User:Mousemambo/Document draft: Difference between revisions

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[''Once again, this whole section should probably be moved to the recently created article "Scale design software."'']

It's important to realize that the words "scale" and "tuning" have ~~very~~ different meanings in different contexts. In the context of scale design software (aka scale designers) and tuning editors, scales can be understood abstractly as an ordered set of notes, whose roughly demarcated structure of intervals is determined by cultural music traditions or based on one of many possible patterns. In this same context, tuning systems can be understood as mathematical specifications for the set of exact pitch frequencies upon which those scale notes ~~may~~ be positioned. Tuning systems can define a large number of possible pitch locations, and a scale may include all or only a subset of them. A broader meaning of the term "tuning system" can encompass both scale and tuning, but splitting these is useful for understanding scale design software.

It's important to realize that the words "scale" and "tuning" have different meanings in different contexts. In the context of scale design software (aka scale designers) and tuning editors, scales can be understood abstractly as an ordered set of notes, whose roughly demarcated structure of intervals is determined by cultural music traditions or based on one of many possible patterns. In this same context, tuning systems can be understood as mathematical specifications for the set of exact pitch frequencies upon which those scale notes are to be be positioned. Tuning systems can define a large number of possible pitch locations, and a scale may include all or only a subset of them. A broader meaning of the term "tuning system" can encompass both scale and tuning, but splitting these is useful for understanding scale design software.

For example, the 12edo tuning system offers 12 possible frequencies per period for placing notes upon, all of which are used by the 12edo Chromatic scale, but only some of which are used by the 12edo Major scale. These examples also ~~point to the fact~~ that an unambiguous, concrete scale description ~~also names~~ the tuning being used. The "12edo Major" scale and "Ptolemy's intense diatonic Major" scale are both Major scales. They are both diatonic (have five large and two maximally separated small intervals per period) and follow the Major mode pattern (L L s L L L s). But they place all their notes besides the tonic on slightly different frequencies, because they follow two different tuning systems — a just intonation in the Ptolemy case and an equal temperament in the 12edo case~~. They sound roughly the same when each is played as a sequential scale, but some strong harmonic differences are audible in dyads and chords~~.

For example, the 12edo tuning system offers 12 possible frequencies per period for placing notes upon, all of which are used by the 12edo Chromatic scale, but only some of which are used by the 12edo Major scale. These examples also highlight that an unambiguous, concrete scale description must name the tuning system being used. The "12edo Major" scale and "Ptolemy's intense diatonic Major" scale are both Major scales. They are both diatonic — have five large (L) and two maximally separated small (s) intervals per period — and follow the Major mode's intervallic pattern (L L s L L L s). But they place all their notes besides the tonic on slightly different frequencies, because they follow two different tuning systems — a just intonation in the Ptolemy case and an equal temperament in the 12edo case.

Therefore, we could define a scale designer as a software tool for indicating the notes of a scale and their exact pitch frequencies. Given that definition, a tuning might could be understood as a more general tool for exploring the various mathematical patterns from which tuning systems are developed. However, you will encounter software that uses these terms differently, as well as many other names that point toward these same functions being fulfilled. And software in this category frequently combines at least some of the functions of a scale designer and tuning editor. Just keep in mind that apart from the abstract meanings of the terms scale and tuning, to play music you will ultimately need to indicate both the notes of your scale and the exact frequencies on which they are placed.

Therefore, we could define a scale designer as a software tool for indicating the notes of a scale and their exact pitch frequencies. Given that definition, a tuning editor might could be understood as a more general tool for exploring the various mathematical patterns from which tuning systems are developed. However, you will encounter software that uses these terms differently, as well as many other names that point toward these same functions being fulfilled. And software in this category frequently combines at least some of the functions of a scale designer and tuning editor. Just keep in mind that apart from the abstract meanings of the terms scale and tuning, to play music you will ultimately need to indicate both the notes of your scale and the exact frequencies on which they are placed.

=== Glossary for scale design software ===

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The implied note, or explicit MIDI note number, on which the tuning file's scale is anchored. In the part of a tuning file that specifies a scale, it is usually the first, usually lowest pitched, scale note defined in a tuning file. In some tuning file systems, the other notes in the scale may be defined with reference to the tuning base (e.g. by frequency ratio or distance in cents). In the part of a tuning file that specifies a keyboard mapping, the tuning base is the MIDI note to which the scale is anchored.

Also called the tuning base note, tuning base MIDI note (in a MIDI context), scale base, base note (easily confused with bass note~~), reference note (which is vague~~), 1/1 (referring to its intervallic relationship with itself), or ~~(least clearly)~~ the "middle note" which is how it's named in the Scala keyboard mapping file (.kbm) specification.

Also called the tuning base note, tuning base MIDI note (in a MIDI context), scale base, base note (too easily confused with bass note), 1/1 (referring to its intervallic relationship with itself), or the "middle note" which (unfortunately) is how it's named in the Scala keyboard mapping file (.kbm) specification.

It can be misleading to refer to the tuning base as the tonic, root, or key, although this is sometime done. The conceptual tool that is a tuning base does not directly appear in Western classical music theory. It's related to the concepts of tonic and key, but the tuning base is just a technical tool that operates in the context of needing to ~~attach~~ a scale to a musical instrument controller. Not every tuning base is also a tonic or key (e.g. in atonal music), and "root" applies most correctly to chords but not scales. Although the lowest note in a scale (~~which is~~ a pitch set usually ordered by pitch frequency), is typically called the scale's tonic in common musicology, it does not have tonical function in atonal music, so "base" is a more general term though not in common use.

A brief aside in support of clarity... It can be misleading to refer to the tuning base as the a tonic, root, or key, although this is sometime done when they point to the same note. The conceptual tool that is a tuning base does not directly appear in Western classical music theory. It's related to the concepts of tonic and key, but the tuning base is just a technical tool that operates in the context of needing to map a scale onto a musical instrument controller like a MIDI keyboard. Not every tuning base is also a tonic or key (e.g. in atonal music), and "root" applies most correctly to chords but not scales. Although the lowest note in a scale (i.e. a pitch set usually ordered by pitch frequency), is typically called the scale's tonic in common musicology terms, it does not have tonical function in atonal music, so "base" is a more general term though not in common use.

'''Reference note'''

The named note, or the MIDI note number, of the reference pitch. Also called the tuning center (e.g. in piano tuning terminology), or in a MIDI context the reference MIDI note. The reference note is ~~sometimes specified~~ with a ~~combined named note, MIDI number, and~~ pitch ~~frequency expression~~, e.g. ~~A4-440Hz-MIDI~~.69, ~~meaning 440 Hz exactly~~ for the ~~A above middle C~~. ~~Notice that~~ 440 Hz exactly is the ISO-16-1975 tuning reference standard pitch for A4 on a piano keyboard.

The named note, or the MIDI note number, of the reference pitch. Also called the tuning center (e.g. in piano tuning terminology), or in a MIDI context the reference MIDI note.

The reference note can also be used as the tuning base note. For simplicity, it is common to use C4 as both tuning base and reference note for EDO scales, with a reference pitch of 261.63 Hz. However, in the case of tonical music using a non-EDO scale (e.g. set to just intonation or meantone tuning systems) carefully setting the tuning base is critical because the uneven intervals require placing the tuning base on the tonic note of the music. Otherwise, the tuning will be off.

But the reference note used for the reference pitch can still be any note of the scale. A4 is commonly used as a reference note because 440 Hz exactly is the ISO-16-1975 tuning reference standard pitch for A4 on a piano keyboard, so no pitch frequency approximation is required. An alternative approach for non-EDO tonical music is to set both the tuning base and reference note to the music's tonic, and set the reference pitch to what the reference note's pitch frequency would have been in a standard 12-EDO concert pitch system.

'''Reference pitch'''

The exact pitch frequency (typically in Hz) based on which all other notes in the scale or tuning system will be assigned a frequency, according to their intervallic relationship to the reference note. Also called the pitch reference or tuning center. In a ~~reference~~ specifier like C4-261Hz-MIDI.60 the "261" is typically an approximation~~, implying~~ a more accurate number with 2-4 digits after a decimal point (e.g. 261.6256).

The exact pitch frequency (typically in Hz) based on which all other notes in the scale or tuning system will be assigned a frequency, according to their intervallic relationship to the reference note. Also called the pitch reference, or tuning center, and sometimes the concert pitch (for an ensemble).

The reference note and pitch are sometimes casually specified with a combined named note, MIDI number, and pitch frequency expression, e.g. A4-440Hz-MIDI.69, meaning 440 Hz exactly for the A above middle C, because A4=440Hz is the international standard. For cases other than A4=440Hz, in a tuning specifier like C4-261Hz-MIDI.60 for example, the "261" is typically an approximation. It implies a more accurate number should be specified in the tuning file itself, with 2-4 digits after a decimal point (e.g. 261.6256).

'''Keyboard mapping'''

@@ Line 196: / Line 196: @@
 [''Once again, this whole section should probably be moved to the recently created article "Scale design software."'']
-It's important to realize that the words "scale" and "tuning" have very different meanings in different contexts. In the context of scale design software (aka scale designers) and tuning editors, scales can be understood abstractly as an ordered set of notes, whose roughly demarcated structure of intervals is determined by cultural music traditions or based on one of many possible patterns. In this same context, tuning systems can be understood as mathematical specifications for the set of exact pitch frequencies upon which those scale notes may be positioned. Tuning systems can define a large number of possible pitch locations, and a scale may include all or only a subset of them. A broader meaning of the term "tuning system" can encompass both scale and tuning, but splitting these is useful for understanding scale design software.
+It's important to realize that the words "scale" and "tuning" have different meanings in different contexts. In the context of scale design software (aka scale designers) and tuning editors, scales can be understood abstractly as an ordered set of notes, whose roughly demarcated structure of intervals is determined by cultural music traditions or based on one of many possible patterns. In this same context, tuning systems can be understood as mathematical specifications for the set of exact pitch frequencies upon which those scale notes are to be be positioned. Tuning systems can define a large number of possible pitch locations, and a scale may include all or only a subset of them. A broader meaning of the term "tuning system" can encompass both scale and tuning, but splitting these is useful for understanding scale design software.
-For example, the 12edo tuning system offers 12 possible frequencies per period for placing notes upon, all of which are used by the 12edo Chromatic scale, but only some of which are used by the 12edo Major scale. These examples also point to the fact that an unambiguous, concrete scale description also names the tuning being used. The "12edo Major" scale and "Ptolemy's intense diatonic Major" scale are both Major scales. They are both diatonic (have five large and two maximally separated small intervals per period) and follow the Major mode pattern (L L s L L L s). But they place all their notes besides the tonic on slightly different frequencies, because they follow two different tuning systems — a just intonation in the Ptolemy case and an equal temperament in the 12edo case. They sound roughly the same when each is played as a sequential scale, but some strong harmonic differences are audible in dyads and chords.
+For example, the 12edo tuning system offers 12 possible frequencies per period for placing notes upon, all of which are used by the 12edo Chromatic scale, but only some of which are used by the 12edo Major scale. These examples also highlight that an unambiguous, concrete scale description must name the tuning system being used. The "12edo Major" scale and "Ptolemy's intense diatonic Major" scale are both Major scales. They are both diatonic — have five large (L) and two maximally separated small (s) intervals per period — and follow the Major mode's intervallic pattern (L L s L L L s). But they place all their notes besides the tonic on slightly different frequencies, because they follow two different tuning systems — a just intonation in the Ptolemy case and an equal temperament in the 12edo case.
-Therefore, we could define a scale designer as a software tool for indicating the notes of a scale and their exact pitch frequencies. Given that definition, a tuning might could be understood as a more general tool for exploring the various mathematical patterns from which tuning systems are developed. However, you will encounter software that uses these terms differently, as well as many other names that point toward these same functions being fulfilled. And software in this category frequently combines at least some of the functions of a scale designer and tuning editor. Just keep in mind that apart from the abstract meanings of the terms scale and tuning, to play music you will ultimately need to indicate both the notes of your scale and the exact frequencies on which they are placed.
+Therefore, we could define a scale designer as a software tool for indicating the notes of a scale and their exact pitch frequencies. Given that definition, a tuning editor might could be understood as a more general tool for exploring the various mathematical patterns from which tuning systems are developed. However, you will encounter software that uses these terms differently, as well as many other names that point toward these same functions being fulfilled. And software in this category frequently combines at least some of the functions of a scale designer and tuning editor. Just keep in mind that apart from the abstract meanings of the terms scale and tuning, to play music you will ultimately need to indicate both the notes of your scale and the exact frequencies on which they are placed.
 === Glossary for scale design software ===
@@ Line 207: / Line 207: @@
 The implied note, or explicit MIDI note number, on which the tuning file's scale is anchored. In the part of a tuning file that specifies a scale, it is usually the first, usually lowest pitched, scale note defined in a tuning file. In some tuning file systems, the other notes in the scale may be defined with reference to the tuning base (e.g. by frequency ratio or distance in cents). In the part of a tuning file that specifies a keyboard mapping, the tuning base is the MIDI note to which the scale is anchored.
-Also called the tuning base note, tuning base MIDI note (in a MIDI context), scale base, base note (easily confused with bass note), reference note (which is vague), 1/1 (referring to its intervallic relationship with itself), or (least clearly) the "middle note" which is how it's named in the Scala keyboard mapping file (.kbm) specification.
+Also called the tuning base note, tuning base MIDI note (in a MIDI context), scale base, base note (too easily confused with bass note), 1/1 (referring to its intervallic relationship with itself), or the "middle note" which (unfortunately) is how it's named in the Scala keyboard mapping file (.kbm) specification.
-It can be misleading to refer to the tuning base as the tonic, root, or key, although this is sometime done. The conceptual tool that is a tuning base does not directly appear in Western classical music theory. It's related to the concepts of tonic and key, but the tuning base is just a technical tool that operates in the context of needing to attach a scale to a musical instrument controller. Not every tuning base is also a tonic or key (e.g. in atonal music), and "root" applies most correctly to chords but not scales. Although the lowest note in a scale (which is a pitch set usually ordered by pitch frequency), is typically called the scale's tonic in common musicology, it does not have tonical function in atonal music, so "base" is a more general term though not in common use.
+A brief aside in support of clarity... It can be misleading to refer to the tuning base as the a tonic, root, or key, although this is sometime done when they point to the same note. The conceptual tool that is a tuning base does not directly appear in Western classical music theory. It's related to the concepts of tonic and key, but the tuning base is just a technical tool that operates in the context of needing to map a scale onto a musical instrument controller like a MIDI keyboard. Not every tuning base is also a tonic or key (e.g. in atonal music), and "root" applies most correctly to chords but not scales. Although the lowest note in a scale (i.e. a pitch set usually ordered by pitch frequency), is typically called the scale's tonic in common musicology terms, it does not have tonical function in atonal music, so "base" is a more general term though not in common use.
 '''Reference note'''
-The named note, or the MIDI note number, of the reference pitch. Also called the tuning center (e.g. in piano tuning terminology), or in a MIDI context the reference MIDI note. The reference note is sometimes specified with a combined named note, MIDI number, and pitch frequency expression, e.g. A4-440Hz-MIDI.69, meaning 440 Hz exactly for the A above middle C. Notice that 440 Hz exactly is the ISO-16-1975 tuning reference standard pitch for A4 on a piano keyboard.
+The named note, or the MIDI note number, of the reference pitch. Also called the tuning center (e.g. in piano tuning terminology), or in a MIDI context the reference MIDI note.
+The reference note can also be used as the tuning base note. For simplicity, it is common to use C4 as both tuning base and reference note for EDO scales, with a reference pitch of 261.63 Hz. However, in the case of tonical music using a non-EDO scale (e.g. set to just intonation or meantone tuning systems) carefully setting the tuning base is critical because the uneven intervals require placing the tuning base on the tonic note of the music. Otherwise, the tuning will be off.
+But the reference note used for the reference pitch can still be any note of the scale. A4 is commonly used as a reference note because 440 Hz exactly is the ISO-16-1975 tuning reference standard pitch for A4 on a piano keyboard, so no pitch frequency approximation is required. An alternative approach for non-EDO tonical music is to set both the tuning base and reference note to the music's tonic, and set the reference pitch to what the reference note's pitch frequency would have been in a standard 12-EDO concert pitch system.
 '''Reference pitch'''
-The exact pitch frequency (typically in Hz) based on which all other notes in the scale or tuning system will be assigned a frequency, according to their intervallic relationship to the reference note. Also called the pitch reference or tuning center. In a reference specifier like C4-261Hz-MIDI.60 the "261" is typically an approximation, implying a more accurate number with 2-4 digits after a decimal point (e.g. 261.6256).
+The exact pitch frequency (typically in Hz) based on which all other notes in the scale or tuning system will be assigned a frequency, according to their intervallic relationship to the reference note. Also called the pitch reference, or tuning center, and sometimes the concert pitch (for an ensemble).
+The reference note and pitch are sometimes casually specified with a combined named note, MIDI number, and pitch frequency expression, e.g. A4-440Hz-MIDI.69, meaning 440 Hz exactly for the A above middle C, because A4=440Hz is the international standard. For cases other than A4=440Hz, in a tuning specifier like C4-261Hz-MIDI.60 for example, the "261" is typically an approximation. It implies a more accurate number should be specified in the tuning file itself, with 2-4 digits after a decimal point (e.g. 261.6256).
 '''Keyboard mapping'''