Dubhe: Difference between revisions
My edits are well reasoned: no other temperament pages have negative steps or bold harmonics to the hundreds, so it's not me who's making unilateral changes. Table notes I have discussed on Discord. Tag: Undo |
make your changes if there is a consensus that supports you; until then there is no consensus. Tag: Undo |
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For technical data, see ''[[No-twos subgroup temperaments#Dubhe]]''. | For technical data, see ''[[No-twos subgroup temperaments#Dubhe]]''. | ||
== Interval | == Interval chains == | ||
In the below, tritave-reduced harmonics | In the below, tritave-reduced harmonics below 243 are indicated in '''bold'''. All ratios are considered to be in the 287-[[odd limit#Nonoctave equaves|throdd limit]]. | ||
<div><div style="display: inline-grid; margin-right: 25px;"> | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|+ style="font-size: 105%;" | Dubhe | |||
|- | |- | ||
! # !! Cents | ! rowspan="2" | # !! rowspan="2" | Cents* !! colspan="1" | Approximate Ratios | ||
|- | |- | ||
| 0 || 0.0 || '''1/1''' | ! 3.5.7.17 subgroup | ||
|- | |||
| -12 || 1160.5 || 49/25, 243/125 | |||
|- | |||
| -11 || 1380.8 || 189/85 | |||
|- | |||
| -10 || 1601.1 || 63/25 | |||
|- | |||
| -9 || 1821.4 || 49/17, 243/85, 357/125 | |||
|- | |||
| -8 || 139.7 || 27/25, 49/45 | |||
|- | |||
| -7 || 360.0 || 21/17, 153/125 | |||
|- | |||
| -6 || 580.3 || 7/5, 243/175 | |||
|- | |||
| -5 || 800.6 || 27/17, 119/75, 245/153 | |||
|- | |||
| -4 || 1020.8 || 9/5, '''49/27''' | |||
|- | |||
| -3 || 1241.1 || 35/17, 51/25, 243/119 | |||
|- | |||
| -2 || 1461.4 || '''7/3''', 81/35 | |||
|- | |||
| -1 || 1681.7 || 45/17, 119/45, 459/175 | |||
|- | |||
| 0 || 0.0 || '''1/1''', 245/243 | |||
|- | |- | ||
| 1 || 220.3 || 17/15, 135/119, 175/153 | | 1 || 220.3 || 17/15, 135/119, 175/153 | ||
|- | |- | ||
| 2 || 440.6 || | | 2 || 440.6 || 9/7, '''35/27''' | ||
|- | |- | ||
| 3 || 660.9 || 25/17, 51/35, 119/81 | | 3 || 660.9 || 25/17, 51/35, '''119/81''' | ||
|- | |- | ||
| 4 || 881.1 || '''5/3''', 81/49 | | 4 || 881.1 || '''5/3''', 81/49 | ||
| Line 22: | Line 50: | ||
| 5 || 1101.4 || '''17/9''', 225/119, 459/245 | | 5 || 1101.4 || '''17/9''', 225/119, 459/245 | ||
|- | |- | ||
| 6 || 1321.7 || 15/7, 175/81 | | 6 || 1321.7 || 15/7, '''175/81''' | ||
|- | |- | ||
| 7 || 1542.0 || 17/7, 125/51 | | 7 || 1542.0 || 17/7, 125/51 | ||
|- | |- | ||
| 8 || 1762.2 || 25/9, 135/49 | | 8 || 1762.2 || '''25/9''', 135/49 | ||
|- | |- | ||
| 9 || 80.5 || 51/49, 85/81, 125/119 | | 9 || 80.5 || 51/49, '''85/81''', 125/119 | ||
|- | |- | ||
| 10 || 300.8 || 25/21 | | 10 || 300.8 || 25/21 | ||
| Line 34: | Line 62: | ||
| 11 || 521.1 || 85/63 | | 11 || 521.1 || 85/63 | ||
|- | |- | ||
| 12 || 741.4 || 75/49, 125/81 | | 12 || 741.4 || 75/49, '''125/81''' | ||
|- | |- | ||
| 13 || 961.7 || 85/49 | | 13 || 961.7 || 85/49 | ||
|- | |- | ||
| 14 || 1181.9 || 125/63 | | 14 || 1181.9 || 125/63 | ||
{{table notes|cols=4 | |||
| In 3.5.7-targeted [[DKW theory|DKW]] tuning for [[BPS]] | |||
}} | |||
|} | |} | ||
</div> | |||
== Tuning spectrum == | == Tuning spectrum == | ||