Extra-Diatonic Intervals

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. A rough approximate tuning range is suggested, based on 72edo, for illustrative purposes; note that these are not definitive measurements and the range will vary from listener to listener, as well as with changes in listening context. Up to four frequency ratios commonly associated with the terms are also included, again for illustrative purposes. The terms should be interpreted as referring to perceptual qualities that are necessarily subjective and flexible.

The Intervals and their Qualities

Interval Name	Qualitative Description	Approximate Range of Cents Values	Commonly Associated Frequency Ratios
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.	17¢ to 50¢	Most small commas, like 81/80 or 135/128
Subminor 2nd	Like a minor 2nd that has been flattened noticeably, but not so far as to sound like an out-of-tune unison.	50¢ to 83¢	25/24, 21/20, 22/21, 33/32
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.	133¢ to 167¢	11/10, 12/11, 13/12, 14/13
Supermajor 2nd	Like a major 2nd that has been sharpened noticeably, but not quite far enough that it begins to sound like a type of minor 3rd; however it may, in some contexts, be mistaken for a very, very flat type of minor 3rd.	217¢ to 250¢	8/7, 15/13
Subminor 3rd	A noticeably darker, flatter version of a minor 3rd. May in some contexts be mistaken for a very, very sharp type of major 2nd.	250¢ to 283¢	7/6, 13/11
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.	333¢ to 366¢	11/9, 16/13, 39/32
Supermajor 3rd	A noticeably sharper and more discordant version of a major 3rd. May in some cases be mistaken for a very, very flat type of 4th, but the obvious discordance in comparison to a typical perfect 4th or major 3rd is typically noticeable in many normal musical contexts.	417¢ to 450¢	14/11, 9/7, 13/10
Sub 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.	450¢ to 483¢	21/16, 17/13, 64/49
Super 4th	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.	517¢ to 533¢	15/11, 27/20
Narrow Tritone	Too sharp and discordant to be mistaken for a mistuned perfect 4th, but still noticeably flat of a traditional 600¢ tritone.	533¢ to 567¢	11/8, 18/13
Wide Tritone	Too flat and discordant to be mistaken for a mistuned perfect 5th, but still noticeably sharp of a traditional 600¢ tritone.	633¢ to 667¢	16/11, 13/9, 23/16
Sub 5th	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.	667¢ to 683¢	22/15, 40/27
Super 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 sixth.	717¢ to 750¢	32/21, 26/17, 49/32
Subminor 6th	A noticeably flatter and darker version of a minor 6th. May in some cases be mistaken for a very, very sharp type of 5th, but the obvious tonal color the interval provides is usually a start contrast to the stable concordance of a typical perfect fifth. With the exception of the very flat end off the subminor 6th spectrum, intervals in this category are noticeably more concordant than sub-5ths.	750¢ to 783¢	20/13, 11/7, 14/9, 25/16
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.	833¢ to 867¢	18/11, 13/8
Supermajor 6th	A noticeably sharper and typically more discordant version of a major 6th. May in some cases be mistaken for a very, very flat type of 7th.	917¢ to 950¢	12/7, 22/13
Subminor 7th	A noticeably darker, flatter version of a minor 7th. May in some contexts be mistaken for a very, very sharp type of major 6th.	950¢ to 983¢	7/4, 26/15
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.	1033¢ to 1067¢	11/6, 13/7, 20/11, 24/13
Supermajor 7th	Like a major 7th that has been sharpened noticeably, but not quite far enough that it begins to sound like a type of octave.	1117¢ to 1150¢	21/11, 31/16
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.	1150¢ to 1183¢	64/33, 160/81, the octave inversions of most small commas