User:Katherinetoast/sandbox - Revision history

FloraC: No categories, thank you

2025-10-28T11:04:12Z

No categories, thank you

← Older revision		Revision as of 11:04, 28 October 2025
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	\| ja = 17平均律		\| ja = 17平均律
	}}		}}
	{{Infobox ET}}		{{Infobox ET\|debug=true}}
	{{ED intro}}		{{ED intro}}
	{{Wikipedia\|17 equal temperament}}		{{Wikipedia\|17 equal temperament}}
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	* [[Lumatone mapping for 17edo]]		* [[Lumatone mapping for 17edo]]

	[[Category:Teentuning]]		<!--[[Category:Teentuning]]-->

Katherinetoast: /* Intervals */

2025-09-23T19:34:10Z

Intervals

← Older revision		Revision as of 19:34, 23 September 2025
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	\| N2		\| N2
	\| UEb, uE		\| UEb, uE
	\|		\|[[File:2step17.mp3]]
	\|-		\|-
	\| 3		\| 3

Katherinetoast: /* Intervals */

2025-09-23T19:31:26Z

Intervals

← Older revision		Revision as of 19:31, 23 September 2025
Line 64:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
	\|		\|[[File:1step17edo.mp3\|318x318px]]
	\|-		\|-
	\| 2		\| 2

Katherinetoast at 19:24, 23 September 2025

2025-09-23T19:24:36Z

← Older revision		Revision as of 19:24, 23 September 2025
Line 64:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
	\|~~[[File:Just_chromatic_semitone_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 2		\| 2

Katherinetoast: /* Intervals */

2025-09-23T19:23:29Z

Intervals

← Older revision		Revision as of 19:23, 23 September 2025
Line 64:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
	\|		\|[[File:Just_chromatic_semitone_on_C.mid\|120x120px]]
	\|-		\|-
	\| 2		\| 2

Katherinetoast: Undo revision 210622 by Katherinetoast (talk)

2025-09-23T19:22:11Z

Undo revision 210622 by Katherinetoast (talk)

← Older revision		Revision as of 19:22, 23 September 2025
Line 64:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
	\|~~[[File:1_step_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 2		\| 2
Line 77:		Line 77:
	\| N2		\| N2
	\| UEb, uE		\| UEb, uE
	\|~~[[File:2_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 3		\| 3
Line 90:		Line 90:
	\| M2		\| M2
	\| E		\| E
	\|~~[[File:3_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 4		\| 4
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	\| m3		\| m3
	\| F		\| F
	\|~~[[File:4_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 5		\| 5
Line 116:		Line 116:
	\| N3		\| N3
	\| UF, uF#		\| UF, uF#
	\|~~[[File:5_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 6		\| 6
Line 129:		Line 129:
	\| M3		\| M3
	\| F#		\| F#
	\|~~[[File:6_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 7		\| 7
Line 142:		Line 142:
	\| P4		\| P4
	\| G		\| G
	\|~~[[File:7_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 8		\| 8
Line 155:		Line 155:
	\| U4/N4		\| U4/N4
	\| UG		\| UG
	\|~~[[File:8_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 9		\| 9
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	\| P5		\| P5
	\| A		\| A
	\|~~[[File:10_steps_in_17-et_on_C.mid\|120x120px]]~~		\|
	\|-		\|-
	\| 11		\| 11

Katherinetoast at 19:21, 23 September 2025

2025-09-23T19:21:42Z

← Older revision		Revision as of 19:21, 23 September 2025
Line 64:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
	\|		\|[[File:1_step_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 2		\| 2
Line 77:		Line 77:
	\| N2		\| N2
	\| UEb, uE		\| UEb, uE
	\|		\|[[File:2_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 3		\| 3
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	\| M2		\| M2
	\| E		\| E
	\|		\|[[File:3_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 4		\| 4
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	\| m3		\| m3
	\| F		\| F
	\|		\|[[File:4_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 5		\| 5
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	\| N3		\| N3
	\| UF, uF#		\| UF, uF#
	\|		\|[[File:5_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 6		\| 6
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	\| M3		\| M3
	\| F#		\| F#
	\|		\|[[File:6_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 7		\| 7
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	\| P4		\| P4
	\| G		\| G
	\|		\|[[File:7_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 8		\| 8
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	\| U4/N4		\| U4/N4
	\| UG		\| UG
	\|		\|[[File:8_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 9		\| 9
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	\| P5		\| P5
	\| A		\| A
	\|		\|[[File:10_steps_in_17-et_on_C.mid\|120x120px]]
	\|-		\|-
	\| 11		\| 11

Katherinetoast: /* Intervals */

2025-09-23T19:19:30Z

Intervals

← Older revision		Revision as of 19:19, 23 September 2025
Line 38:		Line 38:
	! colspan="3" \| [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation\|EUs]]: vvA1 and ^d2)		! colspan="3" \| [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation\|EUs]]: vvA1 and ^d2)
	! colspan="3" \| [[SKULO interval names\|SKULO notation]] {{nowrap\|(U {{=}} 1)}}		! colspan="3" \| [[SKULO interval names\|SKULO notation]] {{nowrap\|(U {{=}} 1)}}
			!Audio
	\|-		\|-
	\| 0		\| 0
Line 50:		Line 51:
	\| P1		\| P1
	\| D		\| D
			\|[[File:Piano_0_1edo.mp3]]
	\|-		\|-
	\| 1		\| 1
Line 62:		Line 64:
	\| U1, m2		\| U1, m2
	\| UD, Eb		\| UD, Eb
			\|
	\|-		\|-
	\| 2		\| 2
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	\| N2		\| N2
	\| UEb, uE		\| UEb, uE
			\|
	\|-		\|-
	\| 3		\| 3
Line 86:		Line 90:
	\| M2		\| M2
	\| E		\| E
			\|
	\|-		\|-
	\| 4		\| 4
Line 98:		Line 103:
	\| m3		\| m3
	\| F		\| F
			\|
	\|-		\|-
	\| 5		\| 5
Line 110:		Line 116:
	\| N3		\| N3
	\| UF, uF#		\| UF, uF#
			\|
	\|-		\|-
	\| 6		\| 6
Line 122:		Line 129:
	\| M3		\| M3
	\| F#		\| F#
			\|
	\|-		\|-
	\| 7		\| 7
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	\| P4		\| P4
	\| G		\| G
			\|
	\|-		\|-
	\| 8		\| 8
Line 146:		Line 155:
	\| U4/N4		\| U4/N4
	\| UG		\| UG
			\|
	\|-		\|-
	\| 9		\| 9
Line 158:		Line 168:
	\| u5/N5		\| u5/N5
	\| uA		\| uA
			\|
	\|-		\|-
	\| 10		\| 10
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	\| P5		\| P5
	\| A		\| A
			\|
	\|-		\|-
	\| 11		\| 11
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	\| m6		\| m6
	\| Bb		\| Bb
			\|
	\|-		\|-
	\| 12		\| 12
Line 194:		Line 207:
	\| N6		\| N6
	\| UBb, uB		\| UBb, uB
			\|
	\|-		\|-
	\| 13		\| 13
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	\| M6		\| M6
	\| B		\| B
			\|
	\|-		\|-
	\| 14		\| 14
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	\| m7		\| m7
	\| C		\| C
			\|
	\|-		\|-
	\| 15		\| 15
Line 230:		Line 246:
	\| N7		\| N7
	\| UC, uC#		\| UC, uC#
			\|
	\|-		\|-
	\| 16		\| 16
Line 242:		Line 259:
	\| M7, u8		\| M7, u8
	\| C#, uD		\| C#, uD
			\|
	\|-		\|-
	\| 17		\| 17
Line 254:		Line 272:
	\| P8		\| P8
	\| D		\| D
			\|
	\|}		\|}
	<references group="note" />		<references group="note" />

Katherinetoast: Created page with "{{interwiki | de = 17-EDO | en = 17edo | es = 17 EDO | ja = 17平均律 }} {{Infobox ET}} {{ED intro}} {{Wikipedia|17 equal temperament}} == Theory == 17edo's perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the hardness of Pythagorean tuning rather than mellowing it out as in meanto..."

2025-09-23T19:11:52Z

Created page with "{{interwiki | de = 17-EDO | en = 17edo | es = 17 EDO | ja = 17平均律 }} {{Infobox ET}} {{ED intro}} {{Wikipedia|17 equal temperament}} == Theory == 17edo's perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the hardness of Pythagorean tuning rather than mellowing it out as in meanto..."

New page

{{interwiki
| de = 17-EDO
| en = 17edo
| es = 17 EDO
| ja = 17平均律
}}
{{Infobox ET}}
{{ED intro}}
{{Wikipedia|17 equal temperament}}

== Theory ==
17edo's [[3/2|perfect fifth]] is around 4 cents sharp of just, and around 6 cents sharp of [[12edo]]'s, lending itself to a [[5L 2s|diatonic]] scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the hardness of [[Pythagorean tuning]] rather than mellowing it out as in [[meantone]]. Meanwhile, it approximates [[harmonic]]s [[7/1|7]], [[11/1|11]], [[13/1|13]], and [[23/1|23]] to reasonable degrees, despite completely missing harmonic [[5/1|5]]. Thus it can plausibly be treated as a temperament of the 2.3.25.7.11.13.23 [[subgroup]], for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers).

Because the 5th harmonic is not well-approximated, using timbres with attenuated 5th harmonics (and its multiples) may reduce audible beating.

The standard major triad is quite [[dissonant]] as the major third is closer to [[9/7]] than the traditional [[5/4]]. Instead, the tonic chords of 17edo could be considered to be the tetrad [[6:7:8:9]] and its utonal inversion (representing [[14:16:18:21]] as [[64/63]] is tempered out), the former of which is a subminor chord with added fourth, and the latter a supermajor chord with added second (resembling the {{w|mu chord}} of {{w|Steely Dan}} fame). These are realized in 17edo as 0–4–7–10 and 0–3–6–10, respectively. Both of these have distinct moods, and are stable and consonant, if somewhat more sophisticated than their classic 5-limit counterparts. To this group we could also add the 0–3–7–10 (a sus2-4 chord). These three chords comprise the three ways to divide the 17edo perfect fifth into two whole tones and one subminor third. Chromatic alterations of them also exist, for example, the 0–3–7–10 chord may be altered to 0–2–7–10 (which approximates 12:13:16:18) or 0–3–8–10 (which approximates 8:9:11:12). The 0–3–8–10 chord is impressive-sounding, resembling a sus4 but with even more tension; it resolves quite nicely to 0–3–6–10.

Another construction of septimal chords involves 4:7:12 and its inversion 7:12:21. These triads span a twelfth, realized in 17edo as 0–14–27 and 0–13–27, respectively. To this we may add 0–12–14–27, representing 8:13:14:24, or 0–13–15–27, representing 7:12:13:21.

=== Odd harmonics ===
{{Harmonics in equal|17|intervals=odd|columns=11}}
{{Harmonics in equal|17|intervals=odd|columns=12|start=12|collapsed=true|title=Approximation of odd harmonics in 17edo (continued)}}

=== Subsets and supersets ===
17edo is the seventh [[prime edo]], following [[13edo]] and coming before [[19edo]]. It does not contain any nontrivial subset edos, though it contains [[17ed4]] and [[17ed8]]. 17ed8, built by taking every third step of 17edo, is a system where all odd harmonics up to the 21st are mapped exactly as in 17edo, except for the 11th. Beyond that, the 27th, 31st, 35th, and 39th harmonics are likewise mapped identically.

[[34edo]], which doubles 17edo, provides a good correction to harmonics 5 and 17; while [[68edo]], which quadruples it, provides additionally the primes 7, 19, and 31.

== Intervals ==
{{See also| 17edo solfege }}

{| class="wikitable center-all right-2 left-3"
|-
! #
! Cents
! Approximate ratios<ref group="note">{{sg|limit=2.3.25.7.11.13.85.23 subgroup}}</ref>
! colspan="2" | [[Circle-of-fifths notation]]<ref group="note">Half-sharps and half-flats (denoted "t" and "d", respectively) can be used to alter the note by a single step, since sharps and flats each span two edosteps. Using half-sharps and half-flats may be preferable for compatibility with the ups-and-downs notation in 34edo, in which an up or down respectively constitute a quarter-sharp or quarter-flat. </ref>
! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and ^d2)
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(U {{=}} 1)}}
|-
| 0
| 0.0
| [[1/1]]
| Unison
| D
| unison
| P1
| D
| unison
| P1
| D
|-
| 1
| 70.6
| [[24/23]], [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Minor 2nd (Semiaugmented 1sn)
| Eb (Dt)
| up unison, minor 2nd
| ^1, m2
| Eb
| uber unison, minor 2nd
| U1, m2
| UD, Eb
|-
| 2
| 141.2
| [[12/11]], [[13/12]], [[14/13]], [[25/23]]
| Augmented 1sn (Neutral 2nd)
| D# (Ed)
| augmented 1sn, mid 2nd
| A1, ~2
| vE
| neutral 2nd
| N2
| UEb, uE
|-
| 3
| 211.8
| [[8/7]], [[9/8]], [[17/15]], [[25/22]], [[26/23]]
| Major 2nd
| E
| major 2nd
| M2
| E
| major 2nd
| M2
| E
|-
| 4
| 282.4
| [[7/6]], [[13/11]], [[20/17]]
| Minor 3rd
| F
| minor 3rd
| m3
| F
| minor 3rd
| m3
| F
|-
| 5
| 352.9
| [[11/9]], [[27/22]], [[16/13]], [[39/32]]
| Diminished 4th (Neutral 3rd)
| Gb (Ft)
| mid 3rd
| ~3
| ^F
| neutral 3rd
| N3
| UF, uF#
|-
| 6
| 423.5
| [[9/7]], [[14/11]], [[23/18]], [[32/25]], [[51/40]]
| Major 3rd (Semidiminished 4th)
| F# (Gd)
| major 3rd
| M3
| F#
| major 3rd
| M3
| F#
|-
| 7
| 494.1
| [[4/3]], [[21/16]], [[85/64]]
| Perfect 4th
| G
| perfect 4th
| P4
| G
| perfect 4th
| P4
| G
|-
| 8
| 564.7
| [[11/8]], [[18/13]], [[25/18]], [[32/23]]
| Diminished 5th (Semiaugmented 4th)
| Ab (Gt)
| mid 4th, diminished 5th
| ~4, d5
| ^G, Ab
| uber 4th/ neutral 4th
| U4/N4
| UG
|-
| 9
| 635.3
| [[13/9]], [[16/11]], [[23/16]], [[36/25]]
| Augmented 4th (Semidiminished 5th)
| G# (Ad)
| augmented 4th, mid 5th
| A4, ~5
| G#, vA
| unter 5th/ neutral 5th
| u5/N5
| uA
|-
| 10
| 705.9
| [[3/2]], [[32/21]], [[128/85]]
| Perfect 5th
| A
| perfect 5th
| P5
| A
| perfect 5th
| P5
| A
|-
| 11
| 776.5
| [[11/7]], [[14/9]], [[25/16]], [[36/23]], [[80/51]]
| Minor 6th (Semiaugmented 5th)
| Bb (At)
| minor 6th
| m6
| Bb
| minor 6th
| m6
| Bb
|-
| 12
| 847.1
| [[13/8]], [[18/11]], [[44/27]], [[64/39]]
| Augmented 5th (Neutral 6th)
| A# (Bd)
| mid 6th
| ~6
| vB
| neutral 6th
| N6
| UBb, uB
|-
| 13
| 917.6
| [[12/7]], [[17/10]], [[22/13]]
| Major 6th
| B
| major 6th
| M6
| B
| major 6th
| M6
| B
|-
| 14
| 988.2
| [[7/4]], [[16/9]], [[23/13]], [[30/17]], [[44/25]]
| Minor 7th
| C
| minor 7th
| m7
| C
| minor 7th
| m7
| C
|-
| 15
| 1058.8
| [[11/6]], [[13/7]], [[24/13]], [[46/25]]
| Diminished 8ve (Neutral 7th)
| Db (Ct)
| mid 7th
| ~7
| ^C
| neutral 7th
| N7
| UC, uC#
|-
| 16
| 1129.4
| [[23/12]], [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Major 7th (Semidiminished 8ve)
| C# (Dd)
| major 7th, down 8ve
| M7, v8
| C#
| major 7th, unter octave
| M7, u8
| C#, uD
|-
| 17
| 1200.0
| [[2/1]]
| Octave
| D
| octave
| P8
| D
| octave
| P8
| D
|}
<references group="note" />

=== Interval quality and chord names in color notation ===
Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:

{| class="wikitable center-all"
|-
! Quality
! Color
! Monzo format
! Examples
|-
| rowspan="2" | minor
| zo
| (a, b, 0, 1)
| 7/6, 7/4
|-
| fourthward wa
| (a, b), b < -1
| 32/27, 16/9
|-
| rowspan="2" | mid
| ilo
| (a, b, 0, 0, 1)
| 11/9, 11/6
|-
| lu
| (a, b, 0, 0, -1)
| 12/11, 18/11
|-
| rowspan="2" | major
| fifthward wa
| (a, b), b > 1
| 9/8, 27/16
|-
| ru
| (a, b, 0, -1)
| 9/7, 12/7
|}

All 17edo chords can be named using ups and downs. Here are the zo, ilo and ru triads:

{| class="wikitable center-all"
|-
! [[Color notation|Color of the 3rd]]
! JI chord
! Notes as edosteps
! Notes of C chord
! Written name
! Spoken name
|-
| zo
| 6:7:9
| 0-4-10
| C Eb G
| Cm
| C minor
|-
| ilo
| 18:22:27
| 0-5-10
| C vE G
| C~
| C mid
|-
| ru
| 14:18:21
| 0-6-10
| C E G
| C
| C major or C
|}

Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).

0-4-9 = C Eb vG = Cm(v5) = C minor down-five

0-5-9 = C vE vG = C~(v5) = C mid down-five

0-6-11 = C E ^G = C(^5) = C up-five

0-4-10-14 = C Eb G Bb = Cm7 = C minor seven

0-5-10-14 = C vE G Bb = C~,7 = C mid add seven

0-6-10-15 = C E G vB = C,~7 = C add mid-seven

0-5-10-15 = C vE G vB = C~7 = C mid-seven

For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].

== Notation ==
=== Ups and downs notation ===
Spoken as up, sharp, upsharp, etc. Note that up can be respelled as downsharp. The gamut runs D, ^D/Eb, D#/vE, E, F etc.
{{Sharpness-sharp2a}}

=== Quarter tone notation ===
Since a sharp raises by 2 steps, 17edo can be notated using quarter-tone accidentals.
{{Sharpness-sharp2}}

=== Sagittal notation ===
This notation uses the same sagittal sequence as edos [[24edo #Sagittal notation|24]], [[31edo #Sagittal notation|31]], and [[38edo #Sagittal notation|38]], and is a subset of the notation for [[34edo #Sagittal notation|34edo]].

==== Evo and Revo flavors ====
<imagemap>
File:17-EDO_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 559 0 719 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:17-EDO_Sagittal.svg]]
</imagemap>

==== Alternative Evo flavor ====
<imagemap>
File:17-EDO_Alternative_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 559 0 719 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:17-EDO_Alternative_Evo_Sagittal.svg]]
</imagemap>

==== Evo-SZ flavor ====
<imagemap>
File:17-EDO_Evo-SZ_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 627 0 687 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 130 106 [[33/32]]
default [[File:17-EDO_Evo-SZ_Sagittal.svg]]
</imagemap>

Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is identical to the Stein-Zimmerman notation.

==== Sagittal songbook diagram ====
From the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 17edo in the Revo flavor of Sagittal:

[[File:17edo Sagittal.png|800px]]

=== 3L 4s (mosh) notation ===
The notation of Neutral[7]. The generator is the perfect 3rd. Notes are denoted as {{nowrap|sLsLsLs {{=}} DEFGABCD}}, and raising and lowering by a chroma {{nowrap|(L − s)}}, 1 edostep in this instance, is denoted by ♯ and ♭.

{| class="wikitable center-all right-2 left-4 left-5 mw-collapsible mw-collapsed"
|-
! #
! Cents
! Note
! Name
! Associated ratios
|-
| 0
| 0.0
| D
| Perfect 1sn
| 1/1
|-
| 1
| 70.6
| D#
| Augmented 1sn
| 33/32
|-
| 2
| 141.2
| Eb
| Minor 2nd
| 12/11
|-
| 3
| 211.8
| E
| Major 2nd
| 9/8
|-
| 4
| 282.4
| Fb
| Diminished 3rd
| 32/27
|-
| 5
| 352.9
| F
| Perfect 3rd
| 11/9, 27/22
|-
| 6
| 423.5
| F#
| Augmented 3rd
| 81/64
|-
| 7
| 494.1
| G
| Minor 4th
| 4/3
|-
| 8
| 564.7
| G#
| Major 4th
| 11/8
|-
| 9
| 635.3
| Ab
| Minor 5th
| 16/11
|-
| 10
| 705.9
| A
| Major 5th
| 3/2
|-
| 11
| 776.5
| Bb
| Diminished 6th
| 128/81
|-
| 12
| 847.1
| B
| Perfect 6th
| 18/11, 44/27
|-
| 13
| 917.6
| B#
| Augmented 6th
| 27/16
|-
| 14
| 988.2
| Cb
| Minor 7th
| 16/9
|-
| 15
| 1058.8
| C
| Major 7th
| 11/6
|-
| 16
| 1129.4
| Db
| Diminished 8ve
| 64/33
|-
| 17
| 1200.0
| D
| Perfect 8ve
| 2/1
|}

== Approximation to JI ==
=== 15-odd-limit interval mappings ===
{{Q-odd-limit intervals|17}}
{{Q-odd-limit intervals|17.04|apx=val|header=none|tag=none|title=15-odd-limit intervals by 17c val mapping}}

=== Selected 13-limit intervals ===
[[File:17ed2-001.svg|alt=alt : Your browser has no SVG support.]]

== Tuning by ear ==
17edo is very close to a circle of seventeen [[25/24]] chromatic semitones: (25/24)17 is only 1.43131 cents sharp of an octave. This means that if you can tune seventeen 25/24's accurately (by say, tuning 5/4 up, 3/2 down and 5/4 up, taking care to minimize the error at each step), you have a shot at approximating 17edo within melodic just noticeable difference.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 27 -17 }}
| {{Mapping| 17 27 }}
| −1.24
| 1.24
| 1.76
|-
| 2.3.7
| 64/63, 17496/16807
| {{Mapping| 17 27 48 }}
| −3.13
| 2.85
| 4.05
|-
| 2.3.7.11
| 64/63, 99/98, 243/242
| {{Mapping| 17 27 48 59 }}
| −3.31
| 2.49
| 3.54
|-
| 2.3.7.11.13
| 64/63, 78/77, 99/98, 144/143
| {{Mapping| 17 27 48 59 63 }}
| −3.00
| 2.31
| 3.28
|}
* 17et is lower in relative error than any previous equal temperaments in the no-5 11- and 13-limit. The next equal temperaments doing better in these subgroups are [[41edo|41]] and [[207edo|207]], respectively.

=== Uniform maps ===
{{Uniform map|edo=17}}

=== Commas ===
17et [[tempering out|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val| 17 27 39 48 59 63 69 }}, cent values rounded to 5 digits.)

{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic limit|Prime limit]]
! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name
|-
| 3
| [[134217728/129140163|(18 digits)]]
| {{Monzo| 27 -17 }}
| 66.765
| Sasawa
| [[17-comma]]
|-
| 5
| [[25/24]]
| {{Monzo| -3 -1 2 }}
| 70.762
| Yoyo
| Dicot comma
|-
| 5
| [[32805/32768]]
| {{Monzo| -15 8 1 }}
| 1.9537
| Layo
| Schisma
|-
| 7
| [[525/512]]
| {{Monzo| -9 1 2 1 }}
| 43.408
| Lazoyoyo
| Avicennma
|-
| 7
| [[64/63]]
| {{Monzo| 6 -2 0 -1 }}
| 27.264
| Ru
| Septimal comma
|-
| 7
| [[245/243]]
| {{Monzo| 0 -5 1 2 }}
| 14.191
| Zozoyo
| Sensamagic comma
|-
| 7
| [[1728/1715]]
| {{Monzo| 6 3 -1 -3 }}
| 13.074
| Triru-agu
| Orwellisma
|-
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| {{Monzo| -6 -8 2 5 }}
| 1.1170
| Quinzo-ayoyo
| [[Wizma]]
|-
| 11
| [[99/98]]
| {{Monzo| -1 2 0 -2 1 }}
| 17.576
| Loruru
| Mothwellsma
|-
| 11
| [[896/891]]
| {{Monzo| 7 -4 0 1 -1 }}
| 9.6880
| Saluzo
| Pentacircle comma
|-
| 11
| [[243/242]]
| {{Monzo| -1 5 0 0 -2 }}
| 7.1391
| Lulu
| Rastma
|-
| 11
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| 4.5026
| Lozoyo
| Keenanisma
|-
| 13
| [[1352/1331]]
| {{Monzo| 3 0 0 0 -3 2 }}
| 27.101
| Bithotrilu
| Lovecraft comma
|-
| 13
| [[364/363]]
| {{Monzo| 2 -1 0 1 -2 1 }}
| 4.763
| Tholuluzo
| Minor minthma
|-
| 17
| [[136/135]]
| {{Monzo| 3 -3 -1 0 0 0 1 }}
| 12.776
| Sogu 2nd
| Diatisma
|}
<references group="note" />
Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, as stated.

=== Rank-2 temperaments ===
* [[List of 17edo rank two temperaments by badness]]
* [[List of edo-distinct 17c rank two temperaments]]
* [[List of edo-distinct 17et rank two temperaments]]
* [[List of edo-distinct 17et no-fives rank two temperaments]]

{| class="wikitable center-all right-3 left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods per 8ve
! Generator
! Cents
! Associated ratio
! Temperament
|-
| 1
| 2\17
| 141.18
| 13/12
| [[Bleu]] / [[progression]] (17c) / [[glacier]]
|-
| 1
| 3\17
| 211.76
| 8/7~9/8
| [[Machine]]
|-
| 1
| 4\17
| 282.35
| 13/11
| [[Huxley]] / [[lovecraft]] / [[subklei]] (17c)
|-
| 1
| 5\17
| 352.94
| 11/9
| [[Suhajira]] / [[neutrominant]] (17c) / [[beatles]] (17c) / [[dicotic]] (17) [[Hemif]] / [[mohamaq]] (17c) / [[salsa]] (17)
|-
| 1
| 6\17
| 423.53
| 9/7
| [[Skwares]] / [[squares]] (17c) / [[sentinel]] (17) / [[sidi]] (17)
|-
| 1
| 7\17
| 494.12
| 4/3
| [[Archy]] / [[supra]] / [[quasisuper]] (17c) / [[dominant (temperament)|dominant]] (17c) / [[superpyth]] (17) / [[schism]] (17) [[Fiventeen]]
|-
| 1
| 8\17
| 564.71
| 7/5
| [[Lee]] / [[liese]] (17c) / [[pycnic]] (17) [[Progress]] (17c)
|}

== Octave stretch or compression ==
17edo's approximations of harmonics 3, 7, 11, and 13 are all tempered sharp, so 17edo adapts well to slightly [[stretched and compressed tuning|compressing the octave]], if that is acceptable. [[44ed6]], [[27edt]] and [[zpi|56zpi]] are good demonstrations of this, where the octaves are flattened by about 1.5, 2.5 cents and 3 cents respectively.

== Scales ==
* [[Antipental blues]]: 4 3 1 2 4 3
* [https://web.archive.org/web/20140215081520/http://microtonalismo.com/proyecto-xvii Blues Peruvian]: 4 3 1 1 1 4 3
* [[Hydra]]: 3 3 1 1 2 3 2 1 1
* [[Maqam|Husayni]] Ascending: 2 2 3 3 2 2 3
* [[Otonal 17]]: 3 2 3 2 2 2 3
* [[Scorp]]: 3 2 3 1 3 2 3
* [[Screamapillar]]: 3 3 2 2 3 3 1
* sLmLs: 2 5 3 5 2

=== MOS scales ===
{{Main| MOS scales of 17edo }}

* diatonic ([[leapfrog]]/[[archy]]) [[5L 2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
* [[neutrominant]] [[3L 4s]] 3 2 3 2 3 2 2 (5\17, 1\1)
* [[neutrominant]] [[7L 3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
* [[squares]] [[3L 5s]] 1 1 4 1 4 1 4 (6\17, 1\1)
* [[squares]] [[3L 8s]] 1 3 1 1 3 1 1 3 (6\17, 1\1)
* lovecraft [[4L 5s]] 3 1 3 1 3 1 3 1 1 (4\17, 1\1)

=== Well temperaments ===
* [[Secor wt17|George Secor's well temperament]]
* [[User:CritDeathX/Sam's 17-note Well Temperament|Nicolai's 17-note well temperament]]
* [[User:FloraC/Flora's 17-note well temperament|Flora's 17-note well temperament]]

== Introductory materials ==
* [[SeventeenTheory]], an introduction to 17edo theory, through the eyes of the [[SeventeenTonePianoProject]].
* [http://anaphoria.com/Secor17puzzle.pdf The 17-tone Puzzle] by George Secor, another introduction into 17edo theory.
* [[17edo tetrachords]]
* [http://microtonalismo.com/proyecto-xvii Proyect 17-Perú] {{forbidden}}

== Music ==
{{Main| 17edo/Music }}
{{Catrel|17edo tracks}}

; [https://www.youtube.com/playlist?list=PLWB50RFxjvduT6F1Mwu0CmPa41LBRdXf5 YouTube playlist of 17edo pieces]
; [https://www.youtube.com/results?search_query=17edo&search=tag YouTube videos tagged with 17edo]

; Compositions from the [[SeventeenTonePianoProject|Seventeen Tone Piano Project]]
* [https://www.archive.org/details/seventeenTPP_01 seventeen-tone piano project phase I]
* [[SeventeenTPPPhaseTwo|Seventeen-tone piano project phase II]]
* [[SeventeenTPPPhaseThree|Seventeen-tone piano project phase III]]


== Instruments ==
* [http://chrisvaisvil.com/?p=436 17 note per octave conversion from a "standard" Stratocaster copy] - conversion by Brad Smith

[[File:17P1050829r.JPG|alt=17P1050829r.JPG|17P1050829r.JPG]]

* 17edo soprano Harmony ukulele with a 3D printed fretboard - conversion by [[User:Tristanbay|Tristan Bay]]

[[File:17edo soprano ukulele with 3D printed fretboard.jpg|frameless|640x640px]]

== See also ==
* [[Lumatone mapping for 17edo]]

[[Category:Teentuning]]