FloraC

Name's Flora Canou (Fumica#5144).  

English & Chinese Mandarin;

Mostly microtonal theory currently.  

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] which has key signatures reordered into fifths for my own use.

I explored and documented the [[sensamagic dominant chord]]. I explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament proposal]].  

[https://github.com/FloraCanou/te_temperament_measures TE Tuning & Temperament Measures Calculator] – I made this Python script 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]]

== Well temperaments ==

I developed well temperaments on [[12edo|12et]] and [[17edo|17et]] which can be seen here. I also tried one on 19et but gave up for multiple reasons.  

* [[User:FloraC/Flora's_12-note_well_temperament|Flora's 12-note well temperament]]

* [[User:FloraC/Flora's_17-note_well_temperament|Flora's 17-note well temperament]]

Q: Why I gave up 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, while in 19et they represent the same ratios better or worse in different keys, and I'm not fond of that. Second, the harmonics of 3, 5, 7, and 13 in 19-et are all flat, so there's not much room to operate. Third, the ambiguity of 4\19 and 15\19 is nice and I want them ''ambiguous in every key''.

== Quick reference ==

 

I call equal temperaments in Tenney-Euclidean tuning "ette".

 

 

 

 

 

 

[math]t_2/v_2 = t_1/v_1[/math]

 

 

Let ''e'' be the [[TE error]] in Breed's RMS, and J be the [[JIP]], then

 

[math]e = ||T - J||_\text {RMS} = \sqrt {\frac {(t_1 - 1)^2 + (t_2 - 1)^2)}{2}}[/math]

 

 

[math]

[/math]

 

 

[math]t_1 = \frac{c + 1}{c^2 + 1} = \frac {v_1 (v_1 + v_2)}{v_1^2 + v_2^2}[/math]

 

and ''f'' (''x'') = sqrt (''x''/2) is a monotonously increasing function

 

 

 

e = \frac {|v_1 - v_2|}{\sqrt {2(v_1^2 + v_2^2)}}

 

This part is deduced from Paul Erlich's ''Middle Path''.

 

[math]

[/math]

This ''e'' is also the amount to stretch or compress each prime.  

This time we have a sequence c = {''c''_''n''}, where

[math]c_i = v_i/v_1, i = 1, 2, \ldots, n[/math]

[math]t_1 = \frac {\sum \vec c}{\vec c^\mathsf T \vec c} = \frac {v_1 \sum V}{VV^\mathsf T}[/math]

Substitute ''t''_''i''/''c''_''i'' for ''t''₁,

e = \sqrt {1 - \frac {(\sum V)^2}{n VV^\mathsf T}}

=== Notes ===

* For ets, TOP tuning and TE tuning are close but not identical.

[[Category:User en-3]]