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

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== Sandboxed rewrite: Naming mos intervals and mos degrees ==

Mos intervals are denoted as a ''quantity'' of mossteps, large or small. An interval that is k mossteps wide is referred to as a ''k-mosstep interval'', or simply ''k-mosstep''. The terms mosoctave and mosunison may be used interchangeably to denote an n-mosstep (where n is the number of tones in the mos) and 0-mosstep respectively.

The prefix of mos- in the terms mosstep, mosunison, and mosoctave may be replace for the mos's prefix, which can be found in the section for mos names below.

This produces the ''generic'' interval classes for a mos, intervals that lack the designation of major, minor, perfect, etc. The following section shows how to find the sizes of these interval classes, and thereby label them as major, minor, or perfect.

=== Rationale for 0-indexed names ===

~~wip~~

Note that a mosunison is a 0-mosstep, rather than a 1st. One might be tempted to generalize diatonic 1-indexed ordinal names: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''

The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

~~There are two types of~~ mos intervals~~: generic~~ mos ~~intervals represent the number of steps that span an interval~~, ~~regardless of the size of those steps~~. ~~Specific mos intervals account for the size~~ of ~~those steps~~, ~~and requires~~ an ~~additional label, such as major or minor. The following section shows how to find and name specific intervals~~.

To overcome this, TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals. Instead of having the mosunison be a mos-1st, it is a 0-mossteps. With our previous example of stacking two fifths to erroneously make a tenth, we now have two 4-mossteps that stack together to make an 8-mosstep.

=== Finding and naming specific mos intervals ===

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 == Sandboxed rewrite: Naming mos intervals and mos degrees ==
+Mos intervals are denoted as a ''quantity'' of mossteps, large or small. An interval that is k mossteps wide is referred to as a ''k-mosstep interval'', or simply ''k-mosstep''. The terms mosoctave and mosunison may be used interchangeably to denote an n-mosstep (where n is the number of tones in the mos) and 0-mosstep respectively.
+The prefix of mos- in the terms mosstep, mosunison, and mosoctave may be replace for the mos's prefix, which can be found in the section for mos names below.
+This produces the ''generic'' interval classes for a mos, intervals that lack the designation of major, minor, perfect, etc. The following section shows how to find the sizes of these interval classes, and thereby label them as major, minor, or perfect.
 === Rationale for 0-indexed names ===
-wip
+Note that a mosunison is a 0-mosstep, rather than a 1st. One might be tempted to generalize diatonic 1-indexed ordinal names: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''
+The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.
-There are two types of mos intervals: generic mos intervals represent the number of steps that span an interval, regardless of the size of those steps. Specific mos intervals account for the size of those steps, and requires an additional label, such as major or minor. The following section shows how to find and name specific intervals.
+To overcome this, TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals. Instead of having the mosunison be a mos-1st, it is a 0-mossteps. With our previous example of stacking two fifths to erroneously make a tenth, we now have two 4-mossteps that stack together to make an 8-mosstep.
 === Finding and naming specific mos intervals ===