User:FloraC: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Project done
No edit summary
 
(30 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


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


== Writings ==
Misc. hemi-idiosyncratic stuff:
* [[User:FloraC/Critique on Functional Just System|Critique on Functional Just System]]
* 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.
* [[User:FloraC/Fundamental principles to musical sense|Fundamental Principles to Musical Sense]]
* 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]].
* [[User:FloraC/There is not a third side of the river|There Is Not a Third Side of the River]]
* Explored the [[canou family]] of temperaments, and a few others in [[User:FloraC/Temperament name proposal]].
* [[User:FloraC/Analysis on the 13-limit just intonation space|Analysis on the 13-Limit Just Intonation Space]]


== Well temperaments ==
== Music ==
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.
* [https://soundcloud.com/floracanou SoundCloud Profile]


* [[User:FloraC/Flora's_12-note_well_temperament|Flora's 12-note well temperament]]
== Tools ==
* [[User:FloraC/Flora's_17-note_well_temperament|Flora's 17-note well temperament]]
* [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.


Q: Why I gave up developing a 19wt
== Selected writings ==
As part of the essay collection ''Notes of the Generation''.


<s>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''. </s>
* [[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/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]]


I'll pick it up soon.
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]]


== Quick reference ==
== Well temperaments ==
I call equal temperaments in Tenney-Euclidean tuning "ette".
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]]
3-limit TE tuning, which is my preferred tuning for most ets, is "ette3".
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]
 
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
I've also been trying to develop one on 19et but no satisfactory result as of now.


[math]c_i &#61; v_i/v_1, i &#61; 1, 2, \ldots, n[/math]
Q: What are the difficulties in developing a 19wt?


And just proceed as before,  
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''.


[math]t_1 &#61; \frac {\sum \vec c}{\vec c^\mathsf T \vec c} &#61; \frac {v_1 \sum V}{VV^\mathsf T}[/math]
Q: What are the solutions?


Substitute ''t''<sub>''i''</sub>/''c''<sub>''i''</sub> for ''t''<sub>1</sub>,  
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.


[math]
Q: It's possible to make octave stretched well temperaments?
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 122: 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]]

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

Retrieved from "https://en.xen.wiki/index.php?title=User:FloraC&oldid=191942"