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FloraC

Joined 30 March 2020
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Name's Flora Canou (Fumica#5144). Age 23. I speak English & Chinese Mandarin. I currently work on mostly microtonal theories especially RTT.  
Flora Canou / Fumica (Discord ID: fumica).  


I contributed to the [https://github.com/euwbah/musescore-n-tet-plugins n-EDO Retuner plugin for MuseScore] and made a [https://github.com/FloraCanou/musescore-n-tet-plugins fork] with key signatures re-ordered into fifths for my own use.  
I speak English and native Mandarin.  


I explored and documented the [[sensamagic dominant chord]] and the [[hemimage bleeding chord]], based on [[Flora's analysis on septimal voice leading|my understanding of septimal voice leading]].
<small>I don't speak conversational Japanese, except for some basic words and how to read kanas and kanjis, so I can read Japanese pages to some degree, but not much beyond that. Please stick to English (or Mandarin if you will) should you wish to have a convo with me. </small>
 
I explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament proposal]].


Long term projects:  
Long term projects:  
* Cleanup for all temperament pages
* Review, maintain and improve temperament pages
* Rework scale trees for mos pages
* Review, maintain and improve the scale trees for mos pages


== Music ==
Important articles of RTT I created:
* [https://soundcloud.com/floracanou Me on SoundCloud]
* [[Optimization]] – an introduction
* [[Constrained tuning]]
* [[Patent val/Properties]]
* [[2.3-equivalent class and Pythagorean-commatic interval naming system]]
* [[Functional harmony in rank-2 temperaments]]


=== Microtonal/xenharmonic releases ===
Misc. hemi-idiosyncratic stuff:
* ''[[Undevicesimal Fugues]]'' (2020)
* Contributed to the [https://github.com/euwbah/musescore-microtonal-edo-plugin Microtonal plugin for MuseScore] and made a [https://github.com/FloraCanou/musescore-n-tet-plugins fork] with key signatures re-ordered into fifths for her own use.
* Explored and documented the [[sensamagic dominant chord]] and the [[hemimage bleeding chord]], based on [[Flora's analysis on septimal voice leading|her understanding of septimal voice leading]].
* Explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament name proposal]].


=== 12et releases ===
== Music ==
* ''Avant l'Avenir'' (2020–2022)
* [https://soundcloud.com/floracanou SoundCloud Profile]
* ''Favonius'' (2018–2020)
* ''Eruption in Silence'' (2016–2018)


== Tools ==
== Tools ==
[https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] – I made this set of Python scripts to compute [[TE tuning]]s, [[badness]]es, [[optimal patent val]]s, etc.
* [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] – Python scripts to compute [[TE tuning]]s, [[badness]]es, [[optimal patent val]]s, etc.
* [https://github.com/FloraCanou/launchpad-tuner Launchpad Tuner] – Python  scripts to tune Novation Launchpads.
 
== Selected writings ==
As part of the essay collection ''Notes of the Generation''.  


== Writings ==
* [[User:FloraC/Critique on Functional Just System|Critique on Functional Just System]]
* [[User:FloraC/Fundamental principles to musical sense|Fundamental Principles to Musical Sense]]
* [[User:FloraC/Fundamental principles to musical sense|Fundamental Principles to Musical Sense]]
* [[User:FloraC/There is not a third side of the river|There Is Not a Third Side of the River]]
* [[User:FloraC/There is not a third side of the river|There Is Not a Third Side of the River]]
* [[User:FloraC/Proposed standard ear-training waveform|Proposed Standard Ear-Training Waveform]]
* [[User:FloraC/Proposed standard ear-training waveform|Proposed Standard Ear-Training Waveform]]
* [[User:FloraC/Analysis on the 13-limit just intonation space|Analysis on the 13-Limit Just Intonation Space]]
* [[User:FloraC/On the canon of music|On the Canon of Music]]
* [[User:FloraC/Analysis on the 13-limit just intonation space: episode i|Analysis on the 13-Limit Just Intonation Space: Episode I]]
* [[User:FloraC/Analysis on the 13-limit just intonation space: episode ii|Analysis on the 13-Limit Just Intonation Space: Episode II]]
* [[User:FloraC/Fokker analysis of rank-3 scales|Fokker Analysis of Rank-3 Scales]]
* [[User:FloraC/Fokker analysis of rank-3 scales|Fokker Analysis of Rank-3 Scales]]
* [[User:FloraC/Hard problems of harmony and psychoacoustically supported optimization|Hard Problems of Harmony and Psychoacoustically Supported Optimization]]
Others
* [[User:FloraC/Critique on Functional Just System|Critique on Functional Just System]]
* <s>[[User:FloraC/Critique on D&D's terminology|Critique on D&D's Terminology]]</s>
* [[User:FloraC/Fumica's edo impressions|Fumica's edo impressions]]


== Well temperaments ==
== Well temperaments ==
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A: Yes it's possible. Just one more argument than pure-octave. Issue is I haven't got a satisfactory result.  
A: Yes it's possible. Just one more argument than pure-octave. Issue is I haven't got a satisfactory result.  


== Quick reference ==
== See also ==
I call equal temperaments in Tenney-Euclidean tuning "ette".
* [[Flora Canou]]
 
3-limit TE tuning, which is my preferred tuning for most ets, is "ette3".
 
Some super easy formulae for such a tuning follows.
 
=== 3-limit TE tuning of ets ===
{{Databox|Detail|
 
Given a val A, we have Tenney-weighted val V &#61; AW, where W is the Tenney-weighting matrix.
 
If T is the Tenney-weighted tuning map, then for any et, for obvious reasons,
 
[math]t_2/v_2 &#61; t_1/v_1[/math]
 
Let ''c'' be the coefficient of TE-weighted tuning map ''c'' &#61; ''t''<sub>2</sub>/''t''<sub>1</sub> &#61; ''v''<sub>2</sub>/''v''<sub>1</sub>
 
Let ''e'' be the [[TE error]] in Breed's RMS, and J be the [[JIP]], then
 
[math]e &#61; {{!}}{{!}}T - J{{!}}{{!}}_\text {RMS} &#61; \sqrt {\frac {(t_1 - 1)^2 + (t_2 - 1)^2)}{2} }[/math]
 
Since
 
[math]
(t_1 - 1)^2 + (t_2 - 1)^2 \\
&#61; t_1^2 - 2t_1 + 1 + c^2 t_1^2 - 2c t_1 + 1 \\
&#61; (c^2 + 1)t_1^2 - 2(c + 1)t_1 + 2
[/math]
 
has minimum at
 
[math]t_1 &#61; \frac{c + 1}{c^2 + 1} &#61; \frac {v_1 (v_1 + v_2)}{v_1^2 + v_2^2}[/math]
 
and ''f'' (''x'') &#61; sqrt (''x''/2) is a monotonously increasing function
 
''e'' has the same minimum point.
 
Now substitute ''t''<sub>2</sub>/''c'' for ''t''<sub>1</sub>,
 
[math]
t_i &#61; \frac {v_i (v_1 + v_2)}{v_1^2 + v_2^2}, i &#61; 1, 2 \\
e &#61; \frac { {{!}}v_1 - v_2{{!}} }{\sqrt {2(v_1^2 + v_2^2)} }
[/math]
 
}}
 
=== 3-limit TOP tuning of ets ===
{{Databox|Detail|
 
This part is deduced from Paul Erlich's ''Middle Path''.
 
[math]
t_i &#61; \frac {2v_i}{v_1 + v_2}, i &#61; 1, 2 \\
e &#61; \frac { {{!}}v_1 - v_2{{!}} }{v_1 + v_2}
[/math]
 
This ''e'' is also the amount to stretch or compress each prime.
 
}}
 
=== General TE tuning of ets ===
{{Databox|Detail|
 
This time we have a sequence c &#61; {''c''<sub>''n''</sub>}, where
 
[math]c_i &#61; v_i/v_1, i &#61; 1, 2, \ldots, n[/math]
 
And just proceed as before,
 
[math]t_1 &#61; \frac {\sum \vec c}{\vec c^\mathsf T \vec c} &#61; \frac {v_1 \sum V}{VV^\mathsf T}[/math]
 
Substitute ''t''<sub>''i''</sub>/''c''<sub>''i''</sub> for ''t''<sub>1</sub>,
 
[math]
t_i &#61; \frac {v_i \sum V}{VV^\mathsf T}, i &#61; 1, 2, \ldots, n \\
e &#61; \sqrt {1 - \frac {(\sum V)^2}{n VV^\mathsf T} }
[/math]
 
}}
 
=== Notes ===
* For the nullity-1 temperament tempering out {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> … ''m''<sub>''n''</sub> }}, each prime ''q<sub>i</sub>'' is tuned to
: <math>-\operatorname {sgn} (m_i) \log_2 (q_i) \frac {\sum_j m_j \log_2 (q_j)}{\sum_j \vert m_j \vert \log_2 (q_j)}</math>
* Even for ets, TOP and TE tuning are not identical, but close.
* The relative interval error space of equal temperaments in TOP tuning seems to be linear.


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[[Category:User zh-N]]
[[Category:User zh-N]]
[[Category:User en-3]]
[[Category:User en-4]]
[[Category:User on Discord]]
[[Category:User on Discord]]
[[Category:User on SoundCloud]]
[[Category:User on SoundCloud]]
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