Formal comma - Revision history

Fredg999: I forgot to remove the todo box...

2025-07-29T20:17:56Z

I forgot to remove the todo box...

← Older revision		Revision as of 20:17, 29 July 2025
Line 10:		Line 10:
	Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. Some notation systems allow one to replace the formal comma for such a prime with its [[chromatic]] and/or [[enharmonic]] counterparts.		Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. Some notation systems allow one to replace the formal comma for such a prime with its [[chromatic]] and/or [[enharmonic]] counterparts.

	~~{{Todo\|inline=1\|text=add ratios}}~~
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	\|+Formal commas used by various JI notations		\|+Formal commas used by various JI notations

Fredg999: /* Usage in JI notations */ Add ratios in table

2025-07-29T20:13:10Z

Usage in JI notations: Add ratios in table

← Older revision		Revision as of 20:13, 29 July 2025
Line 23:		Line 23:
	\|-		\|-
	! [[Color notation]]		! [[Color notation]]
	\| M3		\| [[81/80\|80/81]] (M3)
	\| m7		\| [[64/63\|63/64]] (m7)
	\| P4/A4		\| [[33/32]] (P4)<br>[[729/704\|704/729]] (A4)
	\| m6/M6		\| [[1053/1024]] (m6)<br> [[27/26\|26/27]] (M6)
	\| m2		\| [[4131/4096]] (m2)
	\| m3		\| [[513/512]] (m3)
	\| d5		\| [[16767/16384]] (d5)
	\|-		\|-
	! [[Functional Just System]]		! [[Functional Just System]]
	\| M3		\| 80/81 (M3)
	\| m7		\| 63/64 (m7)
	\| P4		\| 33/32 (P4)
	\| m6		\| 1053/1024 (m6)
	\| m2		\| 4131/4096 (m2)
	\| m3		\| 513/512 (m3)
	\| A4		\| [[736/729]] (A4)
	\|-		\|-
	! [[Helmholtz–Ellis notation]]		! [[Helmholtz–Ellis notation]]
	\| M3		\| 80/81 (M3)
	\| m7		\| 63/64 (m7)
	\| P4		\| 33/32 (P4)
	\| M6		\| 26/27 (M6)
	\| A1		\| [[2187/2176]] (A1)
	\| m3		\| 513/512 (m3)
	\| A4		\| 736/729 (A4)
	\|-		\|-
	! Prime-factor [[Sagittal notation\|Sagittal]]		! Prime-factor [[Sagittal notation\|Sagittal]]
	\| M3		\| 80/81 (M3)
	\| m7		\| 63/64 (m7)
	\| P4		\| 33/32 (P4)
	\| M6		\| 26/27 (M6)
	\| m2		\| 4131/4096 (m2)
	\| m3		\| 513/512 (m3)
	\| A4		\| 736/729 (A4)
	\|}		\|}

FloraC: + prime 23

2025-07-16T10:45:06Z

+ prime 23

← Older revision		Revision as of 10:45, 16 July 2025
Line 11:		Line 11:

	{{Todo\|inline=1\|text=add ratios}}		{{Todo\|inline=1\|text=add ratios}}
	{\| class="wikitable"		{\| class="wikitable center-all"
	\|+Formal commas used by various JI notations		\|+Formal commas used by various JI notations
	!		!
Line 20:		Line 20:
	! 17		! 17
	! 19		! 19
			! 23
	\|-		\|-
	! [[Color notation]]		! [[Color notation]]
Line 28:		Line 29:
	\| m2		\| m2
	\| m3		\| m3
			\| d5
	\|-		\|-
	! [[Functional Just System]]		! [[Functional Just System]]
Line 36:		Line 38:
	\| m2		\| m2
	\| m3		\| m3
			\| A4
	\|-		\|-
	! [[Helmholtz–Ellis notation]]		! [[Helmholtz–Ellis notation]]
Line 44:		Line 47:
	\| A1		\| A1
	\| m3		\| m3
			\| A4
	\|-		\|-
	! Prime-factor [[Sagittal notation\|Sagittal]]		! Prime-factor [[Sagittal notation\|Sagittal]]
Line 52:		Line 56:
	\| m2		\| m2
	\| m3		\| m3
			\| A4
	\|}		\|}

FloraC: Be generic about varying formal commas in a notation system

2025-07-16T10:42:55Z

Be generic about varying formal commas in a notation system

← Older revision		Revision as of 10:42, 16 July 2025
Line 8:		Line 8:
	A JI notation will typically have for each prime ''p'' a pair of [[inflections and alterations\|inflections]] that raise/lower a note by ''p'''s formal comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B♭, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note.		A JI notation will typically have for each prime ''p'' a pair of [[inflections and alterations\|inflections]] that raise/lower a note by ''p'''s formal comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B♭, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note.

	Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. ~~Color~~ notation ~~allows~~ one to replace the formal comma for such a prime with its [[~~apotome~~]] ~~complement~~.		Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. Some notation systems allow one to replace the formal comma for such a prime with its [[chromatic]] and/or [[enharmonic]] counterparts.

	{{Todo\|inline=1\|text=add ratios}}		{{Todo\|inline=1\|text=add ratios}}

FloraC: Formal commas are notation-specific

2025-07-16T10:05:58Z

Formal commas are notation-specific

← Older revision		Revision as of 10:05, 16 July 2025
Line 1:		Line 1:
	A '''formal comma''' (also called a '''mapping comma'''{{idiosyncratic}}) for a prime number ''p'' > 3 is a comma that maps every [[prime subgroup\|2.3.''p''-subgroup]] interval to a nearby conventional [[3-limit]] interval. For example, [[81/80]] maps every 5-limit interval to the 3-limit.		A '''formal comma''' (also called a '''mapping comma'''{{idiosyncratic}}) for a prime number {{nowrap\| ''p'' > 3 }} is a comma in some [[musical notation]] that maps every [[prime subgroup\|2.3.''p''-subgroup]] interval to a nearby conventional [[3-limit]] interval. For example, [[81/80]] maps every 5-limit interval to the 3-limit.

	A formal comma can be identified by the prime ''p'' and the 3-limit interval that ''p''/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major third" and "5/4 = M3" unambiguously indicate 81/80.		A formal comma can be identified by the prime ''p'' and the 3-limit interval that ''p''/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major third" and "5/4 = M3" unambiguously indicate 81/80.

FloraC: Cleanup

2025-07-16T10:04:37Z

Cleanup

← Older revision		Revision as of 10:04, 16 July 2025
Line 1:		Line 1:
	A '''~~mapping~~ comma''' (also called a '''~~formal~~ comma''') for a prime number P > 3 is a comma that maps every [[~~Prime~~ subgroup\|2.3.P]] interval to a nearby conventional 3-limit interval. For example, [[81/80]] maps every 5-limit interval to the 3-limit.		A '''formal comma''' (also called a '''mapping comma'''{{idiosyncratic}}) for a prime number ''p'' > 3 is a comma that maps every [[prime subgroup\|2.3.''p''-subgroup]] interval to a nearby conventional [[3-limit]] interval. For example, [[81/80]] maps every 5-limit interval to the 3-limit.

	A ~~mapping~~ comma can be identified by the prime P and the 3-limit interval that P/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major ~~3rd~~" and "5/4 = M3" unambiguously indicate 81/80.		A formal comma can be identified by the prime ''p'' and the 3-limit interval that ''p''/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major third" and "5/4 = M3" unambiguously indicate 81/80.

	A mapping comma's [[monzo]] or prime-count vector always has a P-count of ±1. The 2-count and 3-count are almost always non-zero, and all other counts are always zero. For example, the usual mapping comma for prime 19 is [[513/512]] ~~= [~~-9 3 0 0 0 0 0 1>.		A mapping comma's [[monzo]] or prime-count vector always has a ''p''-count of ±1. The 2-count and 3-count are almost always non-zero, and all other counts are always zero. For example, the usual mapping comma for prime 19 is [[513/512]] ({{monzo\| -9 3 0 0 0 0 0 1 }}).

	=== Usage in JI notations ===		== Usage in JI notations ==
	A JI notation will typically have for each prime P a pair of [[~~Inflections~~ and alterations\|inflections]] that raise/lower a note by P's ~~mapping~~ comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected ~~B flat~~, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note.		A JI notation will typically have for each prime ''p'' a pair of [[inflections and alterations\|inflections]] that raise/lower a note by ''p'''s formal comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B♭, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note.

			Each JI notation assumes certain formal commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best formal commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289{{c}} to either M2 or M3. Color notation allows one to replace the formal comma for such a prime with its [[apotome]] complement.

	Each JI notation assumes certain mapping commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best mapping commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289¢ to either M2 or M3! Color notation allows one to replace the mapping comma for such a prime with its [[apotome]] complement.
	{{Todo\|inline=1\|text=add ratios}}		{{Todo\|inline=1\|text=add ratios}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+~~Mapping~~ commas used by various JI notations		\|+Formal commas used by various JI notations
	!		!
	!5		! 5
	!7		! 7
	!11		! 11
	!13		! 13
	!17		! 17
	!19		! 19
	\|-		\|-
	![[Color notation]]		! [[Color notation]]
	\|M3		\| M3
	\|m7		\| m7
	\|P4/A4		\| P4/A4
	\|m6/M6		\| m6/M6
	\|m2		\| m2
	\|m3		\| m3
	\|-		\|-
	![[~~FJS\|FJS notation~~]]		! [[Functional Just System]]
	\|M3		\| M3
	\|m7		\| m7
	\|P4		\| P4
	\|m6		\| m6
	\|m2		\| m2
	\|m3		\| m3
	\|-		\|-
	![[~~HEJI\|HEJI~~ notation]]		! [[Helmholtz–Ellis notation]]
	\|M3		\| M3
	\|m7		\| m7
	\|P4		\| P4
	\|M6		\| M6
	\|A1		\| A1
	\|m3		\| m3
	\|-		\|-
	!Prime-factor [[Sagittal notation\|Sagittal]]		! Prime-factor [[Sagittal notation\|Sagittal]]
	\|M3		\| M3
	\|m7		\| m7
	\|P4		\| P4
	\|M6		\| M6
	\|m2		\| m2
	\|m3		\| m3
	\|}		\|}

	== See also ==		== See also ==
	~~https://forum~~.~~sagittal.org/viewtopic.php?t=99~~		* [[Solfege string]], a concise way to indicate a series of formal commas.

	[~~[Solfege string~~]~~], a concise way to indicate a series of mapping commas.~~		== External links ==
			* [https://forum.sagittal.org/viewtopic.php?t=99 The Sagittal Forum \| ''Prime-factor Sagittal JI notation (one symbol per prime)'']

FloraC: FloraC moved page Mapping comma to Formal comma: See talk

2025-07-16T09:58:02Z

FloraC moved page Mapping comma to Formal comma: See talk

← Older revision	Revision as of 09:58, 16 July 2025
(No difference)

VectorGraphics: monzo is the standard term on the wiki

2025-07-16T09:18:20Z

monzo is the standard term on the wiki

← Older revision		Revision as of 09:18, 16 July 2025
Line 3:		Line 3:
	A mapping comma can be identified by the prime P and the 3-limit interval that P/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major 3rd" and "5/4 = M3" unambiguously indicate 81/80.		A mapping comma can be identified by the prime P and the 3-limit interval that P/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major 3rd" and "5/4 = M3" unambiguously indicate 81/80.

	A mapping comma's [[~~Monzo\|~~prime-count vector~~]] or monzo~~ always has a P-count of ±1. The 2-count and 3-count are almost always non-zero, and all other counts are always zero. For example, the usual mapping comma for prime 19 is [[513/512]] = [-9 3 0 0 0 0 0 1>.		A mapping comma's [[monzo]] or prime-count vector always has a P-count of ±1. The 2-count and 3-count are almost always non-zero, and all other counts are always zero. For example, the usual mapping comma for prime 19 is [[513/512]] = [-9 3 0 0 0 0 0 1>.

	=== Usage in JI notations ===		=== Usage in JI notations ===
Line 9:		Line 9:

	Each JI notation assumes certain mapping commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best mapping commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289¢ to either M2 or M3! Color notation allows one to replace the mapping comma for such a prime with its [[apotome]] complement.		Each JI notation assumes certain mapping commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best mapping commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289¢ to either M2 or M3! Color notation allows one to replace the mapping comma for such a prime with its [[apotome]] complement.
			{{Todo\|inline=1\|text=add ratios}}
	{\| class="wikitable"		{\| class="wikitable"
	\|+Mapping commas used by various JI notations		\|+Mapping commas used by various JI notations

TallKite: before you re-title this page as formal comma, please read the discussion tab!

2025-07-16T04:33:52Z

before you re-title this page as formal comma, please read the discussion tab!

New page

A '''mapping comma''' (also called a '''formal comma''') for a prime number P > 3 is a comma that maps every [[Prime subgroup|2.3.P]] interval to a nearby conventional 3-limit interval. For example, [[81/80]] maps every 5-limit interval to the 3-limit.

A mapping comma can be identified by the prime P and the 3-limit interval that P/1 (octave-reduced) maps to. The 3-limit interval is named conventionally. Thus both "prime 5 = major 3rd" and "5/4 = M3" unambiguously indicate 81/80.

A mapping comma's [[Monzo|prime-count vector]] or monzo always has a P-count of ±1. The 2-count and 3-count are almost always non-zero, and all other counts are always zero. For example, the usual mapping comma for prime 19 is [[513/512]] = [-9 3 0 0 0 0 0 1>.

=== Usage in JI notations ===
A JI notation will typically have for each prime P a pair of [[Inflections and alterations|inflections]] that raise/lower a note by P's mapping comma. Thus 5/4 from C is notated as an inflected E, 7/4 as an inflected B flat, etc. Ratios like [[35/32]] and [[49/48]] are inflected twice, and the commas accumulate, so complex ratios may be quite distant from the uninflected 3-limit note.

Each JI notation assumes certain mapping commas. The notations largely agree but do diverge for certain primes, because the exact method for choosing the best mapping commas is disputed. Ideally, both the 3-count and the size in cents is minimized, and there are other considerations as well. The choice for neutral-sounding primes like 11 (P4 vs. A4) and 13 (m6 vs. M6) is particularly tricky. Certain choices map the ratio [[13/11]] = 289¢ to either M2 or M3! Color notation allows one to replace the mapping comma for such a prime with its [[apotome]] complement.
{| class="wikitable"
|+Mapping commas used by various JI notations
!
!5
!7
!11
!13
!17
!19
|-
![[Color notation]]
|M3
|m7
|P4/A4
|m6/M6
|m2
|m3
|-
![[FJS|FJS notation]]
|M3
|m7
|P4
|m6
|m2
|m3
|-
![[HEJI|HEJI notation]]
|M3
|m7
|P4
|M6
|A1
|m3
|-
!Prime-factor [[Sagittal notation|Sagittal]]
|M3
|m7
|P4
|M6
|m2
|m3
|}

== See also ==
https://forum.sagittal.org/viewtopic.php?t=99

[[Solfege string]], a concise way to indicate a series of mapping commas.