User:R-4981/Pepsi: Difference between revisions

(2 intermediate revisions by one other user not shown)

Line 14:

== 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). ~~Ratio~~ 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.

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)9 = 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).

Note that [[3/2]], [[27/8]] and (3/2)9 = 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 32 * ~701.955{{cent}} = (3/2)9.)

{| class="wikitable"

|-

@@ Line 14: / Line 14: @@
 == 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). Ratio 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.
+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> = 19683/16384 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).
+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"
 |-