49edo: Difference between revisions
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| {{UDnote|step=49}} | | {{UDnote|step=49}} | ||
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<nowiki>* | <nowiki />* Based on 49edo's 11-limit patent val {{val| 49 78 114 138 170 }} mapping | ||
== Notation == | == Notation == | ||
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|- | |- | ||
| ϕ | | ϕ | ||
| | | −0.437 | ||
| 34 | | 34 | ||
|- | |- | ||
| ϕ<sup>ϕ<sup>-1</sup></sup> | | ϕ<sup>ϕ<sup>-1</sup></sup> | ||
| | | −0.592 | ||
| 21 | | 21 | ||
|} | |} | ||
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=== Music === | === Music === | ||
* [https://www.youtube.com/watch?v=vZyAm-D3nlk&ab_channel=Sevish Sevish - Star Nursery] uses a scale based on [[acoustic phi]] and ϕ<sup>ϕ<sup> | * [https://www.youtube.com/watch?v=vZyAm-D3nlk&ab_channel=Sevish Sevish - Star Nursery] uses a scale based on [[acoustic phi]] and ϕ<sup>ϕ<sup>−1</sup></sup>. 49edo provides a suitable approximation for this scale with the mode: 5 3 5 5 3 5 3 5 | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve Sstretch (¢) | ! rowspan="2" | Optimal<br />8ve Sstretch (¢) | ||
! colspan="2" | Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all right-3 left-5" | {| class="wikitable center-all right-3 left-5" | ||
|+ Rank-2 temperaments by generators | |+ style="font-size: 105%;" | Rank-2 temperaments by generators | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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|- | |- | ||
| rowspan="2" | 7 | | rowspan="2" | 7 | ||
| rowspan="2" | 20\49<br>(1\49) | | rowspan="2" | 20\49<br />(1\49) | ||
| rowspan="2" | 489.8<br>(24.5) | | rowspan="2" | 489.8<br />(24.5) | ||
| 4/3<br>(250/243) | | 4/3<br />(250/243) | ||
| [[Sevond]] (49) | | [[Sevond]] (49) | ||
|- | |- | ||
| 4/3<br>(25/24) | | 4/3<br />(25/24) | ||
| style="text-align: left" | [[Seville]] (49c) | | style="text-align: left" | [[Seville]] (49c) | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||
== Scales == | == Scales == | ||