Squares: Difference between revisions

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See [[Meantone family #Squares]] and [[Subgroup temperaments #Skwares]] for more technical data.  
See [[Meantone family #Squares]] and [[Subgroup temperaments #Skwares]] for more technical data.  
== Interval chain ==
In the following table, prime harmonics are labeled in '''bold'''.
{| class="wikitable center-1 right-2"
! rowspan="3" | #
! rowspan="3" | Cents *
! colspan="4" | Approximate Ratios
|-
! rowspan="2" | 11-limit
! colspan="3" | 13-limit Extension
|-
! Squares
! Squad
! Agora
|-
| 0
| 0.0
| 1/1
|
|
|
|-
| 1
| 425.6
| 9/7, 14/11
|
| 13/10
|
|-
| 2
| 851.2
| 18/11, 33/20, 44/27
| '''13/8'''
| 21/13
|
|-
| 3
| 76.8
| 21/20, 28/27
|
| 27/26
|
|-
| 4
| 502.4
| '''4/3'''
|
|
|
|-
| 5
| 928.0
| 12/7
|
| 22/13, 26/15
|
|-
| 6
| 153.6
| 11/10, 12/11
| 13/12
| 14/13
|
|-
| 7
| 579.2
| 7/5
|
| 18/13
|
|-
| 8
| 1004.8
| 9/5, 16/9
|
|
|
|-
| 9
| 230.4
| '''8/7'''
|
|
| 15/13
|-
| 10
| 656.0
| '''16/11''', 22/15
| 13/9
|
|
|-
| 11
| 1081.6
| 28/15
| 13/7
| 24/13
|
|-
| 12
| 307.2
| 6/5
| 13/11
|
|
|-
| 13
| 732.8
| 32/21
|
|
| 20/13
|-
| 14
| 1158.4
| 49/25, 64/33, 96/49
| 52/27
|
|
|-
| 15
| 384.0
| 56/45
| 26/21
| '''16/13'''
|
|-
| 16
| 809.6
| '''8/5'''
|
|
| 21/13
|-
| 17
| 35.2
| 36/35, 64/63
|
|
|
|}
<nowiki>*</nowiki> in 11-limit CTE tuning


== Scales ==
== Scales ==

Revision as of 09:59, 31 July 2021

Squares is the rank-2 regular temperament tempering out the syntonic comma, 81/80, and the breedsma, 2401/2400. It has a ~9/7 generator, four of which make a perfect twelfth. Skwares is the no-5 subgroup version of this temperament.

See Meantone family #Squares and Subgroup temperaments #Skwares for more technical data.

Interval chain

In the following table, prime harmonics are labeled in bold.

# Cents * Approximate Ratios
11-limit 13-limit Extension
Squares Squad Agora
0 0.0 1/1
1 425.6 9/7, 14/11 13/10
2 851.2 18/11, 33/20, 44/27 13/8 21/13
3 76.8 21/20, 28/27 27/26
4 502.4 4/3
5 928.0 12/7 22/13, 26/15
6 153.6 11/10, 12/11 13/12 14/13
7 579.2 7/5 18/13
8 1004.8 9/5, 16/9
9 230.4 8/7 15/13
10 656.0 16/11, 22/15 13/9
11 1081.6 28/15 13/7 24/13
12 307.2 6/5 13/11
13 732.8 32/21 20/13
14 1158.4 49/25, 64/33, 96/49 52/27
15 384.0 56/45 26/21 16/13
16 809.6 8/5 21/13
17 35.2 36/35, 64/63

* in 11-limit CTE tuning

Scales

Music

Template:IoT

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