Gentle region: Difference between revisions

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''~~This is the version of Oct 30, 2012.~~ For an alternative version see: [[Gentle region (extended version)]]''

''For an alternative version of the page, see: [[Gentle region (extended version)]].''

~~-----~~

The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of [[29edo]] (~703.4c) and [[17edo]] (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.

[[Margo Schulter]], in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], defined the ~~"gentle~~ region~~" of temperaments with a fifth as generator as that of fifths about~~ 1.49 to 2.65 cents sharp~~; later~~ [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 ~~amending that~~] to ~~from~~ 1.49 to 3.04 cents sharp.

Gentle~~-tempered tone~~ systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for ~~"Neo-gothic"~~ harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish~~, Persian~~|~~middle-eastern (Arabic,~~ Turkish~~, Persian)~~]] tuning systems, with the special property of delivering a common framework for both ~~Arabic and Turkish music~~, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in arabic music. (The interval notated as C-E will have the character of a larger Pythagorean - or super-Pythagorean - major third.)

Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music|Arabic]] and [[Turkish music|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.

We can consider the ~~first~~ region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of ~~[[29edo]]~~, ~~[[46edo]]~~, ~~[[75edo]]~~, ~~[[104edo]]~~, ~~[[109edo]]~~, ~~[[121edo]]~~, ~~[[145edo]]~~, ~~[[155edo]]~~, ~~[[162edo]]~~, ~~[[167edo]]~~, ~~[[179edo]]~~, ~~[[191edo]]~~, ~~[[201edo]]~~, ~~[[213edo]]~~, ~~[[225edo]]~~ and ~~[[237edo]]~~, plus ~~[[63edo]]~~ and ~~[[80edo]]~~ in the extended region.

When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.)

We can consider the originally-defined gentle region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.

The extended gentle region is further divided into two subregions:

* "~~lower~~ gentle": 703.4¢ (near 17\29) to 704.3¢ (near 27\46)

* "Lower gentle": 703.4{{c}} (near 17\29) to 704.3{{c}} (near 27\46)

* "~~upper~~ gentle": 704.3¢ to 705.0¢ (near 10\17, or more accurately 47\80).

* "Upper gentle": 704.3{{c}} to 705.0{{c}} (near 10\17, or more accurately 47\80).

[[46edo]] is effectively the boundary between lower and upper neogothic.

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|703.711

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|Margo Schulter's MET-24 fifth

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-''This is the version of Oct 30, 2012. For an alternative version see: [[Gentle region (extended version)]]''
+''For an alternative version of the page, see: [[Gentle region (extended version)]].''
------
+The '''gentle region''' refers to the set of tuning systems generated by fifths in the region between the fifths of [[29edo]] (~703.4c) and [[17edo]] (~705.9c), which generate [[neogothic]] (specifically, neomajor and neominor) thirds. The region was defined by [[Margo Schulter]] in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], originally defined as the region between 1.49 to 2.65 cents sharp of a just fifth (~703.4 to ~704.6 cents), before being [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 revised] to 1.49 to 3.04 cents sharp (~703.4 to 705 cents). The tuning range shown on this page shows tunings as sharp as 17edo.
-[[Margo Schulter]], in a [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105200.html#105202 tuning list posting], defined the "gentle region" of temperaments with a fifth as generator as that of fifths about 1.49 to 2.65 cents sharp; later [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_106239.html#106239 amending that] to from 1.49 to 3.04 cents sharp.
-Gentle-tempered tone systems are thus "mild" (or, as the name says, "gentle") versions of [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for "Neo-gothic" harmony systems; besides, they are possible temperament frameworks for [[Arabic, Turkish, Persian|middle-eastern (Arabic, Turkish, Persian)]] tuning systems, with the special property of delivering a common framework for both Arabic and Turkish music, differing in the degree of tempering. When the tempering of the fifth is "very gentle"/near-just, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third, as used in Turkish music; while sharper tempering will give this interval the character of a neutral third, as important in arabic music. (The interval notated as C-E will have the character of a larger Pythagorean - or super-Pythagorean - major third.)
+Gentle tuning systems are thus "mild" (or, as the name says, "gentle") versions of tuning systems like [[Superpyth]] temperament. They allow harmony in the style of medieval Pythagorean harmony, usable for neogothic harmony systems; besides, they are possible temperament frameworks for [[Arabic music|Arabic]] and [[Turkish music|Turkish]] tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.
-We can consider the first region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of [[29edo]], [[46edo]], [[75edo]], [[104edo]], [[109edo]], [[121edo]], [[145edo]], [[155edo]], [[162edo]], [[167edo]], [[179edo]], [[191edo]], [[201edo]], [[213edo]], [[225edo]] and [[237edo]], plus [[63edo]] and [[80edo]] in the extended region.
+When the tempering of the fifth is "very gentle"/near-just as in 29edo, the interval notated as C-Fb in standard sheet notation (8 fifths down) will be close to a 5/4 major third (implying [[schismic]] temperament), as used in Turkish music; sharper tempering as in 17edo will give this interval the character of a neutral third, as important in Arabic music. (The interval notated as C-E will have the character of a pythagorean or neomajor third.)
+We can consider the originally-defined gentle region to extend from fifths of size 17\29 to 64\109, and the extended region to reach 47\80. If we remove the restriction to tempering based on chains of fifths, we find that notable equal divisions in the smaller gentle region include multiples of {{EDOs| 29, 46, 75, 104, 109, 121, 145, 155, 162, 167, 179, 191, 201, 213, 225 and 237, plus 63 and 80 }} in the extended region.
 The extended gentle region is further divided into two subregions:
-* "lower gentle": 703.4¢ (near 17\29) to 704.3¢ (near 27\46)
+* "Lower gentle": 703.4{{c}} (near 17\29) to 704.3{{c}} (near 27\46)
-* "upper gentle": 704.3¢ to 705.0¢ (near 10\17, or more accurately 47\80).
+* "Upper gentle": 704.3{{c}} to 705.0{{c}} (near 10\17, or more accurately 47\80).
 [[46edo]] is effectively the boundary between lower and upper neogothic.
 {| class="wikitable"
+|-
 ! colspan="4" | EDO Generator
 ! Fifth
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 | 372.416
 |
+|-
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+|703.711
+|370.312
+|Margo Schulter's MET-24 fifth
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