Calculation formula of pythagorean tuning

The calculation formula of Pythagorean tuning, comprising a generation system, the generation system comprises an input module, a processing and calculation module and an output module, and the processing and calculation module comprises an exponent calculation unit during upward process, a exponent calculation unit during downward process and a frequency value calculation unit, its specific steps are as follows:

• step 1:
• inputting, by the input module, a frequency f0 and the number N of downward tones and the number M of upward tones to be calculated, wherein the frequency f0 is used as the frequency of the starting tone of the tuning;
• step 2:
• obtaining a sequence G by the exponent calculation unit during upward process:
• calculating M values according to an exponent calculation formula gi=└i×log23┘, 1≤i≤M to obtain an exponent sequence G;
• step 3:
• obtaining a sequence G by the exponent calculation unit during downward process:
• calculating N values according to an exponent calculation formula gj′=└j×log23┘+1,1≤j≤N to obtain an exponent sequence G′;
• step 4:
• obtaining, by the frequency value calculation unit, frequency values of the tones needed to be calculated:
• calculating the frequency values of the upward M tones according to a calculation formula to
• f
• i
• =
• f
• 0
• ⨯
• 3
• i
• 2
• g
• i
• ,
• 1
• ≤
• i
• ≤
• M
• to obtain a sequence F of the upward M frequency values;
• and calculating frequency values of the downward N tones according to a calculation formula
• f
• j
• ′
• =
• f
• 0
• ⨯
• 2
• g
• j
• ′
• 3
• j
• ,
• 1
• ≤
• j
• ≤
• N
• to obtain a sequence F′ of the upward N frequency values;
• and
• step 5:
• outputting the tone sequences F and F′by the output module.