Gentle region: Difference between revisions
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'' | ''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]] | |||
Gentle | 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 | 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{{c}} (near 17\29) to 704.3{{c}} (near 27\46) | |||
* "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" | {| class="wikitable" | ||
! colspan="4" | EDO | |- | ||
! | ! colspan="4" | EDO Generator | ||
! | ! Fifth | ||
! | ! Dim 4th | ||
! Comments | |||
|- | |- | ||
| 17\29 | | 17\29 | ||
| Line 25: | Line 32: | ||
| | | | ||
| 703.448 | | 703.448 | ||
|372. | | 372.416 | ||
| | | | ||
|- | |||
| | |||
| | |||
| | |||
| | |||
|703.711 | |||
|370.312 | |||
|Margo Schulter's MET-24 fifth | |||
|- | |- | ||
| | | | ||
| Line 33: | Line 48: | ||
| 61\104 | | 61\104 | ||
| 703.846 | | 703.846 | ||
|369.231 | | 369.231 | ||
| Neo-gothic theory of harmony | | Neo-gothic theory of harmony | ||
|- | |- | ||
| Line 41: | Line 56: | ||
| | | | ||
| 704.000 | | 704.000 | ||
|368.000 | | 368.000 | ||
| | | | ||
|- | |- | ||
| Line 49: | Line 64: | ||
| 71\121 | | 71\121 | ||
| 704.132 | | 704.132 | ||
|366.942 | | 366.942 | ||
| | | | ||
|- | |- | ||
| Line 57: | Line 72: | ||
| | | | ||
| 704.348 | | 704.348 | ||
|365.217 | | 365.217 | ||
| | | | ||
|- | |- | ||
| Line 65: | Line 80: | ||
| 64\109 | | 64\109 | ||
| 704.587 | | 704.587 | ||
|363.303 | | 363.303 | ||
| Boundary of smaller "gentle region" | | Boundary of smaller "gentle region" | ||
|- | |- | ||
| Line 73: | Line 88: | ||
| | | | ||
| 704.762 | | 704.762 | ||
|361.905 | | 361.905 | ||
| | | | ||
|- | |- | ||
| Line 81: | Line 96: | ||
| 47\80 | | 47\80 | ||
| 705.000 | | 705.000 | ||
|360.000 | | 360.000 | ||
| Boundary of larger "gentle region" | | Boundary of larger "gentle region" | ||
|- | |- | ||
| Line 89: | Line 104: | ||
| | | | ||
| 705.882 | | 705.882 | ||
|352.941 | | 352.941 | ||
| | | | ||
|} | |} | ||
| Line 96: | Line 111: | ||
* [[Interseptimal]] | * [[Interseptimal]] | ||
[[Category: | [[Category:EDO theory pages]] | ||
[[Category: | [[Category:Fifth]] | ||
[[Category: | [[Category:Gentle]] | ||
Latest revision as of 00:26, 2 June 2025
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 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 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.
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 and Turkish tuning systems, with the special property of delivering a common framework for both, differing in the degree of tempering.
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 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)
- "Upper gentle": 704.3 ¢ to 705.0 ¢ (near 10\17, or more accurately 47\80).
46edo is effectively the boundary between lower and upper neogothic.
| EDO Generator | Fifth | Dim 4th | Comments | |||
|---|---|---|---|---|---|---|
| 17\29 | 703.448 | 372.416 | ||||
| 703.711 | 370.312 | Margo Schulter's MET-24 fifth | ||||
| 61\104 | 703.846 | 369.231 | Neo-gothic theory of harmony | |||
| 44\75 | 704.000 | 368.000 | ||||
| 71\121 | 704.132 | 366.942 | ||||
| 27\46 | 704.348 | 365.217 | ||||
| 64\109 | 704.587 | 363.303 | Boundary of smaller "gentle region" | |||
| 37\63 | 704.762 | 361.905 | ||||
| 47\80 | 705.000 | 360.000 | Boundary of larger "gentle region" | |||
| 10\17 | 705.882 | 352.941 | ||||