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Oak Blood Three

Joined 8 May 2019
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I'm mostly interested in just intonations (and things approximating them, and alterations of them to accommodate [[Wikipedia:inharmonicity|inharmonicity]]), but not exclusively.
I'm mostly interested in just intonations (and things approximating them, and alterations of them to accommodate [[Wikipedia:inharmonicity|inharmonicity]]), but not exclusively.


Here is a [[Well temperament]] I devised and [https://docs.google.com/spreadsheets/d/1_jBmq1HOHUjMxPgUsWaLLh8iIVhWlZs2muKwljPmUMc/copy the spreadsheet used to calculate it.]
In fact, here are some [[Well temperament|Well temperaments]] I devised and [https://docs.google.com/spreadsheets/d/1_jBmq1HOHUjMxPgUsWaLLh8iIVhWlZs2muKwljPmUMc/copy the spreadsheet used to calculate them.]
  <nowiki>! Cosine C Well.scl
 
  !
They are two related tunings from a family of 12-tone "almost-equal" temperaments, where fifths squeeze and stretch sinusoidally as you go around the circle.
  Kloba's Cosine Well C
 
  12
The first variation is symmetrical about D, with the narrowest fifths (696.05¢) at G–D and D-A and the widest fifths (703.95¢) at C♯–G♯ and G♯–D♯.  The amount of stretch is selected to make the major third from C–E just (5/4). This leaves the major third at F♯–A♯ very wide at 407.82¢ or 5.87¢ wider than Pythagorean.
  !
  ! Cosine D Well C-E Just.scl
  94.65884
  !
  196.61384
  Kloba's Cosine Well D-Centered
  298.56884
    12
  393.22768
  !
  500.52384
    89.21
  593.22768
    193.16
  698.56884
    297.11
  796.61384
    386.31
  894.65884
    501.06
  1000.00000
    586.31
  1092.70384
    697.11
  2/1</nowiki>
    793.16
    889.21
    1000.00
    1085.26
    2/1
 
The second variation is also symmetrical about D, with the amount of stretch selected to make the major third from F♯–A♯ Pythagorean (81/64). The narrowest fifths are 697.74¢ (at G–D and D-A) and the widest fifths are 702.26¢ (at C♯–G♯ and G♯–D♯). This leaves the major third from C–E a little wide at 392.18¢ or 5.87¢ wider than just.
! Cosine D Well F#-A# Pyth.scl
  !
  Kloba's Cosine Well D-Centered
    12
  !
    93.83
    196.09
    298.35
    392.18
    500.60
    592.18
    698.35
    796.09
    893.83
    1000.00
    1091.58
    2/1
[[/sandbox]]
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