Diaschismic/Chords - Revision history

Videogamer1002: spelling

2026-02-09T05:47:51Z

spelling

← Older revision		Revision as of 05:47, 9 February 2026
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	The normal mapping for diaschismic is {{nowrap\|V<sub>dia</sub> {{=}} {{mapping\| 2 0 11 31 45 \| 0 1 -2 -8 -12 }}}}. From this we may derive a val {{nowrap\|'''V''' {{=}} V<sub>dia</sub>[0] − 100 V<sub>dia</sub>[1]}} {{nowrap\|{{=}} {{val\| 2 -100 211 831 1245 }}}} which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by V. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the [[Graham complexity]] of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.		The normal mapping for diaschismic is {{nowrap\|V<sub>dia</sub> {{=}} {{mapping\| 2 0 11 31 45 \| 0 1 -2 -8 -12 }}}}. From this we may derive a val {{nowrap\|'''V''' {{=}} V<sub>dia</sub>[0] − 100 V<sub>dia</sub>[1]}} {{nowrap\|{{=}} {{val\| 2 -100 211 831 1245 }}}} which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by V. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the [[Graham complexity]] of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.

	~~Diaschsmic~~ has [[mos scale]]s of size 10, 12, 22, 34, 46, and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.		Diaschismic has [[mos scale]]s of size 10, 12, 22, 34, 46, and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

	Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has many other connotations. The [[enharmonic unison]] is ^^d2, thus {{nowrap\|^^C {{=}} B#}}. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. {{nowrap\|^1 {{=}} 6''c''}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. For 46edo, {{nowrap\|''c'' {{=}} 4.3¢}} and {{nowrap\|^1 {{=}} 1\46}} = 26.1¢.		Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has many other connotations. The [[enharmonic unison]] is ^^d2, thus {{nowrap\|^^C {{=}} B#}}. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. {{nowrap\|^1 {{=}} 6''c''}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. For 46edo, {{nowrap\|''c'' {{=}} 4.3¢}} and {{nowrap\|^1 {{=}} 1\46}} = 26.1¢.

Lériendil: Lériendil moved page Chords of diaschismic to Diaschismic/Chords

2025-06-22T21:48:11Z

Lériendil moved page Chords of diaschismic to Diaschismic/Chords

← Older revision	Revision as of 21:48, 22 June 2025
(No difference)

TallKite: updated EI to EU

2024-12-29T00:24:43Z

updated EI to EU

← Older revision		Revision as of 00:24, 29 December 2024
Line 5:		Line 5:
	Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46, and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.		Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46, and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

	Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has many other connotations. The enharmonic ~~interval~~ is ^^d2, thus {{nowrap\|^^C {{=}} B#}}. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. {{nowrap\|^1 {{=}} 6''c''}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. For 46edo, {{nowrap\|''c'' {{=}} 4.3¢}} and {{nowrap\|^1 {{=}} 1\46}} = 26.1¢.		Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has many other connotations. The [[enharmonic unison]] is ^^d2, thus {{nowrap\|^^C {{=}} B#}}. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. {{nowrap\|^1 {{=}} 6''c''}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. For 46edo, {{nowrap\|''c'' {{=}} 4.3¢}} and {{nowrap\|^1 {{=}} 1\46}} = 26.1¢.

	In Diaschismic, {{nowrap\|5/4 {{=}} vM3}}, {{nowrap\|7/4 {{=}} vm7}}, and {{nowrap\|11/8 {{=}} vd5}} or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and {{nowrap\|~[[8192/8019]] {{=}} [13 -6 0 0 -1⟩}}. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with {{nowrap\|A4 > d5}}. If {{nowrap\|A4 < d5}}, the arrows flip direction.		In Diaschismic, {{nowrap\|5/4 {{=}} vM3}}, {{nowrap\|7/4 {{=}} vm7}}, and {{nowrap\|11/8 {{=}} vd5}} or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and {{nowrap\|~[[8192/8019]] {{=}} [13 -6 0 0 -1⟩}}. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with {{nowrap\|A4 > d5}}. If {{nowrap\|A4 < d5}}, the arrows flip direction.

ArrowHead294 at 15:12, 21 December 2024

2024-12-21T15:12:57Z

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TallKite: fixed a typo, other changes too

2024-12-21T11:58:27Z

fixed a typo, other changes too

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TallKite: minor clarifications

2024-12-17T03:55:15Z

minor clarifications

← Older revision		Revision as of 03:55, 17 December 2024
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	Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.		Diaschsmic has [[mos scale]]s of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.

	Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.		Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has so many other connotations. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.

	In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.		In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.

TallKite: added more chord names

2024-12-06T21:53:23Z

added more chord names

← Older revision		Revision as of 21:53, 6 December 2024
Line 7:		Line 7:
	Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.		Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf notation guide for rank-2 pergens]. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.

	In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.		In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~[[8192/8019]] = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.

	Because the list is limited to dyadic chords, certain obvious chords like C, Cm, C7 and Cm7 are omitted.		Because the list is limited to dyadic chords, certain obvious chords like C, Cm, C7 and Cm7 are omitted.
Line 169:		Line 169:
	\|783		\|783
	\|11/7		\|11/7
	\|m6		\|m6, vvA5
	!-4		!-4
	\|183		\|183
Line 955:		Line 955:
	\| 1-10/9-7/5-7/4		\| 1-10/9-7/5-7/4
	\| thrush		\| thrush
	\|		\|1-5/4-11/7-9/5
	\|		\|0 -2' -4 4'
	\|		\|Cv^7(vv#5)
	\| 16		\| 16
	\|-		\|-
Line 964:		Line 964:
	\| 1-11/7-7/5-7/4		\| 1-11/7-7/5-7/4
	\| werckismic		\| werckismic
	\|		\|1-14/11-16/9-20/9
	\|		\|0 4 -2 -4'
	\|		\|C7v9no5
	\| 16		\| 16
	\|-		\|-

TallKite: /* Tetrads */ more chord names

2024-12-06T04:10:38Z

Tetrads: more chord names

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TallKite: added more chord names

2024-11-23T10:04:20Z

added more chord names

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TallKite: started adding chord names

2024-11-23T07:49:01Z

started adding chord names

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