Template:MOS degrees/doc: Difference between revisions

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Mos-ordinals support dropped; Degree Notation param deprecated
Ganaram inukshuk (talk | contribs)
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Updated documentation to reflect new features
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| <pre>Step Ratio</pre> || No (optional) || The step ratio of the mos, denoted as a fraction p/q and separated with a slash. If left blank, then the step ratio "2/1" is used by default.
| <pre>Step Ratio</pre> || No (optional) || The step ratio of the mos, denoted as a fraction p/q and separated with a slash. If left blank, then the step ratio "2/1" is used by default.
|-
|-
| <pre>UDP</pre> || No (optional) || The UDP representing the mode for which notation is applied. Due to technical limitations, using the pipe symbol is not advised and the "," character (comma) should be used instead.
| <pre>Show Abbreviations</pre> || No (optional) || Whether to show degree abbreviations. Abbreviations are shown without a mos prefix, and are intended to be an aid with entering JI ratios. Enter "1" to show abbreviations.
|-
|-
| <pre>Notation</pre> || No (optional) || The notation for note names, consisting of the naturals (written without separators), sharp symbol, and flat symbol, each separated by semicolons. For example, standard notation is entered as "CDEFGAB; #; b". If left blank, the default is diamond-MOS notation (JKLMNOP for naturals, & for the sharp symbol, and @ for the flat symbol), or if the scale signature is 5L 2s, the default is standard notation.
| <pre>Number of Alterations</pre> || No (optional) || Whether to show alterations to a mos's specific interval sizes. One alteration shows the large size with +1 chroma and the small size with -1 chroma, or for periods (including the unison and equave), the perfect size with +1 and -1 chroma.
|-
|-
| <pre>Genchain Extend</pre> || No (optional) || Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period.
| <pre>JI Ratios</pre> || No (optional) || Whether to include JI ratios for certain entries. For assistance with entering ratios, see below.
|-
|-
| <pre>Degree Notation</pre> || Deprecated || How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st).
| <pre>UDP</pre> || No (optional) || The UDP representing the mode for which notation is applied; this is to be used in conjunction with notation. Due to technical limitations, using the pipe symbol is not advised and the "," character (comma) should be used instead.
|-
| <pre>Notation</pre> || No (optional) || The notation for note names, consisting of the naturals (written without separators), sharp symbol, and flat symbol, each separated by semicolons. For example, standard notation is entered as "CDEFGAB; #; b". Notation will not be displayed unless entered.
|-
|-
| <pre>MOS Prefix</pre> || No (optional) || If using TAMNAMS mosdegree naming, does the mos have a prefix?
| <pre>MOS Prefix</pre> || No (optional) || If using TAMNAMS mosdegree naming, does the mos have a prefix?
|-
| <pre>Genchain Extend</pre> || Deprecated || Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period.
|-
| <pre>Degree Notation</pre> || Deprecated || How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st).
|}
|}


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A scale signature different from the page's title can be entered as shown.
A scale signature different from the page's title can be entered as shown.


<pre>{{MOS degrees|Scale Signature=5L 2s}}</pre>
<pre>{{MOS degrees
{{MOS degrees|Scale Signature=5L 2s}}
|Scale Signature=5L 2s}}</pre>
{{MOS degrees
|Scale Signature=5L 2s}}
=== Using a different step ratio ===
=== Using a different step ratio ===


By default, cent and step values will be calculated for a step ratio of 2:1. A different step ratio can be entered as shown below. Up to 5 step ratios can be entered, written as p/q and with each ratio separated by semicolons.
By default, cent and step values will be calculated for a step ratio of 2:1. A different step ratio can be entered as shown below. Up to 5 step ratios can be entered, written as p/q and with each ratio separated by semicolons.


<pre>{{MOS degrees|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2}}</pre>
<pre>{{MOS degrees
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2}}
|Scale Signature=5L 2s
=== Using different notation and UDP ===
|Step Ratio=2/1; 3/1; 3/2}}</pre>
{{MOS degrees
|Scale Signature=5L 2s
|Step Ratio=2/1; 3/1; 3/2}}
=== Changing the mos prefix ===
A mos-prefix, if defined under TAMNAMS, is automatically added. For mosses outside of TAMNAMS that have a prefix, enter it as shown below.
<pre>{{MOS degrees
|Scale Signature=2L 5s
|MOS Prefix=pel}}</pre>
{{MOS degrees
|Scale Signature=2L 5s
|MOS Prefix=pel}}
Typing in "NONE" for the prefix will not show any prefixes.
<pre>{{MOS degrees
|Scale Signature=4L 3s
|MOS Prefix=NONE}}</pre>
{{MOS degrees
|Scale Signature=4L 3s
|MOS Prefix=NONE}}
 
=== Using notation and UDP ===


By default, diamond-mos notation is used, or if the scale signature is 5L 2s, standard notation is used. Different notation can be entered as shown below, with semicolons separating the note names, sharp symbol, and flat symbol.
By default, no notation is displayed unless entered as shown in the example below.
<pre>{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b}}</pre>
<pre>{{MOS degrees
{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b}}
|Scale Signature=7L 2s
|Notation=123456789; #; b
}}</pre>
{{MOS degrees
|Scale Signature=7L 2s
|Notation=123456789; #; b
}}
By default, the mode for which nominals are applied is the symmetric mode, corresponding to a UDP of n<nowiki>|</nowiki>n. In the case of a mos with an even number of modes and therefore two "middle" modes (n+1<nowiki>|</nowiki>n and n<nowiki>|</nowiki>n+1), the brighter of the two is used as the default instead. Since some notation schemes may use a different mode as its "default", the UDP can be changed, as shown below. (Use a comma instead of the pipe <nowiki>|</nowiki> symbol.)
By default, the mode for which nominals are applied is the symmetric mode, corresponding to a UDP of n<nowiki>|</nowiki>n. In the case of a mos with an even number of modes and therefore two "middle" modes (n+1<nowiki>|</nowiki>n and n<nowiki>|</nowiki>n+1), the brighter of the two is used as the default instead. Since some notation schemes may use a different mode as its "default", the UDP can be changed, as shown below. (Use a comma instead of the pipe <nowiki>|</nowiki> symbol.)
<pre>{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b|UDP=7,1}}</pre>
<pre>{{MOS degrees
{{MOS degrees|Scale Signature=7L 2s|Notation=123456789; #; b|UDP=7,1}}
|Scale Signature=7L 2s
Typing in "NONE" for notation omits the column for note names. This allows the table to be used to list out interval sizes.
|Notation=123456789; #; b
<pre>{{MOS degrees|Scale Signature=7L 5s|Notation=NONE|}}</pre>
|UDP=7,1}}</pre>
{{MOS degrees|Scale Signature=7L 5s|Notation=NONE|}}
{{MOS degrees
|Scale Signature=7L 2s
|Notation=123456789; #; b|UDP=7,1}}
 
The template will attempt to use default notation with a default UDP if the keyword "Default" is entered. The default is standard notation on C (for 5L 2s) and diamond-mos for any nondiatonic mosses.
<pre>{{MOS degrees
|Scale Signature=4L 3s
|Notation=Default
}}
</pre>
{{MOS degrees
|Scale Signature=4L 3s
|Notation=Default
}}


== Advanced usage ==
== Advanced usage ==
=== Changing the genchain lengths ===
=== Adding JI ratios ===
The values in the table are calculated using a generator chain, or specifically by stacking its bright generator up from the root and down from the note one period up (usually down from the octave). The UDP described previously represents the lengths of the ascending and descending chains to reach all of the nominals, and extending further reaches pitches modified by accidentals.
JI ratios can be added by writing a semicolon-delimited list of entries, where each entry is an abbreviation for a scale degree, followed by a colon, followed by the JI ratio.


The default extend value is the number of large steps ''per period''. This means for multi-period mosses, there is an ascending and descending chain for each period.
To help with entering ratios, set the parameter "Show Abbreviations" to 1 to show scale degrees.


As an example using 5L 2s, a value of 5 effectively shows the two possible note names for all of the black keys on a standard piano.
<pre>{{MOS degrees
<pre>{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=5}}</pre>
|Scale Signature=4L 3s
{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=5}}
|Show Abbreviations=1
Changing this value to 0 means only the naturals are shown.
|JI Ratios=
<pre>{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0}}</pre>
M1md: 8/7;
{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0}}
P2md: 77/64, 6/5;
To show only the minor intervals, consider that the UDP here is 5<nowiki>|</nowiki>1, meaning that the ascending chain starts with 5 generators and the descending chain starts with 1 generator. Going up one more generator produces the augmented 4th, so it's not necessary to extend the ascending chain. Going down 4 more generators produces all of the minor intervals and one more after that produces the diminished 5th, so the descending chain should be extended further by 4.
m3md: 14/11;
M3md:11/8;
m4md: 16/11;
M4md: 11/7;
P5md: 5/3;
m6md: 7/4;
}}
</pre>
{{MOS degrees
|Scale Signature=4L 3s
|Show Abbreviations=1
|JI Ratios=
M1md: 8/7;
P2md: 77/64, 6/5;
m3md: 14/11;
M3md:11/8;
m4md: 16/11;
M4md: 11/7;
P5md: 5/3;
m6md: 7/4;
}}


This template supports entering separate values for the ascending and descending extend values; the first value is for the ascending chain, and the second for the descending chain, as shown below.
=== Showing alterations ===
<pre>{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}</pre>
Alterations refer to raising scale degrees by a chroma beyond the large and small sizes of a mos. For the number of alterations added, an additional altered degree is shown from raising the large size of a scale degree and lowering the small size of a scale degree (or the perfect size for period, unison, and equaves).
{{MOS degrees|Scale Signature=5L 2s|Genchain Extend=0,4}}
<pre>{{MOS degrees
=== Changing the mos prefix ===
|Scale Signature=4L 3s
It may be beneficial to change the prefix in cases where more than one nondiatonic mos is being discussed. The default is "mos", but this can be changed as shown below, using the previous section's example. (Do not add a hyphen to the end of the prefix, as the template will do that automatically.)
|Number of Alterations=2
<pre>{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|MOS Prefix=pel}}</pre>
}}
{{MOS degrees|Scale Signature=2L 5s|UDP=1,5|Notation=CDEFGAB;#;b|MOS Prefix=pel}}
</pre>
Typing in "NONE" for the prefix will not show any prefixes, for both ordinal names and TAMNAMS-named scale degrees.
{{MOS degrees
<pre>{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}</pre>
|Scale Signature=4L 3s
{{MOS degrees|Scale Signature=4L 3s|MOS Prefix=NONE}}
|Number of Alterations=2
}}

Revision as of 04:37, 20 October 2023

Parameters

Parameters Required? Description 
Scale Signature
 Yes (optional on mos pages) The mos's scale signature in the form "xL ys", or for non-octave mosses, "xL ys<p/q>", "xL ys⟨p/q⟩", or "xL ys (p/q-equivalent)". If left blank and used on a mos page, then the page's title will be used. 
Step Ratio
 No (optional) The step ratio of the mos, denoted as a fraction p/q and separated with a slash. If left blank, then the step ratio "2/1" is used by default. 
Show Abbreviations
 No (optional) Whether to show degree abbreviations. Abbreviations are shown without a mos prefix, and are intended to be an aid with entering JI ratios. Enter "1" to show abbreviations. 
Number of Alterations
 No (optional) Whether to show alterations to a mos's specific interval sizes. One alteration shows the large size with +1 chroma and the small size with -1 chroma, or for periods (including the unison and equave), the perfect size with +1 and -1 chroma. 
JI Ratios
 No (optional) Whether to include JI ratios for certain entries. For assistance with entering ratios, see below. 
UDP
 No (optional) The UDP representing the mode for which notation is applied; this is to be used in conjunction with notation. Due to technical limitations, using the pipe symbol is not advised and the "," character (comma) should be used instead. 
Notation
 No (optional) The notation for note names, consisting of the naturals (written without separators), sharp symbol, and flat symbol, each separated by semicolons. For example, standard notation is entered as "CDEFGAB; #; b". Notation will not be displayed unless entered. 
MOS Prefix
 No (optional) If using TAMNAMS mosdegree naming, does the mos have a prefix? 
Genchain Extend
 Deprecated Additional intervals corresponding to the number of additional generators going up and/or down after those represented by the UDP. This value is per period, and the default value is the number of large steps per period. 
Degree Notation
 Deprecated How should degrees be named? Options include TAMNAMS mosdegree naming and ordinal naming (EG, the unison is either called the 0-mosstep or 1st).

Usage

The typical use of this template is for showing a table of scale degrees for a specific step ratio. 

{{MOS degrees}}

Using a different scale signature

A scale signature different from the page's title can be entered as shown. 

{{MOS degrees
|Scale Signature=5L 2s}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-diadegree (unison) 0 0 1/1 (exact)
Minor 1-diadegree 1 100
Major 1-diadegree 2 200
Minor 2-diadegree 3 300
Major 2-diadegree 4 400
Perfect 3-diadegree 5 500
Augmented 3-diadegree 6 600
Diminished 4-diadegree 6 600
Perfect 4-diadegree 7 700
Minor 5-diadegree 8 800
Major 5-diadegree 9 900
Minor 6-diadegree 10 1000
Major 6-diadegree 11 1100
Perfect 7-diadegree (octave) 12 1200 2/1 (exact)

Using a different step ratio

By default, cent and step values will be calculated for a step ratio of 2:1. A different step ratio can be entered as shown below. Up to 5 step ratios can be entered, written as p/q and with each ratio separated by semicolons. 

{{MOS degrees
|Scale Signature=5L 2s
|Step Ratio=2/1; 3/1; 3/2}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 5L 2s
Scale degree 12edo (Basic, L:s = 2:1) 17edo (Hard, L:s = 3:1) 19edo (Soft, L:s = 3:2) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-diadegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-diadegree 1 100 1 70.6 2 126.3
Major 1-diadegree 2 200 3 211.8 3 189.5
Minor 2-diadegree 3 300 4 282.4 5 315.8
Major 2-diadegree 4 400 6 423.5 6 378.9
Perfect 3-diadegree 5 500 7 494.1 8 505.3
Augmented 3-diadegree 6 600 9 635.3 9 568.4
Diminished 4-diadegree 6 600 8 564.7 10 631.6
Perfect 4-diadegree 7 700 10 705.9 11 694.7
Minor 5-diadegree 8 800 11 776.5 13 821.1
Major 5-diadegree 9 900 13 917.6 14 884.2
Minor 6-diadegree 10 1000 14 988.2 16 1010.5
Major 6-diadegree 11 1100 16 1129.4 17 1073.7
Perfect 7-diadegree (octave) 12 1200 17 1200 19 1200 2/1 (exact)

Changing the mos prefix

A mos-prefix, if defined under TAMNAMS, is automatically added. For mosses outside of TAMNAMS that have a prefix, enter it as shown below. 

{{MOS degrees
|Scale Signature=2L 5s
|MOS Prefix=pel}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 2L 5s
Scale degree 9edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-peldegree (unison) 0 0 1/1 (exact)
Minor 1-peldegree 1 133.3
Major 1-peldegree 2 266.7
Minor 2-peldegree 2 266.7
Major 2-peldegree 3 400
Diminished 3-peldegree 3 400
Perfect 3-peldegree 4 533.3
Perfect 4-peldegree 5 666.7
Augmented 4-peldegree 6 800
Minor 5-peldegree 6 800
Major 5-peldegree 7 933.3
Minor 6-peldegree 7 933.3
Major 6-peldegree 8 1066.7
Perfect 7-peldegree (octave) 9 1200 2/1 (exact)

Typing in "NONE" for the prefix will not show any prefixes. 

{{MOS degrees
|Scale Signature=4L 3s
|MOS Prefix=NONE}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-degree (unison) 0 0 1/1 (exact)
Minor 1-degree 1 109.1
Major 1-degree 2 218.2
Perfect 2-degree 3 327.3
Augmented 2-degree 4 436.4
Minor 3-degree 4 436.4
Major 3-degree 5 545.5
Minor 4-degree 6 654.5
Major 4-degree 7 763.6
Diminished 5-degree 7 763.6
Perfect 5-degree 8 872.7
Minor 6-degree 9 981.8
Major 6-degree 10 1090.9
Perfect 7-degree (octave) 11 1200 2/1 (exact)

Using notation and UDP

By default, no notation is displayed unless entered as shown in the example below. 

{{MOS degrees
|Scale Signature=7L 2s
|Notation=123456789; #; b
}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 7L 2s
Scale degree On 1 16edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-armdegree (unison) 1 0 0 1/1 (exact)
Minor 1-armdegree 2b 1 75
Major 1-armdegree 2 2 150
Minor 2-armdegree 3b 3 225
Major 2-armdegree 3 4 300
Minor 3-armdegree 4 5 375
Major 3-armdegree 4# 6 450
Perfect 4-armdegree 5 7 525
Augmented 4-armdegree 5# 8 600
Diminished 5-armdegree 6b 8 600
Perfect 5-armdegree 6 9 675
Minor 6-armdegree 7b 10 750
Major 6-armdegree 7 11 825
Minor 7-armdegree 8 12 900
Major 7-armdegree 8# 13 975
Minor 8-armdegree 9 14 1050
Major 8-armdegree 9# 15 1125
Perfect 9-armdegree (octave) 1 16 1200 2/1 (exact)

By default, the mode for which nominals are applied is the symmetric mode, corresponding to a UDP of n|n. In the case of a mos with an even number of modes and therefore two "middle" modes (n+1|n and n|n+1), the brighter of the two is used as the default instead. Since some notation schemes may use a different mode as its "default", the UDP can be changed, as shown below. (Use a comma instead of the pipe | symbol.) 

{{MOS degrees
|Scale Signature=7L 2s
|Notation=123456789; #; b
|UDP=7,1}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 7L 2s
Scale degree On 1 16edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-armdegree (unison) 1 0 0 1/1 (exact)
Minor 1-armdegree 2b 1 75
Major 1-armdegree 2 2 150
Minor 2-armdegree 3b 3 225
Major 2-armdegree 3 4 300
Minor 3-armdegree 4b 5 375
Major 3-armdegree 4 6 450
Perfect 4-armdegree 5 7 525
Augmented 4-armdegree 5# 8 600
Diminished 5-armdegree 6b 8 600
Perfect 5-armdegree 6 9 675
Minor 6-armdegree 7b 10 750
Major 6-armdegree 7 11 825
Minor 7-armdegree 8b 12 900
Major 7-armdegree 8 13 975
Minor 8-armdegree 9b 14 1050
Major 8-armdegree 9 15 1125
Perfect 9-armdegree (octave) 1 16 1200 2/1 (exact)

The template will attempt to use default notation with a default UDP if the keyword "Default" is entered. The default is standard notation on C (for 5L 2s) and diamond-mos for any nondiatonic mosses. 

{{MOS degrees
|Scale Signature=4L 3s
|Notation=Default
}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree On J 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) J 0 0 1/1 (exact)
Minor 1-smidegree K@ 1 109.1
Major 1-smidegree K 2 218.2
Perfect 2-smidegree L 3 327.3
Augmented 2-smidegree L& 4 436.4
Minor 3-smidegree M@ 4 436.4
Major 3-smidegree M 5 545.5
Minor 4-smidegree N 6 654.5
Major 4-smidegree N& 7 763.6
Diminished 5-smidegree O@ 7 763.6
Perfect 5-smidegree O 8 872.7
Minor 6-smidegree P 9 981.8
Major 6-smidegree P& 10 1090.9
Perfect 7-smidegree (octave) J 11 1200 2/1 (exact)

Advanced usage

Adding JI ratios

JI ratios can be added by writing a semicolon-delimited list of entries, where each entry is an abbreviation for a scale degree, followed by a colon, followed by the JI ratio.

To help with entering ratios, set the parameter "Show Abbreviations" to 1 to show scale degrees. 

{{MOS degrees
|Scale Signature=4L 3s
|Show Abbreviations=1
|JI Ratios=
M1md: 8/7;
P2md: 77/64, 6/5;
m3md: 14/11;
M3md:11/8;
m4md: 16/11;
M4md: 11/7;
P5md: 5/3;
m6md: 7/4;
}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree Abbrev. 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) P0md 0 0 1/1 (exact)
Minor 1-smidegree m1md 1 109.1
Major 1-smidegree M1md 2 218.2 8/7
Perfect 2-smidegree P2md 3 327.3 77/64, 6/5
Augmented 2-smidegree A2md 4 436.4
Minor 3-smidegree m3md 4 436.4 14/11
Major 3-smidegree M3md 5 545.5 11/8
Minor 4-smidegree m4md 6 654.5 16/11
Major 4-smidegree M4md 7 763.6 11/7
Diminished 5-smidegree d5md 7 763.6
Perfect 5-smidegree P5md 8 872.7 5/3
Minor 6-smidegree m6md 9 981.8 7/4
Major 6-smidegree M6md 10 1090.9
Perfect 7-smidegree (octave) P7md 11 1200 2/1 (exact)

Showing alterations

Alterations refer to raising scale degrees by a chroma beyond the large and small sizes of a mos. For the number of alterations added, an additional altered degree is shown from raising the large size of a scale degree and lowering the small size of a scale degree (or the perfect size for period, unison, and equaves). 

{{MOS degrees
|Scale Signature=4L 3s
|Number of Alterations=2
}}
Template:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) Approx. JI Ratios
Steps Cents
Perfect 0-smidegree (unison) 0 0 1/1 (exact)
Augmented 0-smidegree 1 109.1
2× Augmented 0-smidegree 2 218.2
2× Diminished 1-smidegree -1 -109.1
Diminished 1-smidegree 0 0
Minor 1-smidegree 1 109.1
Major 1-smidegree 2 218.2
Augmented 1-smidegree 3 327.3
2× Augmented 1-smidegree 4 436.4
2× Diminished 2-smidegree 1 109.1
Diminished 2-smidegree 2 218.2
Perfect 2-smidegree 3 327.3
Augmented 2-smidegree 4 436.4
2× Augmented 2-smidegree 5 545.5
3× Augmented 2-smidegree 6 654.5
2× Diminished 3-smidegree 2 218.2
Diminished 3-smidegree 3 327.3
Minor 3-smidegree 4 436.4
Major 3-smidegree 5 545.5
Augmented 3-smidegree 6 654.5
2× Augmented 3-smidegree 7 763.6
2× Diminished 4-smidegree 4 436.4
Diminished 4-smidegree 5 545.5
Minor 4-smidegree 6 654.5
Major 4-smidegree 7 763.6
Augmented 4-smidegree 8 872.7
2× Augmented 4-smidegree 9 981.8
3× Diminished 5-smidegree 5 545.5
2× Diminished 5-smidegree 6 654.5
Diminished 5-smidegree 7 763.6
Perfect 5-smidegree 8 872.7
Augmented 5-smidegree 9 981.8
2× Augmented 5-smidegree 10 1090.9
2× Diminished 6-smidegree 7 763.6
Diminished 6-smidegree 8 872.7
Minor 6-smidegree 9 981.8
Major 6-smidegree 10 1090.9
Augmented 6-smidegree 11 1200
2× Augmented 6-smidegree 12 1309.1
2× Diminished 7-smidegree 9 981.8
Diminished 7-smidegree 10 1090.9
Perfect 7-smidegree (octave) 11 1200 2/1 (exact)
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