N2D3P9: Difference between revisions

However, their approach was not able to consider ''all'' possible psychoacoustic reasons for a ratio's popularity. For example, <math>\text{N2D3P9}</math> does not evaluate whether some member of a 2,3-equivalence-class might be very close in pitch to some member of another 2,3-equivalence-class, such as <math>\frac{65}{64}</math> being very close to <math>\frac{1}{1}</math>.

From May to August 2020, a [http://forum.sagittal.org/viewtopic.php?f=4&t=493 collaborative effort] to find such a function, was carried out by members of the [http://forum.sagittal.org/ Sagittal forum], led by Sagittal co-creator [[Dave Keenan]] and [[Douglas Blumeyer]]. Many functions besides <math>\text{N2D3P9}</math> were considered before selecting it as the best function for its purpose.

After deciding upon <math>\text{N2D3P9}</math>, the Sagittal forum members checked the ratios for the existing Sagittal symbols against it, to see how well they'd been served by the Scala archive stats and the earlier <math>\text{sopfr}</math> metric. Each symbol in Sagittal's JI notations has a default value, or primary comma, which allows it to exactly notate ratios in a 2,3-equivalence-class, and based on <math>\text{N2D3P9}</math>, it was found that only a couple of these commas should be changed (these were among the rarest-used symbols in Sagittal). This was as expected; <math>\text{N2D3P9}</math> was developed primarily in order to add new accent marks to Sagittal, to enable it to exactly notate even rarer JI pitches than it already does.

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