Father–3 equivalence continuum/Godtone's approach: Difference between revisions
the father-3 continuum is so bad that i didnt realise it was supposed to be equivalent to this continuum until now. i propose replacing it with this continuum and reworking the temperaments from there into here, but if that isnt acceptable i still believe this continuum should be documented and named as such |
m add two missing exotemperaments and add a high-accuracy temperaments section (neither mutt nor the 3&118 temperament is covered in the original page) |
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| Line 18: | Line 18: | ||
! Ratio | ! Ratio | ||
! Monzo | ! Monzo | ||
|- | |||
| -2 | |||
| [[Smate]] (14 & 17c) | |||
| [[2048/1875]] | |||
| {{monzo| 11 -1 -4 }} | |||
|- | |||
| -1 | |||
| [[Father]] (5 & 8) | |||
| [[16/15]] | |||
| {{monzo| 4 -1 -1 }} | |||
|- | |- | ||
| 0 | | 0 | ||
| Line 70: | Line 80: | ||
! Monzo | ! Monzo | ||
|- | |- | ||
| -1/2 | |||
| [[Very low accuracy temperaments#Yo (2c&3)|Yo]] | |||
| [[10/9]] | |||
| {{monzo| 1 -2 1 }} | |||
|- | |- | ||
| 1/2 | | 1/2 | ||
| Line 91: | Line 105: | ||
| {{ monzo| 55 2 -25 }} | | {{ monzo| 55 2 -25 }} | ||
|} | |} | ||
If we approximate the [[JIP]] with increasing accuracy, (that is, using ''n'' a rational that is an increasingly good approximation of 1.72125...) we find these high-accuracy temperaments: | |||
{| class="wikitable center-1" | |||
|+ style="font-size: 105%;" | Microtemperaments with fractional ''n'' | |||
|- | |||
! rowspan="2" | ''n'' | |||
! rowspan="2" | Temperament | |||
! colspan="2" | Comma | |||
|- | |||
! Ratio | |||
! Monzo | |||
|- | |||
| 5/3 | |||
| [[Mutt]] (84 & 87) | |||
| [[mutt comma]] | |||
| {{ monzo| -44 -3 21 }} | |||
|- | |||
| 7/4 | |||
| 3 & 118 | |||
| (42 digits) | |||
| {{ monzo| 61 4 -29 }} | |||
|} | |||
The simplest of these is [[mutt]] and has interesting properties discussed there. | |||