Xenharmonic Wiki

FloraC

Joined 30 March 2020
← Older edit
VisualWikitext
No edit summary
 
(29 intermediate revisions by the same user not shown)
Line 1: Line 1:
Name's Flora Canou (Fumica#5144). Age 22. 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]]. I explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament proposal]].
<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>


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
 
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]]
 
Misc. hemi-idiosyncratic stuff:
* 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]].
 
== Music ==
* [https://soundcloud.com/floracanou SoundCloud Profile]


== Tools ==
== Tools ==
[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.
* [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/Analysis on the 13-limit just intonation space|Analysis on the 13-Limit Just Intonation Space]]
* [[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 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/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 ==
I developed well temperaments on [[12edo|12et]] and [[17edo|17et]] which can be seen here.  
I developed well temperaments on [[12edo|12et]] and [[17edo|17et]] which can be seen here.  
* [[User:FloraC/Flora's_12-note_well_temperament|Flora's 12-note well temperament]]
* [[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]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]


I've also been trying to develop one on 19et but no satisfactory result as of now.  
I've also been trying to develop one on 19et but no satisfactory result as of now.  
Line 29: Line 56:
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''.  
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 possible solutions?  
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.
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.


== Quick reference ==
Q: It's possible to make octave stretched well temperaments?
I call equal temperaments in Tenney-Euclidean tuning "ette".
 
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]


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


=== Notes ===
== See also ==
* 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
* [[Flora Canou]]
: <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.


------
------
Line 125: Line 72:


[[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]]
Retrieved from "https://en.xen.wiki/w/User:FloraC"