Blackville - Revision history

Lhearne at 04:14, 4 January 2026

2026-01-04T04:14:00Z

← Older revision		Revision as of 04:14, 4 January 2026
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	'''Blackville''' is a rank-3 [[~~Dipentatonic scales~~\|~~dipentatonic~~]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2.		'''Blackville''' is a rank-3 [[Bipentatonic scale\|bipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2.

	Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.		Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.

Lhearne at 02:20, 14 March 2024

2024-03-14T02:20:53Z

← Older revision		Revision as of 02:20, 14 March 2024
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	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	~~[[Category:Generator-offset scales]]~~
	[[Category:GO scales]]		[[Category:GO scales]]
	[[Category:Step-nested scales]]		[[Category:Step-nested scales]]

Lhearne: added category

2024-03-14T02:20:29Z

added category

← Older revision		Revision as of 02:20, 14 March 2024
Line 112:		Line 112:
	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	[[Category:Generator-offset scales]]		[[Category:Generator-offset scales]]
			[[Category:GO scales]]
	[[Category:Step-nested scales]]		[[Category:Step-nested scales]]

FloraC: +lemma; +categories

2024-03-13T04:12:35Z

+lemma; +categories

← Older revision		Revision as of 04:12, 13 March 2024
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	~~Rank~~-3 [[Dipentatonic scales\|dipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2.		'''Blackville''' is a rank-3 [[Dipentatonic scales\|dipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2.

	Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.		Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.
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	\|.0745		\|.0745
	\|}		\|}

			[[Category:10-tone scales]]
			[[Category:Generator-offset scales]]
			[[Category:Step-nested scales]]

Lhearne at 03:47, 13 March 2024

2024-03-13T03:47:28Z

← Older revision		Revision as of 03:47, 13 March 2024
Line 1:		Line 1:
	Rank-3 [[Dipentatonic scales\|dipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.		Rank-3 [[Dipentatonic scales\|dipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10\|2L 5m 3s = (10/9, 16/15, 135/128)]]. It may be generated as a generator offset scale by two chains of 3/2, offset by 16/15, or by the variable generator sequences GS(15/8, 8/5) or GS(16/15, 45/32); or as a step-nested scale by adding 16/15 above the bottom or below the top of every step of the Pythagorean pentatonic scale, which is generated by 3/2.

			Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family\|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.

	Blackville may be used for harmonic tonality by way of it's 3-step triads, which include 5-limit major and minor triads (3 of each, along with wolf major, minor, and augmented triads).		Blackville may be used for harmonic tonality by way of it's 3-step triads, which include 5-limit major and minor triads (3 of each, along with wolf major, minor, and augmented triads).

Lhearne: created page

2024-03-13T03:31:47Z

created page

New page

Rank-3 [[Dipentatonic scales|dipentatonic]] [[generator-offset]] and [[step-nested scale]] with step signature and mapping [[SNS ((2/1, 3/2)-5, 16/15)-10|2L 5m 3s = (10/9, 16/15, 135/128)]]. Tempering ''L'' = ''s'' leads to [[Blackwood]][10], and tempering out ''s'' leads to [[Mavila]][7]. Since tempering ''s'' = ''m'' leads to the pentachordal decatonic of [[Diaschismic family|Srutal/diaschsimic]] temperament, we may name Blackville's modes through extrapolating the modes of the pentachordal decatonic. The first edo to represent Blackville without redundancy is [[17edo]] using the 17c [[val]], where in the standard major mode (smLmsmLmsm) it is 2131213121, i.e., 2L 5m 3s = (3, 1, 2). It may also be tuned without redundancy to [[19edo]] as 1232123212 with 2L 5m 3s = (3, 2, 1), [[26edo]] as 1343134313 with 2L 5m 3s = (4, 3, 1), [[27edo]] as 3242324232 with 2L 5m 3s = (4, 2, 3), [[29edo]] as 2343234323 with 2L 5m 3s = (4, 3, 2), [[31edo]] as 2353235323 with 2L 5m 3s = (5, 3, 2), and [[41edo]] as 3464346434 with 2L 5m 3s = (6, 4, 3), for example.

Blackville may be used for harmonic tonality by way of it's 3-step triads, which include 5-limit major and minor triads (3 of each, along with wolf major, minor, and augmented triads).

Blackville is a superset of [[Nicetone]] / [[Zarlino]], the "just" major scale 9/8 5/4 4/3 3/2 5/3 15/8 2/1, and of it's mirror inverse, the "just" minor scale 9/8 6/5 4/3 3/2 8/5 9/5 2/1 (available in the standard major and standard minor modes respectively as 2112121).

{| class="wikitable"
!Mode number
!Mode in JI
!Step pattern
!Pentachordal
Decatonic
!Pent. Dec.
Mode name
!Blackwood[10]
!UDP
![[Mode height]]
|-
| -5
|16/15 9/8 6/5 81/64 27/20 3/2 8/5 27/16 9/5 2/1
|msmsmLmsmL
|sssssLsssL
|Dark minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
| -.0745
|-
| -4
|135/128 9/8 1215/1024 81/64 45/32 3/2 405/256 27/16 15/8 2/1
|smsmLmsmLm
|ssssLsssLs
|Alternate minor
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
| -.0592
|-
| -3
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 27/16 9/5 2/1
|msmLmsmsmL
|sssLsssssL
|Standard minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
| -.0411
|-
| -2
|135/128 9/8 5/4 4/3 45/32 3/2 405/256 27/16 15/8 2/1
|smLmsmsmLm
|ssLsssssLs
|Dark major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
| -.0258
|-
| -1
|16/15 9/8 6/5 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|msmLmsmLms
|sssLsssLss
|Bright minor
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
| -.0077
|-
|1
|135/128 9/8 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|smLmsmLmsm
|ssLsssLsss
|Standard major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0077
|-
|2
|16/15 32/27 512/405 4/3 64/45 3/2 8/5 16/9 256/135 2/1
|mLmsmsmLms
|sLsssssLss
|Alternate major
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0258
|-
|3
|10/9 32/27 5/4 4/3 45/32 3/2 5/3 16/9 15/8 2/1
|LmsmsmLmsm
|LsssssLsss
|Bright major
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0411
|-
|4
|16/15 32/27 512/405 4/3 64/45 128/81 2048/1215 16/9 256/135 2/1
|mLmsmLmsms
|sLsssLssss
|Dark Augmented
|sLsLsLsLsL
|<nowiki>0|1 (5)</nowiki>
|.0592
|-
|5
|10/9 32/27 5/4 4/3 40/27 128/81 5/3 16/9 15/8 2/1
|LmsmLmsmsm
|LsssLsssss
|Bright Augmented
|LsLsLsLsLs
|<nowiki>1|0 (5)</nowiki>
|.0745
|}