User:Godtone: Difference between revisions

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=== Simple ratios and where I think limits should be drawn ===

== [[User:Godtone/Bird's eye view of temperaments by accuracy|Bird's eye view of temperaments by accuracy]] (W.I.P) ==

If you want to contribute make sure the temperaments make sure to follow the format, such as specifying the exact note count needed for a set of odds separately from the smallest MOS scale that has at least or more than that number of notes. The focus is on practically-useful temperaments of general interest. Many temperaments have not yet been documented there. It's supposed to be a compilation of "cream of the crop" basically, sorted by accuracy so that you can determine your own accuracy-to-simplicity tradeoff that is best for you, but note many higher-accuracy temperaments there are simple ''despite'' being accurate, so I recommend looking at the note counts and set of targetted odds for higher-accuracy stuff first.

== Simple ratios and where I think limits should be drawn ==

This is maybe the obvious place to start. I listen to a variety of dyads in order to judge and try to absorb their qualities and to figure out if and why I like them. My opinions of intervals have changed over time. Anyway, as all positive rationals are ratios of positive naturals (nonzero everyday numbers), I think superparticular intervals are a good place to start. I think the melodic Just Noticeable Difference is important here so that intervals have a reasonable chance at being singable, even if the harmonic JND is significantly lower (partly depending on timbre). For me a reasonable upper limit on the melodic JND is about 11 cents as more than that and I hear something as pretty definitively mistuned, although that doesn't necessarily imply unusabibility as an approximation in a low-complexity system (one with a small amount of average tones per octave). This means that in the series of superparticular intervals (of the form (n+1)/n), the first two that are too close in size to be comfortably distinguished are 14/13 and 13/12, whose difference is 169/168 or about 10.274c.

I also think that powers of 2 in the denominator of an interval, broadly/generally speaking, helps the interval feel less disorienting due to a stronger suggestion of the fundamental, so beyond 13/12, for a bit, the superparticulars of the form (2n+1)/(2n) should be prioritised. This concludes at the following superparticular intervals being of particular (no pun intended) importance to a 'general melodic semi-harmonic system':<br/>

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-=== Simple ratios and where I think limits should be drawn ===
+== [[User:Godtone/Bird's eye view of temperaments by accuracy|Bird's eye view of temperaments by accuracy]] (W.I.P) ==
+If you want to contribute make sure the temperaments make sure to follow the format, such as specifying the exact note count needed for a set of odds separately from the smallest MOS scale that has at least or more than that number of notes. The focus is on practically-useful temperaments of general interest. Many temperaments have not yet been documented there. It's supposed to be a compilation of "cream of the crop" basically, sorted by accuracy so that you can determine your own accuracy-to-simplicity tradeoff that is best for you, but note many higher-accuracy temperaments there are simple ''despite'' being accurate, so I recommend looking at the note counts and set of targetted odds for higher-accuracy stuff first.
+== Simple ratios and where I think limits should be drawn ==
 This is maybe the obvious place to start. I listen to a variety of dyads in order to judge and try to absorb their qualities and to figure out if and why I like them. My opinions of intervals have changed over time. Anyway, as all positive rationals are ratios of positive naturals (nonzero everyday numbers), I think superparticular intervals are a good place to start. I think the melodic Just Noticeable Difference is important here so that intervals have a reasonable chance at being singable, even if the harmonic JND is significantly lower (partly depending on timbre). For me a reasonable upper limit on the melodic JND is about 11 cents as more than that and I hear something as pretty definitively mistuned, although that doesn't necessarily imply unusabibility as an approximation in a low-complexity system (one with a small amount of average tones per octave). This means that in the series of superparticular intervals (of the form (n+1)/n), the first two that are too close in size to be comfortably distinguished are 14/13 and 13/12, whose difference is 169/168 or about 10.274c.
 I also think that powers of 2 in the denominator of an interval, broadly/generally speaking, helps the interval feel less disorienting due to a stronger suggestion of the fundamental, so beyond 13/12, for a bit, the superparticulars of the form (2n+1)/(2n) should be prioritised. This concludes at the following superparticular intervals being of particular (no pun intended) importance to a 'general melodic semi-harmonic system':<br/>