Nicetone: Difference between revisions
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'''Nicetone''' (also known as the '''Zarlino pattern''' or '''Ptolemaic diatonic''') is a 7-note [[Maximum variety| | '''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 | 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]], | 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 | | 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 | | 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, | 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: | ! [[15edo]] <br>(L:M:s = 3:2:1) | ||
! [[41edo]] <br>(L: | ! [[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 | ||
| 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 | ||
| 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 + | | 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 | ||
| | |LMLsLMs <br>RH Nice-Lydian | ||
|- | |- | ||
| | |MLsLMLs <br>LH Nice-Ionian | ||
| | |LMsLMLs <br>RH Nice-Ionian | ||
|- | |- | ||
| | |MLsMLsL <br>LH Nice-Mixolydian | ||
| | |MLsLMsL <br>RH Nice-Mixolydian | ||
|- | |- | ||
| | |LsLMLsM <br>LH Nice-Dorian | ||
| | |MsLMLsL <br>RH Nice-Dorian | ||
|- | |- | ||
| | |LsMLsLM <br>LH Nice-Aeolian | ||
| | |LsLMsLM <br>RH Nice-Aeolian | ||
|- | |- | ||
| | |sLMLsML <br>LH Nice-Phrygian | ||
| | |sLMLsLM <br>RH Nice-Phrygian | ||
|- | |- | ||
| | |sMLsLML <br>LH 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 + | ! Outer generator <br>(''G''<sub>1</sub> = 2L + M + s) | ||
| <math>\displaystyle \frac{4}{7} < G_\text{1} < \frac{2}{3}</math> | | <math>\displaystyle \frac{4}{7} < G_\text{1} < \frac{2}{3}</math> | ||
|- | |- | ||
! RH inner generator <br>(''G''<sub>2R</sub> = L + | ! RH inner generator <br>(''G''<sub>2R</sub> = 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> <br><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} < G_\text{2R} < 4 G_\text{1} - 2 \text{ for } \frac{4}{7} < G_\text{1} ≤ \frac{3}{5}</math> <br><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> | ||
|- | |- | ||
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|+Common Nicetone tunings | |+Common Nicetone tunings | ||
! rowspan="2" | Tuning | ! rowspan="2" | Tuning | ||
! rowspan="2" | L: | ! 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+ | ! rowspan="2" | Outer generator <br>(2L+M+s) | ||
! rowspan="2" | Comments | ! rowspan="2" | Comments | ||
|- | |- | ||
! L | ! L | ||
! | ! M | ||
! s | ! s | ||
! LH (L+s) | ! LH (L+s) | ||
! RH (L+ | ! RH (L+M) | ||
|- | |- | ||
| 5-limit JI || ||203.910||182.404||111.731||315.641||386.314||701.955||L=9/8, | | 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 | * [[Sephipechroid]]: 13-note 3L 5M 5s scale (LMsMLsMsLMsMs and LMsMLsMsMLsMs) | ||
* [[Interoneichro]]: 13-note 5L | * [[Interoneichro]]: 13-note 5L 3M 5s scale (LMsLsLMsLsMLs and LMsLsMLsLsMLs) | ||
* [[Sephimechroid]]: 13-note 5L | * [[Sephimechroid]]: 13-note 5L 5M 3s scale (LMLMsLMLsMLMs and LMLsMLMLsMLMs) | ||
* [[Beatloid]]: 17-note 5L | * [[Beatloid]]: 17-note 5L 5M 7s scale (LMsLsMLsMsLMsLsMs and LMsLsMLsMsLsMLsMs) | ||
* [[Enharoid]]: 17-note 5L | * [[Enharoid]]: 17-note 5L 7M 5s scale (LMsLMsMLMsLMsMLsM and LMsLMsMLsMLMsMLsM) | ||
* [[Moharoid]]: 17-note 7L | * [[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 | * [[Omnidiatonic]] – sister 2L 3M 2s scale | ||
* [[Antinicetone]] – sister 2L | * [[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 |