Kaiveran at 03:52, 1 June 2022

2022-06-01T03:52:58Z

← Older revision		Revision as of 03:52, 1 June 2022
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	==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:
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
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	???		???
	==Properties==		==Properties==
	#The fifth ~~(???)~~ of nupelog must be a [[Sharpness\|superflat]] fifth~~.<!--~~		#The fifth of nupelog must be a [[Sharpness\|superflat]] fifth, as its limit of 4\[[7edo]] is by definition the boundary between diatonic and superflat tunings.
	~~#* (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~~.~~)-->~~
	#???		#???
	#*		#*

Kaiveran at 23:12, 31 May 2022

2022-05-31T23:12:08Z

← Older revision		Revision as of 23:12, 31 May 2022
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	[[Category:GO scales]]		[[Category:GO scales]]
	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]
	[[Category:~~Dipentatonic~~ scales]]		[[Category:Heptatonic scales]]

Kaiveran: meow meow

2022-05-31T23:09:56Z

meow meow

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Kaiveran: Created page with "{{interwiki |de = |en = |es = |ja = }} '''Nupelog''' is a 7-note generator-offset scale with step pattern 2L 2M 3s (sMLssML), equivalent to the 2L 5s MOS with tw..."

2022-05-31T22:51:49Z

Created page with "{{interwiki |de = |en = |es = |ja = }} '''Nupelog''' is a 7-note generator-offset scale with step pattern 2L 2M 3s (sMLssML), equivalent to the 2L 5s MOS with tw..."

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{{interwiki
|de =
|en =
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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),

Unanswered Questions:
*Is it chiral?
*What are the just intervals strongly implied by certain tunings?

"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==
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.

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

==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.)
{| class="wikitable"
|-
! style="text-align:center;" |Pattern
! style="text-align:center;" |Name
|-
| |SLMLSLMLSL
| |Blackdye Bright Aeolian
|-
| |LMLSLMLSLS
| |Blackdye Dark Aeolian
|-
| |MLSLMLSLSL
| |Blackdye Locrian
|-
| |LSLMLSLSLM
| |Blackdye Ionian
|-
| |SLMLSLSLML
| |Blackdye Bright Dorian
|-
| |LMLSLSLMLS
| |Blackdye Dark Dorian
|-
| |MLSLSLMLSL
| |Blackdye Phrygian
|-
| |LSLSLMLSLM
| |Blackdye Lydian
|-
| |SLSLMLSLML
| |Blackdye Bright Mixo
|-
| |LSLMLSLMLS
| |Blackdye Dark Mixo
|}
===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==
#The fifth (3L + M + 2S) of blackdye must be a diatonic fifth.
#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==
{| class="wikitable sortable right-2 right-3 right-4 right-5 right-6 right-7 right-8 right-9 right-10"
|+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==
*[[SNS ((2/1, 3/2)-5, 10/9)-10]]

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

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

User:Kaiveran/Nupelog - Revision history

Kaiveran at 03:52, 1 June 2022

Kaiveran at 23:12, 31 May 2022

Kaiveran: meow meow

Kaiveran: Created page with "{{interwiki |de = |en = |es = |ja = }} '''Nupelog''' is a 7-note generator-offset scale with step pattern 2L 2M 3s (sMLssML), equivalent to the 2L 5s MOS with tw..."