TAMNAMS: Difference between revisions
→Naming specific mos intervals: perfect is period-specific not octave-specific so it seems confusing to un-generalise and then generalise later without explaining that both are actually the same simple rule, also clarified further what is meant by "both generators have two sizes each". furthermore, the term "mosoctave" is very confusing fundamentally (think "mosnonave", etc.) so using "octave" is preferred thus "unison" is used for consistency. |
m →Reasoning for 0-indexed intervals: consistency: mosunison -> unison |
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This section's running example will be 3L 4s. | This section's running example will be 3L 4s. | ||
===Reasoning for 0-indexed intervals === | ===Reasoning for 0-indexed intervals === | ||
Note that a | Note that a unison is a 0-mosstep, rather than a mos1st; likewise, the term 1-mosstep is used rather than a mos2nd. 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. | ||
To overcome this, TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals, which makes the arithmetic needed to understand mos intervals much smoother. Going up a 0-mosstep means to go up zero steps, and stacking two 4-mossteps produces an 8-mosstep, rather than stacking two mos5ths to produce a mos9th. The use of ordinal indexing is generally discouraged when referring to non-diatonic mos intervals. | To overcome this, TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals, which makes the arithmetic needed to understand mos intervals much smoother. Going up a 0-mosstep means to go up zero steps, and stacking two 4-mossteps produces an 8-mosstep, rather than stacking two mos5ths to produce a mos9th. The use of ordinal indexing is generally discouraged when referring to non-diatonic mos intervals. | ||
The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories. | The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories. | ||
===Naming specific mos intervals=== | ===Naming specific mos intervals=== | ||
The phrase ''k-mosstep'' by itself does not specify the exact size of an interval. To refer to specific intervals, the familiar modifiers of ''major'', ''minor'', ''augmented'',''diminished'' and ''perfect'' are used. As mosses are [[Distributional evenness|distributionally even]], every interval (except for the [[1/1|unison]] and [[2/1|octave]]) will be in no more than two sizes. | The phrase ''k-mosstep'' by itself does not specify the exact size of an interval. To refer to specific intervals, the familiar modifiers of ''major'', ''minor'', ''augmented'',''diminished'' and ''perfect'' are used. As mosses are [[Distributional evenness|distributionally even]], every interval (except for the [[1/1|unison]] and [[2/1|octave]]) will be in no more than two sizes. | ||