1ed125c: Difference between revisions
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CompactStar (talk | contribs) 6-digit continued fraction isn't needed |
Propose merge (very similar tunings) |
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{{Infobox ET| | {{todo|merge articles|inline=1|text=Merge [[4ed4/3]] and [[1ed125c]]?}} | ||
{{Infobox ET|48ed32}} | |||
'''1 equal division of 125¢''' ('''1ed125c'''), also known as '''arithmetic pitch sequence of 125¢''' ('''APS125¢'''), is a [[nonoctave]] tuning using equal steps of 125 cents each. This could be considered as dividing the approximate [[perfect fourth]] of 500 cents into 4 equal parts, making it very slightly stretched [[4ed4/3]]. It is equivalent to 9.6[[edo]], and is a subset of [[48edo]] (every fifth step). Therefore, it can be regarded as 48ed32. | |||
{{harmonics in cet|125}} | {{harmonics in cet|125}} | ||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | Degree | ||
! | | ! | Cents | ||
! | | ! | Associated ratios | ||
! | Interval name | |||
|- | |- | ||
| | 0 | | | 0 | ||
| | 0 | | | 0 | ||
| | [[1/1]] | |||
| | unison | | | unison | ||
|- | |- | ||
| | 1 | | | 1 | ||
| | 125 | | | 125 | ||
| | [[14/13]], [[15/14]] | |||
| | 2/3-tone, trienthird | | | 2/3-tone, trienthird | ||
|- | |- | ||
| | 2 | | | 2 | ||
| | 250 | | | 250 | ||
| | [[15/13]], [[22/19]] | |||
| | semifourth | | | semifourth | ||
|- | |- | ||
| | 3 | | | 3 | ||
| | 375 | | | 375 | ||
| | [[5/4]] | |||
| | narrow perde segah, marvelous major third, near just major third | | | narrow perde segah, marvelous major third, near just major third | ||
|- | |- | ||
| | 4 | | | 4 | ||
| | 500 | | | 500 | ||
| | [[4/3]] | |||
| | perfect fourth | | | perfect fourth | ||
|- | |- | ||
| | 5 | | | 5 | ||
| | 625 | | | 625 | ||
| | [[10/7]], [[23/16]] | |||
| | pental diminished fifth, classic diminshed fifth | | | pental diminished fifth, classic diminshed fifth | ||
|- | |- | ||
| | 6 | | | 6 | ||
| | 750 | | | 750 | ||
| | [[17/11]], [[20/13]] | |||
| | septendecimal subminor sixth | | | septendecimal subminor sixth | ||
|- | |- | ||
| | 7 | | | 7 | ||
| | 875 | | | 875 | ||
| | [[5/3]] | |||
| | major sixth | | | major sixth | ||
|- | |- | ||
| | 8 | | | 8 | ||
| | 1000 | | | 1000 | ||
| | [[16/9]] | |||
| | Pythagorean minor seventh | | | Pythagorean minor seventh | ||
|- | |- | ||
| | 9 | | | 9 | ||
| | 1125 | | | 1125 | ||
| | classic ([[5-limit|5-limit]]) diminished octave | | | [[21/11]], [[23/12]] | ||
| | classic ([[5-limit|5-limit]]) diminished octave | |||
|- | |- | ||
| | 10 | | | 10 | ||
| | 1250 | | | 1250 | ||
| | [[33/16]] | |||
| | | | | | ||
|- | |- | ||
| | 11 | | | 11 | ||
| | 1375 | | | 1375 | ||
| | | |||
| | | | | | ||
|- | |- | ||
| | 12 | | | 12 | ||
| | 1500 | | | 1500 | ||
| | | |||
| | | | | | ||
|- | |- | ||
| | 13 | | | 13 | ||
| | 1625 | | | 1625 | ||
| | | |||
| | | | | | ||
|- | |- | ||
| | 14 | | | 14 | ||
| | 1750 | | | 1750 | ||
| | | |||
| | | | | | ||
|- | |- | ||
| | 15 | | | 15 | ||
| | 1875 | | | 1875 | ||
| | | |||
| | | | | | ||
|- | |- | ||
| | 16 | | | 16 | ||
| | 2000 | | | 2000 | ||
| | | |||
| | | | | | ||
|} | |} | ||
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*[http://chrisvaisvil.com/canyon-diablo-fall/ Canyon Diablo Fall] by [[Chris Vaisvil]] | *[http://chrisvaisvil.com/canyon-diablo-fall/ Canyon Diablo Fall] by [[Chris Vaisvil]] | ||
**http://micro.soonlabel.com/125cent/20130317_125cent.mp3 | **http://micro.soonlabel.com/125cent/20130317_125cent.mp3 | ||
*[http://chrisvaisvil.com/crossing-over-125cet/ Crossing Over] by [[Chris Vaisvil]] | *[http://chrisvaisvil.com/crossing-over-125cet/ Crossing Over] by [[Chris Vaisvil]] (125cET is an outdated name for this tuning system, standing for "125-cent equal temperament") | ||
**http://micro.soonlabel.com/125cent/20141011_125ct_crossing_over.mp3 | **http://micro.soonlabel.com/125cent/20141011_125ct_crossing_over.mp3 | ||
[[Category:listen]] | [[Category:listen]] | ||
[[Category:nonoctave]] | [[Category:nonoctave]] | ||
Latest revision as of 01:35, 1 August 2025
| ← 47ed32 | 48ed32 | 49ed32 → |
1 equal division of 125¢ (1ed125c), also known as arithmetic pitch sequence of 125¢ (APS125¢), is a nonoctave tuning using equal steps of 125 cents each. This could be considered as dividing the approximate perfect fourth of 500 cents into 4 equal parts, making it very slightly stretched 4ed4/3. It is equivalent to 9.6edo, and is a subset of 48edo (every fifth step). Therefore, it can be regarded as 48ed32.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +50.0 | -27.0 | -25.0 | -36.3 | +23.0 | +6.2 | +25.0 | -53.9 | +13.7 | -26.3 | -52.0 |
| Relative (%) | +40.0 | -21.6 | -20.0 | -29.1 | +18.4 | +4.9 | +20.0 | -43.1 | +10.9 | -21.1 | -41.6 | |
| Step | 10 | 15 | 19 | 22 | 25 | 27 | 29 | 30 | 32 | 33 | 34 | |
Intervals
| Degree | Cents | Associated ratios | Interval name |
|---|---|---|---|
| 0 | 0 | 1/1 | unison |
| 1 | 125 | 14/13, 15/14 | 2/3-tone, trienthird |
| 2 | 250 | 15/13, 22/19 | semifourth |
| 3 | 375 | 5/4 | narrow perde segah, marvelous major third, near just major third |
| 4 | 500 | 4/3 | perfect fourth |
| 5 | 625 | 10/7, 23/16 | pental diminished fifth, classic diminshed fifth |
| 6 | 750 | 17/11, 20/13 | septendecimal subminor sixth |
| 7 | 875 | 5/3 | major sixth |
| 8 | 1000 | 16/9 | Pythagorean minor seventh |
| 9 | 1125 | 21/11, 23/12 | classic (5-limit) diminished octave |
| 10 | 1250 | 33/16 | |
| 11 | 1375 | ||
| 12 | 1500 | ||
| 13 | 1625 | ||
| 14 | 1750 | ||
| 15 | 1875 | ||
| 16 | 2000 |
Scala file
! E:\cakewalk\scales\125cent.scl ! 125 cent tuning 4 ! 125.00000 250.00000 375.00000 500.00000
Music
- Canyon Diablo Fall by Chris Vaisvil
- Crossing Over by Chris Vaisvil (125cET is an outdated name for this tuning system, standing for "125-cent equal temperament")