28/25: Difference between revisions
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55edo directly approximates this very closely, but maps it inconsistently |
Found in 55edo Approximation to Just Intonation that 55c is not totally out to lunch, and would also work to make 28/25 map consistently |
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| Sound = jid_28_25_pluck_adu_dr220.mp3 | | Sound = jid_28_25_pluck_adu_dr220.mp3 | ||
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'''28/25''', the '''(septimal) middle whole tone''', is the interval between [[5/4]] and [[7/5]], and is intermediate in size between [[10/9]], of which it is [[126/125]] sharp, and [[9/8]], of which it is [[225/224]] flat. It's actually the [[mediant]] of [[19/17]] and [[9/8]]. A [[meantone]] where the tone is tuned to be exactly 28/25 has a fifth of size 2√14/5, or 698.099{{cent}}, which is closely approximated by [[55edo]] (however, 55edo in its patent val maps this interval inconsistently to 8\55 instead of 9\55; 55d is required for proper mapping). | '''28/25''', the '''(septimal) middle whole tone''', is the interval between [[5/4]] and [[7/5]], and is intermediate in size between [[10/9]], of which it is [[126/125]] sharp, and [[9/8]], of which it is [[225/224]] flat. It's actually the [[mediant]] of [[19/17]] and [[9/8]]. A [[meantone]] where the tone is tuned to be exactly 28/25 has a fifth of size 2√14/5, or 698.099{{cent}}, which is closely approximated by [[55edo]] (however, 55edo in its patent val maps this interval inconsistently to 8\55 instead of 9\55; 55c or 55d is required for proper mapping). | ||
== Approximation == | == Approximation == | ||
Latest revision as of 05:02, 5 July 2026
| Interval information |
(septimal) middle whole tone
[sound info]
28/25, the (septimal) middle whole tone, is the interval between 5/4 and 7/5, and is intermediate in size between 10/9, of which it is 126/125 sharp, and 9/8, of which it is 225/224 flat. It's actually the mediant of 19/17 and 9/8. A meantone where the tone is tuned to be exactly 28/25 has a fifth of size 2√14/5, or 698.099 ¢, which is closely approximated by 55edo (however, 55edo in its patent val maps this interval inconsistently to 8\55 instead of 9\55; 55c or 55d is required for proper mapping).
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 6 | 1\6 | 200.00 | +3.80 | +1.90 |
| 12 | 2\12 | 200.00 | +3.80 | +3.80 |
| 18 | 3\18 | 200.00 | +3.80 | +5.70 |
| 24 | 4\24 | 200.00 | +3.80 | +7.60 |
| 25 | 4\25 | 192.00 | -4.20 | -8.75 |
| 30 | 5\30 | 200.00 | +3.80 | +9.50 |
| 31 | 5\31 | 193.55 | -2.65 | -6.85 |
| 37 | 6\37 | 194.59 | -1.60 | -4.95 |
| 43 | 7\43 | 195.35 | -0.85 | -3.04 |
| 49 | 8\49 | 195.92 | -0.28 | -1.14 |
| 55 | 9\55 | 196.36 | +0.17 | +0.76 |
| 61 | 10\61 | 196.72 | +0.52 | +2.66 |
| 67 | 11\67 | 197.01 | +0.82 | +4.56 |
| 73 | 12\73 | 197.26 | +1.06 | +6.46 |
| 74 | 12\74 | 194.59 | -1.60 | -9.89 |
| 79 | 13\79 | 197.47 | +1.27 | +8.36 |
| 80 | 13\80 | 195.00 | -1.20 | -7.99 |
See also
- 25/14 – its octave complement
- 25/21 – its fourth complement
- 29/26 – a co-mediant interval
- Gallery of just intervals
- 25-odd-limit