User:FloraC

From Xenharmonic Wiki
Jump to navigation Jump to search

Name's Flora Canou.

English & Chinese Mandarin;

Mostly microtonal theory currently.

I contributed to the n-EDO Retuner plugin for MuseScore and made a fork which has key signatures reordered into fifths for my own use.

I found this chord – Canovian chord.

I found this temperament – Canou family.

Tools

TE Tuning & Temperament Measures Calculator – how I find all the TE tunings, badnesses, optimal patent vals, etc.

Writings

Well temperaments

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

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

To quickly obtain TOP tuning

  • For any temperament tempering out [m1 m2mn, each prime pi is tuned to log2 (pi)(Σi = 1n mi log2 (pi))/(Σi = 1n |mi| log2 (pi)) (in 8ves).
  • For ets, 3-limit TOP tuning and TE tuning are identical (needs further study in higher limits).
  • For any et tempering out [n m, stretch the octave by δ = (m log23 + n)/(|m| log23 + |n|) to obtain 3-limit TOP/TE tuning (which is my preferred tuning for most ets).