Munit: Difference between revisions

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A '''munit'''{{idiosyncratic}} (pronounced myoo-nit) is the combination of a musical interval, called a '''framing interval''', and a pattern of musical intervals (typically represented in relative step sizes) subdividing that interval. An example munit would be "4/3: LLs," sometimes called the "major tetrachord."

In short, munits are fragments of musical scales, intended in some sense to generalize [[tetrachord~~|tetrachords~~]]. They are both ~~useful~~ as a method of building scales from smaller chunks, and also as a way to analyze our expectations, harmonic or otherwise, regarding how intervals are subdivided differently into step-size patterns in different tuning systems.

In short, munits are fragments of musical scales, intended in some sense to generalize [[tetrachord]]s, jins in [[maqam]], etc. They are useful both as a method of building scales from smaller chunks, and also as a way to analyze our expectations, harmonic or otherwise, regarding how intervals are subdivided differently into step-size patterns in different tuning systems.

The concept of [[~~jins~~]] in ~~[[maqam]] very closely parallels the concept of munit~~.

The concept of munit was proposed by [[Mike Battaglia]] in 2011.

== Interpretation and usefulness ==

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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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* 7/6: LL

* 11/9: LLs

* 9/7: LLL

* 14/11: LLL

* 4/3: LLsL

* 3/2: LLsLLs

So right off the bat we have some very interesting stuff! In the POTE tuning, our large step is 138.674 cents and our small step is 76.427 cents. So we have to learn that, again, 9/8 is not one step, but that there is a passing tone in between. Similarly, we must learn that 7/6 is subdivided into two large steps, and that 11/9 is subdivided into two ~~large and one small step. Perhaps strangely, if we are used to superpyth, 9/7 is now subdivided into three equal parts rather than two, and 4/3 into three~~ large and one small step. 3/2 is now a type of "seventh" rather than a "fifth", and so on. Learning to internalize these munits is an important part of forming the correct expectations regarding what harmonic properties to expect upon hearing a certain pattern of scale steps.

So right off the bat we have some very interesting stuff! In the POTE tuning, our large step is 138.674 cents and our small step is 76.427 cents. So we have to learn that, again, 9/8 is not one step, but that there is a passing tone in between. Similarly, we must learn that 7/6 is subdivided into two large steps, and that 11/9 is subdivided into two large and one small step. 3/2 is now a type of "seventh" rather than a "fifth", and so on. Learning to internalize these munits is an important part of forming the correct expectations regarding what harmonic properties to expect upon hearing a certain pattern of scale steps.

=== Neutral[7] ===

@@ Line 1: / Line 1: @@
 A '''munit'''{{idiosyncratic}} (pronounced myoo-nit) is the combination of a musical interval, called a '''framing interval''', and a pattern of musical intervals (typically represented in relative step sizes) subdividing that interval. An example munit would be "4/3: LLs," sometimes called the "major tetrachord."
-In short, munits are fragments of musical scales, intended in some sense to generalize [[tetrachord|tetrachords]]. They are both useful as a method of building scales from smaller chunks, and also as a way to analyze our expectations, harmonic or otherwise, regarding how intervals are subdivided differently into step-size patterns in different tuning systems.
+In short, munits are fragments of musical scales, intended in some sense to generalize [[tetrachord]]s, jins in [[maqam]], etc. They are useful both as a method of building scales from smaller chunks, and also as a way to analyze our expectations, harmonic or otherwise, regarding how intervals are subdivided differently into step-size patterns in different tuning systems.
-The concept of [[jins]] in [[maqam]] very closely parallels the concept of munit.
+The concept of munit was proposed by [[Mike Battaglia]] in 2011.
 == Interpretation and usefulness ==
@@ Line 29: / Line 29: @@
 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 ==
@@ Line 91: / Line 91: @@
 * 7/6: LL
 * 11/9: LLs
-* 9/7: LLL
+* 14/11: LLL
 * 4/3: LLsL
 * 3/2: LLsLLs
-So right off the bat we have some very interesting stuff! In the POTE tuning, our large step is 138.674 cents and our small step is 76.427 cents. So we have to learn that, again, 9/8 is not one step, but that there is a passing tone in between. Similarly, we must learn that 7/6 is subdivided into two large steps, and that 11/9 is subdivided into two large and one small step. Perhaps strangely, if we are used to superpyth, 9/7 is now subdivided into three equal parts rather than two, and 4/3 into three large and one small step. 3/2 is now a type of "seventh" rather than a "fifth", and so on. Learning to internalize these munits is an important part of forming the correct expectations regarding what harmonic properties to expect upon hearing a certain pattern of scale steps.
+So right off the bat we have some very interesting stuff! In the POTE tuning, our large step is 138.674 cents and our small step is 76.427 cents. So we have to learn that, again, 9/8 is not one step, but that there is a passing tone in between. Similarly, we must learn that 7/6 is subdivided into two large steps, and that 11/9 is subdivided into two large and one small step. 3/2 is now a type of "seventh" rather than a "fifth", and so on. Learning to internalize these munits is an important part of forming the correct expectations regarding what harmonic properties to expect upon hearing a certain pattern of scale steps.
 === Neutral[7] ===