Schismic: Difference between revisions
→Tunings: + a tuning spectrum |
+ more tunings and a link to a Scala file |
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== Notation == | == Notation == | ||
Using schismic can be a challenge because it defies the tradition of {{w|tertian harmony}} in [[chain-of-fifths notation]]. The just major triad on C is C–F♭–G, for example. To address that, an additional module of accidentals such as arrows to represent the comma step may be adopted, allowing the user to write the chord above as C–vE–G. | Using schismic can be a challenge because it defies the tradition of {{w|tertian harmony}} in [[chain-of-fifths notation]]. The just major triad on C is C–F♭–G, for example. To address that, an additional module of accidentals such as arrows to represent the comma step may be adopted, allowing the user to write the chord above as C–vE–G. | ||
== Scales == | |||
=== Scala files === | |||
* [[Clipper32805]] – in a 1–3–5 equal-beating tuning | |||
== Tunings == | == Tunings == | ||
=== Norm-based tunings === | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 701.7187{{c}} | |||
| CWE: ~3/2 = 701.7308{{c}} | |||
| POTE: ~3/2 = 701.7359{{c}} | |||
|} | |||
=== Target tunings === | === Target tunings === | ||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Delta-rational tunings | |||
|- | |||
! Optimized chord !! Generator value !! Polynomial !! Further notes | |||
|- | |||
| 3:4:5 (+1 +1) || ~3/2 = 701.6910{{c}} || ''g''<sup>9</sup> - 4''g''<sup>8</sup> + 64 = 0 || 1–3–5 equal-beating tuning | |||
|- | |||
| 4:5:6 (+1 +1) || ~3/2 = 701.7278{{c}} || ''g''<sup>9</sup> + ''g''<sup>8</sup> - 64 = 0 || 1–3–5 equal-beating tuning | |||
|} | |||
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed" | {| class="wikitable center-all left-5 mw-collapsible mw-collapsed" | ||
|+ style="white-space: nowrap;" | | |+ style="font-size: 105%; white-space: nowrap;" | Odd-limit-based target tunings | ||
! rowspan="2" | Target | ! rowspan="2" | Target | ||
! colspan="2" | Minimax | ! colspan="2" | Minimax | ||