34edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602865014 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 602872548 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 11:24:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602872548</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=Intervals= | =Intervals= | ||
|| | ||~ Degree ||~ Solfege ||~ Cents ||~ approx. ratios of | ||
2.3.5.13.17 | 2.3.5.13.17 [[xenharmonic/subgroup|subgroup]] ||~ additional ratios | ||
of 7 and 11 |||||| | of 7 and 11 ||||||~ [[Ups and Downs Notation|ups and downs ]][[Ups and Downs Notation|notation]] || | ||
||= 0 ||= do ||= | ||= 0 ||= do ||> 0<span style="color: #fff;">.000</span> ||= 1/1 ||= ||= P1 ||= perfect unison ||= D || | ||
||= 1 ||= di || | ||= 1 ||= di ||> 35.294 ||= 128/125 ([[128_125|diesis]]), 51/50 ||= 50/49, 49/48 ||= ^1, vm2 ||= up unison, downminor 2nd ||= D^, Ebv || | ||
downminor 2nd ||= D^, Ebv || | ||= 2 ||= rih ||> 70.588 ||= 25/24, 648/625 ([[648_625|large diesis]]) ||= ||= m2 ||= minor 2nd ||= Eb || | ||
||= 2 ||= rih || | ||= 3 ||= ra ||> 105.882 ||= 17/16, 18/17, 16/15 ||= 15/14 ||= ^m2 ||= upminor 2nd ||= Eb^ || | ||
||= 3 ||= ra || | ||= 4 ||= ru ||> 141.176 ||= 13/12 ||= 14/13, 12/11 ||= ~2 ||= mid 2nd ||= Evv || | ||
||= 4 ||= ru || | ||= 5 ||= reh ||> 176.471 ||= 10/9 ||= 11/10 ||= vM2 ||= downmajor 2nd ||= Ev || | ||
||= 5 ||= reh || | ||= 6 ||= re ||> 211.765 ||= 9/8, 17/15 ||= ||= M2 ||= major 2nd ||= E || | ||
||= 6 ||= re || | ||= 7 ||= raw ||> 247.059 ||= 15/13 ||= 8/7 ||= ^M2, vm3 ||= upmajor 2nd, downminor 3rd ||= E^, Fv || | ||
||= 7 ||= raw || | ||= 8 ||= meh ||> 282.353 ||= 20/17, 75/64 ||= 7/6, 13/11 ||= m3 ||= minor 3rd ||= F || | ||
downminor 3rd ||= E^, Fv || | ||= 9 ||= me ||> 317.647 ||= 6/5 ||= 17/14 ||= ^m3 ||= upminor 3rd ||= F^ || | ||
||= 8 ||= meh || | ||= 10 ||= mu ||> 352.941 ||= 16/13 ||= 11/9 ||= ~3 ||= mid 3rd ||= F^^ || | ||
||= 9 ||= me || | ||= 11 ||= mi ||> 388.235 ||= 5/4 ||= ||= vM3 ||= downmajor 3rd ||= F#v || | ||
||= 10 ||= mu || | ||= 12 ||= maa ||> 423.529 ||= [[51_40|51/40]], 32/25 ||= 14/11, 9/7 ||= M3 ||= major 3rd ||= F# || | ||
||= 11 ||= mi || | ||= 13 ||= maw ||> 458.823 ||= 13/10, 17/13 ||= 22/17 ||= ^M3, v4 ||= upmajor 3rd,down 4th ||= F#^, Gv || | ||
||= 12 ||= maa || | ||= 14 ||= fa ||> 494.118 ||= 4/3 ||= ||= P4 ||= 4th ||= G || | ||
||= 13 ||= maw || | ||= 15 ||= fih ||> 529.412 ||= ||= 15/11 ||= ^4 ||= up 4th ||= G^ || | ||
||= 14 ||= fa || | ||= 16 ||= fu ||> 564.706 ||= 18/13 ||= 11/8 ||= ^^4, d5 ||= double-up 4th, dim 5th ||= G^^, Ab || | ||
||= 15 ||= fih || | ||= 17 ||= fi/se ||> 600<span style="color: #fff;">.000</span> ||= 17/12, 24/17 ||= 7/5, 10/7 ||= vA4, ^d5 ||= downaug 4th, updim 5th ||= G#v, Ab^ || | ||
||= 16 ||= fu || | ||= 18 ||= su ||> 635.294 ||= 13/9 ||= 16/11 ||= A4, vv5 ||= aug 4th, double-down 5th ||= G#, Avv || | ||
||= 17 ||= fi/se ||= | ||= 19 ||= sih ||> 670.588 ||= ||= 22/15 ||= v5 ||= down 5th ||= Av || | ||
||= 18 ||= su || | ||= 20 ||= sol ||> 705.882 ||= 3/2 ||= ||= P5 ||= perfect 5th ||= A || | ||
||= 19 ||= sih || | ||= 21 ||= saw ||> 741.176 ||= 20/13, 26/17 ||= 17/11 ||= ^5, vm6 ||= up 5th, downminor 6th ||= A^, Bbv || | ||
||= 20 ||= sol || | ||= 22 ||= leh ||> 776.471 ||= 25/16, 80/51 ||= 14/9 ||= m6 ||= minor 6th ||= Bb || | ||
||= 21 ||= saw || | ||= 23 ||= le ||> 811.765 ||= 8/5 ||= ||= ^m6 ||= upminor 6th ||= Bb^ || | ||
||= 22 ||= leh || | ||= 24 ||= lu ||> 847.059 ||= 13/8 ||= 18/11 ||= ~6 ||= mid 6th ||= Bvv || | ||
||= 23 ||= le || | ||= 25 ||= la ||> 882.353 ||= 5/3 ||= 28/17 ||= vM6 ||= downmajor 6th ||= Bv || | ||
||= 24 ||= lu || | ||= 26 ||= laa ||> 917.647 ||= [[17_10|17/10]] ||= 12/7, 22/13 ||= M6 ||= major 6th ||= B || | ||
||= 25 ||= la || | ||= 27 ||= law ||> 952.941 ||= 26/15 ||= 7/4 ||= ^M6, vm7 ||= upmajor 6th, downminor 7th ||= B^, Cv || | ||
||= 26 ||= laa || | ||= 28 ||= teh ||> 988.235 ||= 16/9, 30/17 ||= ||= m7 ||= minor 7th ||= C || | ||
||= 27 ||= law || | ||= 29 ||= te ||> 1023.529 ||= 9/5 ||= 20/11 ||= ^m7 ||= upminor 7th ||= C^ || | ||
downminor 7th ||= B^, Cv || | ||= 30 ||= tu ||> 1058.823 ||= 24/13 ||= 13/7, 11/6 ||= ~7 ||= mid 7th ||= C^^ || | ||
||= 28 ||= teh || | ||= 31 ||= ti ||> 1094.118 ||= 32/17, 17/9, 15/8 ||= 28/15 ||= vM7 ||= downmajor 7th ||= C#v || | ||
||= 29 ||= te || | ||= 32 ||= taa ||> 1129.412 ||= 48/25, 625/324 ||= ||= M7 ||= major 7th ||= C# || | ||
||= 30 ||= tu || | ||= 33 ||= da ||> 1164.706 ||= 125/64, 100/51 ||= 49/25, 96/49 ||= ^M7, v8 ||= upmajor 7th, down 8ve ||= C#^, Dv || | ||
||= 31 ||= ti || | ||= 34 ||= do ||> 1200<span style="color: #fff;">.000</span> ||= 2/1 ||= ||= P8 ||= 8ve ||= D || | ||
||= 32 ||= taa || | |||
||= 33 ||= da || | |||
||= 34 ||= do ||= | |||
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]]. | ||
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==Selected just intervals by error== | ==Selected just intervals by error== | ||
The following table shows how [[Just-24|some prominent just intervals]] are represented in 34edo (ordered by absolute error). | The following table shows how [[Just-24|some prominent just intervals]] are represented in 34edo (ordered by absolute error). | ||
|| | ||~ Interval, complement ||~ Error (abs., in [[cent|cents]]) || | ||
||= [[15_13|15/13]], [[26_15|26/15]] ||= 0.682 || | ||= [[15_13|15/13]], [[26_15|26/15]] ||= 0.682 || | ||
||= [[18_13|18/13]], [[13_9|13/9]] ||= 1.324 || | ||= [[18_13|18/13]], [[13_9|13/9]] ||= 1.324 || | ||
| Line 121: | Line 118: | ||
=Commas= | =Commas= | ||
34-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < | 34-EDO [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] < 34 54 79 95 118 126 |.) | ||
|| | ||~ Rational ||~ Monzo ||~ Size (Cents) ||~ Names || | ||
||= | ||= 134217728/129140163 || | 27 -17 > ||> 66.765 ||= 17-comma || | ||
||= 20000/19683 || | 5 -9 4 > ||> 27.660 ||= Minimal Diesis, Tetracot Comma || | ||= 20000/19683 || | 5 -9 4 > ||> 27.660 ||= Minimal Diesis, Tetracot Comma || | ||
||= 2048/2025 || | 11 -4 -2 > ||> 19.553 ||= Diaschisma || | ||= 2048/2025 || | 11 -4 -2 > ||> 19.553 ||= Diaschisma || | ||
||= | ||= 393216/390625 || | 17 1 -8 > ||> 11.445 ||= Würschmidt comma || | ||
||= 15625/15552 || | -6 -5 6 > ||> 8. | ||= 15625/15552 || | -6 -5 6 > ||> 8.107 ||= Kleisma, Semicomma Majeur || | ||
||= | ||= 1212717/1210381 || | 23 6 -14 > ||> 3.338 ||= Vishnuzma, Semisuper || | ||
||= 1029/1000 || | -3 1 -3 3 > ||> 49.492 ||= Keega || | ||= 1029/1000 || | -3 1 -3 3 > ||> 49.492 ||= Keega || | ||
||= [[50_49|50/49]] || | 1 0 2 -2 > ||> 34.976 ||= Jubilisma || | ||= [[50_49|50/49]] || | 1 0 2 -2 > ||> 34.976 ||= Jubilisma || | ||
| Line 134: | Line 131: | ||
||= 126/125 || | 1 2 -3 1 > ||> 13.795 ||= Starling comma, Septimal semicomma || | ||= 126/125 || | 1 2 -3 1 > ||> 13.795 ||= Starling comma, Septimal semicomma || | ||
||= 100/99 || | 2 -2 2 0 -1> ||> 17.399 ||= Ptolemisma, Ptolemy's comma || | ||= 100/99 || | 2 -2 2 0 -1> ||> 17.399 ||= Ptolemisma, Ptolemy's comma || | ||
||= 243/242 || | -1 5 0 0 -2 > ||> 7. | ||= 243/242 || | -1 5 0 0 -2 > ||> 7.139 ||= Rastma, Neutral third comma || | ||
||= 385/384 || | -7 -1 1 1 1 > ||> 4. | ||= 385/384 || | -7 -1 1 1 1 > ||> 4.503 ||= Keenanisma || | ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.120 ||= Superleap || | ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.120 ||= Superleap || | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Degree<br /> | ||
</ | </th> | ||
< | <th>Solfege<br /> | ||
</ | </th> | ||
< | <th>Cents<br /> | ||
</ | </th> | ||
< | <th>approx. ratios of<br /> | ||
2.3.5.13.17 | 2.3.5.13.17 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/subgroup">subgroup</a><br /> | ||
</ | </th> | ||
< | <th>additional ratios<br /> | ||
of 7 and 11<br /> | of 7 and 11<br /> | ||
</ | </th> | ||
< | <th colspan="3"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">ups and downs </a><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a><br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 376: | Line 373: | ||
<td style="text-align: center;">do<br /> | <td style="text-align: center;">do<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">0<span style="color: #fff;">.000</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">1/1<br /> | <td style="text-align: center;">1/1<br /> | ||
| Line 394: | Line 391: | ||
<td style="text-align: center;">di<br /> | <td style="text-align: center;">di<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">35.294<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">128/125 (<a class="wiki_link" href="/128_125">diesis</a>), 51/50<br /> | <td style="text-align: center;">128/125 (<a class="wiki_link" href="/128_125">diesis</a>), 51/50<br /> | ||
| Line 402: | Line 399: | ||
<td style="text-align: center;">^1, vm2<br /> | <td style="text-align: center;">^1, vm2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">up unison, | <td style="text-align: center;">up unison, downminor 2nd<br /> | ||
downminor 2nd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">D^, Ebv<br /> | <td style="text-align: center;">D^, Ebv<br /> | ||
| Line 413: | Line 409: | ||
<td style="text-align: center;">rih<br /> | <td style="text-align: center;">rih<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">70.588<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">25/24, 648/625 (<a class="wiki_link" href="/648_625">large diesis</a>)<br /> | <td style="text-align: center;">25/24, 648/625 (<a class="wiki_link" href="/648_625">large diesis</a>)<br /> | ||
| Line 431: | Line 427: | ||
<td style="text-align: center;">ra<br /> | <td style="text-align: center;">ra<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">105.882<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/16, 18/17, 16/15<br /> | <td style="text-align: center;">17/16, 18/17, 16/15<br /> | ||
| Line 449: | Line 445: | ||
<td style="text-align: center;">ru<br /> | <td style="text-align: center;">ru<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">141.176<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/12<br /> | <td style="text-align: center;">13/12<br /> | ||
| Line 467: | Line 463: | ||
<td style="text-align: center;">reh<br /> | <td style="text-align: center;">reh<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">176.471<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">10/9<br /> | <td style="text-align: center;">10/9<br /> | ||
| Line 485: | Line 481: | ||
<td style="text-align: center;">re<br /> | <td style="text-align: center;">re<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">211.765<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 17/15<br /> | <td style="text-align: center;">9/8, 17/15<br /> | ||
| Line 503: | Line 499: | ||
<td style="text-align: center;">raw<br /> | <td style="text-align: center;">raw<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">247.059<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">15/13<br /> | <td style="text-align: center;">15/13<br /> | ||
| Line 511: | Line 507: | ||
<td style="text-align: center;">^M2, vm3<br /> | <td style="text-align: center;">^M2, vm3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">upmajor 2nd, | <td style="text-align: center;">upmajor 2nd, downminor 3rd<br /> | ||
downminor 3rd<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">E^, Fv<br /> | <td style="text-align: center;">E^, Fv<br /> | ||
| Line 522: | Line 517: | ||
<td style="text-align: center;">meh<br /> | <td style="text-align: center;">meh<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">282.353<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">20/17, 75/64<br /> | <td style="text-align: center;">20/17, 75/64<br /> | ||
| Line 540: | Line 535: | ||
<td style="text-align: center;">me<br /> | <td style="text-align: center;">me<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">317.647<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">6/5<br /> | <td style="text-align: center;">6/5<br /> | ||
| Line 558: | Line 553: | ||
<td style="text-align: center;">mu<br /> | <td style="text-align: center;">mu<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">352.941<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/13<br /> | <td style="text-align: center;">16/13<br /> | ||
| Line 576: | Line 571: | ||
<td style="text-align: center;">mi<br /> | <td style="text-align: center;">mi<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">388.235<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/4<br /> | <td style="text-align: center;">5/4<br /> | ||
| Line 594: | Line 589: | ||
<td style="text-align: center;">maa<br /> | <td style="text-align: center;">maa<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">423.529<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/51_40">51/40</a>, 32/25<br /> | <td style="text-align: center;"><a class="wiki_link" href="/51_40">51/40</a>, 32/25<br /> | ||
| Line 612: | Line 607: | ||
<td style="text-align: center;">maw<br /> | <td style="text-align: center;">maw<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">458.823<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/10, 17/13<br /> | <td style="text-align: center;">13/10, 17/13<br /> | ||
| Line 630: | Line 625: | ||
<td style="text-align: center;">fa<br /> | <td style="text-align: center;">fa<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">494.118<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">4/3<br /> | <td style="text-align: center;">4/3<br /> | ||
| Line 648: | Line 643: | ||
<td style="text-align: center;">fih<br /> | <td style="text-align: center;">fih<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">529.412<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 666: | Line 661: | ||
<td style="text-align: center;">fu<br /> | <td style="text-align: center;">fu<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">564.706<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">18/13<br /> | <td style="text-align: center;">18/13<br /> | ||
| Line 684: | Line 679: | ||
<td style="text-align: center;">fi/se<br /> | <td style="text-align: center;">fi/se<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">600<span style="color: #fff;">.000</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">17/12, 24/17<br /> | <td style="text-align: center;">17/12, 24/17<br /> | ||
| Line 702: | Line 697: | ||
<td style="text-align: center;">su<br /> | <td style="text-align: center;">su<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">635.294<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/9<br /> | <td style="text-align: center;">13/9<br /> | ||
| Line 720: | Line 715: | ||
<td style="text-align: center;">sih<br /> | <td style="text-align: center;">sih<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">670.588<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
| Line 738: | Line 733: | ||
<td style="text-align: center;">sol<br /> | <td style="text-align: center;">sol<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">705.882<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">3/2<br /> | <td style="text-align: center;">3/2<br /> | ||
| Line 756: | Line 751: | ||
<td style="text-align: center;">saw<br /> | <td style="text-align: center;">saw<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">741.176<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">20/13, 26/17<br /> | <td style="text-align: center;">20/13, 26/17<br /> | ||
| Line 774: | Line 769: | ||
<td style="text-align: center;">leh<br /> | <td style="text-align: center;">leh<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">776.471<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">25/16, 80/51<br /> | <td style="text-align: center;">25/16, 80/51<br /> | ||
| Line 792: | Line 787: | ||
<td style="text-align: center;">le<br /> | <td style="text-align: center;">le<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">811.765<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">8/5<br /> | <td style="text-align: center;">8/5<br /> | ||
| Line 810: | Line 805: | ||
<td style="text-align: center;">lu<br /> | <td style="text-align: center;">lu<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">847.059<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">13/8<br /> | <td style="text-align: center;">13/8<br /> | ||
| Line 828: | Line 823: | ||
<td style="text-align: center;">la<br /> | <td style="text-align: center;">la<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">882.353<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">5/3<br /> | <td style="text-align: center;">5/3<br /> | ||
| Line 846: | Line 841: | ||
<td style="text-align: center;">laa<br /> | <td style="text-align: center;">laa<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">917.647<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a><br /> | <td style="text-align: center;"><a class="wiki_link" href="/17_10">17/10</a><br /> | ||
| Line 864: | Line 859: | ||
<td style="text-align: center;">law<br /> | <td style="text-align: center;">law<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">952.941<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">26/15<br /> | <td style="text-align: center;">26/15<br /> | ||
| Line 872: | Line 867: | ||
<td style="text-align: center;">^M6, vm7<br /> | <td style="text-align: center;">^M6, vm7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">upmajor 6th, | <td style="text-align: center;">upmajor 6th, downminor 7th<br /> | ||
downminor 7th<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">B^, Cv<br /> | <td style="text-align: center;">B^, Cv<br /> | ||
| Line 883: | Line 877: | ||
<td style="text-align: center;">teh<br /> | <td style="text-align: center;">teh<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">988.235<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/9, 30/17<br /> | <td style="text-align: center;">16/9, 30/17<br /> | ||
| Line 901: | Line 895: | ||
<td style="text-align: center;">te<br /> | <td style="text-align: center;">te<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1023.529<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/5<br /> | <td style="text-align: center;">9/5<br /> | ||
| Line 919: | Line 913: | ||
<td style="text-align: center;">tu<br /> | <td style="text-align: center;">tu<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1058.823<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">24/13<br /> | <td style="text-align: center;">24/13<br /> | ||
| Line 937: | Line 931: | ||
<td style="text-align: center;">ti<br /> | <td style="text-align: center;">ti<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1094.118<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">32/17, 17/9, 15/8<br /> | <td style="text-align: center;">32/17, 17/9, 15/8<br /> | ||
| Line 955: | Line 949: | ||
<td style="text-align: center;">taa<br /> | <td style="text-align: center;">taa<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1129.412<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">48/25, 625/324<br /> | <td style="text-align: center;">48/25, 625/324<br /> | ||
| Line 973: | Line 967: | ||
<td style="text-align: center;">da<br /> | <td style="text-align: center;">da<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1164.706<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">125/64, 100/51<br /> | <td style="text-align: center;">125/64, 100/51<br /> | ||
| Line 991: | Line 985: | ||
<td style="text-align: center;">do<br /> | <td style="text-align: center;">do<br /> | ||
</td> | </td> | ||
<td style="text-align: | <td style="text-align: right;">1200<span style="color: #fff;">.000</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
| Line 1,015: | Line 1,009: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Interval, complement<br /> | ||
</ | </th> | ||
< | <th>Error (abs., in <a class="wiki_link" href="/cent">cents</a>)<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 1,171: | Line 1,165: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:12 -->Commas</h1> | ||
34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt | 34-EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; 34 54 79 95 118 126 |.)<br /> | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
< | <th>Rational<br /> | ||
</ | </th> | ||
< | <th>Monzo<br /> | ||
</ | </th> | ||
< | <th>Size (Cents)<br /> | ||
</ | </th> | ||
< | <th>Names<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">134217728/129140163<br /> | ||
</td> | </td> | ||
<td>| 27 -17 &gt;<br /> | <td>| 27 -17 &gt;<br /> | ||
| Line 1,216: | Line 1,210: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">393216/390625<br /> | ||
</td> | </td> | ||
<td>| 17 1 -8 &gt;<br /> | <td>| 17 1 -8 &gt;<br /> | ||
| Line 1,230: | Line 1,224: | ||
<td>| -6 -5 6 &gt;<br /> | <td>| -6 -5 6 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">8. | <td style="text-align: right;">8.107<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Kleisma, Semicomma Majeur<br /> | <td style="text-align: center;">Kleisma, Semicomma Majeur<br /> | ||
| Line 1,236: | Line 1,230: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">1212717/1210381<br /> | ||
</td> | </td> | ||
<td>| 23 6 -14 &gt;<br /> | <td>| 23 6 -14 &gt;<br /> | ||
| Line 1,300: | Line 1,294: | ||
<td>| -1 5 0 0 -2 &gt;<br /> | <td>| -1 5 0 0 -2 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">7. | <td style="text-align: right;">7.139<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Rastma, Neutral third comma<br /> | <td style="text-align: center;">Rastma, Neutral third comma<br /> | ||
| Line 1,310: | Line 1,304: | ||
<td>| -7 -1 1 1 1 &gt;<br /> | <td>| -7 -1 1 1 1 &gt;<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">4. | <td style="text-align: right;">4.503<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Keenanisma<br /> | <td style="text-align: center;">Keenanisma<br /> | ||