View source for Mike Sheiman's Alternative Interval Categorizations

People often say xenharmonic intervals like [[16/11]] are "sour" and mathematically similar intervals (e.g. octave inverses like

1/(16/11) or [[11/8]] are "sweet". Doesn't that seem a bit counter intuitive?

We've been told via standard music theory to accept everything, '''even xenharmonic/microtonal intervals, be''' '''pigeon-holed into some sort of [[diatonic]] category'''.

In [[12EDO]] C is the [[tonic]]/"first".

C# (apx. 17/16) is a minor second

D (apx. 9/8) is a major second

D# (apx. 6/5) is a minor third

E (apx. 5/4) is a major third

'''F (apx 4/3) is a perfect fourth''' (Why not a major or minor? Inconsistency...)

'''F# (apx. 7/5) is on the borderline between a fourth and fifth'''

'''G (apx. 3/2) is a perfect fifth''' (Again, no major or minor. Inconsistency...)

G# (apx. 8/5)is a minor sixth

A (apx. 5/3) is a major sixth

A# (apx. 9/5) is a minor seventh

B (apx 15/8) is a major seventh

'''Notice how...even in 12EDO, interval categories seem a bit shaky and inconsistent.'''

So how, then, to you categorize something like an 11/8 or 16/11 between a fourth and a fifth? Or an interval like [[14/9]], between a fifth and a sixth? Furthermore, how do explain when, for example, a 16/11 feels "sour" while an 11/8 slightly below it feels upbeat/sweet?

Usually we simply add additional names as necessary and further complicate the system. 16/11? That's sour because it's a '''diminished''' fifth. Around 14/9? That's upbeat because it's an '''augmented''' fifth. Why not just stick with major ('''more upbeat''') and minor ('''more downbeat''') and neutral ('''in-between upbeat and downbeat and a bit sour''')...equally distributed among 4ths, 5ths, 6ths...?

Here's a proposal for a <u>'''major/minor/neutral-only system'''</u>

C is the tonic/"first".

(15/14 and less) is a minor second

(13/12 to 11/10) is a neutral second

(10/9 to 9/8) is a major second

(8/7) is a minor '''second-half'''

'''(15/13) is a''' neutral '''second-half'''

(7/6) is a major '''second-half'''

(19/16 to 6/5) is a minor third

(11/9) is a neutral third

(5/4-9/7) is a major third

(4/3) is a '''minor fourth''' '''(not a perfect fourth)'''

(15/11) is a neutral fourth

(11/8) is a '''major fourth (a more upbeat fourth)'''

(7/5) is a '''minor fourth-half (not the usual tritone)'''

'''(10/7)''' is a '''neutral fourth-half (not the usual tritone)'''

(13/9) is a '''major fourth-half (a "more upbeat tritone")'''

(16/11) is a minor fifth

(22/15) is a neutral fifth

(3/2) is a '''major fifth (not a perfect fifth)'''

(17/11) is a '''minor fifth-half'''

'''---------------------'''

'''(14/9-11/7)''' is a '''major fifth-half'''

'''(8/5)''' is a minor sixth

(13/8-18/11) is a neutral sixth

'''(5/3)''' is a major sixth

(12/7) is a '''minor sixth-half'''

'''(26/15)''' is a '''neutral sixth-half'''

(7/4) is a '''major sixth-half'''

(16/9-9/5) is a minor seventh

(11/6) is a neutral seventh

(15/8) is a major seventh

'''Note there is only one gap where there isn't an equal minor/neutral/major sub-type categorization for every interval number/type!''' Only the fifth-half isn't perfectly even with two parts instead of 3.

At a quick glance...the point is '''with the latter system, you can hopefully quickly/easily tell which intervals to use to get upbeat (major), downbeat and a tad tense (minor), somewhat tense and mixed-mooded (neutral), or relatively sour (fourth-half) intervals.'''
[[Category:Interval naming]]