Würschmidt: Difference between revisions
Rework the infobox and interval table to reflect that 11 is natural |
→Tunings: tabulate minimax tuning |
||
| (One intermediate revision by the same user not shown) | |||
| Line 103: | Line 103: | ||
== Tunings == | == Tunings == | ||
=== | === Norm-based tunings === | ||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | | |+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | !! colspan="3" | Euclidean | ||
|- | |- | ||
! Constrained !! Destretched | ! Constrained !! Constrained & skewed !! Destretched | ||
|- | |- | ||
! Tenney | ! Tenney | ||
| | | CTE: ~5/4 = 387.734{{c}} || CWE: ~5/4 = 387.776{{c}} || POTE: ~5/4 = 387.7993{{c}} | ||
|- | |- | ||
! | ! Equilateral | ||
| | | CEE: ~5/4 = 387.7224{{c}}<br>(8/65-comma) || || | ||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit add-23 norm-based tunings | |||
|- | |- | ||
! | ! rowspan="2" | !! colspan="3" | Euclidean | ||
| | |- | ||
! Constrained !! Constrained & skewed !! Destretched | |||
|- | |- | ||
! Tenney | ! Tenney | ||
| | | CTE: ~5/4 = 387.734{{c}} || CWE: ~5/4 = 387.781{{c}} ||POTE: ~5/4 = 387.8051{{c}} | ||
| | |||
| | |||
|} | |} | ||
=== Target tunings === | |||
{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+ style="font-size: 105%; white-space: nowrap;" | [[Delta-rational chord|DR]] and equal-beating tunings | |+ style="font-size: 105%; white-space: nowrap;" | [[Delta-rational chord|DR]] and equal-beating tunings | ||
| Line 140: | Line 141: | ||
|- | |- | ||
| 15:18:23 (+3 +5) || ~5/4 = 387.9215 || 4''g''<sup>7</sup> − 3''g''<sup>5</sup> − 10 = 0 || | | 15:18:23 (+3 +5) || ~5/4 = 387.9215 || 4''g''<sup>7</sup> − 3''g''<sup>5</sup> − 10 = 0 || | ||
|} | |||
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Odd-limit-based target tunings | |||
! rowspan="2" | Target | |||
! colspan="2" | Minimax | |||
|- | |||
! Generator | |||
! Eigenmonzo* | |||
|- | |||
| 5-odd-limit | |||
| ~3/2 = 387.7444{{c}} | |||
| 3/2 | |||
|} | |} | ||
=== Tuning spectrum === | === Tuning spectrum === | ||
The below assumes the 2.3.5.11.23 subgroup extension. Note that "e" and "i" are the warts for primes 11 and 23, respectively. | The below assumes the 2.3.5.11.23-subgroup extension. Note that "e" and "i" are the warts for primes 11 and 23, respectively. | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
! Edo<br | ! Edo<br>generator | ||
! [[Eigenmonzo|Eigenmonzo<br | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged interval)]]* | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
|- | |- | ||
| Line 154: | Line 168: | ||
| | | | ||
| 385.7143 | | 385.7143 | ||
| 28ei val, major thirds slightly flatter than this fall under 25&28 or [[magic]] | | 28ei val, major thirds slightly flatter than this fall under 25 & 28 or [[magic]] | ||
|- | |- | ||
| | | | ||
| Line 249: | Line 263: | ||
| [[3/2]] | | [[3/2]] | ||
| 387.7444 | | 387.7444 | ||
| 1/8-comma | | 1/8-comma, 5-odd-limit minimax | ||
|- | |- | ||
| [[294edo|95\294]] | | [[294edo|95\294]] | ||
| Line 359: | Line 373: | ||
=== Other tunings === | === Other tunings === | ||
* [[DKW theory|DKW]] | * 5-limit [[DKW theory|DKW]]: ~5/4 = 387.8015{{c}} | ||
== Music == | == Music == | ||