Pental major and minor: Difference between revisions

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''This article is about two different but related interval qualities. For 5-limit major and minor intervals, see [[5/4]], [[6/5]], [[8/5]], and [[5/3]]. For other uses of "pental", see [[Perfect fifth]] and [[5-limit]].''

: ''This article is about two different but related interval qualities. For 5-limit major and minor intervals, see [[5/4]], [[6/5]], [[8/5]], and [[5/3]]. For other uses of "pental", see [[Perfect fifth]] and [[5-limit]].''

'''Pental major''' intervals are an interval quality denoting tunings close to ptolemaic major intervals. They are sharper than [[submajor]] intervals and flatter than [[novamajor]] intervals. Likewise, '''pental minor''' intervals are an interval quality denoting tunings close to ptolemaic minor intervals. They are sharper than novaminor intervals and flatter than supraminor intervals. Pental major thirds range from about 375–394{{c}}, and pental minor thirds range from about 308–327{{c}}. Pental intervals may also be known as '''classical''', and the terms '''nearmajor/nearminor''' have also been used, though they refer to a somewhat larger band than the definition given here, bleeding into both the submajor/supraminor and novamajor/novaminor categories.

'''Pental major''' intervals are an interval quality denoting tunings close to ptolemaic major intervals. They are sharper than [[submajor]] intervals and flatter than [[novamajor]] intervals. Likewise, '''pental minor''' intervals are an interval quality denoting tunings close to ptolemaic minor intervals. They are sharper than novaminor intervals and flatter than supraminor intervals. Pental major thirds range from about 375–394{{c}}, and pental minor thirds range from about 308–327{{c}}. Pental intervals may also be known as '''classical''', and the terms '''nearmajor/nearminor'''{{idio}} have also been used, though they refer to a somewhat larger band than the definition given here, bleeding into both the submajor/supraminor and novamajor/novaminor categories.

Common pental major/minor intervals can be found as simple 5-limit intervals, and include:

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Optionally, the category of pental may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:

* '''Magimajor''' and '''magiminor''', for thirds, range between about 375–382 and 320–327{{c}}, respectively. These are flat of the 5-limit thirds, and appear in 5-limit temperaments where the chromatic semitone 25/24 is tempered narrow, like in [[garibaldi]], [[magic]] (hence the name), or the minor third in [[flattone]]. Magimajor seconds range from 171–178{{c}}, and thus contain the upper part of the "equable heptatonic" region. For a given [[neutral]] interval ''k'' in cents, the magimajor version is found at around {{nowrap|''k'' + 28}}, and the magiminor version is found at around {{nowrap|''k'' − 28}}.

* '''Magimajor''' and '''magiminor'''{{idio}}, for thirds, range between about 375–382 and 320–327{{c}}, respectively. These are flat of the 5-limit thirds, and appear in 5-limit temperaments where the chromatic semitone 25/24 is tempered narrow, like in [[garibaldi]], [[magic]] (hence the name), or the minor third in [[flattone]]. Magimajor seconds range from 171–178{{c}}, and thus contain the upper part of the "equable heptatonic" region. For a given [[neutral]] interval ''k'' in cents, the magimajor version is found at around {{nowrap|''k'' + 28}}, and the magiminor version is found at around {{nowrap|''k'' − 28}}.

* '''Pentamajor''' and '''pentaminor''', for thirds, range between about 382–394 and 308–320{{c}}, respectively. These are the regions containing 5-limit intervals. Pentamajor seconds range from 178–190{{c}}. For a given [[neutral]] interval ''k'' in cents, the pentamajor version is found at around {{nowrap|''k'' + 35}}, and the pentaminor version is found at around {{nowrap|''k'' − 35}}.

* '''Pentamajor'''/'''classimajor''' and '''pentaminor'''/'''classiminor'''{{idio}}, for thirds, range between about 382–394 and 308–320{{c}}, respectively. These are the regions containing 5-limit intervals. Pentamajor seconds range from 178–190{{c}}. For a given [[neutral]] interval ''k'' in cents, the pentamajor version is found at around {{nowrap|''k'' + 35}}, and the pentaminor version is found at around {{nowrap|''k'' − 35}}.

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-''This article is about two different but related interval qualities. For 5-limit major and minor intervals, see [[5/4]], [[6/5]], [[8/5]], and [[5/3]]. For other uses of "pental", see [[Perfect fifth]] and [[5-limit]].''
+: ''This article is about two different but related interval qualities. For 5-limit major and minor intervals, see [[5/4]], [[6/5]], [[8/5]], and [[5/3]]. For other uses of "pental", see [[Perfect fifth]] and [[5-limit]].''
-'''Pental major''' intervals are an interval quality denoting tunings close to ptolemaic major intervals. They are sharper than [[submajor]] intervals and flatter than [[novamajor]] intervals. Likewise, '''pental minor''' intervals are an interval quality denoting tunings close to ptolemaic minor intervals. They are sharper than novaminor intervals and flatter than supraminor intervals. Pental major thirds range from about 375–394{{c}}, and pental minor thirds range from about 308–327{{c}}. Pental intervals may also be known as '''classical''', and the terms '''nearmajor/nearminor''' have also been used, though they refer to a somewhat larger band than the definition given here, bleeding into both the submajor/supraminor and novamajor/novaminor categories.
+'''Pental major''' intervals are an interval quality denoting tunings close to ptolemaic major intervals. They are sharper than [[submajor]] intervals and flatter than [[novamajor]] intervals. Likewise, '''pental minor''' intervals are an interval quality denoting tunings close to ptolemaic minor intervals. They are sharper than novaminor intervals and flatter than supraminor intervals. Pental major thirds range from about 375–394{{c}}, and pental minor thirds range from about 308–327{{c}}. Pental intervals may also be known as '''classical''', and the terms '''nearmajor/nearminor'''{{idio}} have also been used, though they refer to a somewhat larger band than the definition given here, bleeding into both the submajor/supraminor and novamajor/novaminor categories.
 Common pental major/minor intervals can be found as simple 5-limit intervals, and include:
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 Optionally, the category of pental may be split into two smaller categories. Tuning ranges have been provided in terms of thirds:
-* '''Magimajor''' and '''magiminor''', for thirds, range between about 375–382 and 320–327{{c}}, respectively. These are flat of the 5-limit thirds, and appear in 5-limit temperaments where the chromatic semitone 25/24 is tempered narrow, like in [[garibaldi]], [[magic]] (hence the name), or the minor third in [[flattone]]. Magimajor seconds range from 171–178{{c}}, and thus contain the upper part of the "equable heptatonic" region. For a given [[neutral]] interval ''k'' in cents, the magimajor version is found at around {{nowrap|''k'' + 28}}, and the magiminor version is found at around {{nowrap|''k'' − 28}}.
+* '''Magimajor''' and '''magiminor'''{{idio}}, for thirds, range between about 375–382 and 320–327{{c}}, respectively. These are flat of the 5-limit thirds, and appear in 5-limit temperaments where the chromatic semitone 25/24 is tempered narrow, like in [[garibaldi]], [[magic]] (hence the name), or the minor third in [[flattone]]. Magimajor seconds range from 171–178{{c}}, and thus contain the upper part of the "equable heptatonic" region. For a given [[neutral]] interval ''k'' in cents, the magimajor version is found at around {{nowrap|''k'' + 28}}, and the magiminor version is found at around {{nowrap|''k'' − 28}}.
-* '''Pentamajor''' and '''pentaminor''', for thirds, range between about 382–394 and 308–320{{c}}, respectively. These are the regions containing 5-limit intervals. Pentamajor seconds range from 178–190{{c}}. For a given [[neutral]] interval ''k'' in cents, the pentamajor version is found at around {{nowrap|''k'' + 35}}, and the pentaminor version is found at around {{nowrap|''k'' − 35}}.
+* '''Pentamajor'''/'''classimajor''' and '''pentaminor'''/'''classiminor'''{{idio}}, for thirds, range between about 382–394 and 308–320{{c}}, respectively. These are the regions containing 5-limit intervals. Pentamajor seconds range from 178–190{{c}}. For a given [[neutral]] interval ''k'' in cents, the pentamajor version is found at around {{nowrap|''k'' + 35}}, and the pentaminor version is found at around {{nowrap|''k'' − 35}}.
 {{Navbox intervals}}