Antonian
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
Antonian is an exotemperament that tempers out 10/9, the classic major second. This equates 3/2 with 5/3, 4/3 with 6/5, and 5/4 with 9/8, being even less accurate than more common archetypal exotemperaments like father or dicot. It can be represented by only 3edo in its patent val.
| Antonian |
10/9, 15/14 (7-limit)
7-odd-limit: 161.4 ¢
7-odd-limit: 5 notes
In septimal antonian, 7/6 is equated to 5/4 and 9/8, by tempering out 15/14 and 28/27. An alternative extension is phlegyas, which tempers out 35/32 and 64/63, so 8/7 is equated with 5/4 and 9/8 instead.
For technical data, see Very low accuracy temperaments #Antonian.
Interval chain
In the following table, odd harmonics 1–7 are labeled in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 743 | 3/2, 5/3, 7/5 |
| 2 | 286 | 5/4, 7/6 |
| 3 | 1029 | 7/4 |
* In 7-limit CWE tuning, octave reduced
Tunings
Tunings spectrum
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | Comments |
|---|---|---|---|
| 7/5 | 583 | ||
| 1\2 | 600 | ||
| 3/2 | 702 | ||
| 7/4 | 723 | ||
| 7/6 | 733 | ||
| 5/4 | 793 | ||
| 2\3 | 800 | ||
| 5/3 | 884 |