TAMNAMS: Difference between revisions

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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.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. ''Major'', ''minor'', ''perfect'', etc. would apply as established. The modifier ''neutral'' is used for intervals exactly halfway between major and minor k-steps in a given tuning. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.

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 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.
-Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
+Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. ''Major'', ''minor'', ''perfect'', etc. would apply as established. The modifier ''neutral'' is used for intervals exactly halfway between major and minor k-steps in a given tuning. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
 In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.