Phoenix: Difference between revisions

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The '''phoenix''' tuning continuum ranges consists of a range of [[Equal-step Tuning|equally-tempered scales]] ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf|11edf]]). All of these scales stretch the [[octave]] by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered [[harmonic]]s are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.

The '''phoenix''' tuning continuum ranges consists of a range of [[Equal-step Tuning|equally-tempered scales]] ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts, see [[16ed9/5]]), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf|11edf]]). All of these scales stretch the [[octave]] by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered [[harmonic]]s are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.

[[Mason Green]] chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, "dies" at 24 and rises from the ashes again at 31 or 32.

Revision as of 04:13, 27 January 2024 view source BudjarnLambeth (talk \| contribs) autopatrolled, emailconfirmed 21,264 edits m Added links ← Older edit		Revision as of 01:02, 27 October 2024 view source BudjarnLambeth (talk \| contribs) autopatrolled, emailconfirmed 21,264 edits m Mention 16ed9/5 Newer edit →
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	The '''phoenix''' tuning continuum ranges consists of a range of [[Equal-step Tuning\|equally-tempered scales]] ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf\|11edf]]). All of these scales stretch the [[octave]] by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered [[harmonic]]s are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.		The '''phoenix''' tuning continuum ranges consists of a range of [[Equal-step Tuning\|equally-tempered scales]] ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts, see [[16ed9/5]]), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf\|11edf]]). All of these scales stretch the [[octave]] by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered [[harmonic]]s are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.

	[[Mason Green]] chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, "dies" at 24 and rises from the ashes again at 31 or 32.		[[Mason Green]] chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, "dies" at 24 and rises from the ashes again at 31 or 32.