Munit: Difference between revisions

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The interval of equivalence of a scale, corresponding directly to the framing interval of a munit, has some similar variation in use. For instance, the LLsLLLs scale is typically assumed to have an "octave" as the interval of equivalence, but it is quite common for this "octave" not to be a perfect 1200 cents, but rather stretched or compressed slightly (as is common with pianos, or also the [[TOP tuning]]). Similarly, when we talk about a munit like 4/3: LLs, we typically do not assume the 4/3 needs to be perfectly just; rather it could be tempered with the exact size of the tempered 4/3 varying somewhat.

Lastly, while this article is primarily focused on having a framing interval which has some rational interpretation, there is nothing preventing us from using other framing intervals based on anything, such as irrational tuning systems built on phi or e, etc. We may even take some liberties with the definition such that framing intervals are given as a range of sizes such as those based on[[Interval category|interval categories], so that we can say things like "M3: LsL" (where M3 is a generic "major third"-sized interval, perhaps somewhere in the 370-410 cent size range).

Lastly, while this article is primarily focused on having a framing interval which has some rational interpretation, there is nothing preventing us from using other framing intervals based on anything, such as irrational tuning systems built on phi or e, etc. We may even take some liberties with the definition such that framing intervals are given as a range of sizes such as those based on [[Interval category|interval categories]], so that we can say things like "M3: LsL" (where M3 is a generic "major third"-sized interval, perhaps somewhere in the 370-410 cent size range).

== Examples ==

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 The interval of equivalence of a scale, corresponding directly to the framing interval of a munit, has some similar variation in use. For instance, the LLsLLLs scale is typically assumed to have an "octave" as the interval of equivalence, but it is quite common for this "octave" not to be a perfect 1200 cents, but rather stretched or compressed slightly (as is common with pianos, or also the [[TOP tuning]]). Similarly, when we talk about a munit like 4/3: LLs, we typically do not assume the 4/3 needs to be perfectly just; rather it could be tempered with the exact size of the tempered 4/3 varying somewhat.
-Lastly, while this article is primarily focused on having a framing interval which has some rational interpretation, there is nothing preventing us from using other framing intervals based on anything, such as irrational tuning systems built on phi or e, etc. We may even take some liberties with the definition such that framing intervals are given as a range of sizes such as those based on[[Interval category|interval categories], so that we can say things like "M3: LsL" (where M3 is a generic "major third"-sized interval, perhaps somewhere in the 370-410 cent size range).
+Lastly, while this article is primarily focused on having a framing interval which has some rational interpretation, there is nothing preventing us from using other framing intervals based on anything, such as irrational tuning systems built on phi or e, etc. We may even take some liberties with the definition such that framing intervals are given as a range of sizes such as those based on [[Interval category|interval categories]], so that we can say things like "M3: LsL" (where M3 is a generic "major third"-sized interval, perhaps somewhere in the 370-410 cent size range).
 == Examples ==