Luna and hemithirds: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Cmloegcmluin (talk | contribs)
unchanged interval → unchanged-interval
m Cleanup
Line 1: Line 1:
'''Hemithirds temperament''' has a half of major third interval of [[5/4]] as a generator (hemithird, ~28/25, around 193.2 cents). Aside from two generator represents ~5/4, five generator gives ~7/4 and fifteen gives ~16/3 (tempering out 1029/1024 and 3136/3125 in the 7-limit).
The '''hemithirds''' temperament has a half of major third interval of [[5/4]] as a generator (hemithird, ~28/25, around 193.2 [[cent]]s). Aside from two generator represents ~5/4, five generator gives ~7/4 and fifteen gives ~16/3 (tempering out 1029/1024 and 3136/3125 in the 7-limit).


See [[Hemimean clan #Hemithirds]] or [[Luna family #Hemithirds]] for more information.  
See [[Hemimean clan #Hemithirds]] or [[Luna family #Hemithirds]] for more information.  


== Chords ==
== Chords ==
{{main| Chords of hemithirds }}
{{Main| Chords of hemithirds }}


== Tuning spectrum ==
== Tuning spectrum ==
Gencom: [2 28/25; 196/195 352/351 385/384 625/624]
Gencom: [2 28/25; 196/195 352/351 385/384 625/624]


Gencom mapping: [{{val|1 4 2 2 7 0}}, {{val|0 -15 2 5 -22 23}}]
Gencom mapping: [{{val| 1 4 2 2 7 0 }}, {{val| 0 -15 2 5 -22 23 }}]


{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(Unchanged-interval)]]
! hemithird<br>(¢)
! Generator<br>(¢)
! comments
! Comments
|-
|-
| 14/13
| 14/13
Line 114: Line 114:
[[Category:Luna family]]
[[Category:Luna family]]
[[Category:Hemimean clan]]
[[Category:Hemimean clan]]
[[Category:Gamelismic]]
[[Category:Gamelismic clan]]

Revision as of 03:20, 22 May 2023

The hemithirds temperament has a half of major third interval of 5/4 as a generator (hemithird, ~28/25, around 193.2 cents). Aside from two generator represents ~5/4, five generator gives ~7/4 and fifteen gives ~16/3 (tempering out 1029/1024 and 3136/3125 in the 7-limit).

See Hemimean clan #Hemithirds or Luna family #Hemithirds for more information.

Chords

Tuning spectrum

Gencom: [2 28/25; 196/195 352/351 385/384 625/624]

Gencom mapping: [1 4 2 2 7 0], 0 -15 2 5 -22 23]]

Eigenmonzo
(Unchanged-interval)
Generator
(¢)
Comments
14/13 192.872
12/11 192.948
15/11 192.995
13/10 193.058
16/13 193.066
13/11 193.094
15/13 193.118
13/12 193.120
11/8 193.122
11/10 193.125
18/13 193.144
5/4 193.157
6/5 193.198 5-odd-limit minimax
10/9 193.200
4/3 193.203
16/15 193.210
14/11 193.241 11-odd-limit minimax
9/7 193.283 9-odd-limit minimax
7/6 193.344 7-odd-limit minimax
15/14 193.364
11/9 193.426
8/7 193.765
7/5 194.171