4459/4455: Difference between revisions

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'''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[245/243]] and [[275/273]]. It factors into the superparticular ratio pairs ([[2080/2079]])([[2401/2400]]) or ([[1001/1000]])([[9801/9800]]). Tempering it out and adding the octave back in yields the rank-5 [[tristanismic]] temperament, which is supported by [[EDO|edos]] including {{EDOs | 9, 12, 22, 27, 41, 72, 130, 190, 198, 270, and 311}}.

'''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[245/243]] and [[275/273]], and between [[91/90]] and [[99/98]]. It factors into the superparticular ratio pairs ([[2080/2079]])([[2401/2400]]) or ([[1001/1000]])([[9801/9800]]).

== Etymology ==

This comma was named by [[User:Tristanbay|Tristan Bay]] in early May 2024 after himself.

== Temperaments ==

=== Tristanismic ===

Tempering out 4459/4455 in the full 13-limit leads to this rank-5 temperament.

[[Subgroup]]: 2.3.5.7.11.13

[[Comma list]]: 4459/4455

[[Mapping]]:

{{val| 1 0 0 0 0 0 }}

{{val| 0 1 0 0 0 4 }}

{{val| 0 0 1 0 0 1 }}

{{val| 0 0 0 1 0 -3 }}

[[Optimal tuning]] ([[CWE]]): 2, ~3 = 1902.065, ~5 = 2786.373, ~7 = 3368.568, ~11 = 4151.449

{{Optimal ET sequence|legend=1| 8d, 9, 12, 14cf, 17c, 19e, 22, 31f, 41, 58, 72, 118, 121, 130, 190, 198, 270, 581, 711, 981, 1171, 1441, 1752, 2022, 2463d, 2733d }}

[[Badness]] (Sintel): 0.963

[[Category:Tristanismic]]

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 }}
-'''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[245/243]] and [[275/273]]. It factors into the superparticular ratio pairs ([[2080/2079]])([[2401/2400]]) or ([[1001/1000]])([[9801/9800]]). Tempering it out and adding the octave back in yields the rank-5 [[tristanismic]] temperament, which is supported by [[EDO|edos]] including {{EDOs | 9, 12, 22, 27, 41, 72, 130, 190, 198, 270, and 311}}.
+'''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[245/243]] and [[275/273]], and between [[91/90]] and [[99/98]]. It factors into the superparticular ratio pairs ([[2080/2079]])([[2401/2400]]) or ([[1001/1000]])([[9801/9800]]).
 == Etymology ==
 This comma was named by [[User:Tristanbay|Tristan Bay]] in early May 2024 after himself.
+== Temperaments ==
+=== Tristanismic ===
+Tempering out 4459/4455 in the full 13-limit leads to this rank-5 temperament.
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: 4459/4455
+[[Mapping]]:<br>
+{{val| 1 0 0 0 0 0 }}<br>
+{{val| 0 1 0 0 0 4 }}<br>
+{{val| 0 0 1 0 0 1 }}<br>
+{{val| 0 0 0 1 0 -3 }}<br>
+{{val| 0 0 0 0 1 1 }}
+[[Optimal tuning]] ([[CWE]]): 2, ~3 = 1902.065, ~5 = 2786.373, ~7 = 3368.568, ~11 = 4151.449
+{{Optimal ET sequence|legend=1| 8d, 9, 12, 14cf, 17c, 19e, 22, 31f, 41, 58, 72, 118, 121, 130, 190, 198, 270, 581, 711, 981, 1171, 1441, 1752, 2022, 2463d, 2733d }}
+[[Badness]] (Sintel): 0.963
 [[Category:Tristanismic]]