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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 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''' 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 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 3L 2M 2s. It's also a subset of the 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]].
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]].


{| class="wikitable" style="margin-left: auto; margin-right: auto;"
{| class="wikitable" style="margin-left: auto; margin-right: auto;"
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! Name !! Structure !! Step Sizes !! Graphical Representation
! Name !! Structure !! Step Sizes !! Graphical Representation
|-
|-
| Ptolemaic || 3L 2m 2s || 9\53, 8\53, 5\53 || ├────────┼───────┼────┼────────┼───────┼────────┼────┤
| Ptolemaic || 3L 2M 2s || 9\53, 8\53, 5\53 || ├────────┼───────┼────┼────────┼───────┼────────┼────┤
|-
|-
| Pythagorean || rowspan="2" | 5L 2s || 9\53, 4\53 || ├────────┼────────┼───┼────────┼────────┼────────┼───┤
| Pythagorean || rowspan="2" | 5L 2s || 9\53, 4\53 || ├────────┼────────┼───┼────────┼────────┼────────┼───┤
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| Mosh || 3L 4s || 7\33, 3\33 || ├──┼──────┼──┼──────┼──┼──┼──────┤
| Mosh || 3L 4s || 7\33, 3\33 || ├──┼──────┼──┼──────┼──┼──┼──────┤
|-
|-
| Nicetone || 3L 2m 2s || 7\33, 4\33, 2\33 || ├───┼──────┼─┼──────┼───┼─┼──────┤
| Nicetone || 3L 2M 2s || 7\33, 4\33, 2\33 || ├───┼──────┼─┼──────┼───┼─┼──────┤
|-
|-
| Antipentic || 3L 2s || 7\33, 6\33 || ├─────┼──────┼──────┼─────┼──────┤
| Antipentic || 3L 2s || 7\33, 6\33 || ├─────┼──────┼──────┼─────┼──────┤
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== Intervals ==
== 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"
{| class="wikitable right-2 right-3 right-4 right-5 right-6 right-7"
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! Sizes
! Sizes
! 5-limit JI
! 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"
|- bgcolor="#eaeaff"
!rowspan=3|Second <br>([[TAMNAMS|1-step]])
!rowspan=3|Second <br>([[TAMNAMS|1-step]])
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|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| m
| M
| 10/9, 182.40¢
| 10/9, 182.40¢
| 2\15, 160.00¢
| 2\15, 160.00¢
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!rowspan=3|Third <br>([[TAMNAMS|2-step]])
!rowspan=3|Third <br>([[TAMNAMS|2-step]])
!|<small>small</small>
!|<small>small</small>
| m + s
| M + s
| 32/27, 294.13¢
| 32/27, 294.13¢
| 3\15, 240.00¢
| 3\15, 240.00¢
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|-
|-
!|<small>large</small>
!|<small>large</small>
| L + m
| L + M
| 5/4, 386.31¢
| 5/4, 386.31¢
| 5\15, 400.00¢
| 5\15, 400.00¢
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!rowspan=3|Fourth <br>([[TAMNAMS|3-step]])
!rowspan=3|Fourth <br>([[TAMNAMS|3-step]])
!|<small>small</small>
!|<small>small</small>
| L + m + s
| L + M + s
| 4/3, 498.04¢
| 4/3, 498.04¢
| 6\15, 480.00¢
| 6\15, 480.00¢
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|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| 2L + m
| 2L + M
| 45/32, 590.22¢
| 45/32, 590.22¢
| 8\15, 640.00¢
| 8\15, 640.00¢
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!rowspan=3|Fifth <br>([[TAMNAMS|4-step]])
!rowspan=3|Fifth <br>([[TAMNAMS|4-step]])
!|<small>small</small>
!|<small>small</small>
| L + m + 2s
| L + M + 2s
| 64/45, 609.78¢
| 64/45, 609.78¢
| 7\15, 560.00¢
| 7\15, 560.00¢
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|-
|-
!|<small>medium</small>
!|<small>medium</small>
| L + 2m + s
| L + 2M + s
| 40/27, 680.45¢
| 40/27, 680.45¢
| 8\15, 640.00¢
| 8\15, 640.00¢
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|-
|-
!|<small>large</small>
!|<small>large</small>
| 2L + m + s
| 2L + M + s
| 3/2, 701.96¢
| 3/2, 701.96¢
| 9\15, 720.00¢
| 9\15, 720.00¢
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!rowspan=3|Sixth <br>([[TAMNAMS|5-step]])
!rowspan=3|Sixth <br>([[TAMNAMS|5-step]])
!|<small>small</small>
!|<small>small</small>
| 2L + m + 2s
| 2L + M + 2s
| 8/5, 813.69¢
| 8/5, 813.69¢
| 10\15, 800.00¢
| 10\15, 800.00¢
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|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>medium</small>
!|<small>medium</small>
| 2L + 2m + s
| 2L + 2M + s
| 5/3, 884.36¢
| 5/3, 884.36¢
| 11\15, 880.00¢
| 11\15, 880.00¢
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|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
!|<small>large</small>
!|<small>large</small>
| 3L + m + s
| 3L + M + s
| 27/16, 905.87¢
| 27/16, 905.87¢
| 12\15, 960.00¢
| 12\15, 960.00¢
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!rowspan=3|Seventh <br>([[TAMNAMS|6-step]])
!rowspan=3|Seventh <br>([[TAMNAMS|6-step]])
!| <small>small</small>
!| <small>small</small>
| 2L + 2m + 2s
| 2L + 2M + 2s
| 16/9, 996.09¢
| 16/9, 996.09¢
| 12\15, 960.00¢
| 12\15, 960.00¢
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|-
|-
!|<small>medium</small>
!|<small>medium</small>
| 3L + m + 2s
| 3L + M + 2s
| 9/5, 1017.60¢
| 9/5, 1017.60¢
| 13\15, 1040.00¢
| 13\15, 1040.00¢
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|-
|-
!|<small>large</small>
!|<small>large</small>
| 3L + 2m + s
| 3L + 2M + s
| 15/8, 1088.27¢
| 15/8, 1088.27¢
| 14\15, 1120.00¢
| 14\15, 1120.00¢
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!Right 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
|}
|}


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! Tuning range (in [[octave]]s)
! Tuning range (in [[octave]]s)
|-
|-
! Outer generator <br>(''G''<sub>1</sub> = 2L + m + s)
! Outer generator <br>(''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>(''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>
|-
|-
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|+Common Nicetone tunings
|+Common Nicetone tunings
! rowspan="2" | Tuning
! rowspan="2" | Tuning
! rowspan="2" | L:m:s
! rowspan="2" | L:M:s
! colspan="3" | Size of step (¢)
! colspan="3" | Size of step (¢)
! colspan="2" | Inner generator
! colspan="2" | Inner generator
! rowspan="2" | Outer generator <br>(2L+m+s)
! rowspan="2" | Outer generator <br>(2L+M+s)
! rowspan="2" | Comments
! rowspan="2" | Comments
|-
|-
! L
! L
! m
! M
! s
! s
! LH (L+s)
! LH (L+s)
! RH (L+m)
! 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||L=9/8, M=10/9, 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
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Nicetone has following generator-offset MV3 supersets:
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).
Remarkable non-MV3 generator-offset supersets include [[blackdye]] (10-note, LmLsLmLsLs).
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* [[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.
* [[Zarlino]] – a 5-limit JI scale with the same pattern.
* [[Omnidiatonic]]­­ ­– sister 2L 3m 2s scale
* [[Omnidiatonic]]­­ ­– 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]] – LM-equalized version of nicetone
** [[5L 2s Muddles]] – other diatonic muddles
** [[5L 2s Muddles]] – other diatonic muddles