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Name's Flora Canou (Fumica#5144). Age 23. I speak English & Chinese Mandarin.  
Flora Canou / Fumica (Discord ID: fumica).  


> trained to classical music and interested in expanding common practice harmony thru RTT.  
I speak English and native Mandarin.  


> 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.
<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>


> 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]].
Long term projects:
* Review, maintain and improve temperament pages
* Review, maintain and improve the scale trees for mos pages


> explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament proposal]].  
Important articles of RTT I created:
* [[Optimization]] – an introduction
* [[Constrained tuning]]
* [[Patent val/Properties]]
* [[2.3-equivalent class and Pythagorean-commatic interval naming system]]
* [[Functional harmony in rank-2 temperaments]]


Long term projects:  
Misc. hemi-idiosyncratic stuff:  
* Maintain all temperament pages
* 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.
* Rework scale trees for mos pages
* 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]].


== Music ==
== Music ==
* [https://soundcloud.com/floracanou Me on SoundCloud]
* [https://soundcloud.com/floracanou SoundCloud Profile]


=== Microtonal/xenharmonic releases ===
== Tools ==
* ''[[Undevicesimal Fugues]]'' (2020)
* [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.


=== 12et releases ===
== Selected writings ==
* ''Avant l'Avenir'' (2020–2022)
As part of the essay collection ''Notes of the Generation''.  
* ''Favonius'' (2018–2020)
* ''Eruption in Silence'' (2016–2018)
 
== 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.


== 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/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 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/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]]

Latest revision as of 15:21, 13 April 2025

Flora Canou / Fumica (Discord ID: fumica).

I speak English and native Mandarin.

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.

Long term projects:

  • Review, maintain and improve temperament pages
  • Review, maintain and improve the scale trees for mos pages

Important articles of RTT I created:

Misc. hemi-idiosyncratic stuff:

Music

Tools

Selected writings

As part of the essay collection Notes of the Generation.

Others

Well temperaments

I developed well temperaments on 12et and 17et which can be seen here.

I've also been trying to develop one on 19et but no satisfactory result as of now.

Q: What are the difficulties in developing a 19wt?

A: First, unlike 12- and 17et with ambiguous major and minor thirds, 19et's thirds are close enough to 5-limit JI that interpreting them otherwise is like a force. In 12- and 17et, those intervals can represent different ratios in different keys, whereas in 19et, they represent the same ratios better or worse in different keys. The effect isn't satisfactory. Second, the harmonics of 3, 5, 7, and 13 in 19et are all flat, so there's not much room to operate. Third, the ambiguity of 4\19 and 15\19 is an important characteritics, and those should be ambiguous in every key.

Q: What are the solutions?

A: For 19et to have any room to operate, octave stretch must be employed. For 4\19 and 15\19 not deviating too much, hemitwelfth is used as a generator.

Q: It's possible to make octave stretched well temperaments?

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

See also

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