Xen concepts for beginners: Difference between revisions

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Xen discussion uses two kinds of units:

* ''Frequency ratios''

** The frequency is the absolute pitch of any given tone, usually measured in hertz (Hz). The ratio between frequencies is just a number. Equal intervals have the same frequency ratio.

** The [[frequency]] is the absolute pitch of any given tone, usually measured in [[hertz]] (Hz). The ratio between frequencies is just a number. Equal intervals have the same [[frequency ratio]].

* ''Logarithmic units'' such as cents and edo steps that treat intervals we hear as equal as the same additive unit

* ''Logarithmic units'' such as [[cents]] and [[edo]] steps that treat intervals we hear as equal as the same additive unit

To stack two intervals, we use different types of operations for the two kinds of units. To stack two intervals written as ratios, we *multiply*, whereas to stack two intervals written as cents or edo steps, we *add* the intuitive way. To "unstack" an interval from another interval, we *divide* the respective ratios and *subtract* logarithmic units. To convert between cents and ratios we use the following formulas:

@@ Line 3: / Line 3: @@
 Xen discussion uses two kinds of units:
 * ''Frequency ratios''
-** The frequency is the absolute pitch of any given tone, usually measured in hertz (Hz). The ratio between frequencies is just a number. Equal intervals have the same frequency ratio.
+** The [[frequency]] is the absolute pitch of any given tone, usually measured in [[hertz]] (Hz). The ratio between frequencies is just a number. Equal intervals have the same [[frequency ratio]].
-* ''Logarithmic units'' such as cents and edo steps that treat intervals we hear as equal as the same additive unit
+* ''Logarithmic units'' such as [[cents]] and [[edo]] steps that treat intervals we hear as equal as the same additive unit
 To stack two intervals, we use different types of operations for the two kinds of units.  To stack two intervals written as ratios, we *multiply*, whereas to stack two intervals written as cents or edo steps, we *add* the intuitive way. To "unstack" an interval from another interval, we *divide* the respective ratios and *subtract* logarithmic units. To convert between cents and ratios we use the following formulas: