User:PiotrGrochowski/105edo: Difference between revisions
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105edo, the wonderful meantone
105edo belongs to a meantonic 13–limit system known as grosstone, can be considered an expanded version of 43edo just like how 94edo is an expanded version of 41edo.
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<span style="font-family: 'Verdana';"><center><big><big><big>''105edo, the wonderful meantone</span></center></big></big></big>'' | <span style="font-family: 'Verdana';"><center><big><big><big>''105edo, the wonderful meantone</span></center></big></big></big>'' | ||
<center><span style="font-family: 'Consolas';" style="font-size: 105%;">105edo belongs to a meantonic 13–limit system known as grosstone, can be considered an expanded version of [[43edo]] just like how [[94edo-a|94edo]] is an expanded version of [[41edo]]. | <center><span style="font-family: 'Consolas';"><span style="font-size: 105%;">105edo belongs to a meantonic 13–limit system known as grosstone, can be considered an expanded version of [[43edo]] just like how [[94edo-a|94edo]] is an expanded version of [[41edo]]. | ||
==Selected just intervals by error== | |||
The following table shows how [[15-odd-limit|some prominent just intervals]] are represented in 105edo (ordered by absolute error). | |||
{| class="wikitable" | |||
|- | |||
| | '''Interval, complement''' | |||
| | '''Error (abs., in [[cent]]s)''' | |||
|- | |||
| style="text-align:center;" | [[15/11]], [[22/15]] | |||
| style="text-align:center;" | 0.192 | |||
|- | |||
| style="text-align:center;" | [[7/5]], [[10/7]] | |||
| style="text-align:center;" | 0.345 | |||
|- | |||
| style="text-align:center;" | [[12/11]], [[11/6]] | |||
| style="text-align:center;" | 2.066 | |||
|- | |||
| style="text-align:center;" | [[5/4]], [[8/5]] | |||
| style="text-align:center;" | 2.258 | |||
|- | |||
| style="text-align:center;" | [[16/15]], [[15/8]] | |||
| style="text-align:center;" | 2.554 | |||
|- | |||
| style="text-align:center;" | [[14/13]], [[13/7]] | |||
| style="text-align:center;" | 2.584 | |||
|- | |||
| style="text-align:center;" | [[8/7]], [[7/4]] | |||
| style="text-align:center;" | 2.603 | |||
|- | |||
| style="text-align:center;" | [[11/8]], [[16/11]] | |||
| style="text-align:center;" | 2.747 | |||
|- | |||
| style="text-align:center;" | [[13/10]], [[20/13]] | |||
| style="text-align:center;" | 2.929 | |||
|- | |||
| style="text-align:center;" | [[4/3]], [[3/2]] | |||
| style="text-align:center;" | 4.812 | |||
|- | |||
| style="text-align:center;" | [[11/10]], [[20/11]] | |||
| style="text-align:center;" | 5.004 | |||
|- | |||
| style="text-align:center;" | [[15/14]], [[28/15]] | |||
| style="text-align:center;" | 5.157 | |||
|- | |||
| style="text-align:center;" | [[16/13]], [[13/8]] | |||
| style="text-align:center;" | 5.187 | |||
|- | |||
| style="text-align:center;" | [[14/11]], [[11/7]] | |||
| style="text-align:center;" | 5.349 | |||
|- | |||
| style="text-align:center;" | [[11/9]], [[18/11]] | |||
| style="text-align:center;" | 6.878 | |||
|- | |||
| style="text-align:center;" | [[6/5]], [[5/3]] | |||
| style="text-align:center;" | 7.07 | |||
|- | |||
| style="text-align:center;" | [[7/6]], [[12/7]] | |||
| style="text-align:center;" | 7.415 | |||
|- | |||
| style="text-align:center;" | [[15/13]], [[26/15]] | |||
| style="text-align:center;" | 7.741 | |||
|- | |||
| style="text-align:center;" | [[13/11]], [[22/13]] | |||
| style="text-align:center;" | 7.933 | |||
|- | |||
| style="text-align:center;" | [[9/8]], [[16/9]] | |||
| style="text-align:center;" | 9.624 | |||
|- | |||
| style="text-align:center;" | [[13/12]], [[24/13]] | |||
| style="text-align:center;" | 9.999 | |||
|- | |||
| style="text-align:center;" | [[10/9]], [[9/5]] | |||
| style="text-align:center;" | 11.882 | |||
|- | |||
| style="text-align:center;" | [[9/7]], [[14/9]] | |||
| style="text-align:center;" | 12.227 | |||
|- | |||
| style="text-align:center;" | [[18/13]], [[13/9]] | |||
| style="text-align:center;" | 14.811 | |||
|} | |||
Latest revision as of 03:05, 25 May 2023
Selected just intervals by error
The following table shows how some prominent just intervals are represented in 105edo (ordered by absolute error).
| Interval, complement | Error (abs., in cents) |
| 15/11, 22/15 | 0.192 |
| 7/5, 10/7 | 0.345 |
| 12/11, 11/6 | 2.066 |
| 5/4, 8/5 | 2.258 |
| 16/15, 15/8 | 2.554 |
| 14/13, 13/7 | 2.584 |
| 8/7, 7/4 | 2.603 |
| 11/8, 16/11 | 2.747 |
| 13/10, 20/13 | 2.929 |
| 4/3, 3/2 | 4.812 |
| 11/10, 20/11 | 5.004 |
| 15/14, 28/15 | 5.157 |
| 16/13, 13/8 | 5.187 |
| 14/11, 11/7 | 5.349 |
| 11/9, 18/11 | 6.878 |
| 6/5, 5/3 | 7.07 |
| 7/6, 12/7 | 7.415 |
| 15/13, 26/15 | 7.741 |
| 13/11, 22/13 | 7.933 |
| 9/8, 16/9 | 9.624 |
| 13/12, 24/13 | 9.999 |
| 10/9, 9/5 | 11.882 |
| 9/7, 14/9 | 12.227 |
| 18/13, 13/9 | 14.811 |