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Tetrameantone: Difference between revisions

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The '''tetrameantone''' temperament is a [[nonoctave]] [[meantone]] temperament, tempering out the [[81/80]] in the 4.3.5 subgroup and repeating at the double octave [[4/1]]. It is generated by [[4/3]] and, like in normal meantone temperament, 4 of them make a [[8/5]] plus an octave.
The '''tetrameantone''' temperament is a [[nonoctave]] [[regular temperament|temperament]] [[tempering out]] [[81/80]] in the 4.3.5-[[subgroup]]. It is similar to [[meantone]] but repeats at the double octave [[4/1]]. It is generated by [[3/1]] and, like in normal meantone temperament, four of them make a [[5/1]] plus two double octaves.
 
For technical information see [[Subgroup temperaments#Tetrameantone]].
 
== Interval chain ==
== Interval chain ==
In the following table, odd harmonics 1–5 are '''bolded'''.
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
! Generators
! #
! Cents (POTE)
! Cents*
! Approximate ratios
! Approximate Ratios
|-
| -7
| 1273.671
| 25/12
|-
| -6
| 1777.432
| 45/16
|-
| -5
| 2281.193
| 15/4
|-
| -4
| 384.955
| [[5/4]]
|-
| -3
| 888.716
| [[5/3]]
|-
| -2
| 1392.477
| 9/4, 20/9
|-
| -1
| 1896.239
| [[3/1]]
|-
|-
| 0
| 0
| 0.000
| 0.000
| [[1/1]]
| '''1/1'''
|-
|-
| 1
| 1
| 503.761
| 1896.239
| [[4/3]]
| '''3/1'''
|-
|-
| 2
| 2
| 1007.523
| 1392.477
| [[16/9]], [[9/5]]
| 9/4, 20/9
|-
|-
| 3
| 3
| 1511.284
| 888.716
| 12/5
| 5/3
|-
|-
| 4
| 4
| 2015.045
| 384.955
| 16/5
| '''5/4'''
|-
|-
| 5
| 5
| 118.807
| 2281.193
| [[16/15]]
| 15/4
|-
|-  
| 6
| 6
| 622.568
| 1777.432
| [[64/45]]
| 45/16
|-
|-
| 7
| 7
| 1126.329
| 1273.671
| [[48/25]]
| 25/12
|}
|}
<nowiki>*</nowiki> in 4.3.5-subgroup POTE tuning
== Tetrameantone on tritave ==
== Tetrameantone on tritave ==
Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.
Tritave-repeating tetrameantone (3.4.5 subgroup) is made by cutting off the 4/3 interval range of the tetratave scale. extension will start at 3.4.5.14 subgroup. If we want strict no-twos subgroup, will be 3.5.13.
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|}
|}
=== b15 & b4p ===
=== b15 & b4p ===
: ''Temperament being restricted in different directions: [[No-fives subgroup temperaments #Superflat]]''
Subgroup: 3.5.13
Subgroup: 3.5.13


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[[POTE generator]]: ~325/243 = 508.099
[[POTE generator]]: ~325/243 = 508.099
=== 531441/528125 ===
{{Infobox Interval
| Ratio = 531441/528125
| Name = dinos comma
| Color name = L3uug^51, lathuthuquingu 1sn
| Comma = yes
}}
'''531441/528125''', the '''dinos comma''', is a small 13-limit comma. It can be expressed as (9/5)/(325/243)<sup>2</sup>, (9/5)/(4/3)<sup>2</sup>/(325/324)<sup>2</sup> and (81/80)/(325/324)<sup>2</sup>, among other expressions.
==== Temperaments ====
Tempering out this comma means equating a stack of two 325/243 (tridecimal marvelous fourth) with 9/5. This comma is tempered out in some 13-limit temperaments, e.g. flattone.
==== Etymology ====
The name "dinos" is proposed by Dummy index in 2024. It means: "miNOr Seventh is divided into 2 equal parts".


[[Category:Temperaments]]
[[Category:Tetrameantone| ]] <!-- main article -->
[[Category:Nonoctave]]
[[Category:Non-octave temperaments]]
{{Todo| review }}
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