View source for 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 [[Vector's just notation|VJN]], which names intervals based on commatic alterations, or [[ADIN]], which names intervals based on their position in edos.

== Process ==
To name an interval: 

=== 1. Octave-reduce and determine closest ordinal. ===
The ordinals are as follows:
{| class="wikitable"
|+
!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. 
{| class="wikitable"
|+
!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
|
|
|
|novaminor
|-
| -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
|
|
|
|novamajor
|-
|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:
{| class="wikitable"
|+
!Target
!Replacement
|-
|novamajor unison
|unison
|-
|novaminor fifth
|diminished fifth
|-
|novamajor fifth
|fifth
|-
|novaminor fourth
|fourth
|-
|novamajor fourth
|augmented fourth
|-
|novaminor 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''.