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Extending the chain beyond 13 notes gives good, though irregular, mappings of 3/2 (with -17 generators) and 7/4 (with -15 generators) in the "better" tunings.
Extending the chain beyond 13 notes gives good, though irregular, mappings of 3/2 (with -17 generators) and 7/4 (with -15 generators) in the "better" tunings.
=====Interval chain=====
=====Interval chain=====
{| class="wikitable"
{| class="wikitable center-all right-2 right-6"
|-
|-
! | Generators
! Generators
! | Cents (*)
! Cents <ref name="r1"> using the 2.9.21.5.11.13.17.19 POTE generator; cf. the 44edo generator of 463.64¢ and the 2.9.21.5.11.13 POTE generator of  463.50¢</ref>
! | Ratios (**)
! Ratios <ref name="r2"> 2.9.21.5.11.13.17.19 interpretations; harmonics are in bold</ref>
! | Octatonic notation
! Octatonic notation
! | Generators
! Generators
! | 2/1 inverse (*)
! 2/1 inverse <ref name="r1"/>
! | Ratios (**)
! Ratios <ref name="r2"/>
! | Octatonic notation
! Octatonic notation
|-
|-
|colspan=8|The "diatonic" 8-note scale has the following intervals:
| colspan="8" style="text-align:left" | The "diatonic" 8-note scale has the following intervals:
|-
|-
| style="text-align:center;" | 0
| 0
| style="text-align:right;" | 0
| 0.00
| style="text-align:center;" | 1/1
| 1/1
| style="text-align:center;" | P1
| P1
| style="text-align:center;" | 0
| 0
| style="text-align:right;" | 1200
| 1200.00
| style="text-align:center;" | 2/1
| 2/1
| style="text-align:center;" | P9
| P9
|-
|-
| style="text-align:center;" | 1
| 1
| style="text-align:right;" | 463.17
| 463.17
| style="text-align:center;" | '''21/16''', 13/10, 17/13
| '''21/16''', 13/10, 17/13
| style="text-align:center;" | P4
| P4
| style="text-align:center;" | -1
| -1
| style="text-align:right;" | 736.83
| 736.83
| style="text-align:center;" | 32/21, 20/13
| 32/21, 20/13
| style="text-align:center;" | P6
| P6
|-
|-
| style="text-align:center;" | 2
| 2
| style="text-align:right;" | 926.35
| 926.35
| style="text-align:center;" | 12/7, 17/10
| 12/7, 17/10
| style="text-align:center;" | M7
| M7
| style="text-align:center;" | -2
| -2
| style="text-align:right;" | 273.66
| 273.66
| style="text-align:center;" | 7/6, 20/17
| 7/6, 20/17
| style="text-align:center;" | m3
| m3
|-
|-
| style="text-align:center;" | 3
| 3
| style="text-align:right;" | 189.52
| 189.52
| style="text-align:center;" | '''9/8''', 10/9, 19/17
| '''9/8''', 10/9, 19/17
| style="text-align:center;" | M2
| M2
| style="text-align:center;" | -3
| -3
| style="text-align:right;" | 1010.48
| 1010.48
| style="text-align:center;" | 16/9, 9/5
| 16/9, 9/5
| style="text-align:center;" | m8
| m8
|-
|-
| style="text-align:center;" | 4
| 4
| style="text-align:right;" | 652.69
| 652.69
| style="text-align:center;" | 16/11, 13/9, 19/13
| 16/11, 13/9, 19/13
| style="text-align:center;" | M5
| M5
| style="text-align:center;" | -4
| -4
| style="text-align:right;" | 547.31
| 547.31
| style="text-align:center;" | '''11/8''', 18/13
| '''11/8''', 18/13
| style="text-align:center;" | m5
| m5
|-
|-
| style="text-align:center;" | 5
| 5
| style="text-align:right;" | 1115.86
| 1115.86
| style="text-align:center;" | 40/21, 21/11, 19/10
| 40/21, 21/11, 19/10
| style="text-align:center;" | M8
| M8
| style="text-align:center;" | -5
| -5
| style="text-align:right;" | 84.14
| 84.14
| style="text-align:center;" | 20/19, 21/20, 22/21, 23/22
| 20/19, 21/20, 22/21, 23/22
| style="text-align:center;" | m2
| m2
|-
|-
| style="text-align:center;" | 6
| 6
| style="text-align:right;" | 379.04
| 379.04
| style="text-align:center;" | '''5/4'''
| '''5/4'''
| style="text-align:center;" | M3
| M3
| style="text-align:center;" | -6
| -6
| style="text-align:right;" | 820.97
| 820.97
| style="text-align:center;" | 8/5, 21/13
| 8/5, 21/13
| style="text-align:center;" | m7
| m7
|-
|-
| style="text-align:center;" | 7
| 7
| style="text-align:right;" | 842.21
| 842.21
| style="text-align:center;" | 18/11, '''13/8'''
| 18/11, '''13/8'''
| style="text-align:center;" | A6
| A6
| style="text-align:center;" | -7
| -7
| style="text-align:right;" | 357.79
| 357.79
| style="text-align:center;" | 11/9, 16/13
| 11/9, 16/13
| style="text-align:center;" | d4
| d4
|-
|-
|colspan=8|The "chromatic" 13-note scale also has the following intervals:
| colspan="8" style="text-align:left" | The "chromatic" 13-note scale also has the following intervals:
|-
|-
| style="text-align:center;" | 8
| 8
| style="text-align:right;" | 105.38
| 105.38
| style="text-align:center;" | '''17/16'''
| '''17/16'''
| style="text-align:center;" | A1 (the chroma for oneirotonic)
| A1 (the chroma for oneirotonic)
| style="text-align:center;" | -8
| -8
| style="text-align:right;" | 1094.62
| 1094.62
| style="text-align:center;" | close to '''15/8'''
| close to '''15/8'''
| style="text-align:center;" | d9
| d9
|-
|-
| style="text-align:center;" | 9
| 9
| style="text-align:right;" | 568.55
| 568.55
| style="text-align:center;" | close to 32/23
| close to 32/23
| style="text-align:center;" | A4
| A4
| style="text-align:center;" | -9
| -9
| style="text-align:right;" | 631.45
| 631.45
| style="text-align:center;" | close to '''23/16'''
| close to '''23/16'''
| style="text-align:center;" | d6
| d6
|-
|-
| style="text-align:center;" | 10
| 10
| style="text-align:right;" | 1031.73
| 1031.73
| style="text-align:center;" | 20/11
| 20/11
| style="text-align:center;" | A7
| A7
| style="text-align:center;" | -10
| -10
| style="text-align:right;" | 168.27
| 168.27
| style="text-align:center;" | 11/10
| 11/10
| style="text-align:center;" | d3
| d3
|-
|-
| style="text-align:center;" | 11
| 11
| style="text-align:right;" | 294.90
| 294.90
| style="text-align:center;" | 13/11, '''19/16'''
| 13/11, '''19/16'''
| style="text-align:center;" | A2
| A2
| style="text-align:center;" | -11
| -11
| style="text-align:right;" | 905.10
| 905.10
| style="text-align:center;" | 22/13
| 22/13
| style="text-align:center;" | d8
| d8
|-
|-
| style="text-align:center;" | 12
| 12
| style="text-align:right;" | 758.07
| 758.07
| style="text-align:center;" | close to 14/9
| close to 14/9
| style="text-align:center;" | A5
| A5
| style="text-align:center;" | -12
| -12
| style="text-align:right;" | 441.93
| 441.93
| style="text-align:center;" | close to 9/7
| close to 9/7
| style="text-align:center;" | d5
| d5
|}
|}
(*) using the 2.9.21.5.11.13.17.19 POTE generator; cf. the 44edo generator of 463.64¢ and the 2.9.21.5.11.13 POTE generator of  463.50¢


(**) 2.9.21.5.11.13.17.19 interpretations; harmonics are in bold
<references/>


==="Superpythagorean" tunings===
==="Superpythagorean" tunings===
Retrieved from "https://en.xen.wiki/w/A-team"