User:Vector/Vector's interval naming scheme
Each interval name consists of a quality and an ordinal. Note that this is not the same as VJN, which names intervals based on commatic alterations, or ADIN, which names intervals based on their position in edos. This process is intended to be used to name intervals edo-agnostically. To name intervals in edos, use ADIN.
Process
To name an interval:
1. Octave-reduce and determine closest ordinal.
The ordinals are as follows:
| Ordinal | Neutral location | Cents |
|---|---|---|
| Unison | sqrt(2048/2187) | -57 |
| Second | sqrt(32/27) | 147 |
| Third | sqrt(3/2) | 351 |
| Fourth | sqrt(243/128) | 555 |
| Fifth | sqrt(512/243) | 645 |
| Sixth | sqrt(8/3) | 849 |
| Seventh | sqrt(27/8) | 1053 |
| Octave | sqrt(2187/512) | 1257 |
The unusual placement of the "unison" and "octave" are simply in order to make it so that the perfect unison has the same priority as a Pythagorean major or minor interval. Since intervals outside of the octave are not being considered, this is its only effect. The closest neutral ordinal to the interval's cent value defines the interval's ordinal.
2. Determine quality.
Intervals "in the vicinity" of each of these offsets from their neutral ordinal's location get their corresponding qualities. "In the vicinity" is kept vague. "Priority" here means something different than in ADIN: if you are being non-specific, it determines which offsets to use and which ones to skip, with lower-priority interval categories being more important.
| Offset | Priority 1 | Priority 2 | Priority 3 | Priority 4 |
|---|---|---|---|---|
| -102 | inframinor | inframinor | ||
| -95 | sensaminor | |||
| -85 | subminor | subminor | subminor | |
| -75 | gothminor | |||
| -65 | neominor | neominor | ||
| -55 | triminor | triminor | triminor | |
| -45 | valaminor | |||
| -35 | minor | pentaminor | pentaminor | pentaminor |
| -25 | magiminor | |||
| -20 | supraminor | supraminor | ||
| -10 | subneutral | |||
| 0 | neutral | neutral | neutral | neutral |
| 10 | supraneutral | |||
| 20 | submajor | submajor | ||
| 25 | magimajor | |||
| 35 | major | pentamajor | pentamajor | pentamajor |
| 45 | valamajor | |||
| 55 | trimajor | trimajor | trimajor | |
| 65 | neomajor | neomajor | ||
| 75 | gothmajor | |||
| 85 | supermajor | supermajor | supermajor | |
| 95 | sensamajor | |||
| 102 | ultramajor | ultramajor |
3. Apply special rules
Apply the following replacements:
| Target | Replacement |
|---|---|
| trimajor unison | unison |
| triminor fifth | diminished fifth |
| trimajor fifth | fifth |
| triminor fourth | fourth |
| trimajor fourth | augmented fourth |
| triminor octave | octave |
| major unison | unison |
| minor fifth | diminished fifth |
| major fifth | fifth |
| minor fourth | fourth |
| major fourth | augmented fourth |
| minor octave | octave |
4. Add back additional octaves
This follows standard diatonic interval arithmetic.
Example
What is the interval 462c?
Well, it is closest to the neutral ordinal 555c, so it is a kind of fourth. Additionally, its offset is -93, which places it in the sensaminor category. However, "sensaminor fourth" contains "minor fourth", which gets replaced to "fourth". So it is a sensafourth, or more broadly a subfourth.
What is the interval 71c?
Well, it is closest to the neutral ordinal 147c (remember the neutral unison is -57c) so it is a kind of second. Additionally, its offset is -76, which places it in the "gothminor" category. So it is a gothminor second, or more broadly a subminor second.
The intervals of justly-tuned blackdye
| Interval | Cents | Name |
|---|---|---|
| 1/1 | 0 | unison |
| 10/9 | 182 | pentamajor second |
| 9/8 | 204 | trimajor second |
| 5/4 | 386 | pentamajor third |
| 4/3 | 498 | fourth |
| 40/27 | 680 | pentafifth |
| 3/2 | 702 | fifth |
| 5/3 | 884 | pentamajor sixth |
| 27/16 | 906 | trimajor sixth |
| 15/8 | 1088 | pentamajor seventh |
| 2/1 | 1200 | octave |
