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Diaschismic extensions: Difference between revisions

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srutal is complex enough to necessitate another table
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Both of these can be extended straightforwardly to the [[11-limit|11-]], [[13-limit|13-]], and [[17-limit]] by adding 176/175, 352/351, and 221/220 to the comma list in this order.
Both of these can be extended straightforwardly to the [[11-limit|11-]], [[13-limit|13-]], and [[17-limit]] by adding 176/175, 352/351, and 221/220 to the comma list in this order.


== Interval chains (WIP) ==
== Interval chains ==
=== Diaschismic ===
<div><div style="display: inline-grid; margin-right: 25px;">
<div><div style="display: inline-grid; margin-right: 25px;">
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|+ style="font-size: 105%;" | First period
|+ style="font-size: 105%;" | First period
|-
|-
! rowspan="3" | &#35; !! rowspan="3" | Cents* !! colspan="3" | Approximate Ratios
! rowspan="3" | &#35; !! rowspan="3" | Cents* !! colspan="2" | Approximate Ratios
|-
|-
! rowspan="2" | 2.3.5.17 subgroup !! colspan="2" | Intervals of 7
! rowspan="2" | 2.3.5.17 subgroup !! Intervals of 7
|-
|-
! Srutal !! Diaschismic
| &minus;8 || 220.3 || 100/81 || 21/17, 56/45
|-
|-
| &minus;8 || 220.3 || 100/81 || || 21/17, 56/45
| &minus;7 || 440.6 || 125/96 || '''21/16''', 112/85
|-
|-
| &minus;7 || 440.6 || 125/96 || || '''21/16''', 112/85
| &minus;6 || 660.9 || 25/18 || 7/5
|-
|-
| &minus;6 || 660.9 || 25/18 || || 7/5
| &minus;5 || 881.1 || 25/24 || 21/20
|-
|-
| &minus;5 || 881.1 || 25/24 || || 21/20
| &minus;4 || 1101.4 || 10/9, 75/68 || 28/25
|-
|-
| &minus;4 || 1101.4 || 10/9, 75/68 || || 28/25
| &minus;3 || 1321.7 || 20/17, 32/27 || 119/100
|-
|-
| &minus;3 || 1321.7 || 20/17, 32/27 || || 119/100
| &minus;2 || 1542.0 || '''5/4''', 34/27, 64/51 || 63/50
|-
|-
| &minus;2 || 1542.0 || '''5/4''', 34/27, 64/51 || || 63/50
| &minus;1 || 1762.2 || 4/3, 45/34 || 168/125
|-
|-
| &minus;1 || 1762.2 || 4/3, 45/34 || || 168/125
| 0 || 0.0 || '''1/1''' || 126/125
|-
|-
| 0 || 0.0 || '''1/1''' || ||
| 1 || 220.3 || 16/15, '''17/16''', 18/17 ||  
|-
|-
| 1 || 220.3 || 16/15, '''17/16''', 18/17 || ||  
| 2 || 440.6 || '''9/8''', 17/15 || 125/112
|-
|-
| 2 || 440.6 || '''9/8''', 17/15 || || 125/112
| 3 || 660.9 || 6/5, 81/68 || 25/21
|-
|-
| 3 || 660.9 || 6/5, 81/68 || || 25/21
| 4 || 881.1 || 32/25, 51/40, 81/64 || 80/63
|-
|-
| 4 || 881.1 || 32/25, 51/40, 81/64 || || 80/63
| 5 || 1101.4 || 27/20, 34/25 || 75/56, 85/63
|-
|-
| 5 || 1101.4 || 27/20, 34/25 || || 75/56, 85/63
| 6 || 1321.7 || 51/50, 81/80 || 85/84
|-
|-
| 6 || 1321.7 || 51/50, 81/80 || || 85/84
| 7 || 1542.0 || 27/25 || 15/14, 68/63
|-
|-
| 7 || 1542.0 || 27/25 || || 15/14, 68/63
| 8 || 1762.2 || 144/125 || 8/7
|-
| 8 || 1762.2 || 144/125 || || 8/7
|}
|}
<nowiki />* In 3.5.7-targeted [[DKW theory|DKW]] tuning for [[BPS]]
<nowiki />* In 3.5.7-targeted [[DKW theory|DKW]] tuning for [[BPS]]
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|+ style="font-size: 105%;" | Second period
|+ style="font-size: 105%;" | Second period
|-
|-
! rowspan="3" | &#35; !! rowspan="3" | Cents* !! colspan="3" | Approximate Ratios
! rowspan="3" | &#35; !! rowspan="3" | Cents* !! colspan="2" | Approximate Ratios
|-
! rowspan="2" | 2.3.5.17 subgroup !! colspan="2" | Intervals of 7
|-
|-
! Srutal !! Diaschismic
! rowspan="2" | 2.3.5.17 subgroup !! Intervals of 7
|-
|-
| &minus;8 || 1762.2 || 125/72 || || '''7/4'''
| &minus;8 || 1762.2 || 125/72 || '''7/4'''
|-
|-
| &minus;7 || 1542.0 || 50/27 || || 28/15, 63/34
| &minus;7 || 1542.0 || 50/27 || 28/15, 63/34
|-
|-
| &minus;6 || 1321.7 || 100/51, 160/81 || || 168/85
| &minus;6 || 1321.7 || 100/51, 160/81 || 168/85
|-  
|-  
| &minus;5 || 1101.4 || 40/27, 25/17 || || 112/75, 126/85
| &minus;5 || 1101.4 || 40/27, 25/17 || 112/75, 126/85
|-
|-
| &minus;4 || 881.1 || '''25/16''', 80/51, 128/81 || || 63/40
| &minus;4 || 881.1 || '''25/16''', 80/51, 128/81 || 63/40
|-
|-
| &minus;3 || 660.9 || 5/3, 136/81 || || 42/25
| &minus;3 || 660.9 || 5/3, 136/81 || 42/25
|-
|-
| &minus;2 || 440.6 || 16/9, 30/17 || || 224/125
| &minus;2 || 440.6 || 16/9, 30/17 || 224/125
|-
|-
| &minus;1 || 220.3 || '''15/8''', 17/9, 32/17 || ||
| &minus;1 || 220.3 || '''15/8''', 17/9, 32/17 ||
|-
|-
| 0 || 0.0 || 17/12, 24/17, 45/32, 64/45 || ||
| 0 || 0.0 || 17/12, 24/17, 45/32, 64/45 ||
|-
|-
| 1 || 1762.2 || '''3/2''', 68/45 || || 125/84
| 1 || 1762.2 || '''3/2''', 68/45 || 125/84
|-
|-
| 2 || 1542.0 || 8/5, 27/17, 51/32 || || 100/63
| 2 || 1542.0 || 8/5, 27/17, 51/32 || 100/63
|-
|-
| 3 || 1321.7 || 17/10, '''27/16''' || || 200/119
| 3 || 1321.7 || 17/10, '''27/16''' || 200/119
|-
|-
| 4 || 1101.4 || 9/5, 136/75 || || 25/14
| 4 || 1101.4 || 9/5, 136/75 || 25/14
|-
|-
| 5 || 881.1 || 48/25 || || 40/21
| 5 || 881.1 || 48/25 || 40/21
|-
|-
| 6 || 660.9 || 36/25 || || 10/7
| 6 || 660.9 || 36/25 || 10/7
|-
|-
| 7 || 440.6 || 192/125 || || 32/21, 85/56
| 7 || 440.6 || 192/125 || 32/21, 85/56
|-
|-
| 8 || 220.3 || 81/50 || || 34/21, 45/28
| 8 || 220.3 || 81/50 || 34/21, 45/28
|}
|}
<nowiki />* In 3.5.7-targeted [[DKW theory|DKW]] tuning for [[BPS]]
<nowiki />* In 3.5.7-targeted [[DKW theory|DKW]] tuning for [[BPS]]
Retrieved from "https://en.xen.wiki/w/Diaschismic_extensions"