User:Hkm/Sandbox: Difference between revisions
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{{Editable user page}} | {{Editable user page}} | ||
== | == Sadbox == | ||
=== | === Practicality === | ||
3 | 3 Wedgies | ||
5 | 5 TE | ||
5 | 5 Otonality and utonality (what are the musical implications?) | ||
2 | 2 Balanced word | ||
2 | 2 43ed2 | ||
3 | 3 31ed2 (beginner-friendliness) | ||
=== | === Writing === | ||
5 | 5 Intro to Xenharmonics (can be supplemented with user:hkm/Intro_page) | ||
4 | 4 Concordance | ||
2 | 2 29ed2 (needs a clearer focus on essentially tempered chords in the 2.3.7/5.11/5.13/5 subgroup, less focus on temperaments of 29edo, and less trivia) | ||
4 | 4 Periodicity block | ||
3 | 3 FAQ | ||
=== | === Criticality === | ||
1 | 1 Oodako | ||
1 | 1 Trug | ||
1 | 1 Oviminor | ||
2 A bunch of stub pages | 2 A bunch of stub pages | ||
=== | === Naming === | ||
1 | 1 1025/1024 | ||
=== | === Design === | ||
2 | 2 Ploidacot (why the number names?) | ||
=== | === Formatting === | ||
2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though) | 2 Practically all edo pages <50 (algorithmically generated material, like GPVs and sagittal notations, should be moved to the GPV and sagittal pages, for example. The interval table gets to stay though) | ||
== Badness == | == Badness == | ||
We say that is the score of a "step" is equal to 1/(min_cents + (the motion's error in cents)) * badness_penalty**(the complexity of the motion) / critical_divisor. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament is the critical_divisor necessary to get a score of 2. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) | We say that is the score of a "step" is equal to 1/(min_cents + (the motion's error in cents)) * badness_penalty**(the complexity of the motion) / critical_divisor. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament is the critical_divisor necessary to get a score of 2. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) |