Extra-Diatonic Intervals

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When learning about and discussing xenharmonic intervals, there is not a single agreed-upon terminology. One approach is to describe intervals as being subtle alterations of conventional diatonic interval categories, by adding additional qualifying adjectives to traditional interval names. The origins of this approach are seemingly apocryphal, but its use is somewhat ubiquitous in online xenharmonic communities. This page is an attempt at a glossary of the most common of these extra-diatonic interval terms. It should be stated that these terms are qualitative, not quantitative, and no attempt will be made to definitively associate these interval terms to specific tunings or ranges of tunings. The terms should be interpreted as referring to perceptual qualities that are necessarily subjective and flexible, meant to describe an individual listener's perception, rather than a specific interval size.

Primary Diatonic Intervals

These are the intervals that anyone trained even a little bit in traditional Western music theory should have encountered. Note that here we are using them purely as qualitative descriptors of the sound of intervals, and not in reference to actual functional relationships.

Interval Name 12edo Cents Value
Unison 0
Minor 2nd 100
Major 2nd 200
Minor 3rd 300
Major 3rd 400
Perfect 4th 500
Tritone 600
Perfect 5th 700
Minor 6th 800
Major 6th 900
Minor 7th 1000
Major 7th 1100
Octave 1200

Secondary Intervals

These intervals sound like they occur in between two primary intervals, and may be described with the following qualities.

Interval Name Qualitative Description
Subminor 2nd Between a unison and a minor 2nd, the subminor 2nd typically sounds sharper than a simple out-of-tune unison, but narrower than a "semitone" in that it sounds like less than half of something that would sound like a whole-tone.
Neutral 2nd An ambiguous interval that is between a minor 2nd and a major 2nd, which may sometimes be mistaken for a sharp minor 2nd or a flat major 2nd.
Supermajor 2nd In between a major 2nd and a minor 3rd, sounding closer to a major 2nd, though still noticeably sharper than a traditional major 2nd.
Subminor 3rd In between a major 2nd and a minor 3rd, sounding closer to a minor 3rd, though still noticeably flatter than a traditional minor 3rd.
Neutral 3rd An ambiguous interval that is between a minor 3rd and a major 3rd, which may sometimes be mistaken for a flat major 3rd or a sharp minor 3rd.
Supermajor 3rd In between a major 3rd and a perfect 4th, the supermajor 3rd sounds noticeably sharper than a major 3rd, but still sounds like a type of 3rd, rather than an out-of-tune perfect 4th.
Sub Tritone Too sharp and discordant to be mistaken for a mistuned perfect 4th, but still noticeably flat of a traditional 600¢ tritone.
Super Tritone Too flat and discordant to be mistaken for a mistuned perfect 5th, but still noticeably sharp of a traditional 600¢ tritone.
Subminor 6th In between a perfect 5th and a minor 6th, the subminor 6th sounds noticeably flatter than a minor 6th, but still sounds like a type of 6th, rather than an out-of-tune perfect 5th.
Neutral 6th An ambiguous interval that is between a minor 6th and a major 6th, which may sometimes be mistaken for a flat major 6th or a sharp minor 6th.
Supermajor 6th In between a major 6th and a minor 7th, sounding closer to a major 6th, though still noticeably sharper than a traditional major 6th.
Subminor 7th In between a major 6th and a minor 7th, sounding closer to a minor 7th, though still noticeably flatter than a traditional minor 7th.
Neutral 7th An ambiguous interval that is between a minor 7th and a major 7th, which may sometimes be mistaken for a sharp minor 7th or a flat major 7th.
Supermajor 7th Between a major 7th and an octave, the supermajor 7th typically sounds flatter than a simple out-of-tune octave, but wider than a major 7th.

Tertiary Intervals

These intervals occur in between a primary interval and a secondary interval. For many listeners, these categories may not exist, as they can be subsumed into primary or secondary categories. They are less common in discussion, but may be relevant to some listeners.

Interval Name Qualitative Description
Super-Unison (or Wide Unison) Like a unison that has been obviously detuned in the sharp direction, but not far enough so as to sound like a type of 2nd. Typically noticeably discordant.
Supraminor 2nd In between a minor 2nd and a neutral 2nd. Not sharp enough to sound truly "neutral", but sharp enough to sound distinct from a minor 2nd.
Submajor 2nd In between a neutral 2nd and a major 2nd. Not flat enough to sound truly "neutral", but flat enough to sound distinct from a major 2nd.
Supraminor 3rd In between a minor 3rd and a neutral 3rd. Not sharp enough to sound truly "neutral", but sharp enough to sound distinct from a minor 3rd.
Submajor 3rd In between a neutral 3rd and a major 3rd. Not flat enough to sound truly "neutral", but flat enough to sound distinct from a major 3rd.
Sub 4th In between a supermajor 3rd and a perfect 4th. Like a perfect 4th that has been noticeably detuned in the flat direction, but not far enough so as to sound like a type of 3rd.
Super 4th In between a perfect 4th and a sub tritone. Like a perfect 4th that has been noticeably detuned in the sharp direction, but not far enough so as to sound like a type of tritone.
Sub 5th In between a perfect 5th and a super tritone. Like a perfect 5th that has been noticeably detuned in the flat direction, but not far enough so as to sound like a type of tritone.
Super 5th In between a subminor 6th and a perfect 5th. Like a perfect 5th that has been noticeably detuned in the sharp direction, but not far enough so as to sound like a type of 6th.
Supraminor 6th In between a minor 6th and a neutral 6th. Not sharp enough to sound truly "neutral", but sharp enough to sound distinct from a minor 6th.
Submajor 6th In between a neutral 6th and a major 6th. Not flat enough to sound truly "neutral", but flat enough to sound distinct from a major 6th.
Supraminor 7th In between a minor 7th and a neutral 7th. Not sharp enough to sound truly "neutral", but sharp enough to sound distinct from a minor 7th.
Submajor 7th In between a neutral 7th and a major 7th. Not flat enough to sound truly "neutral", but flat enough to sound distinct from a major 7th.
Sub-Octave (or Narrow Octave) Like an octave that has been obviously detuned in the flat direction, but not far enough so as to sound like a type of 7th. Typically noticeably discordant.