User:Contribution/Chanofreq Project: Difference between revisions

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== WARNING! ==

'''WARNING!''' The Chanofreq project has been replaced by the [[User:Contribution/Chanopif Project|Chanopif project]]!

== Chanofreq Project ==

'''Objective:''' The Chanofreq project seeks to create a standardized file format that allows precise tuning of each note on every MIDI channel to a specific frequency. The aim is to achieve this using a minimalistic data structure that prioritizes efficiency and simplicity.

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'''Answer:'''

* It should be fine to use 64-bit float, as long as no rounding is applied, we stay within the human hearing range, and the number of notes remains reasonable. For example, if [[~~16808edo~~]] is programmed from a base frequency (20 Hz) and a factor (~~3FF0002B3E4564C5~~) with exponents to map the entire multi-channel keyboard, after 10 octaves (20480 Hz), one phase error occurs every 15 days between two adjacent 64-bit float factor values.

* It should be fine to use 64-bit float, as long as no rounding is applied, we stay within the human hearing range, and the number of notes remains reasonable. For example, if [[125000edo|125,000-EDO]] is programmed from a base frequency (20 Hz) and a factor (1.000005545192819) with exponents to map the entire multi-channel keyboard, after 10 octaves (20480 Hz), one phase error occurs every 2.04 days between two adjacent 64-bit float factor values. For the [[402653184edo|402,653,184-EDO]] tuning scheme within chanofreq using factor and exponents, the phase precision between 64-bit float steps is only 78.9 seconds: 1/(440*(2**(-69/12))*1.0000000017214499**(402653184*(32/3)) - 440*(2**(-69/12))*1.0000000017214496**(402653184*(32/3))) = 78.9 seconds.

In comparison, the phase precision between 32-bit steps in 402,653,184-EDO is 12.86 hours, as calculated here: 1/(440*2**((127-69)/12)*2**(1/402653184)-440*2**((127-69)/12))/(60*60) = 12.86 hours.

This shows that even with 64-bit floating-point precision, the factor and exponent solution is far less efficient than other tuning methods, but remains practical for moderately sized musical scales up to approximately [[125000edo|125,000-EDO]], a size that still ensure a precision equivalent to 6 decimal places rounding in cents. However, using Mode B or C as a mediator for [[402653184edo|32-bit MIDI tuning]] should be avoided.

'''Open Questions:'''

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+== WARNING! ==
+'''WARNING!''' The Chanofreq project has been replaced by the [[User:Contribution/Chanopif Project|Chanopif project]]!
 == Chanofreq Project ==
 '''Objective:''' The Chanofreq project seeks to create a standardized file format that allows precise tuning of each note on every MIDI channel to a specific frequency. The aim is to achieve this using a minimalistic data structure that prioritizes efficiency and simplicity.
@@ Line 56: / Line 59: @@
 '''Answer:'''
-* It should be fine to use 64-bit float, as long as no rounding is applied, we stay within the human hearing range, and the number of notes remains reasonable. For example, if [[16808edo]] is programmed from a base frequency (20 Hz) and a factor (3FF0002B3E4564C5) with exponents to map the entire multi-channel keyboard, after 10 octaves (20480 Hz), one phase error occurs every 15 days between two adjacent 64-bit float factor values.
+* It should be fine to use 64-bit float, as long as no rounding is applied, we stay within the human hearing range, and the number of notes remains reasonable. For example, if [[125000edo|125,000-EDO]] is programmed from a base frequency (20 Hz) and a factor (1.000005545192819) with exponents to map the entire multi-channel keyboard, after 10 octaves (20480 Hz), one phase error occurs every 2.04 days between two adjacent 64-bit float factor values. For the [[402653184edo|402,653,184-EDO]] tuning scheme within chanofreq using factor and exponents, the phase precision between 64-bit float steps is only 78.9 seconds: 1/(440*(2**(-69/12))*1.0000000017214499**(402653184*(32/3)) - 440*(2**(-69/12))*1.0000000017214496**(402653184*(32/3))) = 78.9 seconds.
+In comparison, the phase precision between 32-bit steps in 402,653,184-EDO is 12.86 hours, as calculated here: 1/(440*2**((127-69)/12)*2**(1/402653184)-440*2**((127-69)/12))/(60*60) = 12.86 hours.
+This shows that even with 64-bit floating-point precision, the factor and exponent solution is far less efficient than other tuning methods, but remains practical for moderately sized musical scales up to approximately [[125000edo|125,000-EDO]], a size that still ensure a precision equivalent to 6 decimal places rounding in cents. However, using Mode B or C as a mediator for [[402653184edo|32-bit MIDI tuning]] should be avoided.
 '''Open Questions:'''