1ed97.5c: Difference between revisions
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{{Infobox ET|160ed8192}} | {{Infobox ET|160ed8192}} | ||
'''1 equal division of 97.5¢''' ('''1ed97.5c'''), also known as '''APS97.5¢''', is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as [[39ed9]]. It can also be conceived slightly less accurately as [[25ed4]]. In contrast to [[12edo]], which is very similar in step size, it is not considered to approximate the octave ([[2/1]]) or perfect fifth ([[3/2]]), and has a workable, but rather (~10.5c) flat approximation of the perfect fourth ([[4/3]]). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 [[Just intonation subgroup|subgroup]], in which it tempers out [[64/63]], [[100/99]], [[275/273]], and [[325/324]], for example. | '''1 equal division of 97.5¢''' ('''1ed97.5c'''), also known as '''arithmetic pitch sequence of 97.5¢''' ('''APS97.5¢'''), is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as [[39ed9]]. It can also be conceived slightly less accurately as [[25ed4]]. In contrast to [[12edo]], which is very similar in step size, it is not considered to approximate the octave ([[2/1]]) or perfect fifth ([[3/2]]), and has a workable, but rather (~10.5c) flat approximation of the perfect fourth ([[4/3]]). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 [[Just intonation subgroup|subgroup]], in which it tempers out [[64/63]], [[100/99]], [[275/273]], and [[325/324]], for example. | ||
== Intervals == | == Intervals == | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
Revision as of 19:50, 7 November 2023
| ← 159ed8192 | 160ed8192 | 161ed8192 → |
1 equal division of 97.5¢ (1ed97.5c), also known as arithmetic pitch sequence of 97.5¢ (APS97.5¢), is an equal-step tuning with steps of 97.5 cents (or each 13th step of 160edo). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as 39ed9. It can also be conceived slightly less accurately as 25ed4. In contrast to 12edo, which is very similar in step size, it is not considered to approximate the octave (2/1) or perfect fifth (3/2), and has a workable, but rather (~10.5c) flat approximation of the perfect fourth (4/3). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 subgroup, in which it tempers out 64/63, 100/99, 275/273, and 325/324, for example.
Intervals
| Steps | Cents | Ratio approximated* |
|---|---|---|
| 1 | 97.5 | 16/15, 21/20, 35/33, 55/52 |
| 2 | 195.0 | 28/25, 44/39 |
| 3 | 292.5 | 13/11 |
| 4 | 390.0 | 5/4 |
| 5 | 487.5 | 4/3, 33/25 |
| 6 | 585.0 | 7/5 |
| 7 | 682.5 | 49/33 |
| 8 | 780.0 | 11/7, 39/25 |
| 9 | 877.5 | 5/3 |
| 10 | 975.0 | 16/9, 7/4, 44/25 |
| 11 | 1072.5 | 13/7 |
| 12 | 1170.0 | 49/25 |
| 13 | 1267.5 | 27/13 |
| 14 | 1365.0 | 11/5 |
| 15 | 1462.5 | 7/3 |
| 16 | 1560.0 | 27/11, 49/20 |
| 17 | 1657.5 | 13/5 |
| 18 | 1755.0 | 11/4, 36/13 |
| 19 | 1852.5 | 35/12 |
| 20 | 1950.0 | 49/16 |
| 21 | 2047.5 | 13/4, 36/11 |
| 22 | 2145.0 | 45/13 |
| 23 | 2242.5 | 48/13 |
| 24 | 2340.0 | 27/7 |
| 25 | 2437.5 | 45/11 |
| 26 | 2533.0 | 48/11 |
| 27 | 2632.5 | 60/13 |
| 28 | 2730.0 | 63/13 |
| 29 | 2827.5 | 36/7, 81/16 |
| 30 | 2925.0 | 27/5, 60/11 |
| 31 | 3022.5 | 63/11 |
| 32 | 3120.0 | |
| 33 | 3215.5 | 45/7 |
| 34 | 3315.0 | 27/4 |
| 35 | 3412.5 | 36/5 |
| 36 | 3510.0 | 99/13 |
| 37 | 3607.5 | |
| 38 | 3705.0 | 60/7 |
| 39 | 3802.5 | 9/1 |
*some simpler ratios, based on treating 1ed97.5c as a 4/3.5/3.7/3.11/3.13/3.9 subgroup temperament; other approaches are possible.