User:Overthink/Dicot–kleismic equivalence continuum - Revision history

Overthink: table for fractional n

2026-04-20T22:06:31Z

table for fractional n

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 [[:Category:4edo]]
 [[:Category:Equivalence continua]]

Overthink: {{Editable user page}}

2026-04-20T19:40:08Z

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	The '''dicot–kleismic equivalence continuum''' is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] which equate a number of [[25/24\|classical chromatic semitones (25/24)]] with the [[9/8\|Pythagorean major second (9/8)]]. As such, it can also be called the '''dicot–antitonic equivalence continuum'''.		The '''dicot–kleismic equivalence continuum''' is a [[equivalence continuum\|continuum]] of [[5-limit]] [[regular temperament\|temperaments]] which equate a number of [[25/24\|classical chromatic semitones (25/24)]] with the [[9/8\|Pythagorean major second (9/8)]]. As such, it can also be called the '''dicot–antitonic equivalence continuum'''.

Overthink: start draft

2026-04-20T19:39:10Z

start draft

New page

The '''dicot–kleismic equivalence continuum''' is a [[equivalence continuum|continuum]] of [[5-limit]] [[regular temperament|temperaments]] which equate a number of [[25/24|classical chromatic semitones (25/24)]] with the [[9/8|Pythagorean major second (9/8)]]. As such, it can also be called the '''dicot–antitonic equivalence continuum'''.

All temperaments in the continuum satisfy {{nowrap|(25/24)<sup>''n''</sup> ~ 9/8}}. Varying ''n'' results in different temperaments listed in the table below. It converges to [[dicot]] as ''n'' approaches infinity. If we allow non-integer and infinite ''n'', the continuum describes the set of all [[5-limit]] temperaments supported by [[4edo]] due to it being the unique equal temperament that tempers both commas and thus tempers all combinations of them. The just value of ''n'' is approximately 2.8853…, and temperaments having ''n'' near this value tend to be the most accurate ones.

{| class="wikitable center-1"
|+ style="font-size: 105%;" | Temperaments with integer ''n''
|-
! rowspan="2" | ''n''
! rowspan="2" | Temperament
! colspan="2" | Comma
|-
! Ratio
! Monzo
|-
| 0
| [[Very low accuracy temperaments #Antitonic|Antitonic]]
| [[9/8]]
| {{Monzo| -3 2 }}
|-
| 1
| [[Bug|Bug]]
| [[27/25]]
| {{Monzo| 0 3 -2 }}
|-
| 2
| [[Diminished (temperament)|Diminished]]
| [[648/625]]
| {{Monzo| 3 4 -4 }}
|-
| 3
| [[Kleismic]]
| [[15625/15552]]
| {{Monzo| -6 -5 6 }}
|-
| 4
| [[Miscellaneous 5-limit temperaments #Doublewide|Doublewide]]
| [[390625/373248]]
| {{Monzo| -9 -6 8 }}
|-
| …
| …
| …
| …
|-
| ∞
| [[Dicot]]
| [[25/24]]
| {{Monzo| -3 -1 2 }}
|}

'''''Todo:Add fractional n (Myna, etc.)'''''

[[:Category:4edo]]
[[:Category:Equivalence continua]]