User:ArrowHead294/sandbox: Difference between revisions

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Harmonic series with harmonics stretched by 0.25% per octave:
{| class="wikitable center-1 right-2"
{{Powharmonic series|128|expo=1.0025|prec=4}}
|+ style="font-size: 105%;" | Interval chain for {{frac|2|7}}-comma [[superpyth]]
{{Harmonics in equal|311|intervals=odd|prec=2|columns=15}}
|-
{{Harmonics in equal|3159811|intervals=odd|prec=2|columns=31}}
! rowspan="2" | # !! rowspan="2" | Cents !! colspan="2" | Approximate Ratios
{{Harmonics in equal|42586208631|intervals=odd|prec=2|columns=63}}
|-
! 7-limit !! 11-limit
|-
| −10 || {{cents|2^6/(3/2*(64/63)^(2/7))^10|3}} || 16/15, 21/20 ||
|-
| −9 || {{cents|2^6/(3/2*(64/63)^(2/7))^9|3}} || 8/5 ||
|-
| −8 || {{cents|2^5/(3/2*(64/63)^(2/7))^8|3}} || 6/5 || 40/33
|-
| −7 || {{cents|2^5/(3/2*(64/63)^(2/7))^7|3}} || 9/5 || 20/11
|-
| −6 || {{cents|2^4/(3/2*(64/63)^(2/7))^6|3}} || 48/35, 27/20 || 15/11
|-
| −5 || {{cents|2^3/(3/2*(64/63)^(2/7))^5|3}} || 28/27, 36/35 || 45/44
|-
| −4 || {{cents|2^3/(3/2*(64/63)^(2/7))^4|3}} || 14/9 ||
|-
| −3 || {{cents|2^2/(3/2*(64/63)^(2/7))^3|3}} || 7/6 ||
|-
| −2 || {{cents|2^2/(3/2*(64/63)^(2/7))^2|3}} || 7/4, 16/9 ||
|-
| −1 || {{cents|2/(3/2*(64/63)^(2/7))|3}} || 4/3 ||
|-
| 0 || 0 || '''1/1''' ||
|-
| 1 || {{cents|3/2*(64/63)^(2/7)|3}} || '''3/2''' ||
|-
| 2 || {{cents|(3/2*(64/63)^(2/7))^2/2|3}} || '''8/7''', '''9/8''' ||
|-
| 3 || {{cents|(3/2*(64/63)^(2/7))^3/2|3}} || 12/7 ||
|-
| 4 || {{cents|(3/2*(64/63)^(2/7))^4/2^2|3}} || 9/7 ||
|-
| 5 || {{cents|(3/2*(64/63)^(2/7))^5/2^2|3}} || 27/14, 35/18 || 88/45
|-
| 6 || {{cents|(3/2*(64/63)^(2/7))^6/2^3|3}} || 35/24, 40/27 || 22/15
|-
| 7 || {{cents|(3/2*(64/63)^(2/7))^7/2^4|3}} || 10/9 || 11/10
|-
| 8 || {{cents|(3/2*(64/63)^(2/7))^8/2^4|3}} || 5/3 || 33/20
|-
| 9 || {{cents|(3/2*(64/63)^(2/7))^9/2^5|3}} || '''5/4''' ||
|-
| 10 || {{cents|(3/2*(64/63)^(2/7))^10/2^5|3}} || 15/8, 40/21 ||
|-
| 11 || {{cents|(3/2*(64/63)^(2/7))^11/2^6|3}} || 10/7 ||
|-
| 12 || {{cents|(3/2*(64/63)^(2/7))^12/2^7|3}} || 15/14 ||
|-
| 13 || {{cents|(3/2*(64/63)^(2/7))^13/2^7|3}} || 45/28 || 44/27
|-
| 14 || {{cents|(3/2*(64/63)^(2/7))^14/2^8|3}} || 60/49 || 11/9
|-
| 15 || {{cents|(3/2*(64/63)^(2/7))^15/2^8|3}} || 50/27 || 11/6
|-
| 16 || {{cents|(3/2*(64/63)^(2/7))^16/2^9|3}} || 25/18 || '''11/8'''
|-
| 17 || {{cents|(3/2*(64/63)^(2/7))^17/2^10|3}} || 25/24 || 22/21, 33/32
|}

Revision as of 18:52, 29 August 2024

Interval chain for 2⁄7-comma superpyth
# Cents Approximate Ratios
7-limit 11-limit
−10 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^6/(3/2*(64/63)^(2/7))^10|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 16/15, 21/20
−9 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^6/(3/2*(64/63)^(2/7))^9|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 8/5
−8 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^5/(3/2*(64/63)^(2/7))^8|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 6/5 40/33
−7 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^5/(3/2*(64/63)^(2/7))^7|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 9/5 20/11
−6 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^4/(3/2*(64/63)^(2/7))^6|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 48/35, 27/20 15/11
−5 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^3/(3/2*(64/63)^(2/7))^5|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 28/27, 36/35 45/44
−4 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^3/(3/2*(64/63)^(2/7))^4|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 14/9
−3 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^2/(3/2*(64/63)^(2/7))^3|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 7/6
−2 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2^2/(3/2*(64/63)^(2/7))^2|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 7/4, 16/9
−1 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 2/(3/2*(64/63)^(2/7))|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 4/3
0 0 1/1
1 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: 3/2*(64/63)^(2/7)|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 3/2
2 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^2/2|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 8/7, 9/8
3 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^3/2|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 12/7
4 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^4/2^2|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 9/7
5 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^5/2^2|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 27/14, 35/18 88/45
6 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^6/2^3|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 35/24, 40/27 22/15
7 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^7/2^4|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 10/9 11/10
8 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^8/2^4|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 5/3 33/20
9 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^9/2^5|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 5/4
10 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^10/2^5|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 15/8, 40/21
11 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^11/2^6|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 10/7
12 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^12/2^7|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 15/14
13 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^13/2^7|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 45/28 44/27
14 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^14/2^8|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 60/49 11/9
15 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^15/2^8|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 50/27 11/6
16 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^16/2^9|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 25/18 11/8
17 ^(.*?)[Cc]?$|\1}}) / ln(2)}}|3|.|}}{{subst:#switch: {{subst:#rmatch: (3/2*(64/63)^(2/7))^17/2^10|^.*?([Cc]?)$|\1}}|c= ¢|C= ¢|#default=}} 25/24 22/21, 33/32
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