User:Kaiveran/Nupelog: Difference between revisions

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'''Nupelog''' is a 7-note [[generator-offset]] scale with step pattern 2L 2M 3s (sMLssML), equivalent to the [[2L 5s]] [[MOS]] with two of the small steps made larger.  It occupies a broad triangle on the chart of MV3 scales, whose vertices are generators 0\1,1\2 (degenerate to 2edo),
'''Nupelog''' is a 7-note [[generator-offset]] scale with step pattern 2L 2M 3s (sMLssML), equivalent to the [[2L 5s]] [[MOS]] with two of the small steps made larger.  It occupies a broad triangle on the [https://en.xen.wiki/images/d/da/MV3-Labeled.png chart of MV3 scales], whose vertices are generators [0\1,1\2] degenerate to [[2edo]], [2\7,4\7] degenerate to [[7edo]], and [1\2,1\2] again degenerate to [[2edo]].
 
 
<span style="color: #ff0000;">Unanswered Questions:</span>
 
<span style="color: #ff0000;">*Is it chiral?</span>
 
<span style="color: #ff0000;">*What are the just intervals strongly implied by certain tunings?</span>


<span style="color: #ff0000;">Unanswered Questions:
*Is it chiral?
*What are the just intervals strongly implied by certain tunings?</span>


"Nupelog" is a name given to this region by [[User:Kaiveran|Kaiveran]], reflecting both the [[Pelogic family|pelogic]] family of temperaments, and the fact that several measured tunings of the Indonesian ''pelog'' have a very similar step pattern.
"Nupelog" is a name given to this region by [[User:Kaiveran|Kaiveran]], reflecting both the [[Pelogic family|pelogic]] family of temperaments, and the fact that several measured tunings of the Indonesian ''pelog'' have a very similar step pattern.


==Intervals==
==Intervals==
The following is a table of blackdye 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 blackdye using the following expressions.  
The following is a table of nupelog 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 nupelog using the following expressions.  


{| class="wikitable right-2 right-3 right-4 right-5"
{| class="wikitable right-2 right-3 right-4 right-5"
|+Interval sizes in blackdye
|+Interval sizes in nupelog
|-
|-
! |Interval class
! |Interval class
!Sizes
!Sizes
![[5-limit]] JI
!???
![[32edo]] (L:m:s = 5:2:1)
!???
![[34edo]] (L:m:s = 5:3:1)
! ???
|-
|-
!|[[TAMNAMS|1-step]]
!|[[TAMNAMS|1-step]]
|s<br />m<br />L
|
|81/80, 21.51¢<br />16/15, 111.73¢<br />10/9, 182.40¢
|
|1\32, 37.50¢<br />2\32, 75.00¢<br />5\32, 187.50¢
|
|1\34, 35.29¢<br />3\34, 105.88¢<br />5\34, 176.47¢
|
|-
|-
!|[[TAMNAMS|2-step]]
!|[[TAMNAMS|2-step]]
|L + s<br />L + m
|
|9/8, 203.91¢<br />32/27, 294.14¢
|
|6\32, 225.00¢<br />7\32, 262.50¢
|
|6\34, 211.77¢<br />8\34, 282.35¢
|  
|-  
|-  
!|[[TAMNAMS|3-step]]
!|[[TAMNAMS|3-step]]
|L + 2s<br />L + m + s<br />2L + s<br />2L + m
|
|729/640‚ 225.42¢<br />6/5, 315.64¢<br />5/4, 386.31¢<br />320/243, 476.54¢
|
|7\32, 262.50¢<br />8\32, 300.00¢<br />11\32, 412.50¢<br />12\32, 450.00¢
|
|7\34, 247.06¢<br />9\34, 317.65¢<br />11\34, 388.24¢<br />13\34, 458.82¢
|
|-  
|-  
!|[[TAMNAMS|4-step]]
!|[[TAMNAMS|4-step]]
|2L + 2s<br />2L + m + s
|
|81/64, 407.82¢<br />4/3, 498.04¢
|
|12\32, 450.00¢<br />13\32, 487.50¢
|
|12\34, 423.53¢<br />14\34, 494.12¢
|
|-
|-
!|[[TAMNAMS|5-step]]
!|[[TAMNAMS|5-step]]
|2L + m + 2s<br />2L + 2m + s<br />3L + 2s<br />3L + m + s
|
|27/20, 519.55¢<br />64/45, 609.78¢<br />45/32, 590.22¢<br />40/27, 680.45¢
|
|14\32, 525.00¢<br />15\32, 562.50¢<br />17\32, 637.50¢<br />18\32, 675.00¢
|
|15\34, 529.41¢<br />17\34, 600.00¢<br />17\34, 600.00¢<br />19\34, 670.59¢
|
|-
|-
!|[[TAMNAMS|6-step]]
!|[[TAMNAMS|6-step]]
|3L + m + 2s<br />3L + 2m + s
|
|3/2, 701.96¢<br />128/81, 792.18¢
|
|19\32, 712.50¢<br />20\32, 750.00¢
|
|20\34, 705.88¢<br />22\34, 776.47¢
|
|-
!|[[TAMNAMS|7-step]]
|3L + m + 3s<br />3L + 2m + 2s<br />4L + m + 2s<br />4L + 2m + s
|243/160, 723.46¢<br />8/5, 813.69¢<br />5/3, 884.36¢<br />1280/729, 974.58¢
|20\32, 750.00¢<br />21\32, 787.50¢<br />24\32, 900.00¢<br />25\32, 937.50¢
|21\34, 741.18¢<br />23\34, 811.77¢<br />25\34, 882.35¢<br />27\34, 952.94¢
|-
!|[[TAMNAMS|8-step]]
|4L + m + 3s<br />4L + 2m + 2s
|27/16, 905.87¢<br />16/9, 996.09¢
|25\32, 937.50¢<br />26\32, 975.00¢
|26\34, 917.65¢<br />28\34, 988.24¢
|-
!|[[TAMNAMS|9-step]]
|5L + 2m + s<br />5L + m + 2s<br />4L + 2m + 2s
|9/5, 1017.60¢<br />15/8, 1088.27¢<br />160/81, 1178.49¢
|27\32, 1012.50¢<br />30\32, 1125.00¢<br />31\32, 1162.50¢
|29\34, 1023.53¢<br />31\34, 1094.12¢<br />33\34, 1164.71¢
|}
|}
The octave in blackdye can be called the "perfect 10-step" in TAMNAMS.
Since nupelog is heptatonic, there is little issue with calling the "perfect 7-step" the octave, as in diatonic music.


==Modes==
==Modes ==
===Cyclic order===
===Cyclic order===
The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)
The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)
Line 89: Line 75:
! style="text-align:center;" |Name
! style="text-align:center;" |Name
|-
|-
| |SLMLSLMLSL
| |sMLssML
| |Blackdye Bright Aeolian
| |Nupelog Anti-Ionian
|-
|-
| |LMLSLMLSLS
| |MLssMLs
| |Blackdye Dark Aeolian
| |Nupelog Anti-Dorian
|-
|-
| |MLSLMLSLSL
| |LssMLsM
| |Blackdye Locrian
| |Nupelog Anti-Phrygian
|-
|-
| |LSLMLSLSLM
| |ssMLsML
| |Blackdye Ionian
| |Nupelog Anti-Lydian
|-
|-
| |SLMLSLSLML
| |sMLsMLs
| |Blackdye Bright Dorian
| |Nupelog Anti-Mixolydian
|-
|-
| |LMLSLSLMLS
| |MLsMLss
| |Blackdye Dark Dorian
| |Nupelog Anti-Aeolian
|-
|-
| |MLSLSLMLSL
| |LsMLssM
| |Blackdye Phrygian
| |Nupelog Anti-Locrian
|-
| |LSLSLMLSLM
| |Blackdye Lydian
|-
| |SLSLMLSLML
| |Blackdye Bright Mixo
|-
| |LSLMLSLMLS
| |Blackdye Dark Mixo
|}
|}
===By generator chain===
===By generator chain===
Because blackdye has two chains of 5 fifth generators, it has two chains of 5 modes each separated by one generator:
???
#LSLSLMLSLM (Lydian) > LSLMLSLSLM (Ionian) > LSLMLSLMLS (Dark Mixo) > LMLSLSLMLS (Dark Dorian) > LMLSLMLSLS (Dark Aeolian)
#SLSLMLSLML (Bright Mixo) > SLMLSLSLML (Bright Dorian) > SLMLSLMLSL (Bright Aeolian) > MLSLSLMLSL (Phrygian) > MLSLMLSLSL (Locrian)
 
==Properties==
==Properties==
#The fifth (3L + M + 2S) of blackdye must be a diatonic fifth.<!--
#The fifth (???) of nupelog must be a [[Sharpness|superflat]] fifth.<!--
#* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7M + 14S - (20L + 8M + 12S) = L - M + 2S. Since L - M >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s|2L' 3s']] subset of blackdye with L' = ML and s' = SL.)-->
#* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7M + 14S - (20L + 8M + 12S) = L - M + 2S. Since L - M >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s|2L' 3s']] subset of blackdye with L' = ML and s' = SL.)-->
#The fifth is:
#???
#*sharper than 700¢, if L + 3S > 2M
#*
#*equal to 700¢, if L + 3S = 2M
#*flatter than 700¢, if L + 3S < 2M


==Tunings==
==Tunings==
{| class="wikitable sortable right-2 right-3 right-4 right-5 right-6 right-7 right-8 right-9 right-10"
==Examples==
|+Blackdye tunings
! rowspan="2" |Tuning
! rowspan="2" |L:M:S
! colspan="9" |Degrees of the mode SLMLSLMLSL
|-
!1!!2!!3!!4!!5!!6!!7!!8!!9
|-
| colspan="2" align="center" |5-Limit Interpretation
||81/80||9/8||6/5||4/3||27/20||3/2||8/5||16/9||9/5
|-
|JI||8.481:5.195:1
||21.506||203.910||315.641||498.045||519.551||701.955||813.686||996.090||1017.596
|-
|22edo||3:2:1
||54.545||218.182||327.273||490.909||545.455||709.090||818.182||981.818||1036.364
|-
|27edo||4:2:1
||44.444||222.222||311.111||488.889||533.333||711.111||800.000||977.778||1022.222
|-
|29edo||4:3:1
||41.379||206.897||331.034||496.551||537.931||703.448||827.586||993.103||1034.483
|-
|32edo||4:3:2
||75.000||225.000||337.500||487.500||562.500||712.500||825.000||975.000||1050.000
|-
|32edo||5:2:1
||37.500||225.000||300.000||487.500||525.000||712.500||787.500||975.000||1012.500
|-
|34edo||5:3:1
||35.294||211.765||317.647||494.117||529.412||705.882||811.764||988.235||1023.529
|-
|37edo||5:3:2
||64.865||227.027||324.324||486.486||551.351||713.514||810.810||972.973||1037.838
|-
|36edo||5:4:1
||33.333||200.000||333.333||500.000||533.333||700.000||833.333||1000.000||1033.333
|-
|39edo||5:4:2
||61.538||215.385||338.462||492.308||553.846||707.692||830.769||984.615||1046.154
|-
|42edo||5:4:3
||85.714||228.571||342.857||485.714||571.429||714.286||828.571||971.429||1057.143
|-
|39edo||5:4:2
||61.538||215.385||338.462||492.308||553.846||707.692||830.769||984.615||1046.154
|-
|37edo||6:2:1
||32.432||227.027||291.892||486.486||518.919||713.514||778.378||972.973||1005.405
|-
|39edo||6:3:1
||30.769||215.385||307.692||492.308||523.077||707.692||800.000||984.615||1015.384
|-
|42edo||6:3:2
||57.143||228.571||314.286||485.714||542.857||714.286||800.000||971.429||1028.571
|-
|41edo||6:4:1
||29.268||204.878||321.951||497.561||526.829||702.439||819.512||995.122||1024.390
|-
|47edo||6:4:3
||76.596||229.787||331.915||485.106||561.702||702.439||714.894||970.213||1046.809
|-
|42edo||7:2:1
||28.571||228.571||285.714||485.714||514.286||714.286||771.429||971.429||1000.000
|-
|44edo||7:3:1
||27.273||218.182||300.000||490.909||518.182||709.091||790.901||981.818||1009.091
|-
|46edo||7:4:1
||26.087||208.696||313.043||495.652||521.739||704.348||808.696||991.304||1017.391
|-
|53edo||8:5:1
||22.642||203.773||316.981||498.113||520.755||701.887||815.094||996.226||1018.868
|}
 
==Example==
An example in Blackdye Bright Aeolian, SLMLSLMLSL ([[:File:Blackdye Aeolian Example Score.pdf|score]])
 
[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:M:S = 3:2:1)
 
[[File:Blackdye Aeolian Example 27edo.mp3]] [[27edo]] (L:M:S = 4:2:1)
 
[[File:Blackdye Aeolian Example 29edo.mp3]] [[29edo]] (L:M:S = 4:3:1)
 
[[File:Blackdye Aeolian Example 32edo 5_2_1.mp3]] [[32edo]] (L:M:S = 5:2:1)
 
[[File:Blackdye Aeolian Example 34edo.mp3]] [[34edo]] (L:M:S = 5:3:1)
 
[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:M:S = 5:4:1)


==Scala files==
==Scala files==
*[[SNS ((2/1, 3/2)-5, 10/9)-10]]
*[[SNOGO-Nupelog]] (playable live [https://sevish.com/scaleworkshop/?name=Nupelog%20(sMLssML%2C%2014%2F13%20-%2011%2F10%20-%2015%2F13)&data=14%2F13%0A77%2F65%0A231%2F169%0A3234%2F2197%0A45276%2F28561%0A249018%2F142805%0A747054%2F371293&freq=256&midi=69&vert=7&horiz=1&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=harmonicbell&ampenv=perc-long here])


==See also==
==See also==
*[[Diasem]], a similar diatonic-like mos detempering but for 2.3.7
*???
*[[Indonesian]]


[[Category:GO scales]]
[[Category:GO scales]]
[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]
[[Category:Dipentatonic scales]]
[[Category:Dipentatonic scales]]

Revision as of 23:09, 31 May 2022

Nupelog is a 7-note generator-offset scale with step pattern 2L 2M 3s (sMLssML), equivalent to the 2L 5s MOS with two of the small steps made larger. It occupies a broad triangle on the chart of MV3 scales, whose vertices are generators [0\1,1\2] degenerate to 2edo, [2\7,4\7] degenerate to 7edo, and [1\2,1\2] again degenerate to 2edo.


Unanswered Questions:

*Is it chiral?

*What are the just intervals strongly implied by certain tunings?


"Nupelog" is a name given to this region by Kaiveran, reflecting both the pelogic family of temperaments, and the fact that several measured tunings of the Indonesian pelog have a very similar step pattern.

Intervals

The following is a table of nupelog 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 nupelog using the following expressions.

Interval sizes in nupelog
Interval class Sizes ??? ??? ???
1-step
2-step
3-step
4-step
5-step
6-step

Since nupelog is heptatonic, there is little issue with calling the "perfect 7-step" the octave, as in diatonic music.

Modes

Cyclic order

The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)

Pattern Name
sMLssML Nupelog Anti-Ionian
MLssMLs Nupelog Anti-Dorian
LssMLsM Nupelog Anti-Phrygian
ssMLsML Nupelog Anti-Lydian
sMLsMLs Nupelog Anti-Mixolydian
MLsMLss Nupelog Anti-Aeolian
LsMLssM Nupelog Anti-Locrian

By generator chain

???

Properties

  1. The fifth (???) of nupelog must be a superflat fifth.
  2. ???

Tunings

Examples

Scala files

See also

Retrieved from "https://en.xen.wiki/index.php?title=User:Kaiveran/Nupelog&oldid=92262"