Gentle region (extended version): Difference between revisions
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[[Margo_Schulter|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. | [[Margo_Schulter|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 | 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.) | ||
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|29edo]], [[46edo|46edo]], [[75edo|75edo]], [[104edo|104edo]], [[109edo|109edo]], [[121edo|121edo]], [[145edo|133edo]], [[155edo|155edo]], [[162edo|162edo]], [[167edo|167edo]], [[179edo|179edo]], [[191edo|191edo]], [[201edo|201edo]], [[213edo|213edo]], [[225edo|225edo]] and [[237edo|237edo]], plus [[63edo|63edo]] and [[80edo|80edo]] in the extended region. | 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|29edo]], [[46edo|46edo]], [[75edo|75edo]], [[104edo|104edo]], [[109edo|109edo]], [[121edo|121edo]], [[145edo|133edo]], [[155edo|155edo]], [[162edo|162edo]], [[167edo|167edo]], [[179edo|179edo]], [[191edo|191edo]], [[201edo|201edo]], [[213edo|213edo]], [[225edo|225edo]] and [[237edo|237edo]], plus [[63edo|63edo]] and [[80edo|80edo]] in the extended region. | ||
| Line 11: | Line 11: | ||
|- | |- | ||
! colspan="2" | Generator | ! colspan="2" | Generator | ||
! | ! Cents | ||
! | ! 2-3-7(b)-11-13(b) | ||
! <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span> | ! <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">Half 8/7+ 1\3 7/6<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">1\3 8/7+ Half 7/6</span></span></span> | ||
! | ! 8/7+7/6 | ||
! | ! | ||
|- | |- | ||
| (7+10)\29 | |||
| | |||
| style="text-align:center;" |289.655+413.793 | | style="text-align: center;" | 289.655+413.793 | ||
| | | | {{val| 29 46 81 100 107 }} | ||
| style="text-align:center;" |2\29+ | | style="text-align: center;" | 2\29+3\29 | ||
82.759+124.138 | 82.759+124.138 | ||
| style="text-align:center;" |6\29+6\29 | | style="text-align: center;" | 6\29+6\29 | ||
248.276+248.276 | 248.276+248.276 | ||
| | |||
|- | |- | ||
| (25+36)\104 | |||
| | |||
| style="text-align:center;" |288.4615+415.385 | | style="text-align: center;" | 288.4615+415.385 | ||
| | | | {{val| 104 165 292 360 385 }} | ||
| style="text-align:center;" |5\52+''23\312'' | | style="text-align: center;" | 5\52+''23\312'' | ||
115.385+''88.4615'' | 115.385+''88.4615'' | ||
| Line 40: | Line 40: | ||
<span style="background-color: rgba(255,255,255,0); text-align: start;">''76.923+132.692''</span> | <span style="background-color: rgba(255,255,255,0); text-align: start;">''76.923+132.692''</span> | ||
| style="text-align:center;" |5\52+23\104 | | style="text-align: center;" | 5\52+23\104 | ||
230.769+265.385 | 230.769+265.385 | ||
| | |||
|- | |- | ||
| (18+26)\75 | |||
| | |||
| style="text-align:center;" |288+416 | | style="text-align: center;" | 288+416 | ||
| < 75 119 210~211 259 277| | |||
| style="text-align:center;" |7\75+''17\225'' | | style="text-align: center;" | 7\75+''17\225'' | ||
112+''90.667'' | 112+''90.667'' | ||
| Line 56: | Line 56: | ||
<span style="background-color: rgba(255,255,255,0); text-align: start;">''74.667+136''</span> | <span style="background-color: rgba(255,255,255,0); text-align: start;">''74.667+136''</span> | ||
| style="text-align:center;" |14\75+17\75 | | style="text-align: center;" | 14\75+17\75 | ||
224+272 | 224+272 | ||
| | |||
|- | |- | ||
| | |||
| (47+68)\196 | |||
| style="text-align:center;" |287.755+416.3265 | | style="text-align: center;" | 287.755+416.3265 | ||
| < 196 311 549-551 678 725| | |||
| style="text-align:center;" |''37\392+44\588'' | | style="text-align: center;" | ''37\392+44\588'' | ||
''113.265+89.796'' | ''113.265+89.796'' | ||
| Line 72: | Line 72: | ||
<span style="background-color: rgba(255,255,255,0); text-align: start;">''75.51''+134.694</span> | <span style="background-color: rgba(255,255,255,0); text-align: start;">''75.51''+134.694</span> | ||
| style="text-align:center;" |37/196+44/196 | | style="text-align: center;" | 37/196+44/196 | ||
226.531+269.388 | 226.531+269.388 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |287.713+416.382 | | style="text-align: center;" | 287.713+416.382 | ||
| | | | {{val| 29 46 81 100 107 }} + {{val| 46 73 129 159 170 }}</span><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small; line-height: 1.5;">φ</span> | ||
| style="text-align:center;" |119.283+85.7795 | | style="text-align: center;" | 119.283+85.7795 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">79.522+128.769</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">79.522+128.769</span> | ||
| style="text-align:center;" |238.566+257.3385 | | style="text-align: center;" | 238.566+257.3385 | ||
| | |||
|- | |- | ||
| | |||
| (29+42)\121 | |||
| style="text-align:center;" |287.603+416.529 | | style="text-align: center;" | 287.603+416.529 | ||
| | | | {{val| 121 192 339~340 419 448 }} | ||
| style="text-align:center;" |''23\242''+9\121 | | style="text-align: center;" | ''23\242''+9\121 | ||
''114.05''+89.256 | ''114.05''+89.256 | ||
| Line 98: | Line 98: | ||
<span style="background-color: rgba(255,255,255,0);">''76.033+133.884''</span> | <span style="background-color: rgba(255,255,255,0);">''76.033+133.884''</span> | ||
| style="text-align:center;" |23\121+27\121 | | style="text-align: center;" | 23\121+27\121 | ||
228.099+267.769 | 228.099+267.769 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |287.267+416.978 | | style="text-align: center;" | 287.267+416.978 | ||
| | | | {{val| 29 46 81 100 107 }} + {{val| 109 173 306 377 403 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |116.8205+87.323 | | style="text-align: center;" | 116.8205+87.323 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">78.617+130.984</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">78.617+130.984</span> | ||
| style="text-align:center;" |235.85+261.969 | | style="text-align: center;" | 235.85+261.969 | ||
| | |||
|- | |- | ||
| (11+16)\46 | |||
| | |||
| style="text-align:center;" |286.9565+417.391 | | style="text-align: center;" | 286.9565+417.391 | ||
| | | | {{val| 46 73 129 159 170 }} | ||
| style="text-align:center;" |''9\92+5\69'' | | style="text-align: center;" | ''9\92+5\69'' | ||
''117.391+86.9565'' | ''117.391+86.9565'' | ||
| Line 124: | Line 124: | ||
<span style="background-color: rgba(255,255,255,0);">78.261+130.435</span> | <span style="background-color: rgba(255,255,255,0);">78.261+130.435</span> | ||
| style="text-align:center;" |9\46+5\23 | | style="text-align: center;" | 9\46+5\23 | ||
234.783+260.87 | 234.783+260.87 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |286.587+417.884 | | style="text-align: center;" | 286.587+417.884 | ||
| | | | {{val| 29 46 81 100 107 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |117.925+88.626 | | style="text-align: center;" | 117.925+88.626 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.635+132.9395</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.635+132.9395</span> | ||
| style="text-align:center;" |232.936+265.879 | | style="text-align: center;" | 232.936+265.879 | ||
| | |||
|- | |- | ||
| | |||
| (48+70)\201 | |||
| style="text-align:center;" |286.567+417.91 | | style="text-align: center;" | 286.567+417.91 | ||
| | | | {{val| 201 319 564 695 703 }} | ||
| style="text-align:center;" |''13\134+44\603'' | | style="text-align: center;" | ''13\134+44\603'' | ||
''116.418+87.56'' | ''116.418+87.56'' | ||
| Line 150: | Line 150: | ||
<span style="background-color: rgba(255,255,255,0);">77.612+131.343</span> | <span style="background-color: rgba(255,255,255,0);">77.612+131.343</span> | ||
| style="text-align:center;" |39\201+44\201 | | style="text-align: center;" | 39\201+44\201 | ||
232.836+262.687 | 232.836+262.687 | ||
| | |||
|- | |- | ||
| | |||
| (37+54)\155 | |||
| style="text-align:center;" |286.452+418.0645 | | style="text-align: center;" | 286.452+418.0645 | ||
| | | | {{val| 155 246 435 536 573 }} | ||
| style="text-align:center;" | 3\31+''34\465'' | | style="text-align: center;" | 3\31+''34\465'' | ||
116.129+''87.742'' | 116.129+''87.742'' | ||
| Line 166: | Line 166: | ||
<span style="background-color: rgba(255,255,255,0);">77.419+131.613</span> | <span style="background-color: rgba(255,255,255,0);">77.419+131.613</span> | ||
| style="text-align:center;" |30\155+34\155 | | style="text-align: center;" | 30\155+34\155 | ||
232.258+263.226 | 232.258+263.226 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |286.387+418.151 | | style="text-align: center;" | 286.387+418.151 | ||
| | | | {{val| 46 73 129 159 170 }} + {{val| 109 173 306 377 403 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |115.968+87.842 | | style="text-align: center;" | 115.968+87.842 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.312+131.7365</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.312+131.7365</span> | ||
| style="text-align:center;" |231.935+263.527 | | style="text-align: center;" | 231.935+263.527 | ||
| | |||
|- | |- | ||
| | |||
| (63+92)\264 | |||
| style="text-align:center;" |286.364+418.182 | | style="text-align: center;" | 286.364+418.182 | ||
| | | | {{val| 264 419 741 913 976 }} | ||
| style="text-align:center;" |''51\528+29\396'' | | style="text-align: center;" | ''51\528+29\396'' | ||
''115.909+87.87'' | ''115.909+87.87'' | ||
| Line 192: | Line 192: | ||
<span style="background-color: rgba(255,255,255,0);">77.273+131.818</span> | <span style="background-color: rgba(255,255,255,0);">77.273+131.818</span> | ||
| style="text-align:center;" | 51\264+58\264 | | style="text-align: center;" | 51\264+58\264 | ||
231.818+263.636 | 231.818+263.636 | ||
| | |||
|- | |- | ||
| (26+38)\109 | |||
| | |||
| style="text-align:center;" |286.2385+418.349 | | style="text-align: center;" | 286.2385+418.349 | ||
| | | | {{val| 109 173 306 377 403 }} | ||
| style="text-align:center;" |''21\218''+8\109 | | style="text-align: center;" | ''21\218''+8\109 | ||
''115.596''+88.07 | ''115.596''+88.07 | ||
| Line 208: | Line 208: | ||
<span style="background-color: rgba(255,255,255,0);">77.064+132.11</span> | <span style="background-color: rgba(255,255,255,0);">77.064+132.11</span> | ||
| style="text-align:center;" |21\109+24\109 | | style="text-align: center;" | 21\109+24\109 | ||
231.192+264.22 | 231.192+264.22 | ||
| Boundary of smaller "gentle region" | |||
|- | |- | ||
| | |||
| (67+98)\281 | |||
| style="text-align:center;" |286.121+418.505 | | style="text-align: center;" | 286.121+418.505 | ||
| | | | {{val| 281 446 789 972 1039 }} | ||
| style="text-align:center;" |27\281+''62\843'' | | style="text-align: center;" | 27\281+''62\843'' | ||
115.3025+''88.256'' | 115.3025+''88.256'' | ||
| Line 224: | Line 224: | ||
<span style="background-color: rgba(255,255,255,0);">76.868+132.384</span> | <span style="background-color: rgba(255,255,255,0);">76.868+132.384</span> | ||
| style="text-align:center;" |54\281+62\281 | | style="text-align: center;" | 54\281+62\281 | ||
230.605+264.769 | 230.605+264.769 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |286.101+418.533 | | style="text-align: center;" | 286.101+418.533 | ||
| | | | {{val| 46 73 129 159 170 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |116.526+89.264 | | style="text-align: center;" | 116.526+89.264 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.684+133.8965</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">77.684+133.8965</span> | ||
| style="text-align:center;" |233.052+267.793 | | style="text-align: center;" | 233.052+267.793 | ||
| | |||
|- | |- | ||
| | |||
| (41+60)\172 | |||
| style="text-align:center;" |286.0465+418.605 | | style="text-align: center;" | 286.0465+418.605 | ||
| | | | {{val| 172 273 483 595 636 }} | ||
| style="text-align:center;" |''33\344+19\258'' | | style="text-align: center;" | ''33\344+19\258'' | ||
''115.116+88.372'' | ''115.116+88.372'' | ||
| Line 250: | Line 250: | ||
<span style="background-color: rgba(255,255,255,0);">76.744+132.558</span> | <span style="background-color: rgba(255,255,255,0);">76.744+132.558</span> | ||
| style="text-align:center;" |33\172+38\172 | | style="text-align: center;" | 33\172+38\172 | ||
230.232+265.116 | 230.232+265.116 | ||
| | |||
|- | |- | ||
| | |||
| (56+82)\235 | |||
| style="text-align:center;" |285.957+418.723 | | style="text-align: center;" | 285.957+418.723 | ||
| | | | {{val| 235 373 660 813 869 }} | ||
| style="text-align:center;" |''9\94+52\705'' | | style="text-align: center;" | ''9\94+52\705'' | ||
114.894+81.511 | 114.894+81.511 | ||
| Line 266: | Line 266: | ||
<span style="background-color: rgba(255,255,255,0);">76.596+132.766</span> | <span style="background-color: rgba(255,255,255,0);">76.596+132.766</span> | ||
| style="text-align:center;" |9\47+52\235 | | style="text-align: center;" | 9\47+52\235 | ||
229.787+265.532 | 229.787+265.532 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |285.852+418.864 | | style="text-align: center;" | 285.852+418.864 | ||
| | | | {{val| 109 173 306 377 403 }} + {{val| 63 100 177 218 233 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |114.963+88.4675 | | style="text-align: center;" | 114.963+88.4675 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">76.642+132.701</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">76.642+132.701</span> | ||
| style="text-align:center;" |229.926+265.402 | | style="text-align: center;" | 229.926+265.402 | ||
| | |||
|- | |- | ||
| <span style="display: block; text-align: center;">(15+22)\63</span> | |||
| | |||
| style="text-align:center;" |<span style="display: block; text-align: center;">285.714+419.048</span> | | style="text-align: center;" | <span style="display: block; text-align: center;">285.714+419.048</span> | ||
| | | | {{val| 63 100 177 218 233 }} | ||
| style="text-align:center;" |2\21+''2\27'' | | style="text-align: center;" | 2\21+''2\27'' | ||
114.286+''88.889'' | 114.286+''88.889'' | ||
| Line 292: | Line 292: | ||
<span style="background-color: rgba(255,255,255,0); text-align: start;">76.1905+133.333</span> | <span style="background-color: rgba(255,255,255,0); text-align: start;">76.1905+133.333</span> | ||
| style="text-align:center;" |4\21+2\9 | | style="text-align: center;" | 4\21+2\9 | ||
228.571+266.667 | 228.571+266.667 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" |285.513+419.316 | | style="text-align: center;" | 285.513+419.316 | ||
| | | | {{val| 46 73 129 159 170 }} + {{val| 80 127 225 277 296 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">113.7825+89.20</span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0);">75.855+133.80</span></span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"></span> | | style="text-align: center;" | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">113.7825+89.20</span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"><span style="background-color: rgba(255,255,255,0);">75.855+133.80</span></span><span style="background-color: rgba(255,255,255,0); display: block; text-align: center;"></span> | ||
| style="text-align:center;" |227.565+267.606 | | style="text-align: center;" | 227.565+267.606 | ||
| | |||
|- | |- | ||
| | |||
| <span style="display: block; text-align: center;">(49+72)\206</span> | |||
| style="text-align:center;" |<span style="display: block; text-align: center;">285.437+419.4175</span> | | style="text-align: center;" | <span style="display: block; text-align: center;">285.437+419.4175</span> | ||
| | | | {{val| 206 327 578~579 713 762 }} | ||
| style="text-align:center;" |10\103+15\206 | | style="text-align: center;" | 10\103+15\206 | ||
116.505+87.37 | 116.505+87.37 | ||
| Line 316: | Line 316: | ||
<span style="background-color: rgba(255,255,255,0);">''77.67+131.068''</span> | <span style="background-color: rgba(255,255,255,0);">''77.67+131.068''</span> | ||
| style="text-align:center;" |20\103+45\206 | | style="text-align: center;" | 20\103+45\206 | ||
233.01+262.136 | 233.01+262.136 | ||
| | |||
|- | |- | ||
| <span style="display: block; text-align: center;">(34+50)\143</span> | |||
| | |||
| style="text-align:center;" |<span style="display: block; text-align: center;">285.315+419.58</span> | | style="text-align: center;" | <span style="display: block; text-align: center;">285.315+419.58</span> | ||
| | | | {{val| 143 227 401~402 495 529 }} | ||
| style="text-align:center;" |''14\143+31\429'' | | style="text-align: center;" | ''14\143+31\429'' | ||
117.4825+86.71 | 117.4825+86.71 | ||
| Line 332: | Line 332: | ||
<span style="background-color: rgba(255,255,255,0);">''78.322+130.07''</span> | <span style="background-color: rgba(255,255,255,0);">''78.322+130.07''</span> | ||
| style="text-align:center;" |28\143+31\143 | | style="text-align: center;" | 28\143+31\143 | ||
234.965+260.14 | 234.965+260.14 | ||
| | |||
|- | |- | ||
| | |||
| | |||
| style="text-align:center;" | 285.234+419.688 | | style="text-align: center;" | 285.234+419.688 | ||
| | | | {{val| 63 100 177 218 233 }} + {{val| 80 127 225 277 296 }}<span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ</span> | ||
| style="text-align:center;" |113.085+89.636 | | style="text-align: center;" | 113.085+89.636 | ||
<span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">75.39+134.454</span> | <span style="background-color: rgba(255,255,255,0); display: block; text-align: center;">75.39+134.454</span> | ||
| style="text-align:center;" | 226.169+268.909 | | style="text-align: center;" | 226.169+268.909 | ||
| | |||
|- | |- | ||
| <span style="display: block; text-align: center;">(54+78)\223</span> | |||
| | |||
| style="text-align:center;" | | | style="text-align: center;" | | ||
<span style="display: block; text-align: center;">285.202+419.731</span> | <span style="display: block; text-align: center;">285.202+419.731</span> | ||
| | | | {{val| 223 354 626~627 771 825 }} | ||
| style="text-align:center;" |''43\446+49\669'' | | style="text-align: center;" | ''43\446+49\669'' | ||
115.695+87.892 | 115.695+87.892 | ||
| Line 359: | Line 359: | ||
<span style="background-color: rgba(255,255,255,0);">''77.13+131.839''</span> | <span style="background-color: rgba(255,255,255,0);">''77.13+131.839''</span> | ||
| style="text-align:center;" |43\223+49\223 | | style="text-align: center;" | 43\223+49\223 | ||
231.39+263.677 | 231.39+263.677 | ||
| | |||
|- | |- | ||
| <span style="display: block; text-align: center;">(19+28)\80</span> | |||
| | |||
| style="text-align:center;" |<span style="display: block; text-align: center;">285+420</span> | | style="text-align: center;" | <span style="display: block; text-align: center;">285+420</span> | ||
| | | | {{val| 80 127 225 277 296 }} | ||
| style="text-align:center;" |''3\32+3\40'' | | style="text-align: center;" | ''3\32+3\40'' | ||
''112.5+90'' | ''112.5+90'' | ||
| Line 375: | Line 375: | ||
<span style="background-color: rgba(255,255,255,0);">75+135</span> | <span style="background-color: rgba(255,255,255,0);">75+135</span> | ||
| style="text-align:center;" |3\16+9\40 | | style="text-align: center;" | 3\16+9\40 | ||
225+270 | 225+270 | ||
| Boundary of larger "gentle region" | |||
|- | |- | ||
| style="text-align:center;" | (4+6)\17 | | style="text-align: center;" | (4+6)\17 | ||
| | | | ||
| style="text-align:center;" |282.353+423.529 | | style="text-align: center;" | 282.353+423.529 | ||
|<nowiki>< 17 27 48 60 63|</nowiki> | |<nowiki>< 17 27 48 60 63|</nowiki> | ||
| style="text-align:center;" |1\17+''4\51'' | | style="text-align: center;" | 1\17+''4\51'' | ||
70.588+''93.1765'' | 70.588+''93.1765'' | ||
| Line 390: | Line 390: | ||
''105.882''+70.588 | ''105.882''+70.588 | ||
| style="text-align:center;" |3\17+4\17 | | style="text-align: center;" | 3\17+4\17 | ||
211.765+282.353 | 211.765+282.353 | ||
| | | | ||
|} | |} | ||
[[Category:Gentle]] | [[Category:Gentle]] | ||
[[Category:Interval region]] | [[Category:Interval region]] | ||
[[Category:Tables]] | [[Category:Tables]] | ||