41edo: Difference between revisions
Add the ratios of 19 and 21. Complete the ratios of 13. I speculated it consistent in 19- and 21-odd-limit if treated as a no-17s tuning. |
m Cleanup |
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| Line 491: | Line 491: | ||
If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups_and_Downs_Notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone. | If "red" is replaced by "up", "blue" by "down", and "neutral" by "mid", and if "gray" is omitted, this notation becomes essentially the same as [[Ups_and_Downs_Notation|ups and downs notation]]. The only difference is the use of minor tritone and major tritone. | ||
=Selected just intervals by error= | ==Selected just intervals by error== | ||
{| class="wikitable" style="text-align:center;" | {| class="wikitable" style="text-align:center;" | ||
! | | ! | | ||
| Line 641: | Line 641: | ||
|- | |- | ||
|" | |" | ||
| | | style="text-align:center;" | | ||
|31.57 | |31.57 | ||
|<nowiki> | -25 7 6 </nowiki>> | |<nowiki> | -25 7 6 </nowiki>> | ||
| Line 673: | Line 673: | ||
|- | |- | ||
|" | |" | ||
|32805/32768 | | style="text-align:center;" | 32805/32768 | ||
|1.95 | |1.95 | ||
|<nowiki> | -15 8 1 </nowiki>> | |<nowiki> | -15 8 1 </nowiki>> | ||
| Line 689: | Line 689: | ||
|- | |- | ||
|" | |" | ||
| | | style="text-align:center;" | | ||
|22.41 | |22.41 | ||
|<nowiki> | -10 7 8 -7 </nowiki>> | |<nowiki> | -10 7 8 -7 </nowiki>> | ||
| Line 705: | Line 705: | ||
|- | |- | ||
|" | |" | ||
|3125/3087 | | style="text-align:center;" | 3125/3087 | ||
|21.18 | |21.18 | ||
|<nowiki> | 0 -2 5 -3 </nowiki>> | |<nowiki> | 0 -2 5 -3 </nowiki>> | ||
| Line 714: | Line 714: | ||
|" | |" | ||
| | | | ||
|19.95 | | style="text-align:center;" | 19.95 | ||
|<nowiki> | 10 -11 2 1 </nowiki>> | |<nowiki> | 10 -11 2 1 </nowiki>> | ||
|Sazoyoyo | |Sazoyoyo | ||
| Line 721: | Line 721: | ||
|- | |- | ||
|" | |" | ||
|33075/32768 | | style="text-align:center;" | 33075/32768 | ||
|16.14 | |16.14 | ||
|<nowiki> | -15 3 2 2 </nowiki>> | |<nowiki> | -15 3 2 2 </nowiki>> | ||
| Line 729: | Line 729: | ||
|- | |- | ||
|" | |" | ||
|245/243 | | style="text-align:center;" | 245/243 | ||
|14.19 | |14.19 | ||
|<nowiki> | 0 -5 1 2 </nowiki>> | |<nowiki> | 0 -5 1 2 </nowiki>> | ||
| Line 737: | Line 737: | ||
|- | |- | ||
|" | |" | ||
|4000/3969 | | style="text-align:center;" | 4000/3969 | ||
|13.47 | |13.47 | ||
|<nowiki> | 5 -4 3 -2 </nowiki>> | |<nowiki> | 5 -4 3 -2 </nowiki>> | ||
| Line 745: | Line 745: | ||
|- | |- | ||
|" | |" | ||
| | | style="text-align:center;" | | ||
|9.15 | |9.15 | ||
|<nowiki> | -15 0 -2 7 </nowiki>> | |<nowiki> | -15 0 -2 7 </nowiki>> | ||
| Line 753: | Line 753: | ||
|- | |- | ||
|" | |" | ||
|1029/1024 | | style="text-align:center;" | 1029/1024 | ||
|8.43 | |8.43 | ||
|<nowiki> | -10 1 0 3 </nowiki>> | |<nowiki> | -10 1 0 3 </nowiki>> | ||
| Line 761: | Line 761: | ||
|- | |- | ||
|" | |" | ||
|225/224 | | style="text-align:center;" | 225/224 | ||
|7.71 | |7.71 | ||
|<nowiki> | -5 2 2 -1 </nowiki>> | |<nowiki> | -5 2 2 -1 </nowiki>> | ||
| Line 769: | Line 769: | ||
|- | |- | ||
|" | |" | ||
|16875/16807 | | style="text-align:center;" | 16875/16807 | ||
|6.99 | |6.99 | ||
|<nowiki> | 0 3 4 -5 </nowiki>> | |<nowiki> | 0 3 4 -5 </nowiki>> | ||
| Line 777: | Line 777: | ||
|- | |- | ||
|" | |" | ||
|10976/10935 | | style="text-align:center;" | 10976/10935 | ||
|6.48 | |6.48 | ||
|<nowiki> | 5 -7 -1 3 </nowiki>> | |<nowiki> | 5 -7 -1 3 </nowiki>> | ||
| Line 785: | Line 785: | ||
|- | |- | ||
|" | |" | ||
|5120/5103 | | style="text-align:center;" | 5120/5103 | ||
|5.76 | |5.76 | ||
|<nowiki> | 10 -6 1 -1 </nowiki>> | |<nowiki> | 10 -6 1 -1 </nowiki>> | ||
| Line 793: | Line 793: | ||
|- | |- | ||
|" | |" | ||
| | | style="text-align:center;" | | ||
|3.80 | |3.80 | ||
|<nowiki> | 25 -14 0 -1 </nowiki>> | |<nowiki> | 25 -14 0 -1 </nowiki>> | ||
| Line 801: | Line 801: | ||
|- | |- | ||
|" | |" | ||
|2401/2400 | | style="text-align:center;" | 2401/2400 | ||
|0.72 | |0.72 | ||
|<nowiki> | -5 -1 -2 4 </nowiki>> | |<nowiki> | -5 -1 -2 4 </nowiki>> | ||
| Line 809: | Line 809: | ||
|- | |- | ||
|11 | |11 | ||
| | | style="text-align:center;" | | ||
|29.72 | |29.72 | ||
|<nowiki> | 15 0 1 0 -5 </nowiki>> | |<nowiki> | 15 0 1 0 -5 </nowiki>> | ||
| Line 817: | Line 817: | ||
|- | |- | ||
|" | |" | ||
|245/242 | | style="text-align:center;" | 245/242 | ||
|21.33 | |21.33 | ||
|<nowiki> | -1 0 1 2 -2 </nowiki>> | |<nowiki> | -1 0 1 2 -2 </nowiki>> | ||
| Line 825: | Line 825: | ||
|- | |- | ||
|" | |" | ||
|100/99 | | style="text-align:center;" | 100/99 | ||
|17.40 | |17.40 | ||
|<nowiki> | 2 -2 2 0 -1 </nowiki>> | |<nowiki> | 2 -2 2 0 -1 </nowiki>> | ||
| Line 833: | Line 833: | ||
|- | |- | ||
|" | |" | ||
|1344/1331 | | style="text-align:center;" | 1344/1331 | ||
|16.83 | |16.83 | ||
|<nowiki> | 6 1 0 1 -3 </nowiki>> | |<nowiki> | 6 1 0 1 -3 </nowiki>> | ||
| Line 841: | Line 841: | ||
|- | |- | ||
|" | |" | ||
|896/891 | | style="text-align:center;" | 896/891 | ||
|9.69 | |9.69 | ||
|<nowiki> | 7 -4 0 1 -1 </nowiki>> | |<nowiki> | 7 -4 0 1 -1 </nowiki>> | ||
| Line 849: | Line 849: | ||
|- | |- | ||
|" | |" | ||
|65536/65219 | | style="text-align:center;" | 65536/65219 | ||
|8.39 | |8.39 | ||
|<nowiki> | 16 0 0 -2 -3 </nowiki>> | |<nowiki> | 16 0 0 -2 -3 </nowiki>> | ||
| Line 857: | Line 857: | ||
|- | |- | ||
|" | |" | ||
|243/242 | | style="text-align:center;" | 243/242 | ||
|7.14 | |7.14 | ||
|<nowiki> | -1 5 0 0 -2 </nowiki>> | |<nowiki> | -1 5 0 0 -2 </nowiki>> | ||
| Line 865: | Line 865: | ||
|- | |- | ||
|" | |" | ||
|385/384 | | style="text-align:center;" | 385/384 | ||
|4.50 | |4.50 | ||
|<nowiki> | -7 -1 1 1 1 </nowiki>> | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| Line 1,033: | Line 1,033: | ||
|- | |- | ||
|" | |" | ||
|256/255 | | style="text-align:center;" | 256/255 | ||
|6.78 | |6.78 | ||
|<nowiki> | 8 -1 -1 0 0 0 -1 </nowiki>> | |<nowiki> | 8 -1 -1 0 0 0 -1 </nowiki>> | ||
| Line 1,041: | Line 1,041: | ||
|- | |- | ||
|" | |" | ||
|715/714 | | style="text-align:center;" | 715/714 | ||
|2.42 | |2.42 | ||
|<nowiki> | -1 -1 1 -1 1 1 -1 </nowiki>> | |<nowiki> | -1 -1 1 -1 1 1 -1 </nowiki>> | ||
| Line 1,057: | Line 1,057: | ||
|- | |- | ||
|" | |" | ||
|361/360 | | style="text-align:center;" | 361/360 | ||
|4.80 | |4.80 | ||
|<nowiki> | -3 -2 -1 0 0 0 0 2 </nowiki>> | |<nowiki> | -3 -2 -1 0 0 0 0 2 </nowiki>> | ||
| Line 1,063: | Line 1,063: | ||
|19oog2 | |19oog2 | ||
|go comma | |go comma | ||
|- | |- | ||
|" | |" | ||
| Line 1,079: | Line 1,071: | ||
|L19o | |L19o | ||
| | undevicesimal comma, Boethius' comma | | | undevicesimal comma, Boethius' comma | ||
|- | |||
|" | |||
| style="text-align:center;" | 1216/1215 | |||
|1.42 | |||
|<nowiki> | 6 -5 -1 0 0 0 0 1 </nowiki>> | |||
|Sanogu | |||
|s19og | |||
|Eratosthenes' comma | |||
|- | |- | ||
|23 | |23 | ||
|736/729 | | style="text-align:center;" | 736/729 | ||
|16.54 | |16.54 | ||
|<nowiki> | 5 -6 0 0 0 0 0 0 1 </nowiki>> | |<nowiki> | 5 -6 0 0 0 0 0 0 1 </nowiki>> | ||
| Line 1,089: | Line 1,089: | ||
|- | |- | ||
|29 | |29 | ||
|145/144 | | style="text-align:center;" | 145/144 | ||
|11.98 | |11.98 | ||
|<nowiki> | -4 -2 1 0 0 0 0 0 0 1 </nowiki>> | |<nowiki> | -4 -2 1 0 0 0 0 0 0 1 </nowiki>> | ||