Taylor-53CS, a 13-limit JI well-temperament: introduction and demo

Описание: I designed this tuning last week, along with a couple of other JI CSs which act like well-temperaments or circulating irregular detempered equal temperaments. This tuning basically acts like a laser-tuned 53-equal, with almost all of the obvious intervals focused into actual JI (as opposed to just being a few cents out). It seems to be just about the perfect tuning for a whole bunch of music, containing all of the standard pythagorean and classic intonations as well as slightly more far out JI ratios from many world musics up through the 13 prime-limit.

53-equal does the 13-prime limit incredibly well, but in my mind doesn't really nail most ratios involving prime 11, and prime 7 is also noticeably slightly mistuned. This is the hyper-focused one, and I love the interval variety it provides (hoping one day I can remember the interval sizes in more than just a couple of keys!). Of course, it contains only 53 tones from the potentially infinite 13-limit lattice, but I think they're some of the best to provide a solid listening foundation in JI. I hope to use this tuning in future to demonstrate JI textures and movements.

The tuning, from C (1/1):
1/1 81/80 33/32 28/27 256/243 16/15 13/12 12/11 10/9 9/8 8/7 15/13 7/6 32/27 6/5 39/32 16/13 5/4 81/64 9/7 13/10 21/16 4/3 27/20 11/8 18/13 45/32 64/45 13/9 16/11 40/27 3/2 32/21 20/13 14/9 128/81 8/5 13/8 64/39 5/3 27/16 12/7 26/15 7/4 16/9 9/5 11/6 24/13 15/8 243/128 27/14 64/33 160/81 2/1

or, if you're a fan of cents
0.000000 21.506290 53.272943 62.960904 90.224996 111.731285 138.572661 150.637059 182.403712 203.910002 231.174094 247.741053 266.870906 294.134997 315.641287 342.482663 359.472338 386.313714 407.820003 435.084095 454.213948 470.780907 498.044999 519.551289 551.317942 563.382340 590.223716 609.776284 636.617660 648.682058 680.448711 701.955001 729.219093 745.786052 764.915905 792.179997 813.686286 840.527662 857.517337 884.358713 905.865003 933.129094 952.258947 968.825906 996.089998 1017.596288 1049.362941 1061.427339 1088.268715 1109.775004 1137.039096 1146.727057 1178.493710 1200.000000


Pedantic notes: I didn't prepare anything to play or say, so a couple of times I forget a ratio or confuse myself with the position in the chain of fifths, although I almost always correct myself. I forgot to introduce a couple of notes in the light purple row: 16/11 "G" and 12/11 "D". I think I probably went through everything else.

Speaking of "purple", I should have been consistent with my other rainbow layout videos and called the outside rows "violet" instead of "purple", but hopefully most of this makes sense. The colours are just mapped straight as they would be with 53EDO, and I did think about making a custom coloured mapping for this, but it proved way too complex and hard to see what was really going on.

The instrument is the Lumatone keyboard, and I'm running a slightly modified MKI Organish 2 patch on Pianoteq 6.

The intro music is a recording I did on a piano patch the other day in the same tuning.


My book "Microtonality in 55 keys", a guide to intervals, scales, chords on generalised keyboards and how to use them in a wide range of microtonal tunings, is available on my website here (follow the PayPal link)
https://cametaylor.wixsite.com/home/p...

Get in touch if you want to organise lessons on keyboards, audiation, microtonality, or just want to learn more about music in general:
Here on YouTube @camtaylormusic
via email at [email protected]
my website https://cametaylor.wixsite.com/home
Facebook   / camtaylorpianolessons  


Listen to more of my music on
Archive https://archive.org/details/@iamcamta...
SoundCloud   / camtaylor-1  
  / cam-taylor-2-1  
More to come soon.