Kite Giedraitis's Categorizations of 41edo Scales - Revision history

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:30:23Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:30, 17 April 2025
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	\| Layo		\| Layo
	Saruyo&Ruyoyo		Saruyo&Ruyoyo
	\| [[Schismatic]] ([[Helmholtz temperament\|Helmholtz]],		\| [[Schismatic]] ([[Helmholtz (temperament)\|Helmholtz]],
	[[Garibaldi]], [[Cassandra]])		[[Garibaldi]], [[Cassandra]])
	\| (P8, P5)		\| (P8, P5)

Sintel: fix helmholtz link

2025-04-16T15:38:39Z

fix helmholtz link

← Older revision		Revision as of 15:38, 16 April 2025
Line 906:		Line 906:
	\| Layo		\| Layo
	Saruyo&Ruyoyo		Saruyo&Ruyoyo
	\| [[Schismatic]] ([[Helmholtz]],		\| [[Schismatic]] ([[Helmholtz temperament\|Helmholtz]],
	[[Garibaldi]], [[Cassandra]])		[[Garibaldi]], [[Cassandra]])
	\| (P8, P5)		\| (P8, P5)

ArrowHead294 at 18:49, 13 March 2025

2025-03-13T18:49:17Z

Show changes

TallKite: /* (TO DO / Notes to myself) */

2023-04-20T01:19:38Z

(TO DO / Notes to myself)

← Older revision		Revision as of 01:19, 20 April 2023
Line 736:		Line 736:
	\|5 = ~2		\|5 = ~2
	\|146.34		\|146.34
	\|Zozoyo Noca; Zozoyo&Rutribiyo		\|Zozoyo Noca
			Zozoyo&Rutribiyo
	\|[[Bohlen-Pierce]], [[Bohpier]]		\|[[Bohlen-Pierce]], [[Bohpier]]
	\|(P8, P12/13)		\|(P8, P12/13)
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	\|7 = M2		\|7 = M2
	\|204.88		\|204.88
	\|Wawa Layo / Wawa Layo&Ruyoyo		\|Wawa Layo
			Wawa Layo&Ruyoyo
	\|[[Baldy]]		\|[[Baldy]]
	\|(P8, c<sup>3</sup>P4/20)		\|(P8, c<sup>3</sup>P4/20)
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	\|11 = ^m3		\|11 = ^m3
	\|321.95		\|321.95
	\|Tritriyo / Latrizo&Zotriyo		\|Tritriyo
			Latrizo&Zotriyo
	\|[[Superkleismic]]		\|[[Superkleismic]]
	\|(P8, ccP4/9)		\|(P8, ccP4/9)
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	\|13 = vM3		\|13 = vM3
	\|380.49		\|380.49
	\|Laquinyo&Ruyoyo / Ruyoyo&Zozoyo / Saquinzo&Zozoyo		\|Laquinyo&Ruyoyo
			Ruyoyo&Zozoyo

			Saquinzo&Zozoyo
	\|[[Magic]]		\|[[Magic]]
	\|(P8, P12/5)		\|(P8, P12/5)
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	\|15 = ^M3		\|15 = ^M3
	\|439.02		\|439.02
	\|Sasa-tritribizo = {{monzo\| 5 -35 0 18 }}; Wawa Laquinyo / Wawa Ruyoyo&Zozoyo		\|Sasa-tritribizo = {{monzo\| 5 -35 0 18 }};
			Wawa Laquinyo

			Wawa Ruyoyo&Zozoyo
	\|		\|
	\|(P8, c<sup>6</sup>P5/18)		\|(P8, c<sup>6</sup>P5/18)
Line 878:		Line 887:
	\|17 = P4		\|17 = P4
	\|497.56		\|497.56
	\|Layo / Saruyo&Ruyoyo		\|Layo
			Saruyo&Ruyoyo
	\|[[Schismatic]] ([[Helmholtz]],		\|[[Schismatic]] ([[Helmholtz]],
	[[Garibaldi]], [[Cassandra]])		[[Garibaldi]], [[Cassandra]])

AthiTrydhen: /* (TO DO / Notes to myself) */

2023-04-19T05:25:17Z

(TO DO / Notes to myself)

← Older revision		Revision as of 05:25, 19 April 2023
Line 821:		Line 821:
	\|13 = vM3		\|13 = vM3
	\|380.49		\|380.49
	\|Laquinyo&Ruyoyo / Ruyoyo&Zozoyo		\|Laquinyo&Ruyoyo / Ruyoyo&Zozoyo / Saquinzo&Zozoyo
	\|[[Magic]]		\|[[Magic]]
	\|(P8, P12/5)		\|(P8, P12/5)

AthiTrydhen: /* (TO DO / Notes to myself) */

2023-04-19T01:48:39Z

(TO DO / Notes to myself)

← Older revision		Revision as of 01:48, 19 April 2023
Line 842:		Line 842:
	\|15 = ^M3		\|15 = ^M3
	\|439.02		\|439.02
	\|Sasa-tritribizo = {{monzo\| 5 -35 0 18 }}		\|Sasa-tritribizo = {{monzo\| 5 -35 0 18 }}; Wawa Laquinyo / Wawa Ruyoyo&Zozoyo
	\|		\|
	\|(P8, c<sup>6</sup>P5/18)		\|(P8, c<sup>6</sup>P5/18)

AthiTrydhen: /* (TO DO / Notes to myself) */ Thou shalt not mix color names and conventional temperament names!

2023-04-19T01:47:46Z

(TO DO / Notes to myself): Thou shalt not mix color names and conventional temperament names!

Show changes

TallKite: /* Chromaticism: semitonal, trientonal and microtonal scales */

2023-04-16T20:16:42Z

Chromaticism: semitonal, trientonal and microtonal scales

← Older revision		Revision as of 20:16, 16 April 2023
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	In practice, 41-equal scales tend to be "fuzzy", meaning that one or two scale notes may sometimes shift by an edostep. For example, a major scale may contain both a M2 and a vM2, and use whichever one is required by the harmony at the moment.		In practice, 41-equal scales tend to be "fuzzy", meaning that one or two scale notes may sometimes shift by an edostep. For example, a major scale may contain both a M2 and a vM2, and use whichever one is required by the harmony at the moment.

	There are five broad categories of 41-equal scales: pentatonic, diatonic, semitonal, ~~trientonal~~ and microtonal. The three latter ones fall under the general category of chromatic.		There are five broad categories of 41-equal scales: pentatonic, diatonic, semitonal, fretwise and microtonal. The three latter ones fall under the general category of chromatic.

	=== Pentatonic scales ===		=== Pentatonic scales ===
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	\|}		\|}

	=== Chromaticism: semitonal, ~~trientonal~~ and microtonal scales ===		=== Chromaticism: semitonal, fretwise and microtonal scales ===
	Most 41-equal intervals suggest a specific ratio, but those only a few edosteps wide don't. Thus the remaining categories don't imply any prime subgroups. Traditional 12-equal chromaticism, which translates to runs played on every other fret, is called '''semitonal''', a conventional term referring to the 12-equal semitone. Playing a run of notes one fret apart is ~~called '''trientonal''', which means "by third-tones". In a guitar context, it can be~~ called '''fretwise'''. '''Microtonal''' scales differ from fuzzy scales in having many sequential ^1 intervals, and no steps larger than a vm2. Thus fuzzy means partly but not fully microtonal, and a fuzzy diatonic scale could be called a diatonic/microtonal scale. '''Chromatic''' is an umbrella term that includes semitonal, ~~trientonal/~~fretwise and microtonal.		Most 41-equal intervals suggest a specific ratio, but those only a few edosteps wide don't. Thus the remaining categories don't imply any prime subgroups. Traditional 12-equal chromaticism, which translates to runs played on every other fret, is called '''semitonal''', a conventional term referring to the 12-equal semitone. Playing a run of notes one fret apart is called '''fretwise'''. '''Microtonal''' scales differ from fuzzy scales in having many sequential ^1 intervals, and no steps larger than a vm2. Thus fuzzy means partly but not fully microtonal, and a fuzzy diatonic scale could be called a diatonic/microtonal scale. '''Chromatic''' is an umbrella term that includes semitonal, fretwise and microtonal.
	{\| class="wikitable" style="text-align:center;"		{\| class="wikitable" style="text-align:center;"
	!scale type -->		!scale type -->
	! colspan="4" \|semitonal		! colspan="4" \|semitonal
	! colspan="2" \|~~trientonal or~~ fretwise		! colspan="2" \|fretwise
	! colspan="2" \|microtonal		! colspan="2" \|microtonal
	\|-		\|-
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	On the Kite guitar, going up an "even" interval (one that has an even number of edosteps) keeps one on the same string, and an "odd" one takes you to the next string. An octave spans 3 strings, thus a scale often has only 3 odd intervals. The exceptions are generally either fuzzy or awkward to play. The latter include wa, ila and zala diatonic, and microtonal scales with many ^1 steps.		On the Kite guitar, going up an "even" interval (one that has an even number of edosteps) keeps one on the same string, and an "odd" one takes you to the next string. An octave spans 3 strings, thus a scale often has only 3 odd intervals. The exceptions are generally either fuzzy or awkward to play. The latter include wa, ila and zala diatonic, and microtonal scales with many ^1 steps.

	From this we can deduce that ~~trientonal/~~fretwise scales are often 19 tones, and microtonal ones are often 22. We can also deduce that a semitonal scale of 12 notes usually has two vm2's. If there are more vm2's, the scale is semitonal/~~trientonal~~. Scales of 1, 2 and 3 edosteps are ~~trientonal~~/microtonal.		From this we can deduce that fretwise scales are often 19 tones, and microtonal ones are often 22. We can also deduce that a semitonal scale of 12 notes usually has two vm2's. If there are more vm2's, the scale is semitonal/fretwise. Scales of 1, 2 and 3 edosteps are fretwise/microtonal.

	=== Harmonic scales ===		=== Harmonic scales ===
	In Western music, harmonies often require notes that the melody doesn't. For example, "Auld Lang Syne" has a pentatonic melody but diatonic harmonies. Often the melody is diatonic but the harmonies are at least somewhat chromatic. The score will have accidentals in the piano part but not the vocal part. The scale used by the melody is the melodic scale, and the one used to construct chords is the harmonic scale. 41-equal yaza harmonic scales are usually semitonal or ~~trientonal~~.		In Western music, harmonies often require notes that the melody doesn't. For example, "Auld Lang Syne" has a pentatonic melody but diatonic harmonies. Often the melody is diatonic but the harmonies are at least somewhat chromatic. The score will have accidentals in the piano part but not the vocal part. The scale used by the melody is the melodic scale, and the one used to construct chords is the harmonic scale. 41-equal yaza harmonic scales are usually semitonal or fretwise.

	In 12-equal, a song is generally in a major or minor key, and uses a major or minor scale. A ya piece in 41-equal often is as well. But unlike 12-equal, 41-equal allows the use of yaza chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor 3rd and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.		In 12-equal, a song is generally in a major or minor key, and uses a major or minor scale. A ya piece in 41-equal often is as well. But unlike 12-equal, 41-equal allows the use of yaza chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor 3rd and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.

TallKite: /* 41-equal MOS scales */ added a few JI interpretations

2023-03-27T21:42:18Z

41-equal MOS scales: added a few JI interpretations

@@ Line 491: / Line 491: @@
 L=4, s=3
 |alternate frets
 L 7s 1xs = 10
@@ Line 572: / Line 582: @@
 L=8, s=3
 |every 4th fret
 dots only
@@ Line 623: / Line 641: @@
 |}
-=== (Notes to myself) ===
+=== (TO DO / Notes to myself) ===
 Changing awkward very-near-equal scales to non-awkward less-equal scales:

TallKite: /* Harmonic scales */ dup and dud

2022-09-14T20:55:18Z

Harmonic scales: dup and dud

← Older revision		Revision as of 20:55, 14 September 2022
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	A scale needn't have every single step size on the list in order to be in the category, just most of them. In practice, a non-wa pentatonic scale will often lack a m3 step, as in the examples. But a fuzzy pentatonic scale often will have a m3, e.g. C D vE G vA/A C. Ya and za scales generally contain an off-5th (either an ^5 or a v5), and would often become fuzzy to avoid the wolf.		A scale needn't have every single step size on the list in order to be in the category, just most of them. In practice, a non-wa pentatonic scale will often lack a m3 step, as in the examples. But a fuzzy pentatonic scale often will have a m3, e.g. C D vE G vA/A C. Ya and za scales generally contain an off-5th (either an ^5 or a v5), and would often become fuzzy to avoid the wolf.

	In addition to these broad categories, every 41-equal scale has a unique name that uses ups and downs. The 4 pentatonic examples above are major pentatonic, downmajor pentatonic, downminor pentatonic and ~~double-upminor~~ pentatonic. [[Kite Guitar Exercises and Techniques by Kite Giedraitis\|Rotating]] these scales makes the minor (wa), upminor (ya), upmajor (za) and ~~double-downmajor~~ (ila) pentatonic scales.		In addition to these broad categories, every 41-equal scale has a unique name that uses ups and downs. The 4 pentatonic examples above are major pentatonic, downmajor pentatonic, downminor pentatonic and dupminor pentatonic. [[Kite Guitar Exercises and Techniques by Kite Giedraitis\|Rotating]] these scales makes the minor (wa), upminor (ya), upmajor (za) and dudmajor (ila) pentatonic scales.

	These subgroups can be combined to make another four subgroups. Yala pentatonic scales tend to have ~~wolf~~ 5ths, and thus may be fuzzy. A yazala pentatonic scale must be fuzzy, in order to contain so many different step sizes.		These subgroups can be combined to make another four subgroups. Yala pentatonic scales tend to have off 5ths, and thus may be fuzzy. A yazala pentatonic scale must be fuzzy, in order to contain so many different step sizes.
	{\| class="wikitable" style="text-align:center;"		{\| class="wikitable" style="text-align:center;"
	!scale type -->		!scale type -->
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	=== Diatonic scales ===		=== Diatonic scales ===
	There are four basic categories of diatonic scales. In practice, a non-wa scale will often lack a m2 step, unless it's fuzzy. The ya and za diatonic scales have ~~wolf~~ 5ths, and thus tend to be fuzzy. The ila scale is the most equally distributed, thus arguably the most diatonic-friendly. Ya is also fairly equal. Za scales tend to have a very lopsided L/s ratio.		There are four basic categories of diatonic scales. In practice, a non-wa scale will often lack a m2 step, unless it's fuzzy. The ya and za diatonic scales have off 5ths, and thus tend to be fuzzy. The ila scale is the most equally distributed, thus arguably the most diatonic-friendly. Ya is also fairly equal. Za scales tend to have a very lopsided L/s ratio.
	{\| class="wikitable" style="text-align:center;"		{\| class="wikitable" style="text-align:center;"
	!scale type -->		!scale type -->
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	In 12-equal, a song is generally in a major or minor key, and uses a major or minor scale. A ya piece in 41-equal often is as well. But unlike 12-equal, 41-equal allows the use of yaza chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor 3rd and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.		In 12-equal, a song is generally in a major or minor key, and uses a major or minor scale. A ya piece in 41-equal often is as well. But unlike 12-equal, 41-equal allows the use of yaza chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor 3rd and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.

	For 12-equal ya scales, one chooses a 7-note subset of the 12 notes, and lets the imperfect degrees be either major or minor, or some combination. For 41-equal yaza scales, choose a 12-note subset, and let all but the tonic, 4th and 5th be either upped or downed. (The M2 and m7 may also be plain.) Up is utonal and down is otonal. Combining upped and downed intervals in a 41-equal scale creates ~~double-up~~ and ~~double-down~~ intervals, i.e. mid intervals. This increases the odd limit and/or the prime limit, so yaza scales tend not to mix up and down.		For 12-equal ya scales, one chooses a 7-note subset of the 12 notes, and lets the imperfect degrees be either major or minor, or some combination. For 41-equal yaza scales, choose a 12-note subset, and let all but the tonic, 4th and 5th be either upped or downed. (The M2 and m7 may also be plain.) Up is utonal and down is otonal. Combining upped and downed intervals in a 41-equal scale creates dup and dud intervals, i.e. mid intervals. This increases the odd limit and/or the prime limit, so yaza scales tend not to mix up and down.

	Harmonic scales aren't played sequentially to create melodies, and having more than 3 odd intervals isn't awkward. Often a harmonic scale is fuzzy, and uses pitch shifts of one edostep. Such a scale could be classified as diatonic/microtonal or semitonal/microtonal.		Harmonic scales aren't played sequentially to create melodies, and having more than 3 odd intervals isn't awkward. Often a harmonic scale is fuzzy, and uses pitch shifts of one edostep. Such a scale could be classified as diatonic/microtonal or semitonal/microtonal.