User:R-4981/Pepsi: Difference between revisions
→Interval chain: per request of the designer of the scale, to add more interpretations and to fix implausible ones, and to fix the page generally |
m Lériendil moved page Pepsi to User:R-4981/Pepsi: seems niche enough |
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== Interval chain == | == Interval chain == | ||
In this table, the intervals are [[octave-reduced]]. It is up to the user whether they want to use this reduced version of the scale as an octave-repeating scale, or whether they want to use the non-octave version of this scale (in which case one must keep in mind that the octave-reductions shown are only to help simplify analysis). | In this table, the intervals are [[octave-reduced]]. It is up to the user whether they want to use this reduced version of the scale as an octave-repeating scale, or whether they want to use the non-octave version of this scale (in which case one must keep in mind that the octave-reductions shown are only to help simplify analysis). Ratios given in the below rows are approximated by the corresponding pitch of the tuning (or are exact in the few cases without a tilde ('''~''')). The ratios are shown in order of size, so that the most plausible interpretations tend to be near the middle, while alternative interpretations that may harmonize better in various contexts are shown above and below. | ||
Note that [[3/2]], [[27/8]] and (3/2)<sup>9</sup> = 19683/512 (which when octave-reduced is [[19683/16384]]) are tuned perfectly, hence the otherwise-surprising inclusion of the last ratio (although for practically all purposes it is more useful to think of it as an approximation of 6/5). (This is because 3<sup>2</sup> * ~701.955{{cent}} = (3/2)<sup>9</sup>.) | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 38: | Line 40: | ||
|- | |- | ||
| [[3/2]] | | [[3/2]] | ||
| | | [[100/99]] | ||
| | | [[76/45]] | ||
| | | [[36/35]] | ||
| | | [[6/5]] | ||
| | | [[12/11]] | ||
| | | [[45/26]] | ||
| | | [[9/7]] | ||
| | | [[13/10]] | ||
| | | [[21/20]] | ||
| | | [[10/9]] | ||
| | | [[15/13]] | ||
| | | [[15/11]] | ||
| | | [[49/32]] | ||
| | | [[56/45]] | ||
| | | [[25/14]] | ||
| | | [[25/13]] | ||
| | | [[64/45]] | ||
|- | |- | ||
| [[3/2]] | | [[3/2]] | ||
| | | [[105/104]] | ||
| [[27/16]] | | [[27/16]] | ||
| | | [[39/38]] | ||
| | | [[6/5]] | ||
| | | [[38/35]] | ||
| | | [[26/15]] | ||
| | | [[32/25]] | ||
| | | [[43/33]] | ||
| | | [[43/41]] | ||
| | | [[31/28]] | ||
| | | [[38/33]] | ||
| | | [[19/14]] | ||
| | | [[55/36]] | ||
| | | [[41/33]] | ||
| | | [[57/32]] | ||
| | | [[48/25]] | ||
| | | [[27/19]] | ||
| ... | | ... | ||
|- | |- | ||
| [[3/2]] | | [[3/2]] | ||
| | | [[121/120]] | ||
| | | [[32/19]] | ||
| | | [[40/39]] | ||
| [[19683/16384]] | | [[19683/16384]] | ||
| | | [[13/12]] | ||
| | | [[19/11]] | ||
| | | [[14/11]] | ||
| | | [[56/43]] | ||
| | | [[22/21]] | ||
| | | [[21/19]] | ||
| | | [[38/33]] | ||
| | | [[35/26]] | ||
| | | [[50/33]] | ||
| | | [[31/25]] | ||
| | | [[16/9]] | ||
| | | [[21/11]] | ||
| | | [[78/55]] | ||
| ... | | ... | ||
|} | |} | ||
[[Category:Tuning]] | [[Category:Tuning]] | ||