Xenharmonic Wiki

Reversed meantone: Difference between revisions

← Older edit
VisualWikitext
No edit summary
m - parent category
 
(5 intermediate revisions by 4 users not shown)
Line 24: Line 24:
[[TOP tuning|TOP generator]]s: ~2 = 1199.6961, ~4/3 = 494.3834
[[TOP tuning|TOP generator]]s: ~2 = 1199.6961, ~4/3 = 494.3834


[[Optimal GPV sequence]]: {{Val list| 5, 12, 17 }}
{{Optimal ET sequence|legend=1| 5, 12, 17 }}
</div></div>
</div></div>




<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (5&amp;12, 2.3.7.41 subgroup)'''</div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (5&amp;12, 2.3.7.41 subgroup)'''</div>
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">
Subgroup: 2.3.7.41
Subgroup: 2.3.7.41
Line 42: Line 43:
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029


[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 49 }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }}
</div></div>
</div></div>


Line 61: Line 62:
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454
[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454


[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 39d }}
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }}
</div></div>
</div></div>


==Non-octave==
=== Other tunings ===
As [[meantone]] is based within the octave and on the syntonic comma, 81/80, tempering the fifth flat, and the thirds to be simple rational intervals, basing it within the third or fifth harmonic or the perfect fifth or the major tenth, sixth or third instead still may temper 81/80, even if it might as well be called reverse meantone. Of these, the major third of 5/4 is the least recognizable as an interval, though still very recognizable. Additionally, the major third of 5/4 is a very narrow interval to base a temperament within, so if its use is intended as more than a joke it might as well be the [[Augmented family|augmented]] temperament 4ned5/2.
* [[DKW theory|DKW]] (2.3.41): ~2 = 1\1, ~3/2 = 706.8411 (~4/3 = 493.1589)
 
* DKW (2.3.6561/160<ref>Mathematically identical to [[meantone]], but optimized for the "retroptolemaic" thirds, [[2560/2187]] and [[6561/5120]], rather than 6/5 and 5/4</ref>): ~2 = 1\1, ~3/2 = 706.8984 (~4/3 = 493.1016)
==Temperament data==
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (b11&amp;b19, 3.2.5 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3.2.5
 
[[Comma list]]: 81/80
 
[[Gencom]]: [3 3/2; 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 1 0 }}, {{val| 0 -1 4 }}]
 
[[POTE generator]]: ~3/2 = 698.3375
 
[[TOP tuning|TOP generator]]s: ~3 = 1898.4460, ~3/2 = 697.0491
 
[[Optimal GPV sequence]]: {{Val list| b11, b19, b30 }}
</div></div>
 
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (b11&amp;b19, 3.2.5.7 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3.2.5.7
 
[[Comma list]]: 64/63, 81/80
 
[[Gencom]]: [3 3/2; 64/63 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 1 0 3}}, {{val| 0 -1 4 -13}}]
 
[[POTE generator]]: ~3/2 = 698.5001
 
[[TOP tuning|TOP generator]]s: ~3 = 1898.4580, ~3/2 = 697.2159
 
[[Optimal GPV sequence]]: {{Val list| b11, b19, b30, b41, b71 }}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (b11de&amp;b19e, 3.2.5.7.11 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3.2.5.7.11
 
[[Comma list]]: 64/63, 81/80, 99/98
 
[[Gencom]]: [2 3/2; 64/63 81/80 99/98]
 
[[Mapping|Sval mapping]]: [{{val| 1 1 0 4 7}}, {{val| 0 -1 4 -6 -13}}]
 
[[POTE generator]]: ~3/2 = 702.7738
 
[[TOP tuning|TOP generator]]s: ~3 = 1893.9031, ~3/2 = 699.7986
 
[[Optimal GPV sequence]]: {{Val list| b8, b11de, b19e, b27, b38dee, b46cde }}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (c16&amp;c28, 5.2.3 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5.2.3 (3/2.5)
 
[[Comma list]]: 81/80
 
[[Gencom]]: [3/2 10/9; 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 4 2 3 }}, {{val| 0 -1 —1 }}]
 
[[POTE generator]]: ~3/2 = 696.5784, ~10/9 = 192.5712
 
[[TOP tuning|TOP generator]]s: ~3/2 = 697.0491, ~10/9 = [[Tel:192.7014|192.7014]]
 
[[Optimal GPV sequence]]: {{Val list| c16, c28, c44 }}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (c12d&amp;c16dee, 5.2.3.7 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5.2.3.7
 
[[Comma list]]: 64/63, 81/80
 
[[Gencom]]: [3/2 10/9; 64/63 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 4 2 3 6}}, {{val| 0 -1 —1 -4}}]
 
[[POTE generator]]: ~3/2 = 696.5784, ~10/9 = 201.7001
 
[[TOP tuning|TOP generator]]s: ~3/2 = 697.2159, ~10/9 = 202.3697
 
[[Optimal GPV sequence]]: {{Val list| c12d, c16dee, c28, c40, c52d, c64 }})
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (c12de&amp;c16dee, 5.2.3.7.11 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5.2.3.7.11
 
[[Comma list]]: 64/63, 81/80, 99/98
 
[[Gencom]]: [3/2 10/9; 64/63 81/80 99/98]
 
[[Mapping|Sval mapping]]: [{{val| 4 2 3 6 8}}, {{val| 0 -1 —1 -4 -7}}]
 
[[POTE generator]]: ~3/2 = 696.5784, ~10/9 = 204.5471
 
[[TOP tuning|TOP generator]]s: ~3/2 = 699.7986, ~10/9 = 205.4927
 
[[Optimal GPV sequence]]: {{Val list| c12de, c16dee, c28, c40e, c52dee, c64 }})
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q4&amp;q7, 3/2.2.3.5 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3/2.2.3.5
 
[[Comma list]]: 81/80
 
[[Gencom]]: [3/2 9/8; 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -1 -1 0 }}]
 
[[POTE generator]]: ~9/8 = 198.7378
 
[[TOP tuning|TOP generator]]s: ~3/2 = 699.3710, ~9/8 = 198.0062
 
[[Optimal GPV sequence]]: {{Val list| q4, q7, q11}}
</div></div>
 
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (q3&amp;q7, 3/2.2.3.5.7 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3/2.2.3.5.7
 
[[Comma list]]: 64/63, 81/80
 
[[Gencom]]: [3/2 9/8; 64/63 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 3 4 6}}, {{val| 0 -1 -1 0 -4}}]
 
[[POTE generator]]: ~9/8 = 205.3121
 
[[TOP tuning|TOP generator]]s: ~3/2 = 700.2305, ~9/8 = 204.8077
 
[[Optimal GPV sequence]]: {{Val list| q3, q7, q10, q17, q24, q31 }}
</div></div>
 
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q7e&amp;q11, 3/2.2.3.5.7.11 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 3/2.2.3.5.7.11
 
[[Comma list]]: 64/63, 81/80, 99/98
 
[[Gencom]]: [3/2 9/8; 64/63 81/80 99/98]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 3 4 4 4}}, {{val| 0 -1 -1 0 3 7}}]
 
[[POTE generator]]: ~9/8 = 195.0236
 
[[TOP tuning|TOP generator]]s: ~3/2 = 698.2079, ~9/8 = 193.9826
 
[[Optimal GPV sequence]]: {{Val list| q7e, q11, q18, q25 }}
 
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q16&amp;q25, 5/2.2.3.5 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/2.2.3.5
 
[[Comma list]]: 81/80
 
[[Gencom]]: [5/2 3/2; 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 -1 -1 0 }}, {{val| 0 4 5 4 }}]
 
[[POTE generator]]: ~3/2 = 696.9241
 
[[TOP tuning|TOP generator]]s: ~5/2 = 1586.4184, ~3/2 = 696.9702
 
[[Optimal GPV sequence]]: {{Val list| q16, q25, q41 }}
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (q16&amp;q25, 5/2.2.3.5.7 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/2.2.3.5.7
 
[[Comma list]]: 64/63, 81/80
 
[[Gencom]]: [5/2 3/2; 64/63 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 -1 -1 0 3}}, {{val| 0 4 5 4 -2}}]
 
[[POTE generator]]: ~3/2 = 696.7420
 
[[TOP tuning|TOP generator]]s: ~5/2 = 1587.1426, ~3/2 = 697.1060
 
[[Optimal GPV sequence]]: {{Val list| q16, q25, q41 }}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q16&amp;q41, 5/2.2.3.5.7.11 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/2.2.3.5.7.11
 
[[Comma list]]: 81/80, 126:125, 176:175
 
[[Gencom]]: [5/2 3/2; 81/80 126:125 176:175]
 
[[Mapping|Sval mapping]]: [{{val| 1 -1 -1 0 3 7}}, {{val| 0 4 5 4 -2 -10}}]
 
[[POTE generator]]: ~3/2 = 696.3353
 
[[TOP tuning|TOP generator]]s: ~5/2 = 1587.1426, ~3/2 = 697.2531
 
[[Optimal GPV sequence]]: {{Val list|q16, q25, q41, q57}}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q9&amp;q14, 5/3.2.3.5 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/3.2.3.5
 
[[Comma list]]: 81/80
 
[[Gencom]]: [5/3 10/9; 81/80]
 
[[Mapping|Val mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -3 -4 -4 }}]
 
[[POTE generator]]: ~10/9 = 189.0028
 
[[TOP tuning|TOP generator]]s: ~5/3 = 884.9987, ~10/9 = 189.1396
 
[[Optimal GPV sequence]]: {{Val list| q9, q14, q23 }}
</div></div>
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"><div style="line-height:1.6;">'''Reversed meantone (q9&amp;q14d, 5/3.2.3.5.7 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/3.2.3.5.7
 
[[Comma list]]: 126/125, 81/80
 
[[Gencom]]: [5/3 10/9; 126/125 81/80]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 3 4 6}}, {{val| 0 -3 -4 -4 -10}}]
 
[[POTE generator]]: ~10/9 = 192.2011
 
[[TOP tuning|TOP generator]]s: ~5/3 = 887.4720, ~10/9 = 192.8777
 
[[Optimal GPV sequence]]: {{Val list| q9, q14d, q23 }}
</div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Reversed meantone (q9&amp;q14, 5/3.2.3.5.7.11 subgroup)'''</div>
<div class="mw-collapsible-content">
Subgroup: 5/3.2.3.5.7.11
 
[[Comma list]]: 81/80, 126/125, 100/99
 
[[Gencom]]: [5/3 ; 81/80 126/125 100/99]
 
[[Mapping|Sval mapping]]: [{{val| 1 2 3 4 4 6}}, {{val| 0 -3 -4 -4 -1 -6}}]
 
[[POTE generator]]: ~10/9 = 190.2709
 
[[TOP tuning|TOP generator]]s: ~5/3 = 886.3893, ~10/9 = 190.7078
 
[[Optimal GPV sequence]]: {{Val list| q9, q14, q23, q37}}
</div></div>


[[Category:41-limit]]
[[Category:Reversed meantone| ]] <!-- main article -->
[[Category:Temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Reversed_meantone"