25/16: Difference between revisions
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'''25/16''', the '''classic(al) | '''25/16''', the '''classic(al) augmented fifth''' is the interval obtained by stacking two [[5/4]] major thirds, however, it gains additional [[isoharmonic chord|isoharmonic]] identity from its position between [[11/8]] and [[7/4]], so it can frequently be used in conjunction with those, even in chords. | ||
While this interval has been referred to as the ''classic augmented fifth'' or ''classical augmented fifth'' for some time, the term ''diptolemaic'' [https://discord.com/channels/332357996569034752/516067802864549890/912167264789364736 was coined on Discord] by [[Flora Canou]] while discussing a proposal for a consistent naming scheme for different 5-limit intervals with [[Aura]]. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the '''diptolemaic augmented fifth'''. | |||
== Approximation == | |||
{{Interval edo approximation|25/16}} | |||
== See also == | == See also == | ||
* [[32/25]] – its [[octave complement]] | * [[32/25]] – its [[octave complement]] | ||
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[[Category:Fifth]] | [[Category:Fifth]] | ||
[[Category:Augmented fifth]] | [[Category:Augmented fifth]] | ||
Latest revision as of 13:07, 3 November 2025
| Interval information |
diptolemaic augmented fifth
reduced harmonic
[sound info]
25/16, the classic(al) augmented fifth is the interval obtained by stacking two 5/4 major thirds, however, it gains additional isoharmonic identity from its position between 11/8 and 7/4, so it can frequently be used in conjunction with those, even in chords.
While this interval has been referred to as the classic augmented fifth or classical augmented fifth for some time, the term diptolemaic was coined on Discord by Flora Canou while discussing a proposal for a consistent naming scheme for different 5-limit intervals with Aura. Specifically, since "diptolemaic" intervals have two instances of prime 5 in their factorization, this interval is also referred to as the diptolemaic augmented fifth.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | +27.37 | +6.84 |
| 11 | 7\11 | 763.64 | -8.99 | -8.24 |
| 14 | 9\14 | 771.43 | -1.20 | -1.40 |
| 17 | 11\17 | 776.47 | +3.84 | +5.44 |
| 25 | 16\25 | 768.00 | -4.63 | -9.64 |
| 28 | 18\28 | 771.43 | -1.20 | -2.80 |
| 31 | 20\31 | 774.19 | +1.57 | +4.05 |
| 42 | 27\42 | 771.43 | -1.20 | -4.20 |
| 45 | 29\45 | 773.33 | +0.71 | +2.65 |
| 48 | 31\48 | 775.00 | +2.37 | +9.49 |
| 56 | 36\56 | 771.43 | -1.20 | -5.59 |
| 59 | 38\59 | 772.88 | +0.25 | +1.25 |
| 62 | 40\62 | 774.19 | +1.57 | +8.09 |
| 70 | 45\70 | 771.43 | -1.20 | -6.99 |
| 73 | 47\73 | 772.60 | -0.02 | -0.15 |
| 76 | 49\76 | 773.68 | +1.06 | +6.69 |
See also
- 32/25 – its octave complement