Xenharmonic Reference - User contributions [en]

Talk:Mojannab

2026-03-06T10:44:33Z

Iniðil: add sign

I will create larger article on the dastgah and then merge this one with it.</br>
- [[User:Iniðil|Iniðil]]

Talk:Mojannab

2026-03-06T10:42:40Z

Iniðil: Created page with "I will create larger article on the dastgah and then merge this one with it."

I will create larger article on the dastgah and then merge this one with it.

Mojannab

2026-03-06T10:39:58Z

Iniðil: more correct interpretation

'''Mojannab''' is a type of neutral interval in Iranian classical music corresponding to the [[neutral second]]. It is derived by dividing the small minor third on two unequal parts, or by stacking two [[Pythagorean tuning|Pythagorean limmas]]. Applicable theoretical definitions and classifications were introduced by al-Farabi[https://en.wikipedia.org/wiki/Al-Farabi] (870–951 CE) and Safī al-Dīn al-Urmawī[https://en.wikipedia.org/wiki/Safi_al-Din_al-Urmawi] (1216-1294 CE).

== Categorization ==
{| class="wikitable"
|+
!Type
!Range
!JI
!Western name
|-
|Small
|112-120c
|15/14, 16/15, 2187/2048
|Large semitone
|-
|Medium
|128-151c
|12/11, 14/13, 13/12, 64/59
|Supraminor/neutral second
|-
|Large
|165-182c
|11/10, 10/9, 65536/59049
|Submajor/nearmajor second
|}

Mojannab

2026-03-06T10:20:45Z

Iniðil: fix of error

'''Mojannab''' is a type of neutral interval in Iranian classical music corresponding to the [[neutral second]]. Functionally, it represents two unequal divisions of the minor third. Applicable theoretical definitions and classifications were introduced by al-Farabi[https://en.wikipedia.org/wiki/Al-Farabi] (870–951 CE) and Safī al-Dīn al-Urmawī[https://en.wikipedia.org/wiki/Safi_al-Din_al-Urmawi] (1216-1294 CE).

== Categorization ==
{| class="wikitable"
|+
!Type
!Range
!JI
!Western name
|-
|Small
|112-120c
|15/14, 16/15, 2187/2048
|Large semitone
|-
|Medium
|128-151c
|12/11, 14/13, 13/12, 64/59
|Supraminor/neutral second
|-
|Large
|165-182c
|11/10, 10/9, 65536/59049
|Submajor/nearmajor second
|}

Mojannab

2026-03-05T23:57:40Z

Iniðil: language improvement

'''Mojannab''' is a type of neutral interval in Iranian classical music corresponding to the spectrum of intervals between [[neutral second]] and [[Minor third|subminor third]]. Functionally, it represents two unequal divisions of the minor third. Applicable theoretical definitions and classifications were introduced by al-Farabi[https://en.wikipedia.org/wiki/Al-Farabi] (870–951 CE) and Safī al-Dīn al-Urmawī[https://en.wikipedia.org/wiki/Safi_al-Din_al-Urmawi] (1216-1294 CE).

== Categorization ==
{| class="wikitable"
|+
!Type
!Range
!JI
!Western name
|-
|Small
|112-120c
|15/14, 16/15, 2187/2048
|Small neutral second
|-
|Medium
|128-151c
|12/11, 14/13, 13/12, 64/59
|Neutral second
|-
|Large
|165-182c
|11/10, 10/9, 65536/59049
|Large neutral second
|}

Mojannab

2026-03-05T23:55:06Z

Iniðil: definition of interval from Iranian classical music theory

'''Mojannab''' is type of neutral interval in Iranian classical music corresponding to spectrum of intervals between [[neutral second]] and [[Minor third|subminor third]]. Functionally, it represents two unequal divisions of the minor third. Theoretical definition and classifications for this type of intervals were introduced by al-Farabi[https://en.wikipedia.org/wiki/Al-Farabi] (870–951 CE) and Safī al-Dīn al-Urmawī[https://en.wikipedia.org/wiki/Safi_al-Din_al-Urmawi] (1216-1294 CE).

== Categorization ==
{| class="wikitable"
|+
!Type
!Range
!JI
!Western name
|-
|Small
|112-120c
|15/14, 16/15, 2187/2048
|Small neutral second
|-
|Medium
|128-151c
|12/11, 14/13, 13/12, 64/59
|Neutral second
|-
|Large
|165-182c
|11/10, 10/9, 65536/59049
|Large neutral second
|}

14edo

2026-03-04T20:13:31Z

Iniðil: /* Intrvals */ typo

'''14edo''', or 14 equal divisions of the octave, is the equal tuning featuring steps of (1200/14) ~≃ 85.714 cents, 14 of which stack to the perfect octave 2/1. While it approximates the 5:7:9:11:17:19 harmony relatively well for its size, it lacks a convincing realization of other low-complexity just intervals. Consequently, [[Delta-rational chord|DR]]-based approaches may be more practically useful.

== Theory ==
=== Edostep interpretations ===
The edostep of 14edo allows several interpretations within the [[19-limit]]:
* 20/19 (the third part of dividing 7/6)
* 21/20 (the difference between 4/3 and 7/5)
* 256/243 (the difference between 4/3 and two 9/8)
* 28/27 (the difference between 15/14 and 10/9)
* 22/21 (the difference between 12/11 and 8/7)

=== JI approximation ===
Some recognizably approximated low-complexity just intervals include 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10, which can allow to interpret 14edo as high damage 11-limit temperament.

{{Harmonics in ED|14|31|0}}
{| class="wikitable"
|+Thirds in 14edo
!Quality
|'''Subminor'''
|'''Neutral'''
|'''Supermajor'''
|-
!Cents
|'''257.143'''
|'''342.857'''
|'''428.571'''
|-
!Just interpretation
|'''22/19'''
|'''17/14'''
|'''22/17'''
|}

==== Chords ====
As a superset of the popular 7edo scale, it offers recognizable triadic harmonies built on subminor, neutral, and supermajor thirds; however, its poor approximation of perfect fourths and fifths gives it a distinctly xenharmonic character.

Its equally-spaced [[MOS]] [[diatonic]] scale (equivalent to 7edo) allows all intervals to have a "minor", "neutral/perfect", and "major" variant, wherein (for instance) a minor third is the same pitch as a major second. [[21edo]] provides distinctions between these categories.

14edo can also support Western functional harmony. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.

== Intervals ==
Here is a table of 14edo's intervals:
{| class="wikitable"
|+
!Name
!Degree
!Cents
!Approximate Ratios
|-
|Unison
|0
|0
|1/1
|-
|Narrow minor second
|1
|85.714
|'''20/19,''' 21/20
|-
|Neutral second
|2
|171.429
|'''11/10''', 10/9
|-
|Subminor third
|3
|257.143
|'''7/6''', 22/19, 15/13
|-
|Neutral third
|4
|342.857
|'''11/9''', 17/14
|-
|Supermajor third
|5
|428.571
|'''9/7''', 22/17, 14/11
|-
|Wide fourth
|6
|514.286
|'''4/3''', 19/14
|-
|Tritone
|7
|600.000
|'''7/5''', 10/7
|-
|Narrow fifth
|8
|685.714
|'''3/2''', 28/19
|-
|Subminor sixth
|9
|771.429
|'''14/9''', 11/7
|-
|Neutral sixth
|10
|857.143
|'''18/11''', 28/17
|-
|Supermajor sixth
|11
|942.857
|'''12/7''', 17/10, 19/11
|-
|Neutral seventh
|12
|1028.571
|'''9/5''', 20/11
|-
|Wide Major 7th
|13
|1114.286
|'''17/9''', 36/19, 21/11
|-
|Octave
|14
|1200
|2/1
|}

{{Navbox EDO}}
{{Cat|Edos}}

14edo

2026-03-04T16:58:37Z

Iniðil: add interval table

'''14edo''', or 14 equal divisions of the octave, is the equal tuning featuring steps of (1200/14) ~≃ 85.714 cents, 14 of which stack to the perfect octave 2/1. While it approximates the 5:7:9:11:17:19 harmony relatively well for its size, it lacks a convincing realization of other low-complexity just intervals. Consequently, [[Delta-rational chord|DR]]-based approaches may be more practically useful.

== Theory ==
=== Edostep interpretations ===
The edostep of 14edo allows several interpretations within the [[19-limit]]:
* 20/19 (the third part of dividing 7/6)
* 21/20 (the difference between 4/3 and 7/5)
* 256/243 (the difference between 4/3 and two 9/8)
* 28/27 (the difference between 15/14 and 10/9)
* 22/21 (the difference between 12/11 and 8/7)

=== JI approximation ===
Some recognizably approximated low-complexity just intervals include 7/5, 7/6, 9/7, 10/7, 10/9, 11/7, 11/9, and 11/10, which can allow to interpret 14edo as high damage 11-limit temperament.

{{Harmonics in ED|14|31|0}}
{| class="wikitable"
|+Thirds in 14edo
!Quality
|'''Subminor'''
|'''Neutral'''
|'''Supermajor'''
|-
!Cents
|'''257.143'''
|'''342.857'''
|'''428.571'''
|-
!Just interpretation
|'''22/19'''
|'''17/14'''
|'''22/17'''
|}

==== Chords ====
As a superset of the popular 7edo scale, it offers recognizable triadic harmonies built on subminor, neutral, and supermajor thirds; however, its poor approximation of perfect fourths and fifths gives it a distinctly xenharmonic character.

Its equally-spaced [[MOS]] [[diatonic]] scale (equivalent to 7edo) allows all intervals to have a "minor", "neutral/perfect", and "major" variant, wherein (for instance) a minor third is the same pitch as a major second. [[21edo]] provides distinctions between these categories.

14edo can also support Western functional harmony. The most stable chords are [0 3 8] and [0 4 8], including extensions with the 11th and 12th steps.

== Intrvals ==
Here is a table of 14edo's intervals:
{| class="wikitable"
|+
!Name
!Degree
!Cents
!Approximate Ratios
|-
|Unison
|0
|0
|1/1
|-
|Narrow minor second
|1
|85.714
|'''20/19,''' 21/20
|-
|Neutral second
|2
|171.429
|'''11/10''', 10/9
|-
|Subminor third
|3
|257.143
|'''7/6''', 22/19, 15/13
|-
|Neutral third
|4
|342.857
|'''11/9''', 17/14
|-
|Supermajor third
|5
|428.571
|'''9/7''', 22/17, 14/11
|-
|Wide fourth
|6
|514.286
|'''4/3''', 19/14
|-
|Tritone
|7
|600.000
|'''7/5''', 10/7
|-
|Narrow fifth
|8
|685.714
|'''3/2''', 28/19
|-
|Subminor sixth
|9
|771.429
|'''14/9''', 11/7
|-
|Neutral sixth
|10
|857.143
|'''18/11''', 28/17
|-
|Supermajor sixth
|11
|942.857
|'''12/7''', 17/10, 19/11
|-
|Neutral seventh
|12
|1028.571
|'''9/5''', 20/11
|-
|Wide Major 7th
|13
|1114.286
|'''17/9''', 36/19, 21/11
|-
|Octave
|14
|1200
|2/1
|}

{{Navbox EDO}}
{{Cat|Edos}}

14edo

2026-03-04T16:21:01Z

Iniðil: /* Edostep interpretations */ language

14edo

2026-03-04T16:20:12Z

Iniðil: /* Chords */

14edo

2026-03-04T16:18:41Z

Iniðil: provide more information