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, see [[16ed9/5]]), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf|11edf]]). All of these scales [[Stretched ~~octave~~|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 [[Stretched and compressed tuning|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.

== Etymology ==

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== Instruments ==

Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic~~. Pianos are good instruments for phoenix because they have stretched octaves already~~.

Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic.

== Intervals ==

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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, see [[16ed9/5]]), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf|11edf]]). All of these scales [[Stretched octave|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 [[Stretched and compressed tuning|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.
 == Etymology ==
@@ Line 39: / Line 39: @@
 == Instruments ==
-Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already.
+Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic.
 == Intervals ==