Frequency temperament: Difference between revisions

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m FloraC moved page Arithmetic interval chain to User:CompactStar/Arithmetic interval chain without leaving a redirect: Not ready for the main namespace. See talk
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I am going to rework this page and add some of my more recent ideas so it can be moved into mainspace.
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'''Arithmetic interval chains''' are interval chains similar to [[regular temperament]]s. Whereas regular temperaments are created by reducing integer powers of a [[generator]], an arithmetic interval chain is created by reducing integer multiples of a generator. The n-th interval in an arithmetic interval chain prior to octave-reduction is given by n*g + 1, where g is the generator.


For example, this is an arithmetic interval chain with a generator of 0.29 and period [[2/1]]:
<pre>
1+0.29 = 1.29
1+2*0.29 = 1.58
1+3*0.29 = 1.87
1+4*0.29 = 2.16 -> 1.08
1+5*0.29 = 2.45 -> 1.225
1+6*0.29 = 2.74 -> 1.37
...
</pre>
== List of arithmetic interval chains ==
* [[Sqrttwo]]
* [[Neutrino]]
[[Category:Arithmetic interval chains]]

Revision as of 07:24, 19 May 2023

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