Editing Generic and specific intervals (section)

==Myhill's property<!--'Myhill's property' redirects here-->==
'''Myhill's property'''<!--boldface per WP:R#PLA--> is the quality of [[musical scale]]s or collections with exactly two specific intervals for every generic interval, and thus also have the properties of [[cardinality equals variety]], [[structure implies multiplicity]], and being a [[well formed generated collection]]. In other words, each generic interval can be made from one of two possible different specific intervals. For example, there are major or minor and perfect or augmented/diminished variants of all the diatonic intervals:

{| class="wikitable"
! Diatonic<br/> interval
! Generic<br/> interval
! Diatonic<br/> intervals
! Specific<br/> intervals
|-
|2nd
|1
|m2 and M2
|1 and 2
|-
|3rd
|2
|m3 and M3
|3 and 4
|-
|4th
|3
|P4 and A4
|5 and 6
|-
|5th
|4
|d5 and P5
|6 and 7
|-
|6th
|5
|m6 and M6
|8 and 9
|-
|7th
|6
|m7 and M7
|10 and 11
|}

The [[diatonic scale|diatonic]] and [[pentatonic collection]]s possess Myhill's property. The concept appears to have been first described by John Clough and [[Gerald Myerson]] and named after their associate the mathematician [[John Myhill]]. (Johnson 2003, p.&nbsp;106, 158)