Third<br />([[TAMNAMS|2-step]])
 ! style="font-size: 0.75em;" | Small
 | M + s
@@ Line 72: / Line 72: @@
 | 13\41, 380.49¢
 |- style="background-color: "#eaeaff;"
-! rowspan="3" | Fourth <br />([[TAMNAMS|3-step]])
+! rowspan="3" | Fourth<br />([[TAMNAMS|3-step]])
 ! style="font-size: 0.75em;" | Small
 | L + M + s
@@ Line 91: / Line 91: @@
 | 20\41, 585.37¢
 |-
-! rowspan="3" | Fifth <br />([[TAMNAMS|4-step]])
+! rowspan="3" | Fifth<br />([[TAMNAMS|4-step]])
 ! style="font-size: 0.75em;" | Small
 | L + M + 2s
@@ Line 110: / Line 110: @@
 | 24\41, 702.44¢
 |- style="background-color: "#eaeaff;"
-! rowspan="3" | Sixth <br />([[TAMNAMS|5-step]])
+! rowspan="3" | Sixth<br />([[TAMNAMS|5-step]])
 ! style="font-size: 0.75em;" | Small
 | 2L + M + 2s
@@ Line 129: / Line 129: @@
 | 31\41, 907.32¢
 |-
-! rowspan="3" | Seventh <br />([[TAMNAMS|6-step]])
+! rowspan="3" | Seventh<br />([[TAMNAMS|6-step]])
 ! style="font-size: 0.75em;" | Small
 | 2L + 2M + 2s
@@ Line 158: / Line 158: @@
 ! Left handed !! Right handed
 |-
-| LMLsMLs <br />LH Nice-Lydian
+| LMLsMLs<br />LH Nice-Lydian
-| LMLsLMs <br />RH Nice-Lydian
+| LMLsLMs<br />RH Nice-Lydian
 |-
-| MLsLMLs <br />LH Nice-Ionian
+| MLsLMLs<br />LH Nice-Ionian
-| LMsLMLs <br />RH Nice-Ionian
+| LMsLMLs<br />RH Nice-Ionian
 |-
-| MLsMLsL <br />LH Nice-Mixolydian
+| MLsMLsL<br />LH Nice-Mixolydian
-| MLsLMsL <br />RH Nice-Mixolydian
+| MLsLMsL<br />RH Nice-Mixolydian
 |-
-| LsLMLsM <br />LH Nice-Dorian
+| LsLMLsM<br />LH Nice-Dorian
-| MsLMLsL <br />RH Nice-Dorian
+| MsLMLsL<br />RH Nice-Dorian
 |-
-| LsMLsLM <br />LH Nice-Aeolian
+| LsMLsLM<br />LH Nice-Aeolian
-| LsLMsLM <br />RH Nice-Aeolian
+| LsLMsLM<br />RH Nice-Aeolian
 |-
-| sLMLsML <br />LH Nice-Phrygian
+| sLMLsML<br />LH Nice-Phrygian
-| sLMLsLM <br />RH Nice-Phrygian
+| sLMLsLM<br />RH Nice-Phrygian
 |-
-| sMLsLML <br />LH Nice-Locrian
+| sMLsLML<br />LH Nice-Locrian
-| sLMsLML <br />RH Nice-Locrian
+| sLMsLML<br />RH Nice-Locrian
 |}
@@ Line 189: / Line 189: @@
 ! 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>
 |-
-! 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>
 |-
-! 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>
 |-
-! 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>
 |-
-! 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>
 |-
-! 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>
 |}