User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions

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Intervals that are more than x+y mossteps above the root share the same designation as the same mosstep that is octave-reduced. Given our example of 3L 4s, if there is a 10-mosstep, it is the same designation (in this case, either major or minor) as a 3-mosstep. Octave-reduction on a general k-mosstep can be done by finding the remainder of k divided by (x+y).

Additional consideration is needed for multi-period mosses. ~~If the mos is a multi-period mos~~, there will be at least one additional interval only seen as one size rather than two. These intervals occur every period and such intervals, specific to multi-period mosses, are referred to as perfect. This is to say that multiples of the period are perfect, just like multiples of the mosoctave are perfect. Generators of a multi-period mos that are raised or lowered by some amount of periods are also perfect, just like generators raised or lowered by multiples of a mosoctave are perfect. If, however, the mos is of the form nL ns, the generators use the labels of major and minor, rather than augmented, perfect, and diminished. The reason for this exception is to prevent ambiguity over every interval being referred to as perfect.

Additional consideration is needed for multi-period mosses. In this case, there will be at least one additional interval only seen as one size rather than two. These intervals occur every period and such intervals, specific to multi-period mosses, are referred to as perfect. This is to say that multiples of the period are perfect, just like multiples of the mosoctave are perfect. Generators of a multi-period mos that are raised or lowered by some amount of periods are also perfect, just like generators raised or lowered by multiples of a mosoctave are perfect. If, however, the mos is of the form nL ns, the generators use the labels of major and minor, rather than augmented, perfect, and diminished. The reason for this exception is to prevent ambiguity over every interval being referred to as perfect.

In summary, bright generators are either a perfect k-mosstep or diminished k-mosstep, dark generators are either an augmented k-mosstep or a perfect k-mosstep, and all other intervals that are not the mosunison, mosoctave, or an integer multiple of the period ~~(for multi~~-~~period mosses)~~ are either major or minor k-mossteps. If the mos is nL ns, then the generators are either major or minor instead, and all other intervals are perfect. If context allows, "k-mosstep" may be shortened to "k-step", and to refer to generic intervals, the modifiers of major/minor or augmented/perfect/diminished are omitted.

In summary, bright generators are either a perfect k-mosstep or diminished k-mosstep, dark generators are either an augmented k-mosstep or a perfect k-mosstep, and all other intervals that are not the mosunison, mosoctave, or an integer multiple of the period if applicable - all of which are perfect - are either major or minor k-mossteps. If the mos is nL ns, then the generators are either major or minor instead, and all other intervals are perfect. If context allows, "k-mosstep" may be shortened to "k-step", and to refer to generic intervals, the modifiers of major/minor or augmented/perfect/diminished are omitted.

==== Naming mos degrees ====

Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.

==== Naming ~~intervals and degrees raised~~ by a chroma ====

==== Naming alterations by a chroma ====

Mos intervals are altered by raising or lowering it by a moschroma, the difference between a large step and a small step. This process is exactly like using sharps and flats in standard notation. Raising and lowering a major k-mosstep by a chroma produces an augmented and minor k-mosstep respectively, and raising and lowering a minor k-mosstep by a chroma produces a major and diminished k-mosstep respectively. The same applies with raising a perfect mos interval (such as mosunison, mosoctave, or generator) by a chroma to make it augmented, and lowering a perfect mos interval by a chroma to make it diminished. This process of raising and lowering by a chroma can be repeated multiple times; after an augmented and diminished mos interval is a doubly-augmented and doubly-diminished mos interval, and after that a triply-augmented and triply-diminished mos interval. These additional labels also apply to mosdegrees.

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==== Naming intervals smaller than a chroma ====

~~A type~~ of ~~interval that is sometimes used is~~ the diesis~~, which is the absolute difference between~~ a ~~large step and two small steps. In our running example~~ of 3L 4s, we have a major 1-mosstep, equivalent to a large mosstep. Lowering a major 1-mosstep by a chroma produces a a minor 1-mosstep, and lowering again produces a diminished 1-mosstep, which is equivalent to a mosdiesis. Depending on the ~~step ratio, the diminished 1-mosdegree will either be higher, if soft-of-basic~~, ~~or lower, if hard~~-~~of-basic, than the tonic by a mosdiesis. If the step ratio is basic, then the size of the mosdiesis is 0.~~

* Mosdiesis (a generalization of the diesis as commonly found in meantone theories): |L - 2s|

* Moskleisma (a generalization of the kleisma, also found in meantone theories): |L - 3s|

=== Reasoning for names ===

@@ Line 70: / Line 70: @@
 Intervals that are more than x+y mossteps above the root share the same designation as the same mosstep that is octave-reduced. Given our example of 3L 4s, if there is a 10-mosstep, it is the same designation (in this case, either major or minor) as a 3-mosstep. Octave-reduction on a general k-mosstep can be done by finding the remainder of k divided by (x+y).
-Additional consideration is needed for multi-period mosses. If the mos is a multi-period mos, there will be at least one additional interval only seen as one size rather than two. These intervals occur every period and such intervals, specific to multi-period mosses, are referred to as perfect. This is to say that multiples of the period are perfect, just like multiples of the mosoctave are perfect. Generators of a multi-period mos that are raised or lowered by some amount of periods are also perfect, just like generators raised or lowered by multiples of a mosoctave are perfect. If, however, the mos is of the form nL ns, the generators use the labels of major and minor, rather than augmented, perfect, and diminished. The reason for this exception is to prevent ambiguity over every interval being referred to as perfect.
+Additional consideration is needed for multi-period mosses. In this case, there will be at least one additional interval only seen as one size rather than two. These intervals occur every period and such intervals, specific to multi-period mosses, are referred to as perfect. This is to say that multiples of the period are perfect, just like multiples of the mosoctave are perfect. Generators of a multi-period mos that are raised or lowered by some amount of periods are also perfect, just like generators raised or lowered by multiples of a mosoctave are perfect. If, however, the mos is of the form nL ns, the generators use the labels of major and minor, rather than augmented, perfect, and diminished. The reason for this exception is to prevent ambiguity over every interval being referred to as perfect.
-In summary, bright generators are either a perfect k-mosstep or diminished k-mosstep, dark generators are either an augmented k-mosstep or a perfect k-mosstep, and all other intervals that are not the mosunison, mosoctave, or an integer multiple of the period (for multi-period mosses) are either major or minor k-mossteps. If the mos is nL ns, then the generators are either major or minor instead, and all other intervals are perfect. If context allows, "k-mosstep" may be shortened to "k-step", and to refer to generic intervals, the modifiers of major/minor or augmented/perfect/diminished are omitted.
+In summary, bright generators are either a perfect k-mosstep or diminished k-mosstep, dark generators are either an augmented k-mosstep or a perfect k-mosstep, and all other intervals that are not the mosunison, mosoctave, or an integer multiple of the period if applicable - all of which are perfect - are either major or minor k-mossteps. If the mos is nL ns, then the generators are either major or minor instead, and all other intervals are perfect. If context allows, "k-mosstep" may be shortened to "k-step", and to refer to generic intervals, the modifiers of major/minor or augmented/perfect/diminished are omitted.
 ==== Naming mos degrees ====
 Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.
-==== Naming intervals and degrees raised by a chroma ====
+==== Naming alterations by a chroma ====
 Mos intervals are altered by raising or lowering it by a moschroma, the difference between a large step and a small step. This process is exactly like using sharps and flats in standard notation. Raising and lowering a major k-mosstep by a chroma produces an augmented and minor k-mosstep respectively, and raising and lowering a minor k-mosstep by a chroma produces a major and diminished k-mosstep respectively. The same applies with raising a perfect mos interval (such as mosunison, mosoctave, or generator) by a chroma to make it augmented, and lowering a perfect mos interval by a chroma to make it diminished. This process of raising and lowering by a chroma can be repeated multiple times; after an augmented and diminished mos interval is a doubly-augmented and doubly-diminished mos interval, and after that a triply-augmented and triply-diminished mos interval. These additional labels also apply to mosdegrees.
@@ Line 173: / Line 173: @@
 ==== Naming intervals smaller than a chroma ====
-A type of interval that is sometimes used is the diesis, which is the absolute difference between a large step and two small steps. In our running example of 3L 4s, we have a major 1-mosstep, equivalent to a large mosstep. Lowering a major 1-mosstep by a chroma produces a a minor 1-mosstep, and lowering again produces a diminished 1-mosstep, which is equivalent to a mosdiesis. Depending on the step ratio, the diminished 1-mosdegree will either be higher, if soft-of-basic, or lower, if hard-of-basic, than the tonic by a mosdiesis. If the step ratio is basic, then the size of the mosdiesis is 0.
+* Mosdiesis (a generalization of the diesis as commonly found in meantone theories): |L - 2s|
+* Moskleisma (a generalization of the kleisma, also found in meantone theories): |L - 3s|
 === Reasoning for names ===