MOS inflection: Difference between revisions

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If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.

A scale ~~constructed in this way lacks many useful structural properties of~~ a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.

A scale being a MODMOS guarantees a number of useful characteristics, most importantly [[epimorphism]]. A MOS inflection ''might'' sometimes have these properties, but it often doesn't. Compared to a MODMOS, it also typically preserves less of the 'character' of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.

== Types of MOS inflection ==

{{Idiosyncratic terms|The terms for the different kinds of MOS inflection, proposed by [[Budjarn Lambeth]]}}

It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.

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=== Robust MOS inflection ===

Robust MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.

Robust MOS inflection is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.

This will result in a scale which is a subset of some larger MOS scale with the same generator and period.

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=== Semirobust MOS inflection ===

Semirobust MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.

Semirobust MOS inflection is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.

For example, if you take this Negri[8] MOS:

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=== Frankenstein MOS inflection ===

Frankenstein MOS inflection~~{{idiosyncratic}}~~ is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).

Frankenstein MOS inflection is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).

For example, if you take this Negri[7] MOS in [[67edo]]:

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=== Aspirational MOS inflection ===

Aspirational MOS inflection~~{{idiosyncratic}}~~ is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.

Aspirational MOS inflection is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.

For example, if you take this Negri[7] MOS in 67edo:

@@ Line 9: / Line 9: @@
 If we take a MOS scale, and adjust one or more its notes up or down by some ''other'' consistent interval besides a chroma, we instead obtain an inflected MOS scale. This process is called '''MOS inflection'''.
-A scale constructed in this way lacks many useful structural properties of a MODMOS, most importantly [[epimorphism]]. Compared to a MODMOS, it also preserves less of the character of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.
+A scale being a MODMOS guarantees a number of useful characteristics, most importantly [[epimorphism]]. A MOS inflection ''might'' sometimes have these properties, but it often doesn't. Compared to a MODMOS, it also typically preserves less of the 'character' of the original MOS scale, which could be useful or detrimental depending on one’s goals in making the scale.
 == Types of MOS inflection ==
+{{Idiosyncratic terms|The terms for the different kinds of MOS inflection, proposed by [[Budjarn Lambeth]]}}
 It’s likely that many more types could be conceived of. Feel free to edit this page and add any which you find useful or interesting.
@@ Line 17: / Line 18: @@
 === Robust MOS inflection ===
-Robust MOS inflection{{idiosyncratic}} is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.
+Robust MOS inflection is where the interval of adjustment is one of the intervals which was already present within the original MOS scale.
 This will result in a scale which is a subset of some larger MOS scale with the same generator and period.
@@ Line 49: / Line 50: @@
 === Semirobust MOS inflection ===
-Semirobust MOS inflection{{idiosyncratic}} is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.
+Semirobust MOS inflection is where the interval of adjustment is an interval which was not already present within the original MOS scale, but which is present within a larger MOS of the same generator and period.
 For example, if you take this Negri[8] MOS:
@@ Line 79: / Line 80: @@
 === Frankenstein MOS inflection ===
-Frankenstein MOS inflection{{idiosyncratic}} is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).
+Frankenstein MOS inflection is where the interval of adjustment is the chroma of another MOS. This approach lends itself to situations where the two MOS scales are tuned using the same [[equal temperament]] (though that isn’t compulsory).
 For example, if you take this Negri[7] MOS in [[67edo]]:
@@ Line 105: / Line 106: @@
 === Aspirational MOS inflection ===
-Aspirational MOS inflection{{idiosyncratic}} is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.
+Aspirational MOS inflection is where one step of a MOS is adjusted by exactly the right amount to tune it to a pure [[JI]] ratio, relative to the [[tonic]]. Then any other step(s) may be adjusted by increments of the same amount that initial interval was modified by.
 For example, if you take this Negri[7] MOS in 67edo: