Hemififths: Difference between revisions
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→Interval chain: added ups and downs notation |
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! rowspan="2" | Cents* | ! rowspan="2" | Cents* | ||
! colspan="2" | Approximate Ratios | ! colspan="2" | Approximate Ratios | ||
! rowspan="2" |ups and downs | |||
notation ** | |||
|- | |- | ||
! 7-limit | ! 7-limit | ||
| Line 19: | Line 21: | ||
| '''1/1''' | | '''1/1''' | ||
| | | | ||
|P1 | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 24: | Line 27: | ||
| 49/40, 60/49 | | 49/40, 60/49 | ||
| 11/9, '''16/13''', 27/22, 39/32 | | 11/9, '''16/13''', 27/22, 39/32 | ||
|~3 = ^m3 = vM3 | |||
|- | |- | ||
| 2 | | 2 | ||
| Line 29: | Line 33: | ||
| '''3/2''' | | '''3/2''' | ||
| | | | ||
|P5 | |||
|- | |- | ||
| 3 | | 3 | ||
| Line 34: | Line 39: | ||
| 90/49 | | 90/49 | ||
| 11/6, 24/13 | | 11/6, 24/13 | ||
|~7 = ^m7 = vM7 | |||
|- | |- | ||
| 4 | | 4 | ||
| Line 39: | Line 45: | ||
| '''9/8''' | | '''9/8''' | ||
| | | | ||
|M2 | |||
|- | |- | ||
| 5 | | 5 | ||
| Line 44: | Line 51: | ||
| 112/81 | | 112/81 | ||
| '''11/8''', 18/13 | | '''11/8''', 18/13 | ||
|~4 = ^4 = vA4 | |||
|- | |- | ||
| 6 | | 6 | ||
| Line 49: | Line 57: | ||
| 27/16 | | 27/16 | ||
| 22/13 | | 22/13 | ||
|M6 | |||
|- | |- | ||
| 7 | | 7 | ||
| Line 54: | Line 63: | ||
| 28/27 | | 28/27 | ||
| 33/32, 27/26 | | 33/32, 27/26 | ||
|^1 = \m2 | |||
|- | |- | ||
| 8 | | 8 | ||
| Line 59: | Line 69: | ||
| 80/63, 81/64 | | 80/63, 81/64 | ||
| 14/11, 33/26 | | 14/11, 33/26 | ||
|M3 | |||
|- | |- | ||
| 9 | | 9 | ||
| Line 64: | Line 75: | ||
| 14/9 | | 14/9 | ||
| | | | ||
|^5 = \m6 | |||
|- | |- | ||
| 10 | | 10 | ||
| Line 69: | Line 81: | ||
| 40/21 | | 40/21 | ||
| 21/11 | | 21/11 | ||
|M7 | |||
|- | |- | ||
| 11 | | 11 | ||
| Line 74: | Line 87: | ||
| 7/6 | | 7/6 | ||
| | | | ||
|^M2 = \m3 | |||
|- | |- | ||
| 12 | | 12 | ||
| Line 79: | Line 93: | ||
| 10/7 | | 10/7 | ||
| | | | ||
|A4 = \~5 | |||
|- | |- | ||
| 13 | | 13 | ||
| Line 84: | Line 99: | ||
| '''7/4''' | | '''7/4''' | ||
| | | | ||
|^M6 = \m7 | |||
|- | |- | ||
| 14 | | 14 | ||
| Line 89: | Line 105: | ||
| 15/14 | | 15/14 | ||
| 14/13 | | 14/13 | ||
|A1 = \~2 | |||
|- | |- | ||
| 15 | | 15 | ||
| Line 94: | Line 111: | ||
| '''21/16''' | | '''21/16''' | ||
| | | | ||
|^M3 = \4 | |||
|- | |- | ||
| 16 | | 16 | ||
| Line 99: | Line 117: | ||
| 45/28 | | 45/28 | ||
| 21/13 | | 21/13 | ||
|A5 = \~6 | |||
|- | |- | ||
| 17 | | 17 | ||
| Line 104: | Line 123: | ||
| 63/32, 160/81 | | 63/32, 160/81 | ||
| | | | ||
|^M7 = \8 | |||
|- | |- | ||
| 18 | | 18 | ||
| Line 109: | Line 129: | ||
| 98/81, 135/112 | | 98/81, 135/112 | ||
| 40/33 | | 40/33 | ||
|A2 = \~3 | |||
|- | |- | ||
| 19 | | 19 | ||
| Line 114: | Line 135: | ||
| 40/27 | | 40/27 | ||
| | | | ||
|^A4 = \5 | |||
|- | |- | ||
| 20 | | 20 | ||
| Line 119: | Line 141: | ||
| 49/27 | | 49/27 | ||
| 20/11 | | 20/11 | ||
|A6 = \~7 | |||
|- | |- | ||
| 21 | | 21 | ||
| Line 124: | Line 147: | ||
| 10/9 | | 10/9 | ||
| | | | ||
|^A1 = \M2 | |||
|- | |- | ||
| 22 | | 22 | ||
| Line 129: | Line 153: | ||
| 49/36 | | 49/36 | ||
| 15/11 | | 15/11 | ||
|A3 = \~4 | |||
|- | |- | ||
| 23 | | 23 | ||
| Line 134: | Line 159: | ||
| 5/3 | | 5/3 | ||
| | | | ||
|^A5 = \M6 | |||
|- | |- | ||
| 24 | | 24 | ||
| Line 139: | Line 165: | ||
| 49/48, 50/49 | | 49/48, 50/49 | ||
| 40/39, 45/44, 55/54, 65/64 | | 40/39, 45/44, 55/54, 65/64 | ||
|A7 - P8 = -d2 = ^\1 | |||
|- | |- | ||
| 25 | | 25 | ||
| Line 144: | Line 171: | ||
| '''5/4''' | | '''5/4''' | ||
| | | | ||
|^A2 = \M3 | |||
|- | |- | ||
| 26 | | 26 | ||
| Line 149: | Line 177: | ||
| 49/32 | | 49/32 | ||
| 20/13 | | 20/13 | ||
|AA4 = ^\5 | |||
|- | |- | ||
| 27 | | 27 | ||
| Line 154: | Line 183: | ||
| '''15/8''' | | '''15/8''' | ||
| | | | ||
|^A6 = \M7 | |||
|- | |- | ||
| 28 | | 28 | ||
| Line 159: | Line 189: | ||
| 147/128 | | 147/128 | ||
| 15/13 | | 15/13 | ||
|AA1= ^\2 | |||
|- | |- | ||
| 29 | | 29 | ||
| Line 164: | Line 195: | ||
| 45/32 | | 45/32 | ||
| | | | ||
|^A3 = \A4 | |||
|} | |} | ||
<nowiki /> | <nowiki>*</nowiki> In 7-limit CTE tuning, generator = 351.445¢, P5 = 702.89¢, c = 2.89¢ | ||
<nowiki>**</nowiki> Enharmonic equivalences: vvA1 and v\m2. Cents: ^1 = 50¢ + 3.5c and /1 = 50¢ - 8.5c | |||
== Notation == | == Notation == | ||
| Line 172: | Line 206: | ||
# The Pythagorean comma (+24 gensteps, inverse diminished second). | # The Pythagorean comma (+24 gensteps, inverse diminished second). | ||
Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma. | Below is tabulated how to notate the prime harmonics with an arrow representing a syntonic~septimal comma (thus ^C = Ddb). | ||
{| class="wikitable center-1 center-3" | {| class="wikitable center-1 center-3" | ||
|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals | |+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals | ||
| Line 201: | Line 235: | ||
|} | |} | ||
Below is tabulated how to notate the prime harmonics with an arrow representing a Pythagorean comma. | Below is tabulated how to notate the prime harmonics with an arrow representing a Pythagorean comma (thus ^C = B#). | ||
{| class="wikitable center-1 center-3" | {| class="wikitable center-1 center-3" | ||
|+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals | |+ style="font-size: 105%;" | Hemififths nomenclature<br />for selected intervals | ||